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The Quantitative section measures your basic mathematical skills, understanding of elementary mathematical concepts, and the ability to reason quantitatively and solve problems in a quantitative setting. There is a balance of questions requiring basic knowledge of arithmetic, algebra, geometry, and data analysis. These are essential content areas usually studied at the high school level. The questions in the quantitative section can also be from • • • Di screte Quanti tative Questi on Quanti tative Compari son Questi on Data Interpretati on Questi on etc.
The distribution in this guide is only to facilitate the candidates. This distribution is not a part of test template, so, a test may contain all the questions of one format or may have a random number of questions of different formats. This chapter is divided into 4 major sections. The first discusses the syllabus /contents in each section of the test respectively and the remaining three sections address the question format, guide lines to attempt the questions in each format and some example questions.
2.1
2.1.1
General Mathematics Review
Arithmetic
The following are some key points, which are phrased here to refresh your knowledge of basic arithmetic principles.
Basic arithmetic
• For any number a, exactl y one of the fol l owi ng i s true: o a i s n egativ e o a i s z ero o a i s posi ti ve Th e on l y nu m ber th at i s equ al to i ts opposi te i s 0 (e. g.
•
a = − a only if a = 0 )
• •
If 0 i s m ul ti pli ed to any oth er n um ber, i t will m ak e i t zero ( a × 0 = 0 ) . Product or quoti ent of two numbers of t h e same si gn are al ways posi ti ve and of a d i fferent si gn are al ways negati ve. E. g. i f a po si ti ve number i s mul ti pli ed to a negati ve number the r esul t wi ll be nega ti ve and i f a negati ve number i s d i vi ded by another ne gati ve number the r esul t will be posi ti ve.
Every i n teger has a fini te set of factor s (di v i sors) an d an i nfi ni te set of m u l t i p l i e r s. If a and o o o o b are two i n tegers, the f oll owi n g four terms are synonyms a i s a divisor o f b a i s a factor o f b b i s a divisible b y a b i s a multiple o f a
They al l mean that when a i s divi ded by b there i s no r e m a i n der . • • • Posi ti ve i n tegers, other than 1, have at l east two posi tive factors. Posi ti ve i n tegers, other than 1, whi ch have exactl y two factors, are known as p r i m e nu m b e r s. Every i n teger greater than 1 that i s not a pri m e can be wri tten as a product of pri m es. T o f i n d t h e p r i m e f a c to r i z a ti o n of a n i n t e g e r , fi n d a n y t w o f a c t o r s o f t h a t number, i f both are pr i m es, you are done; i f not, continue factorizati on until each factor i s a pri m e. E. g. to fi nd the pri m e factori z ati on of 48, two factors are 8 and 6. Both of them are not pri m e numbers, so conti nue to factor them. Factors of 8 are 4 and 2, and of 4 are 2 and 2 (2 × 2 × 2). Factors of 6 are 3 and 2 (3 × 2). S o the number 48 ca n be wri tten as 2 × 2 × 2 × 2 × 3. Th e Leas t C om m on Mu l ti pl e (LCM) of tw o in tegers a a n d b i s th e sm all est i n teger which i s di vi sibl e by both a and b, e. g. the LCM of 6 and 9 i s 18.
•
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• • The Greatest Common Di vi sor (GCD) of tw o integers a and b is th e largest i n teger which di vi des both a and b, e. g. the GCD of 6 and 9 i s 3. The produc t of GCD an d LCM of two i n tegers i s equ al to th e prod u cts of n u m bers i tsel f . E. g. 6 × 9 = 54 3 × 18 = 54 (where 3 i s GCD and 18 i s LCM of 6 and 9). Even numbers are al l the mul ti ples of 2 e. g. (… , −4, −2, 0, 2, 4, …) Odd numbe rs are all integers no t di vi si bl e by 2 ( … , −5, −3, −1, 1, 3, 5, … ) If two i n tegers are bo th even or both odd, t h ei r sum and di fference are even. If one i n teger i s even and the other i s odd, thei r sum and di fference are odd. The produc t of two i n tegers i s even unl ess both of them are odd. When an equati on invol v es more than one operati on, i t i s i m portant to carry them out i n the correct order. The correct order i s P arentheses, Exponents, Mu l ti pli cati on an d Div i si on , Add i ti on an d Subtracti on, or just the fi rst l etters PEM D AS to remember th e proper or der.
Mul ti pl yi n g or di vi di ng an i n equali ty by a negati ve number reve rses i t. If
a b < c c.
a < b and c i s
•
a negati ve number, then
and
If si des of an i n equality are both posi ti ve and both ne gati ve, taki ng the reci procal reverses th e i n equali ty . If If
a b > c c.
• •
0 < x < 1 and a i s
pos i t i v e , t h en
xa < a .
m>n,
t h en
0 < x < 1 and m and n are 0 < x < 1,
integers wi th
xm < xn < x .
•
If
t h en
x > x.
•
If
0 < x < 1 , then
1 1 >x >1 x and x
Pro per ties of Ze ro
• • • • • • • 0 i s the only number that i s nei ther negati ve nor posi ti ve. 0 i s smal l er than every posi tive number and great er than every negati ve number. 0 i s an even i n teger. 0 i s a m ul ti pl e of ev ery i n teger. For every number For every number
a a
:
a + 0 = a and a − 0 = a .
: a×0 = 0.
For every posi ti ve i n teger
n : 0n = 0 .
•
For every number
a
(incl u di ng 0):
a ÷ 0 and
a 0
are undefi n ed symbol s.
•
For every number
a
(other than 0):
0÷a =
0 = 0. a
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• • 0 i s th e only n u m ber th at i s equ al to i ts opposi te:
a f o ot. I f one work s for 8 hours a d a y , he works e ig ht of a day . If a hock ey sti ck i s 40 i n ches l on g, i t
m e a s u r e s f o r t y t w e l f th s • The numbe rs such as
(
1 , 8
40 ) of a 12 1 8 , 24 24
f o ot. and
40 , 12
in w hi ch one i n teger is w ri tten
over the second i n teger, are called fr actio n s . The center li ne i s call ed the fracti on bar. The number abov e the bar i s call ed the n u m e r a to r , a n d t he number bel ow the bar i s call ed d e n o m i n a t o r . • • The denom i nator of a fracti on can never be 0. A f r a c ti o n , s u c h a s
i s al s o k n ow n a s a n im proper fraction . B u t, Its v al ue i s on e. Every fracti on can be express ed i n deci mal form (or as a whol e number) by di vi di ng the number by the denomi nator.
3 = 0.3, 10
•
3 8 48 100 = 0.75, = 1, = 3, = 12.5 4 8 16 8
Unli ke the exampl es above, when most fracti ons are converted to deci mal s, the di vi si on does not termi n ate, after 2 or 3 or 4 deci mal pl aces; rather i t goes on forever wi th some set of di gi ts repeati n g i t.
If the numbers do no t have the same number of di gits to the right of the deci mal poi n t, add zeroes to the end of the shorter one to make them equal in l ength. Now compare the numbers i gnoring the deci mal point. For examp l e, to compare 1. 83 and 1. 823, add a 0 t o the end of 1. 83 forming 1. 830. Now compare them, thi n ki ng of them as whol e numbers wi thout decimal poi n t: si nce 1830 > 182 3, then 1.830 >1. 823.
Ra tio s and Proportions
• A rati o i s a fracti on that compares two quanti ti es that are measured i n the s a m e u n i t s . Th e f i r s t q u a nt i t y i s t he nume ra t or a nd t h e se con d qua nt i t y i s denomi nator. For exampl e, i f there are 16 boys and 4 gi rl s, we say that the rati o of the number of boys to the numbe r of gi rl s on the team i s 16 to 4, or
16 . 4
Th i s i s of ten w ri tten as 16: 4. S in ce a rati o i s j u st a f racti on , i t can
be reduc e d or converted to a deci mal or a perce n t. The Foll owi n g are di fferent ways to expr ess the sa me r ati o:
16 to 4 ,
•
16 : 4 , 16 , 4 , 4 1
a of a+b
0.25 ,
25%
If a set of obj ects i s di vi ded i nto two gro u ps i n the rati on fi rst group contai ns
the techni cal name for these ki nd of averages i s A ri thmeti c Mean. • • • If you know the average of n numbers, mul ti pl y that average w i th n to get the s u m o f n u m b e r s . If all the numbers i n a set are the same, then that number i s the average . Assume that the average of a set of numbers i s A. If a new number x i s added to that set, the new average wi ll be; o o o • • G r e a t er i f x i s g r e a t e r t h a n t h e e x i s t i n g a ve r a g e S m a l l e r i f x i s s m a ll e r t h a n t h e e x i s t i n g a v e r a g e Unchanged if x is e q ual to th e existing average
sum of n numbers n
or si mply
A=
Sum n
A ri thmeti c sequenc e i s an order ed set of numbers, such that, the di fference between tw o consecuti v e numbers i s the same. If there i s an ari thmeti c sequen ce of n ter m s, then the averag e cal cul ati on can be made si mpl e by usi n g these rul es. o The avera g e of the te rms i n that sequ ence wil l be the mi ddl e t erm, i f n i s odd. o If n i s even, the average wi ll be the average of two mi ddl e terms.
2.1.2
Algebra
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Polynomia ls
• A monomi al i s any number or va ri abl e or product of n u mbers an d vari abl es. For exampl e •
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Solving Equations and Inequalities • The basi c pri n ci pl e in sol vi n g equati ons and i n equali ti es i s th at you can m an i pu l ate th em i n an y w ay as l on g as y ou do the same thin g to both sides. For exampl e you may add a nu mber to b oth si des, or you may di vi de or mul ti pl y both si des wi th same number etc. By usi n g the foll owi n g six-step metho d, you can sol v e most of the equati ons and i n equ ali ti es. The method i s expl ained wi th the hel p of a n exampl e. Example : if
When you have to so l v e one vari abl e and the equat i on/i nequali ty i nvol v e more than one vari abl e, treat all other vari abl es as pl ai n numbers an d apply the six-step method. Example :
a = 3b − c , if S o l u tio n :
Step 1 2 3 4
w h at
is
th e
v al u e
of
b
in
term s
of
a
and
c?
What to d o … There ar e no fracti ons and deci mal s. There are no parenth eses. There are no li ke terms. By addi ng and subtra cti n g get all the variabl es on one si de. By addi ng or subtra cti n g get all pl ai n numbers on the other si de.
Example
Rememb er there i s onl y one v a r i a b l e b , w h i ch i s on on e si d e onl y. Re me mb e r we a re a and c as con si deri ng p l a i n n u mb e r . A d d c to each si de to get:
5
a + c = 3b
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6 D ivi de both si des by the coeffi ci ent of the variabl e. D ivi de both si des by 3 to get:
a+c =b 3
•
It i s not necessary to foll ow these steps i n the order s peci f i ed. Some ti mes i t makes the probl em much easi er, i f you change the o rder of these steps. Example : If
D oi n g the same thi n g on each side of an eq uati on does n o t mean doi n g the same thi n g to each term of the equati on. Th i s i s very i m portant if you are doi n g di vi si ons, or deali n g wi th exponents and roots. Example : If
A system of equati ons i s a set of two or more equati ons havi ng tw o or more vari abl es. To sol v e such equati ons, you must fi nd the val u e of each v a r i a b l e t ha t w i l l m a ke e a c h e q u at i o n t r u e . To sol v e a system of equati ons, add or subtract them to get a third equati on. If there are more than two equati ons you can just add them. Example : If
•
x + y = 10
and
x − y = 10
w h at i s th e val u e of
y?
S o l u tio n :
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x + y = 10 x− y = 2
Add two equati ons: Now repl aci n g •
2x
= 12 ⇒ x = 6
x
wi th 6 i n the fi rst equati on:
6 + y = 10 ⇒
y=4
If you know the val u e of one va ri abl e i n a system of t w o equati ons, you can use thi s val u e to get the value of the other vari able. As i t i s done i n the previ ous questi on.
Javed was two years younger than Saleem. Bilal has at most Rs.10,000. The product of 2 and a number exceeds that number by 5 (is 5 more than that number).
5 + x = 13 J = S −2 B ≤ 10000 2N = N + 5
• •
In word probl ems, you must be sure about what you are answer i n g. Do not answer the wrong questi on. In probl em s i n v ol vi n g ages, rem em ber that "years ago" means you need t o subtract, and "years from now" means you need to add.
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• Di stance probl ems all depend on three vari ati ons of the same formul a:
The two di agonal s bi sect each ot her. and BE = ED A di agonal di vi des the paral l elogram i n to two tri angl es that are congruent.
AE = EC
A re ctangle i s a parall el ogram in whi ch all four angl es are ri ght angl es. It has all the properti es of a parall el ogram. In addi ti on i t has the foll owi n g properti es: o o The measu re of each angl e i n a rectangl e is 90° . The di agon al s of a rectangl e are equal i n l ength.
•
A square is a rectangl e that has the foll owing addi ti onal properti es: o A square has all i ts sides equal i n l ength. o In a square, di agonals are perpendi cul ar to each other.
•
To cal cul ate the area, the foll owing formul as are requi red: o o o For a parall el ogram, h e i gh t . For a rectangl e, width. For a square,
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Circles
• A circle co nsi sts of all the poi n ts that are the same di stance from one fi xed poi n t call ed the c e n t e r . Th at di stan ce i s call ed th e r a d i u s of a ci rcl e. Th e word radi us i s al so used to re p resent any of the l i ne se gment s joi ni n g the center and a poi n t on the ci rcl e. The pl ural of radi us i s r a d i i.
An arc consi sts of two poi n ts i n a ci rcl e and al l the poi n ts between them. E . g . PQ i s an arc i n the di agram.
•
A n angl e whose verte x i s at the center of the ci rcl e i s call ed the central angle .
∠PCQ
i n the di agram above i s a central angle .
•
The de gree measure of a compl ete ci rcl e i s
360° .
•
The de gree measure of an arc i s the measure of the central angl e that i n tercepts i t. E. g. the degr ee me asure of
PQ
i s equal to the measure of
∠PCQ
i n the di agram above.
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x
•
If
i s the degre e mea sure of an arc, i ts l ength can be cal cul ated as
x C, 360
where C i s the ci rcumference. • • The area o f a ci rcl e can be cal cul ated as
π r2 .
The area of a sector formed by the arc and two radii can be x A , where A is the area of a circle. calculated as 360
2.2
Discrete Quantitative Questions
These are standard multiple-choice questions. Most of such questions require you to do some computations and you have to choose exactly one of the available choices based upon those computations. This section will teach you the basic tactics to attempt such questions.
2.2.1
Question format
Each question will consist of a question statement and the choices labeled from A to E. The number of choices may vary from 2 to 5, but exactly one choice will be correct for each question.
2.2.2
How to attempt?
Following are some tactics, which will lead you to the correct answer. • Whenever you know how to answer a questi on di rectl y , just do i t. The tacti cs shoul d be used onl y when you do not know the exact sol u ti on, and you just want to eli mi n ate the choi ces. Rem em b er th at n o probl em requ i res l en gth y or di fficu l t com pu tati on s. If y ou f i n d y ou rsel f doin g a l ot of com pl ex a ri th m eti c, th i n k agai n. You m ay be goi n g i n the wrong di recti on. Whenever there i s a questi on wi th some unknowns (vari abl es), repl ace them wi th the appro p ri ate numeri c val u es for ease of cal cul ati on. When you need to repl ace vari abl es wi th val u es, choose easy-to-us e numbers, e. g. the number 1 00 i s app ropri ate i n most per cent-rel ate d probl ems and the LCD (l east common denomi nator) i s best sui ted in questi ons that i n vol v e fracti ons. A ppl y "back-sol vi n g" whenever you know what to do to answer the questi on but you want to avoi d doi n g algebra. To understan d thi s tacti c read the f o l l o wi n g exampl e: On Monday , a storeo wner recei v ed a shi pment of bo oks. On Tuesday, sh e sol d hal f of them. On Wedn esday after two more were so l d, she had exactl y 2/5 of the books l eft. How many were i n the sh i pment? (A) 10 (B) 20 (C) 30 (D) 40 (E) 50
•
• •
•
now by this tacti c: Assume that (A) i s the correct answer, i f so; she must have 3 books on Wedne sday . But 2/5 of 10 are 4, so, (A ) i s i n correct; Assume that (B) i s the correct answer, i f so; she must have 8 books on Wedne sday . 2/5 of 20 are 8, so, (B) i s the correct cho i ce, and as there may
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be onl y one correct c h oi ce, there i s no nee d to che ck for remai n ing choi ces. Th i s tacti c i s v ery h elpf u l w h en a n orm al al gebrai c sol u ti on f or th e probl em i n v ol v es com pl ex or l en gth y cal cu l ati on s. If you are not sure how to answer the questi on, do not l eave i t unanswered. Try to eli mi n ate absurd choi ces and gue ss from the remai n ing ones. Most of the ti mes four of the choi ces are absu rd and you r answer i s no l onger a guess. Man y th i ngs m ay h e l p y ou to real i z e th at a parti cu l ar ch oi ce i s absu rd. S ome of them are li sted bel ow. o o o The answe r must be posi ti ve but some of the choi ces are nega ti ve so el imi n ate all the negati ve ones. The answer must be even but some of the choi ces are odd so el i mi n ate all th e odd ch oi ces. The answe r must be l ess then 100, but some of the choi ces are greater tha n 100 (or any other val u e) so eli mi n ate all choi ces that are out of range. The answe r must be a whol e number, but some of the choi ces are fracti ons so eli mi n ate all fracti on s. These are some exampl es. Th ere may be numero u s si tuati ons where you can appl y thi s tacti c and fi nd the correct an swer even i f you do not know the ri ght way to sol v e the probl em.
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Example
If a school cafeteri a needs C cans of soup each week for each student an d there are S students, for how many weeks will X cans of soup l ast? ( A) C X/ S (B ) X S /C (C) S /C X (D) X/C S (E ) C SX
Some of the questi ons i n the Quanti tati ve secti on of the test may be quanti tati ve compari son questi ons. The Fol l owi ng text wi ll expl ai n you the format and techni ques u need to attempt th e questi ons of thi s format.
2.3.1 Question format
Such ques ti ons consist of two quanti ti es, one i n co l u mn A and the other i n col u mn B. You have to compare the two quanti ti es. The i n form ati on concerni ng one or bot h quanti ti es i s presented b efore them. Only the foll owi n g four choi ces will be given: A. B. C. D. Th e Th e The Th e qu an ti ty i n col u mn A i s greater qu an ti ty i n col u mn B i s greater two quanti ti es i n both col u mn s are equ al rel ati on sh i p can not be det er m i n ed f rom th e i n f ormati on giv en
And as it is clear from the choices, only one will be correct at one time. Your job is to choose one of them after careful comparison. The following text explains some simple tactics to attempt such questions.
2.3.2 How to attempt
Whenever you encounter a quanti tative compari son questi on, the foll ow i n g gu i del i n es w ill h el p you to fi n d th e correct an sw er qu i ck l y. • If the questi on i n volves some vari abl es, repl ace them wi th appropri at e numbers. Here are some gui deli n es i n choosi ng an appropri ate number: o The very best number s to use are –1, 0 and 1. o Often fracti ons between 0 and 1 are useful (e. g. 1/2, 3/4 etc. ). o Occasi onally, "l arge" numbers s u ch as 10 or 100 can be used. o If there i s more than one vari able, i t i s permi ssi bl e to repl ace ea ch wi th the same number . o Do not i mpose any un-speci f i ed condi ti ons on numbers. Cho ose t h e m r a n d o m l y. Eli mi n ate the choi ces and choos e from the remai n i n g ones. For exampl e If you found the quanti ti es ever equal , the correct choi ce coul d never be A or B , so, eli mi n ate A and B . A quanti tati ve compari son question can be treated as a n equati on or i n equali ty. Ei ther: Column A < Column B, or Column A = Column B, or
•
•
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Column A > Column B So, you can perform si mi l ar operati on on both col u mns to si mplify the probl em j u st as i n equ ati on s (or i n equ ali ti es).
Once agai n there i s no need for cal cul ati on, as the sp eed i n col u mn B i s higher than that in col u mn A. It i s obvi ous that i t will take less ti me to travel shorter di stance at a greater spee d. S o the val u e in col u mn A i s l arger. The answer i s opti on (A).
for column B. A s there are no c o l u mn A an d be grea ter than, l ess than or equal to 0. So the correct choi ce i s (D).
15 y − 13 y = 2 y
13 y − 13 y = 0 f o r 2 y can restri ctions,
2.4
Data Interpretation Questions
These ques ti ons are based on th e i n formation that i s present ed i n the form of a graph, chart or tabl e. Most of the data i s presente d graphi call y. The most common types of gra phs are l i ne gra phs, bar gr aphs and ci rcl e graph s. Th e objecti v e of such que sti ons i s to test you r abi li ty to understan d and anal yze stati sti cal data.
2.4.1
Data i n terpretati on questi ons al ways appear i n sets , you are present ed wi th some data i n any format (chart , graph or tabl e), an d you wi ll then be as ked wi th some questi ons about that data. The fol l owing exampl e expl ai ns the format of such questi ons.
Question 2:
For which year, the percentage increase in sales from the previous year is the greatest. (A) 1995 (B) 1996 (C) 1999 (D) 2000 (E) 2001
2.4.2 How to attempt
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• Do not try to answer such ques ti ons i mmedi atel y, fi rst of all read th e present ed data car efull y. You must be ve ry cl ear ab out the dat a and i ts meani n gs even before readi n g the fi rst questi on. Do not confuse numbers wi th percents. Thi s confusion i s most li kely to occur whe n data i s pres ented i n pi e graphs. F or exampl e i n the foll owi n g graph
•
Sales in million Rs.
12 10 8 6 4 2 0 1994 1995 1996 1997 1998 1999 2000 2001 Years
Now i t woul d be a great mi stake here to thi n k that sales of "TVs & VCRs" is 15% mor e than the sal es of Computers i n 2001 by XYZ Corporati on. To k n o w t hi s y o u h a v e to c a l c ul a t e i t a s • Try to avoi d un-necessary cal cul ati ons. Most of the questi ons coul d easi l y be sol v ed by observati on and e s ti mati on. Use esti mati on to el i mi n ate th e choi ces, if you are not abl e to fi nd th e correct answer wi thout calcul ati on. For exampl e to sol v e "Questi on 1" present e d i n the exampl e at the start of thi s secti on, i f you are not sure of the correc t answer, you can then try to cut down the number of possi bl e choi ces by observati on. You a re bei n g asked to tel l the percentage i n crease. Where as, i n year 2000, the sal e i s decrea si ng i n stead of i n creasi ng, so, y ou can i mm edi atel y el i mi n ate ch oi ce (D ) i n th at qu esti on .
15 × 100 = 60% 25 .
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• Your answers must be ba sed upon the i n formati on present ed i n the gi ven charts and grap hs. If your knowl edge contradi c ts any of t h e dat a present ed, i gnore what you know and sti ck to the presente d da ta. The present ed data shoul d be the onl y base for your cal cul ati ons and esti mati ons. A lways use the prope r uni ts, there may b e some qu esti ons that ask you to compar e di fferent data i tems possi bl y from di fferent data s ets. Be careful about the uni ts used to repres ent t h e data. Because gr aphs and c h arts pres ent data i n a form that enabl e s you to readi l y see th e rel ati on sh i ps am on g v al u es an d to m ak e qu i ck compari sons, you shou l d al ways try to vi su ali z e you answer i n th e same format as the original data was presented. Be sure th at your answer i s reasonabl e. For exam pl e, the pr ofi t coul d never i n crease the act u al sal es, or the ex p enses coul d never be negati ve etc. While answering the questi on , fi rst of al l el i mi n ate su ch u n reasonabl e choi ces, an d then choose from the remai n i n g ones.
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2.5
1
Practice exercise
( A ) 49 ( B ) 49. 5 ( C ) 50 ( D ) 50. 5 ( E ) 51
What i s the average of posi tive i n tegers from 1 to 100 i n cl usive?
2
If
x + y = 6, y + z = 7,
and
x+ z =9,
what is the average of
x, y
and (E)
z?
11 (A) 3
3 In the
11 (B) 2
di agram bel ow,
(C) li nes
22 3
l and
( D ) 11 m are not
22
para ll el.
If A repres ents the a v erage me asure of al l the ei ght angl es, what i s the val u e of A?
Six actors ---- Bob, Carol , Dave Ed, Frank, and Grace audi ti on for a part i n an off-Broadway pl ay. The au di tions wi ll take pl ace o v er four c onsecuti v e days, starti ng on a Thursda y . Each actor wi ll have one au di ti on; the days on w h i ch t h e d i f f e r e n t a c t o r s w i l l a u d i ti o n m u s t con form to th e f oll owi n g con di ti on s. i. ii . iii . i v. v. vi. vii. 1 At l east one audi ti on will take place each day. No more than two audi ti ons will take pl ace on any day. No more than thr ee audi ti ons wil l take pl ace on any two consecuti v e days. Bob's audi ti on must take pl ace on S aturday. Carol 's audi ti on must take pl ace on the same day as another audi ti on. Frank's au di ti ons must take pl ace on th e day bef ore Grac e' s audi ti on. Dave's audi ti on must take pl ace on a day after Ed's au di ti on.
Questions 6-10:
Duri ng the fi rst hal f of the year, from January through June, the chai rperson of the mathe m ati cs dep artment wi ll be on sa bbati cal . The dean of the col l ege has asked each of the si x professors i n the de partment -- - Arkes, Borofsky, Chang, Denture, Hobbes, a n d Le e--- to serve a s acti ng c h ai rperson duri ng one of
1 0 The onl y professors that can serve i n Janu ary are A and L, so, one of th em must serve i n January, and nei ther serves i n February . So choi ce A cannot be true.
3.2
Logical Reasoning
Each l ogi cal reasoni n g questi on requi res you to anal yze an argu ment prese n ted i n a short pa ssage. Oft en you are asked ei th er to fi nd a concl u si on that i s a l ogi cal consequen ce of the p assage, or to choose a statemen t that, if true, strengt h en or weakens the argumen t.
Questions, whi ch test your abi li ty to go beyon d the auth or's expl i ci t statements an d see what these stat ements i mpl y, may be worded l i k e these. o It can be i n ferred from the passage a bove that the auth or bel i ev es that … o Wh i ch of th e f oll owi ng i s i m pli ed by th e p assage a bo v e? o From the informati on above, whi ch of the foll owi n g i s the most reasonabl e i n ference?
Techniques for Sentence Completion
For the se ntence co mpl eti on a few choi ces are gi ven that co ul d be sel ected for compl eti ng the sente n ces. Only one choice i s correct out of the several choi ces. You have t o compl ete the sente n ce by sel ecti n g the correct ch oi ce accordi n g to the gramm ar or voca bul ary. For maki ng the ri ght ch oi ce you can benefi t from the foll owi n g techni ques; • After you read the i n compl ete s entence do not l ook at the choi ces. Try to t h i n k a b o ut t h e c o r r e c t a n s w e r y o u r s e l f. If you think that you have compl eted the sent ence and found the cor rect choi ce you can c onsul t your li st of choi ces. If th e answer you thought match es one of the choi ces menti oned i n the li st that i s most probabl y the ri ght choi ce to be marked. If i t does not mat ch wi th the choi ce you can l ook for a synonym repl acem e n t. Thi s tacti c i s very h el pf ul i n fi n di n g th e ri gh t an sw er, it prevents y ou from confusi n g yoursel f wi th the wrong choi ces. Do not select the choi ce hastil y. Even i f you are satisfi ed wi th your choi ce try to substi tute i t wi th the other choi ces so that you are more sati sfi ed wi th your deci si on. Someti mes the other choi ce fi ts more appr opri atel y to the senten ce. When you are asked to compl ete a sent en ce, whi ch has two spaces to be fill ed i n , try to put th e fi rst word of every choi ce i n the fi rst bl ank. Note down the choi ce that you fi nd best. Now for the second bl ank try every second ch oi ce of al l choi ces. Note the choi ce that you think i s most appropri at e. Check i f the two sel ected choi ces are matchi ng one of t h e gi ven pai r of choi ces. If i t does then s el ect i t as your correct ch oi ce, i f not then consider thi s pai r as a wron g choi ce and try wi th the other choi ces. If you fi nd di ffi cul ty in maki ng sense out o f certai n words an d y ou are not very familiar wi th them you can try to ma ke a gue ss wi th reference to the
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context of the sentence. Try to break the word into vari ous parts and anal yze i ts meani n g e.g. i f you do not know the meani n g of the wor d " ci vili z ati on " break i t i n to tw o i. e. 'ci vili z e' an d 'ati on ' n ow y ou m ay k n ow the meani n g of ci vi lize and thro ugh the term 'ati on' you can m ake out th at the word i s a noun of ci vili ze. If you fi nd the word unfamili ar wi th prefi x es and suffi xes di vi de the word i n to i ts part s e. g. prer ecordi ng. Thi s word consi sts of both prefi x and suffix. You can break the word l ike pre-recor d i n g. Here you know that pre me ans before, record means to stor e and -i ng i s a term of conti nuous tense. So you can fi nd thi s break up of words qui te hel pful in maki ng out the ri ght sense. If none of the techni que works try maki ng a gu ess wi th reference to the context. • When l ong and compl ex sente n ces confuse you then try to break th at sentence i n to smal l er more sen tences by rephrasi ng i t. After you di vi de i t compare wi th the origi n al sentence to avoi d any mi sinterpretati on. If you are sati sfi ed read the small er sentences to get the i de a more cl earl y.
Exclude the choice from your consideration that you think is incorrect, e.g. the choices that do not have the same grammatical unit as of the original pair cannot match the original pair in anyway. Spend more time on considering the more possible choices. You should know about the various kinds of analogies that are more frequently asked. Some of the common analogy types are as follows; Synonyms Some words are linked together in a pair which means the same or has a similar dictionary definition.e.g Pretty- Beautiful Overseas Scholarship Scheme for PhD Studies
•
i.
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ii. Describing Qualities Some pairs have some words in which one word describes the other word. Heavy- Rain Class and Member Some pairs have words which are based on class and member basis e.g. Electronics-Radio Antonyms Some pairs consist of the words that are opposite to each other e.g. Love- Hate Describing Intensity Some pairs consist of the intensity of the other e.g. Smile-Laughter words in which one describes the
iii.
iv.
v.
vi.
Function In some pairs a word describes the function of the other word e.g. Pen-Write Manners Some words in a speech describe the manners and behavior e.g. Polite-Speech Worker-Workplace Some pairs in a word describe the profession and its workplace e.g. Doctor-Clinic
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Questi ons rel ated to cri ti cal readi n g try to j u dge your readi n g skill s and how you understand and i n terpret what you read. The paper i n cl udes a few passages that ask answeri n g questi on s rel ated to the pass age.
Techniques for Critical Reading Exercises
There are a few techniques related to the Critical Reading Questions that prove to be a good guideline for solving such questions. • Do not read the questions before reading the whole passage. Try to skim through the whole passage and then read the questions to look for a more specific answer. Read the passage quickly with understanding but do not panic. Try to analyze what the whole passage is about and what the author really intends to convey. While reading mark the lines where you think the passage carries the most important points. These strategies would definitely help you find the answers. When you find yourself stuck with a question, do not waste your time on it and go ahead for the next questions. Sometimes, answering other questions guide you about the earlier question. But, if you still do not find the answer mark it for doing in the end more calmly, having enough time to think. Try to familiarize yourself with the types of critical reading questions. Once you know the nature of such questions, you will be able to find the answers more quickly even when you are reading the passage. The examples of some commonly asked questions are as follows: o Central Idea Mostly, questions are asked to explain the central idea or main theme of the whole passage, which analyzes how you skim through it. Sometimes, the opening and closing lines can give you a better clue about answering such questions properly. Specific Details Sometimes to analyze your scanning abilities you are asked to answer some specific details about the passage. Such questions are about 'when', 'where', 'which' and 'who'. You can get the answers of this kind of questions from the area of the passage which you marked in the first reading, where you think the most important and informational remarks of the author lies. Making Inferences Most of the questions ask you to infer from the passages, making your opinion about what is said in the paragraph, implying meaning and making your own point of view. These questions try to assess your judgment; you must be clear in your mind about what the author is referring to and then make your own opinion according to your understanding and comprehension. Read and think about all the choices and analyze each of it logically according to your comprehension rather than the author's point of view. Overseas Scholarship Scheme for PhD Studies
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o
o
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o
Meaning in Context Some selected words from the passage are pointed out to explain them with reference to the context to check your reading comprehension. Sometimes the word that describes something in a dictionary portrays it the other way when it appears in the context. The test tries to judge your ability to make sense of the word in the context. Author's Approach Some questions ask you to explain the mood in which the author is writing whether it is sarcastic, humorous, witty, sad etc. When you are asked questions like these you can look for certain expressions, words, phrases or exclamations, which describe the tone, mood or style of the author. The feelings of the writer are mostly exhibited through choice of words. While answering these questions read the message carefully observing particularly the use of words. Title Selection Some passages ask for selecting a title that best suits the passage. Remember that the chosen title should not be narrowly or broadly selected. Try to avoid choosing those titles that describes only one or two paragraphs but the one, which is applicable to the whole passage and portrays it best.
o
o
Example Questions Passage I: National Testing Service Pakistan Overseas Scholarship Scheme for PhD Studies
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behavior 1 The main idea of this excerpt is A. to provide evidence of the origin of language. B. to present the need for language. C. to discuss how early man communicated. D. to present the culture of early man. E. to narrate the story of English. Theories of the origin of language include all of the following EXCEPT A. Changes occurring through the years. B. The need to communicate. C. Language of children. D. The first man's extensive vocabulary. E. Communication among primitive men. The purpose of the discussion of the word, "Doll," is intended to A. Trace the evolution of a noun. B. Support the fact that naming things is most important. C. Indicate how adults teach language to children. D. Show the evolution of many meanings for one word. E. Evince man's multiple uses of single words The implication of the author regarding the early elements of language is that A. There were specific real steps followed to develop our language. B. Care must be exercised when exhuming what we consider the roots of language. C. We owe a debt of gratitude to the chimpanzee contribution. D. Adults created language in order to instruct their children. E. Language was fully developed by primitive man. If we accept that primitive man existed for a very long period of time without language, then we may assume that A. Language is not necessary to man's existence. B. Language developed with the developing culture of primitives. C. Primitives existed in total isolation from one another. Overseas Scholarship Scheme for PhD Studies
2
F.
3
4
5
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D. E.
6 Children brought about a need for language. Mankind was not intended to communicate.
COMMON QUERIES
Q. How to take NTS Online Test? You will go through the following screen shots to learn how to take NTS Online test. Step: 1 This is the first screen named as Candidate Login Screen. You will enter your Candidate ID and Password provided to you by NTS
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Step: 2 You will see Test Instructions' Screen after you successfully login. Please read the instructions carefully to avoid any confusion during the test. After reading the instructions, press Start Test button on center bottom of the page.
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Step: 3 After you click on the Start Test button your test starts and a page appears which shows your first question of the test. Each question has various choices, if you know the answer you can select the correct choice for your answer and press Next Question button. You can also add this question in the Pass Box to answer it at some another stage. You will also find some additional information about your test on this page. This information includes: • • • Total Number of Questions in the Test Total Number of Questions Answered by you Total Number of Questions in the Pass box to be attempted later
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Step: 4 If you place a question in Pass Box you will notice that the Questions in Pass Box field will increase by one.
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Step: 5 If you want to answer the questions in Pass Box, simply click on Questions in Pass Box link at the top. It will take you on the following screen. Now click Answer this Question button for the question you want to answer.
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Step: 6 You have selected this question from Pass Box now select its answer and proceed for next question.
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Step: 7 You have attempted all questions and now this last screen will show your detailed result.
Wish You Good Luck with your Test. National Testing Service
Q. How is NTS Online Test different from paper-based Test? For the Paper-based Test, • • • • A pencil, eraser and a sharpener is required to attempt the paper-based test. You can make the changes in the answer that you have already marked. The announcement of results is delayed than the online tests. You have to fill in a separate answer sheet to mark your answers.
Where as for the Online Test, • • • • • No stationery items are required to attempt online test. If you want to attempt a question at the end, you can place it in the Pass Box for attempting later. You can not reattempt a question that you have already answered. As soon as you finish the test, the result is displayed on the screen. In case of a system failure during the test, you will have to log-in again and the test will start from the same question where you had left. No information will be lost while the system was unavailable.
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Q. How Can I Ask for Result Reporting? Your result is reported to you right after you finish your test. You are given the certificate fifteen days after the conduct of the test of the last batch. If you still do not get the result you can Contact Us. You can also visit the website of NTS to check your result. The final result is sent to you by email. Q. Is There Any Negative Marking While Scoring? There is no negative marking for wrong answers. However the negative marking may be activated if it is required by the allied institute or organization. Q. What are the Rules and Regulations that apply to me in the Test Center when taking the Online General Test? Rules and Regulations: • If you do not appear with the Identity Card (NIC) on the Test Center, you will not be allowed to take the test. • The test will be given on the day and at the scheduled time. You are asked to observe punctuality. Arriving late at the center may disqualify you from taking the test. • You are not allowed to bring any testing aids inside the test center. Nothing, except the original Identity Card is required to be taken along. • You are not allowed to smoke, eat or drink inside the test center. • No discussion or any form of communication with the fellow candidates is allowed during the testing session. • You will also not be allowed to leave the test center without the permission of the supervisor. • Test centers do not have large waiting areas. Friends or relatives who accompany you to the test center will not be permitted to wait in the test center or contact you while you are taking the test. • You will be required to sign the attendance sheet before and after the test session and any time you leave or enter the premises where the test is being conducted. • If you need to leave your seat at any time during the test (which shall only be allowed in case of serious illness), raise your hand and ask the invigilator. • Repeated unscheduled breaks will be documented and reported to NTS. NTS reserves the right to videotape all or any of Testing Sessions and use it to determine any misconduct, etc. • If at any time during the test you believe that you have a problem with your test, or need the Invigilation Staff for any reason, raise your hand to notify the Invigilation Staff.
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NOTE: The rest of the queries regarding the test format, contents and other procedures have almost the same answers as of the paper based tests, given above.
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DRILL TESTS General
Note: The sample papers do not include quantitatively the same number of questions as there would be in the actual papers. They are merely meant to provide conceptual guidance to the users or prospective candidates.
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Drill Test I
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I Quantitative Section No. Of Questions 10
Choose the correct answer for each question and shade the corresponding CIRCLE on the answer sheet
1. The number of degrees through which the hour hand of a clock moves in 2 hours and 12 minutes is
A. B. C. D. E. A
66 72 732 723 None of these B C D E
2. A cylindrical container has a diameter of 14 inches and a height of 6 inches. Since one gallon equals 231 cubic inches, the capacity of the tank is approximately A. B. C. D. E. A 2-2/7 gallons 4 gallons 1-1/7 gallons 2-2/7 gallons None of these B C D E
3. A train running between two towns arrives at its destination 10 minutes late when it goes 40 miles per hour and 16 minutes late when it goes 30 miles per hour. The distance between the two towns is A. B. C. D. E. A 720 miles 12 miles 8-6/7 miles 12-7/7 miles None of these B C D E
4. If the base of a rectangle is increased by 30% and the altitude is decreased by 20% the area is increased by A. B. C. D. E. A 25% 10% 5% 1% 4% B C D E
5. If the sum of the edges of a cube is 48 inches, the volume of the cube is A. 512 inches B. 96 cubic inches C. 64 cubic inches National Testing Service Pakistan Overseas Scholarship Scheme for PhD Studies
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D. 698 cubic inches E. None of these A B C D E
6. A certain triangle has sides, which are, respectively, 6 inches, 8 inches, and 10 inches long. A rectangle equal in area to that of the triangle has a width of 3 inches. The Perimeter of the rectangle, expressed in inches, is A. B. C. D. E. A 11 16 22 23 24 B C D E
7. The cube of 1/3 is A. B. C. D. E. A 3/9 3/27 1/81 1/27 1/9 B C D E
8. In general, the sum of the squares of two numbers is greater than twice the product of the numbers. The pair of numbers for which this generalization is not valid is A. B. C. D. E. A 8,9 9,9 9,10 9,8 8,10 B C D E
9. A piece of wire 132 inches long is bent successively in the shape of an equilateral triangle, a square, a regular hexagon, a circle. The plane surface of the largest area is included when the wire is bent into the shape of a A. B. C. D. E. A Circle Square Hexagon Triangle Line B C D E
10. If pencils are bought at 35 cents per dozen and sold at 3 for 10 cents the total profit on 5 1/2 dozen is National Testing Service Pakistan Overseas Scholarship Scheme for PhD Studies
Choose the correct answer for each question and shade the corresponding CIRCLE in the answer sheet
Three first. Each bench has room for exactly three people. Everyone must sit in a seat or on a bench, and seating is subject to the following restrictions: An adult must sit on each bench. Either R or S must sit in the driver's seat. J must sit immediately beside M. 1. Which of the following can sit in the front passenger seat? A: J B: L C: R D: S E: V A B C D E
24. If S sits on a bench that is behind where J is sitting, which of the following must be true? A: H sits in a seat or on a bench that is in front of where M is sitting. B: L sits in a seat or on a bench that is in front of where F is sitting. C: F sits on the same bench as H. D: L sits on the same bench as S National Testing Service Pakistan Overseas Scholarship Scheme for PhD Studies
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E: M sits on the same bench as V. A B C D E
For question 5 to 9 not serve unless Ms. K and O also serve. Neither Mr. M nor Mr. N will serve without the other. If P serves, neither Q nor R can serve. 5. Which of the following is an acceptable committee? A: J, L, M, N, O B: K, L, N, O, P C: K, M, N, O, R D: L, M, N, O, R E: M, N, O, P, Q A B C D E
7. If Q and R are both on the committee, who else must be on the committee? A: J B: K C: L D: M E: O A B C D E
8. If M is not on the committee, each of the following must be on the committee EXCEPT A: J B: L C: O D: Q E: R B C D E 9. In how many different ways can the principal select an acceptable committee? A: Fewer than 3 B: 3 National Testing Service Pakistan Overseas Scholarship Scheme for PhD Studies A
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C: 5 D: 7 E: More than 7 A B C D E
For question 10 to 13 A contractor will build five houses in a certain town on a street that currently has no houses on it. The contractor will select from seven different models of houses—T, U, V, W, X, Y, and Z. The town's planning board has placed the following restrictions on the contractor: No model can, be selected for more than one house. Either model W must be selected or model Z must be selected, but both cannot be selected. If model Y is selected, then model V must also be selected. If model U is selected, then model W cannot be selected. 10. If model U is one of the models selected for the street, then which of the following models must also be selected? A: T B: W C: X D: Y E: Z A B C D E
11. If T, U, and X are three of the models selected for the street, then which of the following must be the other two models selected? A: V and W B: V and Y C: V and Z D: W and Y E: Y and Z A B C D E
13. If model Z is one model not selected for the street, then the other model NOT selected must be which of the following? A: T B: U C: V D: W E: X A B C D E
For question 14 to 16 Seven children—F, J, K, M, R, S, and T—are eligible to enter a spelling contest. From these seven, two teams must be formed, a red team and a green team, each team consisting of exactly three of the children. No child can be selected for more than one team. Team selection is subject to the following restrictions: If M is on the red team, K must be selected for the green team. If F is on the red team, R, if selected, must be on the green team. R cannot be on the same team as S. J cannot be on the same team as K. 14. Which of the following can be the three members of the Red team?
15. If M and F are both on the red team, the green team can consist of which of the following? A: J, K, and R B: J, S, and T C: K, R, and S D: K, R, and T E: R, S, and T A B C D E Overseas Scholarship Scheme for PhD Studies
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16. If M is on the red team, which of the following, if selected, must also be on the red team? A: F B: J C: R D: S E: T A B C D E
For question 17 to 20 A mail carrier must deliver mail by making a stop at each of six buildings: K, L, M, O, P, and S. Mail to be delivered are of two types, ordinary mail and priority mail. The delivery of both types of mail is subject to the following conditions: Regardless of the type of mail to be delivered, mail to P and mail to S must be delivered before mail to M is delivered. Regardless of the type of mail to be delivered, mail to L and mail to K must be delivered before mail to S is delivered. Mail to buildings receiving some priority mail must be delivered, as far as the above conditions permit, before mail to buildings receiving only ordinary mail. 17. If K is the only building receiving priority mail, which of the following lists the buildings in an order, from first through sixth, in which they can receive their mail? A: L, K, P, S, O, M B: L, K, S, P, M, O C: K, L, P, M, S, O D: K, P, L, S, O, M E: O, K, L, P, S, M A B C D E
19. If the sequence of buildings to which mail is delivered is O, P, L, K, S, M and if S is receiving priority mail, which of the following is a complete and accurate list of buildings that must also be receiving priority mail? A: O, L B: O, P C: P, L D: P, M E: O, P, L, K A B C D E
20. If only one building is to receive priority mail, and, as a result, O can be no earlier than fourth in the order of buildings, which of the following must be the building receiving priority mail that day? A: K B: L C: M D: P E: S A B C D E
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III VERBAL Section No. Of Questions 20
Choose the correct answer for each question and shade the corresponding CIRCLE in the answer sheet
Each sentence below has one or two blanks, each blank indicating that something has been omitted. Beneath the sentence are five lettered words or sets of words. Choose the word or set of words that, when inserted in the sentence, best fits the meaning of the sentence as a whole. 1. Florence Nightingale was ___ in the development of modern medicine, ___ such practices as sanitization of hospital wards and isolation of actively infected patients. A. B. C. D. E. A a collaborator…rejecting a maverick…protesting an innovator…initiating a pioneer…criticizing an individualist…standardizing B C D E
4. Roberto Clement was seen as ___ during his life because of both his selflessness on the baseball field and his humanitarian work in his native Nicaragua. A. B. C. D. E. A An individualist a grandstander a sybarite an altruist an opportunist B C D E
5. His habit of spending more than he earned left him in a state of perpetual-----but he------------hoping to see a more affluent day. A. B. C. D. A indigence: persevered in confusion: compromised by enervation: retaliated by motion: responded B C D E
Each question below consists of a related pair of words or phrases, followed by five lettered pairs of words or phrases. Select the lettered pair that best expresses a relationship similar to that expressed in the original pair. National Testing Service Pakistan Overseas Scholarship Scheme for PhD Studies
Read the passages and answer the questions given at the end: Recent technological advances in manned undersea vehicles have overcome some of the limitations of divers and diving equipment. Without vehicles, divers often become sluggish and their mental concentration was limited. Because of undersea pressure that affected their speech organs, communication among divers was difficult or impossible. But today, most oceanographers make observations by the means of instruments that are lowered into the ocean or from samples taken from the water direct observations of the ocean floor are made not only by divers of more than seven miles and cruise at the depth of fifteen thousand feet. Radio equipment buoys can be operated by remote National Testing Service Pakistan Overseas Scholarship Scheme for PhD Studies
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control in order to transmit information back to land based laboratories, including data about water temperature, current and weather. Some of mankind's most serous problems, especially those concerning energy and food, may be solved with the help of observations made by these undersea vehicles. 19. With what topic is the passage primarily concerned? A. Recent technological advances. B. Communication among divers. C. Direct observation of the ocean floor D. Undersea vehicles A B C D E
20. Divers have problems in communicating underwater because? A. The pressure affected their speech organs B. The vehicles they used have not been perfected. C. They did not pronounce clearly D. The water destroyed their speech organs. A B C D E
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Drill Test II
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I Quantitative Section Choose the correct answer for each question and shade the corresponding CIRCLE in the answer sheet
The tiles in the floor of a bathroom are 15/16 inch squares. The cement between the tiles is 1/16 inch. There are 3240 individual tiles in this floor. The area of the floor is A. B. C. D. E. 225 sq. yds. 2.5 sq. yds. 250 sq. ft. 22.5 sq. yds 225 sq. ft.
A
3.
B
C
D
E
He was given successive discounts of
A man bought a TV set that was listed at $160. 20% and 10%. The price he paid was A. B. C. D. E. $129.60 $119.60 $118.20 $115.20 $112.00
A
4.
B
C
D
E
Mr. Jones' income for a year is $15,000. He pays 15% of this in federal taxes and 10% of the remainder in state taxes. How much is left? A. B. C. D. E. $12,750 $9,750 $14,125 $13,500 $11,475
A
5.
B
C
D
E
The radius of a circle which has a circumference equal to the perimeter of a hexagon whose sides are each 22 inches long is closest in length to which one of the following? A. B. C. D. E. 7 21 14 28 24
A
B
C
D
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6. If a, is a multiple of 5 and b = 5a, which of the following could be the value of a + b? I. A. B. C. D. E. 60 I only III only I and III only II and III only None of these II. 100 III. 150
The integral part of logarithm is called A. Characteristic B. Mantissa C. Solution D. Root E. None of these
A
A. B. C. D. E.
B
1 ∞ zero -∞ –1
C
D
E
10. On the y-axis, the x-coordinate is
A
B
C
D
E
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II ANALYTICAL Section No. Of Questions 20
Choose the correct answer for each question and shade the corresponding CIRCLE in the answer sheet
For question 1 to 3 A volunteer uses a truck to pick up donations of unsold food and clothing from stores and to deliver them to locations where they can be distributed. He drives only along a certain network of roads. In the network there are two-way roads connecting each of the following pairs of points: 1 with 2, 1 with 3, 1 with 5, 2 with 6, 3 with 7, 5 with 6, and 6 with 7. There are also one-way roads going from 2 to 4, from 3 to 2, and from 4 to 3. There are no other roads in the network, and the roads in the network do not intersect. To make a trip involving pickups and deliveries, the volunteer always takes a route that for the whole trip passes through the fewest of the points 1 through 7, counting a point twice if the volunteer passes through it twice. The volunteer's home is at point 3. Donations can be picked up at a supermarket at point 1, a clothing store at point 5, and a bakery at point 4. Deliveries can be made as needed to a tutoring center at point 2, a distribution center at point'6, and a shelter at point 7. 1. If the volunteer starts at the supermarket and next goes to the shelter, the first intermediate point his route passes through must be A: 2 B: 3 C: 5 D: 6 E: 7 A B C D E
2. If, starting from home, the volunteer is then to make pickups for the shelter at the supermarket and the bakery (in either order), the first two intermediate points on his route, beginning with the first, must be A: 1 and 2 B: 1 and 3 C: 2 and 1 D: 2 and 4 E: 4 and 2 A B C D E
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3. If, starting from the clothing store, the volunteer next is to pick up bread at either the supermarket or the bakery (whichever stop makes his route go through the fewest of the points) and then is to go to the shelter, the first two points he reaches after the clothing store, beginning with the first, must be A: 1 and 2 B: 1 and 3 C: 4 and 2 D: 6 and 2 E: 6 and 4 A B C D E
For question 4 to 5 There are seven cages next to each other in a zoo. The following is known about the cages. Each cage has only one animal, which is either a monkey or a bear. There is a monkey in each of the first and last cages. The cage in the middle has a bear. No two adjacent cages have bears in them. The bear's cage in the middle has two monkey cages on either side. Each of the two other bear cages are between and next to two monkey cages 4. How many cages have monkeys in them? A: 2 B: 3 C: 4 D: 5 E: 6 A B C D E
5. The bear cage in the middle must have A: No other bear cage to its left B: No monkey cage on its right. C: A bear cage to its left and to its right D: Other bear cages next to it. E: No monkey cage to its left. A B C D E
For question 6 to 8 A nursery class in a school has a circular table with eleven seats around it. Five girls (Kiran, Lado, Maryam, Omera and Parveen) and five boys (Farhan, Ghaus, Haris, Imdad and Jahangir) are seated around the table. None of the girls are seated in a seat adjacent to another girl. Kiran sits between Farhan and Ghaus, and next to each of them. Jahangir does not sit next to Imdad. 6. Which of the following is a possible seating order around the table? A: Empty seat, Farhan, Kiran, Ghaus, Lado, Omera, Haris, Imdad, Parveen, Jahangir, and Maryam. National Testing Service Pakistan Overseas Scholarship Scheme for PhD Studies
8. If Jahangir leaves his seat and occupies the empty seat, his new seating position would be between: A : Farhan and Kiran B : Maryam and Ghaus C : Kiran and Ghaus D : Imdad and Lado E : Parveen and Lado A B C D E
For question 9 to 11 Four telephone operators (Abid, Baqir, Chauhan, and Daud) each have to perform duties at the telephone exchange on four different days, Thursday through Sunday. The following is known about their duty schedule: Chauhan has his duty day before Abid. Daud has his duty day later than Baqir. 9. Which of the following is a possible order of duty days for the four operators? A: Chauhan, Daud, Abid and Baqir. B: Daud, Chauhan, Abid, and Baqir. C: Baqir, Chauhan, Daud and Abid. D: Abid, Chauhan, Daud and Baqir. E: Abid, Baqir, Daud and Chauhan. A B C D E
10. If Chauhan has his duty day on Saturday, who must have his duty day on Thursday? A: Either Abid or Daud. National Testing Service Pakistan Overseas Scholarship Scheme for PhD Studies
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B: Daud C: Abid D: Either Baqir or Daud. E: Baqir. A B C D E
11. Each of the following is possible EXCEPT: A: Chauhan has his duty on Thursday. B: Baqir has his duty on Thursday. C: Daud has his duty on Saturday. D: Baqir has his duty on Sunday E: Abid has his duty on Sunday. A B C D E
For question 12 to 13 There are 12 seats facing the blackboard in a classroom, four seats (A1, A2, A3 & A4) in that order are in row A, the first row from the blackboard. Immediately behind row A is row B with four seats (B1, B2, B3 & B4) in that order. Immediately behind row B, is the last row C with four seats (C1, C2, C3 & C4) in that order. Six students attend the class the following is known about there seating arrangement: Ejaz sits exactly in front of Comil, Seat A2 is always unoccupied Daud does not sit next to Farhat, Gharuy sits in seat A4 Hamid does not sit in seat B4 All the seats in row C always remain empty 12. If Daud sits in seat B3, then Farhat must sit in seat: A: A3 B: A1 C: B4 D: B2 E: C2 A B
C
D
E
13. Suppose that Hamid and Ejaz are sitting in seats A1 and A3 respectively, then it CANNOT be true that seat: A: B1 is occupied by Daud. B: B2 is empty C: B1 is empty D: B3 is OCCUPIED BY Comil E: B4 is empty A B C D E
For question 14 to 17 National Testing Service Pakistan Overseas Scholarship Scheme for PhD Studies
16. If Q and R are both on the committee, who else must be on the committee? A: J B: K C: L D: M E: O A B C D E
17. In how many different ways can the principal select an acceptable committee? A: Fewer than 3 B: 3 C: 5 D: 7 E: More than 7 A B C D E
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For question 18 to 20 Three other. Each bench has room for exactly three people. Everyone must at in a seat or on a bench, and seating is subject to the following restrictions: An adult must sit on each bench. Either R or S must sit in the driver's seat. J must sit immediately beside M. 18. Which of the following can sit in the front passenger seat? A: J B: L C: R D: S E: V A B C D E
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III VERBAL Section No. Of Questions 20 Choose the correct answer for each question and shade the corresponding CIRCLE in the answer sheet
Each sentence below has one or two blanks; Surprisingly enough, it is more difficult to write about the--------than about the--and strange. A. B. C. D. A specific, foreign abstract, prosaic commonplace, exotic simple, routine B C D E
7. Consumers refused to buy meat products from the company because of rumors that the water supply at the meat processing plant was ______; the rumors, however, were quite ______, with no hard evidence to back them up. A. B. C. D. E. A uninspected .. reckless contaminated .. unsubstantiated impure .. damaging misdirected .. scandalous unscrupulous .. vicious B C D E
8. Many kinds of harmful viruses are unhindered when passing through different parts of the host organism; indeed, there are few organic substances which such viruses' cannot______. A. B. C. D. E. A undermine disseminate aerate exterminate perforate B C D E
9. Their conversation was unsettling, for the gravity of their topic contrasted so oddly with the ______ of their tone A. B. C. D. E. A uniqueness rapidity lightness precision reverence B C D E Overseas Scholarship Scheme for PhD Studies
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10. Throughout the animal kingdom, ____ bigger than the elephant. A. B. C. D. E. A whale is only the only the whale is is the whale only only whale is the whale is only B C D E
Each question below consists of a related pair of words or phrases, followed by five lettered pairs of words or phrases. Select the lettered pair that best expresses a relationship similar to that expressed in the original pair. 11. YAWN: BOREDOM :: A. dream : sleep B. anger : madness C. smile : amusement D. face : expression E. impatience : rebellion A B C D E
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For Question 15-20 read the following passage: A popular theory explaining the evolution of the universe is known as the Big Bang Model. According to the model at some time between twenty billion years ago, all present matter and energy were compressed into a small ball only a few kilometers in diameter. It was, in effect, an atom that contained in the form of pure energy all of the components of the entire universe. Then, at a moment in time that astronomers refer to as T = 0, the ball exploded, hurling the energy into space. Expansion occurred. As the energy cooled most of it became matter in the form of protons, neutrons and electrons. These original particles combined to form hydrogen and helium and continued to expand. Matter formed into galaxies with stars and planets. 15. Which sentence best summarizes this passage? A. The big band theory does not account for the evolution of the universe B. According to the Big Bang Model, an explosion caused the formation of the universe C. The universe is made of hydrogen and helium D. The universe is more than ten billion years old A B C D E 16. According to this passage when were the galaxies formed? A. B. C. D. A Ten Billion Years ago Fifteen billion Years ago At T = 0 Twenty billion years ago B C D E
17. The word "compressed" in the passage could best be replaced by A. B. C. D. A Excited Balanced Reduced Controlled B C D E
18. It may be inferred that A. B. C. D. A Energy and matter are the same Protons, neutrons, and electrons are not matter Energy may be converted into matter The galaxies stopped expanding as energy cooled B C D E
20. The environment before the Big Bang is described as all the following EXCEPT A. B. C. D. A Compressed matter Energy All the components of the universe Protons, electrons and neutrons B C D E
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Drill Test III
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I Quantitative Section No. Of Questions 20
Choose the correct answer for each question and shade the corresponding OVAL in the answer sheet
1. If the pattern of dots shown above is continued so that each row after Row One contains 1 dot more than the row immediately above it, which row will contain 12 dots? A. B. C. D. E. A Seven Eight Nine Ten Twelve B C D E
2. Each of Steve's buckets has a capacity of 11 gallons, while each of Mark's buckets can hold 8 gallons. How much more water in gallons can 7 of Steve's bucket's hold compared to 7 of Mark's buckets? A. B. C. D. E. A 3 7 21 24 56 B C D E
3. Two integers have a sum of 42 and a difference of 22. The greater of the two integers is A. B. C. D. E. A 22 25 28 31 32 B C D E
4. The average of five numbers is 34. If three of the numbers are 28, 30 and 32, what is the average of the other two? A. 40 B. 50 C. 60 D. 70 National Testing Service Pakistan
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E. 80 A B C D E
6. In a certain cake, two straight cuts (made along two different radii) succeed in removing 4/15 of the total cake. What is the central angle in degrees of the piece cut? A. B. C. D. E. A 26 60 85 92 96 B C D E
78. If 2 and 4 each divide q without remainder, which of the following must q divide without remainder. National Testing Service Pakistan Overseas Scholarship Scheme for PhD Studies
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A. B. C. D. E. A
1 2 4 8 It cannot be determined from the information given. B C D E
9. The ratio of boys to girls in a certain classroom was 2 : 3. If boys represented five more than one third of the class, how many people were there in the classroom? A. B. C. D. E. A 15 25 30 45 75 B C D E
1214. Which is greater? Column A (10/4) / (3/2) * (3/7) A. B. C. D. E. A if if if if if Column B (3/4) * (10/7) / (3/2)
the quantity in Column A is greater the quantity in Column B is greater the two quantities are equal there is no relationship between these two quantities the relationship cannot be determined from the information given C D E
Choose the correct answer for each question and shade the corresponding CIRCLE in the answer sheet
The office staff of the XYZ Corporation presently consists of three bookkeepers (L, M and N ) and five secretaries (O, P, Q, R and S). Management is planning to open a new office in another city sending three secretaries and two bookkeepers from the present staff. To do so they plan to separate certain individuals who do not function well together. The following guidelines were established to set up the new office: (a) Bookkeepers L and N are constantly finding faults with one another therefore should not be sent together to the new office. (b) N and P function well alone but not as a team. They should be separated. (c) O and R have not been on speaking terms for many months. They should not go together. (d) Since O and Q have been competing for a promotion, they should not be in one team. Based on the information given above find the correct answers to the following Questions: 1. If M insists on staying back then how many combinations are possible? A. B. C. D. 1 2 3 None
A
2.
B
C
D
E
If L is to be moved as one of the bookkeepers, which of the following CANNOT be a possible working unit? A. B. C. D. LMOPS LMPQS LMORS LMPRS
A
3.
B
C
D
E
If N is sent to the new Office which member of the staff CANNOT be sent? A. B. C. D. O M Q R
A
4.
B
C
D
E
If O is sent to the new office then which of the following is a possible team? A. B. C. D. LMOPR MNOQS MNOPS LMOPS
A
5.
B
C
D
E
If both N and Q are moved to the new office, how many combinations are possible? A. 2 B. 3 C. 4
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D. 1
A
6.
B
C
D
E
Adjacent countries
A map representing countries R, S, W, X, Y and Z is to be drawn. cannot have the same color in the map. The countries adjacent to each other are as follows: Each of R, S, X and Y is adjacent to W. X is adjacent to Y. Each of R and S is adjacent to Z. If X is the same color as Z then it must be true that A. B. C. D. W is a different color from any other country. S is a different color from any other country. X is the same color as Y. S is the same color as X.
A
B
C
D
E
Two statements, labeled I. & II, follow each of the following questions. The statements contain certain information. In the questions you do not actually have to compute an answer, rather you have to decide whether the information given in the statements I. and II. is sufficient to find a correct answer by using basic mathematics and every day facts?
7. A long distance runner has just completed running 28 miles. How long did it take him to finish the journey? I. His record speed is 8.25 miles per hour. II. His average speed through the journey was 8 miles per hour8.
B
C
D
E
Captain of the national cricket team has to be the most popular member of the team. Who is the captain of Pakistan's national cricket team? I. Waqar is the best player on the team. II. Waseem is the senior-most memberNational Testing Service Pakistan
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A
9.
B
C
D
E
How many boys
In a BCE class at CIIT, 30 boys and 10 girls registered Calculus II. passed the course? I. 5 students could not pass. II. There were 2 girls who obtained A grade.
A
this this but and
A
B
C
D
E
10. A horse ran 100 miles without stopping. What was its average speed in miles per hour? I. The journey started at 8 PM and ended at 4 AM the following day. II. The horse ran 20 miles per hour for the first 50 miles sufficient11. How much time will computer a need to solve 150 problems? I. The computer needs 50 seconds to solve one problem. II. Computer never takes more than 60 seconds to solve a problem12. How many pencils does Raheel have? I. He bought two boxes each containing 10 pencils. II. He lent two pencils to Khaleel13. In a certain farm there are 47 goats. How many large brown goats are there? I. 16 of the goats are large. II. There are 18 brown goats in the farm14. Can there be more than 200 pictures in a 60-page book? I. There is at least one picture in each page. II. There are no more than 3 pictures in any page Overseas Scholarship Scheme for PhD Studies
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15. If P > Q and R > S, then, P + R > Q + S. Is X > Y? I. X + A > Y + B II. A > B
III VERBAL Section
No of Questions
Choose the correct answer for each question and shade the corresponding CIRCLE in the answer sheet 10 Although its publicity has been ___, the film itself is intelligent, well-acted, handsomely produced and altogether ___ A. tasteless … respectable B. extensive … moderate C. sophisticated … moderate D. risqué … crude E. perfect … spectacular A 2. B C D E
Ants live in colonies based on ___; each member contributes to the good of all by actively working with others in performing necessary tasks. A. B. C. D. E. A Heredity Individualism Cooperation Reasoning Instinct B C D E
Each question below consists of a related pair of words or phrases, followed by five lettered pairs of words or phrases. Select the lettered pair that best expresses a relationship similar to that expressed in the original pair. 4. STUDYING: LEARNING:: A. running : jumping B. investigating : discovering C. reading : writing Overseas Scholarship Scheme for PhD Studies
Read the passages and answer the questions asked at its end. Almost a century ago Alfred Binet, a gifted psychologist, was asked by the French Ministry of Education to help determine who would experience difficulty in school. Given the influx of provincials to the capital, along with immigrants of uncertain stock, Parisian officials believed they needed to know who might not advance smoothly through the system. Proceeding in an empirical manner, Binet posed many questions to youngsters of different ages. He ascertained which questions when answered correctly predicted success in school, and which questions when answered incorrectly foretold school difficulties. The items that discriminated most clearly between the two groups became, in effect, the first test of intelligence. Binet is a hero to many psychologists. He was a keen observer, a careful scholar, an inventive technologist. Perhaps even more important for his followers, he devised the instrument that is often considered psychology's greatest success story. Millions of people who have never heard Binet's name have had aspects of their fate influenced by instrumentation that the French psychologist inspired. And thousands of psychometricians — specialists in the measurement of psychological variables — earn their living courtesy of Binet's invention. National Testing Service Pakistan Overseas Scholarship Scheme for PhD Studies
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Although it has prevailed over the long run, the psychologist's version of intelligence is now facing its biggest threat. Many scholars and observers — and even some iconoclastic psychologists — feel that intelligence is too important to be left to the psychometricians. Experts are extending the breadth of the concept — proposing much intelligence, including emotional intelligence and moral intelligence. They are experimenting with new methods of ascertaining intelligence, including some that avoid tests altogether in favor of direct measures of brain activity. They are forcing citizens everywhere to confront a number of questions: What is intelligence? How ought it to be assessed? And how do our notions of intelligence fit with what we value about human beings? In short, experts are competing for the "ownership" of intelligence in the next century. 8. According to the passage, which of the following is most similar to the "barometer" developed by Binet? A. B. C. D. E. A 9. The S.A.T. or other standardized college admission test. The written portion of a driver's license test. Open tryouts for a varsity athletic team An electronic scan of brain-wave activity. The trivia questions of a game show. B C D E
The author suggests which of the following about "citizens everywhere"? A. They do not have a sufficiently accurate definition of intelligence to evaluate recent scientific developments. B. They stand to benefit from recent progress in the scientific assessment of intelligence. C. The experiments they are performing with new methods of intelligence measurement are valuable and interesting. D. They are at odds with the experts over who should have the right to define "intelligence." E. Traditionally they have not given careful consideration to some important issues concerning intelligence.
Choose the correct answer for each question and shade the corresponding CIRCLE in the answer sheet
1
1. If the length of BC is twice the length of AC, what are the coordinates of B where A=(x,y)? A. B. C. D. E. A (x,2y) (-x,2y) (2x,y) (-2x,y) (-2x,2y) B C D E
2. The average of five numbers is 34. If three of the numbers are 28, 30 and 32, what is the average of the other two? A. 40 B. 50 C. 60 D. 70 E. 80 A B C D E
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G 3. In the figure above, rectangle AEJL has been divided into 8 congruent squares with each of the 8 squares having an area of 16. What is the length of AE + MF + LG+ AL + BK + CJ + DH + EG? A. B. C. D. E. A 32 44 88 128 176 B C D E which of the following is an
5. In a certain town, p gallons of gasoline are needed per month for each car. How long will q gallons last at this rate given that there are r cars in town? A. B. C. D. E. A pr/q qr/p r/pq q/pr pqr B C D E
810. If the vertices of a triangle are at (0,0), (-3, 4) and (3, 4), what is the area of the triangle? A. B. C. D. E. A 4 6 12 14 18 B C D E
11. A water-tank has a base with dimensions 2 feet by 6 feet. If a cube with each side 1 foot is totally immersed in the water, how many inches will the water rise? (12inches = 1 foot) A. B. C. D. E. A 1 2 4 8 It cannot be determined from the information given B C D E
12. In the figure above, the quadrilateral ABCD is a trapezoid with x = 2. The diameter of each semicircle is a side of the trapezoid. What is the sum of the lengths of the four drawn semicircles? (Round to the nearest whole number.) A. B. C. D. E. A 13 16 19 22 31 B C D E
1415. A restaurant has a special whereby both parents can eat for $20 and each child can eat for $5. Assuming a family group consists of both parents and at least one child, what is the maximum number of family groups that could have attended given that the restaurant took $115? A. B. C. D. E. A 6 5 4 3 2 B C D E
16. Which of the following points lays in the interior of the circle whose radius is 10 and whose center is at the origin? A. B. C. D. E. A (-9, 4) (5, -19) (0, -10) (10, -1) (0,15) B C D E
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Choose the correct answer for each question and shade the corresponding CIRCLE in the answer Analytical No. Of 15 sheet Reasoning Questions 17. If the perimeter of the rectangle ABCD is 14, what is the perimeter of ∆BCD? A. B. C. D. E. 7 12 7 + √29 86 It cannot be determined from the information given. B C D E
Two statements labeled I & II, follow each of the following questions. The statements contain certain information. In the questions you do not actually have to compute an answer, rather you
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have to decide whether the information given in the statements I. and II. is sufficient to find a correct answer by using basic mathematics and every day facts? 1. What day of the week is today? I. Today is March 25. II. Akram left Pakistan on Wednesday2.
B
C
D
E
Can any of the four rivers be more than 300 meters wide? I. The narrowest of the four rivers is 240 meters wide. II. Average width of the four rivers is 300 meters this this but and
A
3.
B
C
D
E
If it is raining then there must be clouds. Are there clouds? I. It is not raining. II. It rained yesterdayRead the passage to answer the question 4-5 A map representing countries R, S, W, X, Y and Z is to be drawn. Adjacent countries cannot have the same color in the map. The countries adjacent to each other are as follows: Each of R, S, X and Y is adjacent to W. X is adjacent to Y. National Testing Service Pakistan Overseas Scholarship Scheme for PhD Studies
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Each of R and S is adjacent to Z. 4. Which of the following countries can be the same color as W? A. B. C. D. A
5.
S X Y Z B C D E
Which of the following is a pair of countries that can be the same color? A. B. C. D. R and S S and W W and X X and Y
A
B
C
D
E
Questions 6 to 11 depends on the following passage A college president wishes to select four members of a faculty-student committee as special representatives to meet with the college's board of trustees. The faculty-student committee consists of eight members four of which (F, G, H and I) are faculty members whereas the other four (R, S, T and U) are students. The president can select any four of the eight committee members as long as the following rules are observed: The four representatives must consist of exactly two faculty members and two students. Either F or G must be one of the representatives but F and G both cannot be the representatives. If R is a representative then H must also be a representative. If T is a representative then G cannot be a representative. 6. If T is a representative but H is not a representative then the whole group can be determined if it were also true that: A. B. C. D. F is a representative. I is a representative. R is not a representative. U is not a representative.
A
7.
B
C
D
E
If R is a representative then which of the following CANNOT be a representative? A. B. C. D. H I S T
A
8.
B
C
D
E
If G is a representative then which of the following can be the other three representatives? A. B. C. D. F, S and U H, I and R H, R and S I, R and U
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A B C D E
9.
If neither S nor U is a representative then which of the following is the pair of facultymember representatives? A. B. C. D. F and G F and H F and I G and H
A
B
C
D
E
10. If G, I and S are representatives then which of the following must also be a representative? A. B. C. D. H R T U
A
B
C
D
E
11. If F and I are representatives then which of the following is not a representative? A. B. C. D. I S U R
A
B
C
D
E
Questions 12 to 14 depends on the following passage
At a congress of the Ruling Party, the seven top party leaders, who are all cabinet ministers, are seated on a platform in order of rank the Prime Minister being in the center. The closer a person is to the Prime Minister; the higher is his/her rank. Moreover, a person sitting on the right of the PM outranks the one sitting equidistant on the left of the PM. The seven leaders are T, U, V, W, X, Y, and Z. Y is four places to the left of the Minister of Agriculture, who is two places to the right of V. U's neighbors are T and the Minister of Agriculture. Z is two places to the left of W. The Ministers of Education, Mining and Culture are seated together, in order, from left to right. The remaining Ministers are those of Social Welfare and Defense. 12. The fifth ranking person in the party hierarchy is: A. Z, the Minister of Mining B. Y, the Minister of Culture C. W, the Prime Minister. D. X, the minister of Defense. A B C D E
13. How many of the seven party leaders outrank the Minister of Education? National Testing Service Pakistan Overseas Scholarship Scheme for PhD Studies
15. "A meadow in springtime is beautiful, even if no one is there to appreciate it." This statement would be a logical opposite to which of the following claims? A. People will see only what they want to see. B. Beauty exits only in the eyes of the beholder. C. Beauty does not depend on seasons. D. The greatest pleasure available to mankind is the contemplation of beauty. A B C D E
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III VERBAL Section No. Of Questions 10 Choose Some illnesses such as smallpox, which have been almost eliminated in the United States are still ____ in many places abroad. A. discussed B. prevalent C. scarce D. unknown E. hospitalized A 2. B C D E
A recent study indicates that the crime rate in the United States remains ____ and that one in three households ____ some form of major crime in any year A. incredible ... witnesses B. astronomical ... experiences C. simultaneous ... perpetrates D. unsuccessful ... initiates E. defeated ... prosecutes A B C D E
Each question below consists of a related pair of words or phrases, followed by five lettered pairs of words or phrases. Select the lettered pair that best expresses a relationship similar to that expressed in the original pair. 3. SALVAGE : TREASURE A. settle : argument B. incorporate : company C. send : correspondence D. rescue : victim E. recycle : newspaper A 4. B C D E
Read the passages and answer the questions given at its end: National Testing Service Pakistan Overseas Scholarship Scheme for PhD Studies
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behavior 5. The main idea of this excerpt is (A) to provide evidence of the origin of language. (B) to present the need for language. (C) to discuss how early man communicated. (D) to present the culture of early man. (E) to narrate the story of English. A 6. B C D E
Theories of the origin of language include all of the following EXCEPT (A) changes occurring through the years. (B) the need to communicate. (C) language of children. (D) the first man's extensive vocabulary. (E) communication among primitive men. Overseas Scholarship Scheme for PhD Studies
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A 7. B C D E
The purpose of the discussion of the word, "Doll," is intended to (A) Trace the evolution of a noun. (B) Support the fact that naming things is most important. (C) Indicate how adults teach language to children. (D) Show the evolution of many meanings for one word. (E) Evince man's multiple uses of single words A B C D E
8.
The implication of the author regarding the early elements of language is that (A) There were specific real steps followed to develop our language. (B) Care must be exercised when exhuming what we consider the roots of language. (C) We owe a debt of gratitude to the chimpanzee contribution. (D) Adults created language in order to instruct their children. (E) Language was fully developed by primitive man. A B C D E
9.
If we accept that primitive man existed for a very long period of time without language, then we may assume that (A) language is not necessary to man's existence. (B) language developed with the developing culture of primitives. (C) primitives existed in total isolation from one another. (D) children brought about a need for language. (E) mankind was not intended to communicate. A B C D E
10. After a reading of this article, one might infer that (A) society creates problems with language. (B) language is for adults to instruct children. (C) society uses language to improve itself. (D) with the evolution of language came wisdom. (E) language brings power. A B C D E
Note: The Sample Test does not include quantitatively the same number of questions as there would be in the actual papers. They are merely meant to provide conceptual guidance to the users or prospective candidates.
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I VERBAL Section No. Of Questions 15
Choose Despite the millions of dollars spent on improvements, the telephone system in India remains ________ and continues to ___________ the citizens who depend upon it. A. B. C. D. E. Primitive…inconvenience Bombastic...upset Suspicious...connect Outdated...elate Impartial...vex
3. A good trial lawyer will argue only what is central to an issue, eliminating ___________ information or anything else that might __________ the client. A. B. C. D. E. Seminal...amuse Extraneous...jeopardize Erratic...enhance Prodigious...extol Reprehensible…initiate
4. Pollen grains and spores that are 200 millions old are now being extracted from shale and are ____________ the theory that the breakup of the continents occurred in stages; in fact, it seems that the breakups occurred almost __________ . A. B. C. D. E. refining...blatantly reshaping...simultaneously countermanding...imperceptibly forging...vicariously supporting...haphazardly
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Each question below consists of a related pair of words or phrases, followed by five lettered pairs of words or phrases. Select the lettered pair that best expresses a relationship similar to that expressed in the original pair. 5. DETENTION : RELEASE :: A. B. C. D. E. viciousness : attack calamity : repair qualification : employ induction : discharge therapy : confuse
Read the passages and answer the questions asked at its end. Art, like words, is a form of communication. Words, spoken and written, render accessible to humans of the latest generations all the knowledge discovered by the experience and reflection, both of preceding generations and of the best and foremost minds of their own times. Art renders accessible to people of the latest generations all the feelings experienced by their predecessors, and those already felt by their best and foremost contemporaries. Just as the evolution of knowledge proceeds by dislodging and replacing that which is mistaken, so too the evolution of feeling proceeds through art. Feelings less kind and less necessary for the well-being of humankind are replaced by others kinder and more essential to that end. This is the purpose of art, and the more art fulfills that purpose the better the art; the less it fulfills it, the worse the art. 13.The author develops the passage primarily by A. B. C. D. E. theory and refutation example and generalization comparison and contrast question and answer inference and deduction
14.According to the author, knowledge is A. B. C. D. E. evolutionary and emotional cumulative and progressive static and unmoving dynamic and cyclical practical and directionless
15.According to the passage, all of the following are true EXCEPT: A. B. C. D. E. Art is a form of communication. Art helps to refine sensibilities. Art is a repository of experience. Real art can never be bad. Art is a progressive human endeavor.
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II Analytical Reasoning Section No. Of Questions 20 Choose the correct answer for each question and shade the corresponding CIRCLE in the answer sheet
Questions 16-19 are based on the following. The Western Derby is a race held annually at Bayshore Racetrack. There are eight gates at the racetrack, but only seven horses are entered in this race—Julius Caesar, King's Bounty, Longshot, Man Among Boys, Nocturnal, Odyssey, and Phantom. One of the gates is left empty. The horses are at the gate, waiting for the race to begin. Gate 1, on the inside of the racetrack, is occupied. Phantom is at a gate inside of Nocturnal. The number of gates separating Julius Caesar and King's Bounty equals the number of gates separating Longshot and Man among Boys. Nocturnal and Odyssey are next to each other.
16. If Odyssey is at Gate 2, which of the following must be true? A. B. C. D. E. Nocturnal is at the innermost gate. King's Bounty is at the outermost gate. A horse occupies the outermost gate. Phantom is at the innermost gate. The outermost gate is not empty.
I and II only II and III only II and IV only I, II, and III only I, II, III, and IV
19. If Julius Caesar and King's Bounty are at the second and fourth gates, respectively, all of the following can be true EXCEPT A. B. C. D. E. Phantom is at Gate 1 Man Among Boys is at Gate 3 Longshot is at Gate 6 Odyssey is at Gate 7 Nocturnal is at Gate 7
20.Studies have shown that families who install smoke detectors and own fire extinguishers have a reduced risk of losing a child in a house fire. Therefore, no family who installs smoke detectors and owns a fire extinguisher will lose a child in a house fire. Of the following, the best criticism of the argument above is that the argument does not take into account the possibility of losing a child in a house fire despite all precautionary measures B. indicate that fire extinguishers are effective during early stages of a fire C. cite the fact that smoke detectors have proven to be effective in waking sleeping children during a house fire D. differentiate between the two major causes of house fires: cooking and heating E. take into account that families who buy smoke detectors are also more likely to purchase fire insurance 21.LSD is a drug known to cause synesthesia, a phenomenon in which sensory input somehow becomes interchanged in the brain: a person with synesthesia might smell a symphony, hear sun light, or taste a pinprick. While most cases are drug induced, some people suffer from synesthesia in various forms since birth. Which of the following can be most safely inferred from the information above? Synesthesia is not always a drug-induced phenomenon. Some great artists of this century have been known for their synesthetic proclivities. C. LSD is an addictive drug. D. Synesthesia is rarely bothersome to those who experience it. E. Synesthesia at birth is a result of mothers who have tried LSD. 22.Palindromes are easier to solve than acrostics, but acrostics are more difficult to create than palindromes. Rebuses are more difficult to solve than acrostics, yet rebuses are easier to create than palindromes. A. B. A.
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If the above information is true, then it must also be true that A. B. C. D. E. acrostics are more difficult to create than rebuses palindromes are more difficult to solve than rebuses rebuses are easier to solve than acrostics acrostics are easier to create than rebuses rebuses are easier to solve than palindromes
Questions 23-25 are based on the following. A university has a procedure for registering and recording complaints. Due to strict bureaucratic regulations, the following system of passing complaints must be observed: A is the first registrar to receive all incoming complaints. F is the recorder and final administrator to handle a complaint. Personnel B, C, D, and E may pass complaints only as follows: A to B B to either C or D C to either B or E D to C E to either D or F 23.Which is an acceptable path for a complaint to follow, passing from A? A. B. C. D. E. B to C to D to F B to D to C to F B to C to E to F B to E to F D to C to F
24.If a complaint is received and is handled by each personnel member only one time, which of the following could be one of the passes? A. B. C. D. E. A to C C to B C to F D to C E to D
25.Between which two personnel may a complaint pass by means of two different paths without any duplication of passes? A. B. C. D. E. B to E C to D C to E D to B E to B
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Questions 26-31 are based on the following. In a baseball field, one team can practice at a time. There are seven teams—the Aces, the Bears, the Cubs, the Ducks, the Eagles, the Falcons, and the Giants. The baseball field is open seven evenings a week from Monday to Sunday (Sunday being considered the last day of the week), and the allocation of practice times is governed by the following rules: On any evening, only one team can play. The Aces must practice on Monday. The Ducks practice exactly one day before the Falcons practice. The Falcons practice exactly one day before the Giants practice. The Cubs and the Bears must practice earlier in the week than the Eagles. 26.The latest day in the week that the Bears can practice is A. B. C. D. E. Tuesday Wednesday Thursday Friday Saturday
27.If a person went to the baseball field on three consecutive evenings, he or she could see which of the following teams in the order listed? A. B. C. D. E. the the the the the Falcons, the Giants, the Cubs Falcons, the Giants, the Ducks Aces, the Ducks, the Cubs Bears, the Cubs, the Falcons Ducks, the Eagles, the Falcons
28.One week, the Cubs practiced on Wednesday and the Ducks practiced the next day. That week, the Bears must have practiced on A. B. C. D. E. Monday Tuesday Friday Saturday Sunday
29.If the Giants practice on Thursday, the Eagles and the Ducks must practice on which days, respectively? A. B. C. D. E. Sunday and Tuesday Saturday and Tuesday Friday and Wednesday Wednesday and Thursday Tuesday and Monday
30.If the Falcons practice on Saturday, the Eagles must practice on what day? A. Tuesday
31.The practice schedule has to adhere to which of the following? A. B. C. D. E. The The The The The Ducks practice earlier in the week than the Eagles. Falcons practice on a later day than the Eagles. Falcons practice earlier in the week than the Giants. Cubs practice earlier in the week than the Ducks. Bears practice earlier in the week than the Cubs.
32.Wine, cheese, butter, and raisins are all examples of early techniques to preserve food. In modern times, food scientists have developed other techniques such as dehydration, hermetic sealing, and radiation. Of these, radiation is the most controversial because preliminary studies have shown that radiation alters the natural chemical bonds in fruits and vegetables. Instead of providing salutary effects, eating radiated produce may well introduce irritating chemicals into the body, creating a possible health hazard. Which of the following, if true, supports the conclusion that eating radiated produce poses a possible health hazard? A. Radiation affects only those chemical bonds associated with water, that is, hydrogen and oxygen. B. Radiation kills microorganisms that hasten food decay. C. The radiation-induced bonds are unlike any of those found in non-radiated produce. D. Certain microorganisms, namely those found in yogurt cultures, are essential for proper digestion. E. Radiation has no effect on foods preserved by drying. 33.Blue Blood, Inc., is a private blood products company that buys blood only from qualified donors. To qualify, a person must weigh at least 105 pounds, must not have taken malaria medication in the last three years, must never have had hepatitis, and must never have used intravenous drugs. Blue Blood nurses know that traveling has an effect on the possibilities for blood donation: Everyone who travels to Malaysia is required to take malaria medication; no one who enters Singapore can have ever used intravenous drugs; everyone traveling to Gorisimi gets hepatitis. Which of the following situations would not automatically disqualify a person from selling blood to Blue Blood? A. B. C. D. E. traveling to Malaysia two years ago having once weighed 110 pounds and now weighing 95 pounds being denied admission to Singapore traveling to Gorisimi five years ago using intravenous drugs that were legal at the time
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34.Before marriage, couples should be tested for AIDS and any other sexually communicable diseases. Negative results will guarantee the health and safe-ness of their marriage. Which of the following is an assumption of the argument in the passage above? A. Current state laws require couples who are planning to get married to be tested for infectious disease in order to prevent possible health problems in the future. B. There are many infectious diseases that can be sexually transmitted from one individual to another. C. Fortunately even if a test proves positive for a communicable disease, couples can still lead healthy marriages by taking the proper precautions. D. Due to advances in medical research over the years, infectious diseases that used to be fatal can now be effectively treated. E. All the diseases detectable through testing have no incubation period and the results of these tests can immediately indicate whether or not the individual has the disease. Question 35 is based on the following. Nine athletes attend a sports banquet. Three of the athletes—}, K, and L—are varsity football players; two of the athletes—M and N—are varsity basketball players. The other four athletes— O, P, Q, and R—belong to the hockey club. All nine athletes will be seated at three small tables, each seating three athletes. The athletes must be seated according to the following rules: O and J do not sit at the same table. P sits together with at least one of K or M. There can be at most only one football player at a table. There can be at most only one basketball player at a table. 35.Suppose just one varsity athlete sits at a certain table, and that athlete happens to be J. If so, who else sits with J? A. B. C. D. E. P, Q P, R Q, R O, Q O, P
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III Quantitative Section
No of Questions
15
Choose the correct answer for each question and shade the corresponding CIRCLE in the answer sheet
38.Cindy wants to paint her office. She can buy three cans of the same-priced paint and three identical brushes for $21, or she can buy four cans of the same paint and one brush for $22. How much does a can of paint cost? A. B. C. D. E. $2 $3 $4 $5 $6
40.The sum of a and 9 - 2a is less than 8. Which of the following is (are) the value(s) of a? I. a<-1 II. a< 1
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Building Standards in Educational and Professional Testing
III. a>1 A. B. C. D. E. I only II only III only I and II only I and III only
41.Susan is having a party. At 7:00 P.M., guests begin arriving at a uniform rate of 8 people every 15 minutes. If this pattern continues, how many guests will have arrived by 9:30 P.M.? F. G. H. I. J. 10 20 40 64 80
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44.In the figure above, if the radius of the circle is 8, and triangle TRS is inscribed in the circle, then the length of arc TRS is A. B. C. D. E. 16π/3 (32 π)/3 16 π (128 π)/3 64 π
45.For developing pictures, XYZ Photo Lab charges a service fee of $3 for every order it receives in addition to a printing fee. If the order consists of 12 pictures or less, the printing fee per picture is $0.36. If the order consists of more than 12 pictures, the printing fee per picture is $0.24. What is the total cost per picture for an order consisting of 30 pictures? A. B. C. D. E. $0.11 $0.24 $0.34 $0.46 $3.24
46.Lisa found an easy way to add up a sequence of positive even integers with an even number of terms. She formed pairs of equal sums by adding the first integer to the last, the second integer to the next-to-last, and so on. She then computed the total by adding these equal sums. If the total Lisa obtained was 930, how many terms were there in the sequence of positive even integers if the sequence started with the number 2? A. B. C. D. E. 30 39 40 60 465
47.December is the busiest month at Lamont's Gift Shoppe, where sales in December are 40 percent higher than average. If sales in February are typically 20 percent lower than average, what is the ratio of February sales to December sales? A. B. C. D. E. 1:2 4:2 4:5 4:7 6:7
50.Box A and box B have 6 cards each. Each card is marked with one integer, 1 through 6. Both boxes can have more than one card with the same integer, but the sum of all the integers in each box must be 18. Two of the cards in box/1 are 6's and two of the cards in box B are 5's. If one card is drawn from box A and one from box B, but neither a 6 nor a 5 is drawn, what is the largest possible sum of the integers on the cards drawn from the two boxes? A. B. C. D. E. 3 4 7 8 12 | 677.169 | 1 |
Geometry GMAT Preparation GuidePaperback
Item is available through our marketplace sellers.
OverviewThe book offers a unique balance between two competing emphases: test-taking strategies and in-depth content understanding. Practice problem sets build specific foundational skills in each topic and include the most advanced content that many other prep books ignore. As the average GMAT score required to gain admission to top b-schools continues to rise, this guide provides test takers with the depth and volume of advanced material essential for succeeding on the GMAT's computer adaptive format. Book also includes online access to 6 full-length Simulated Practice GMAT Exams at Manhattan GMAT's website.
Special Features:
*Each of the 8 Guides covers 1 major topic in extensive depth, providing students with many more pages-per-topic than found in all in-one books. Single-topic focus of each guide allows the student to purchase only those guides that pertain to his/her weaknesses.
*Purchase includes 6 Full-Length Computer Adaptive Online Practice GMAT Exams and Bonus Geometry Online Question Bank developed exclusively by Manhattan GMAT. Your book includes a unique access code that enables you to access these online resources.
*Cleanly-presented strategies, problems sets, and explanations with sidebars that highlight key concepts; no need to wade through cramped pages in small typeface.
*Each chapter builds comprehensive contentunderstanding in the given topic area by providing rules, strategies and in-depth examples of how the GMAT tests a given topic and how you can respond accurately and quickly. Each chapter is followed by 15 challenging practice problems, progressively increasing in difficulty and designed to increase your ability from novice to expert in the given topic. Answers with comprehensive explanations follow each problem set.
*A special chapter provides specific strategies for attacking GMAT Data Sufficiency Problems that involve the use of Geometry. Data Sufficiency problems are uniquely challenging problems that account for more than one-third of the quantitative problems you will see on the GMAT.
*After mastering all the Geometry topics and completing Manhattan GMAT's comprehensive problem sets, you can test your knowledge on Geometry problems that have appeared on past GMAT exams. These problems are contained in The Official Guides For GMAT Review (sold separately), published by GMAC, the organization that administers the GMAT. Manhattan GMAT has categorized all the problems in The Official Guides by topic and the comprehensive list of categorized Geometry problems appears in the back of the Geometry Strategy Guide.
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Manhattan GMAT's 8 preparation guides were developed by Manhattan GMAT's talented staff of real teachers, all of whom have scored in the 99th percentile on the official GMAT. As the company focuses solely on the GMAT (no other tests), it continually updates the guides to reflect the GMAT's most current trends. Questions are refined and strategies enhanced, blending the academic and test-taking skills that have been essential to the success of Manhattan GMAT students around the world. The nation's largest GMAT-exclusive preparation provider, Manhattan GMAT was founded by Zeke Vanderhoek. A Yale graduate, Zeke taught as a member of Teach for America at New York City public junior-high school, earned a Masters in Philosophy & Education from Columbia University's Teachers College, and supplemented his day-job by tutoring individuals in various subjects at all educational levels. Word-of-mouth referrals soon brought in a remarkably high number of GMAT test-takers, and thus Manhattan GMAT and its prep guides were born. | 677.169 | 1 |
[Study material by JSUNIL for Central public school, Samastipur] What is set (in mathematics)?
The collection of well-defined distinct objects is known as a set. The word well-defined refers to a specific property which makes it easy to identify whether the given object belongs to the set or not. The word 'distinct' means that the objects of a set must be all different. Sets are denoted by Capital l letters
Examples:
A = {Color of rainbow] Þ express set of the Color of rainbow
A = [1,2,3,……..} Þ Represent the set of natural numbers
B = [a, e, i, o, u] Þ Represent the set of vowels
M = {1/2, 2/3,3/4………….99/100}
Elements of Set:
The different objects that form a set are called the elements of a set. The elements of the set are written in any order under curly bracket. Elements are denoted by small letters.
B = [a, e, i, o, u] Þ Represent the set of vowels
Here element of set B are a, e, i, o, u
Notation of a Set: Download full study material Download Set Theory - ● Sets ● Objects Form a Set ● Elements of a Set ● Properties of Sets ● Representation of a Set ● Different Notations in Sets ● Standard Sets of Numbers ● Types of Sets ● Pairs of Sets ● Subset ● Subsets of a Given Set ● Operations on Sets ● Union of Sets ● Intersection of Sets ● Difference of two Sets ● Complement of a Set ● Cardinal number of a set ● Cardinal Properties of Sets ● Venn Diagrams | 677.169 | 1 |
Mathematics at Work is a book that challenges our assumptions about our subject. This is the fourth edition of a book devoted to
Practical Applications of Arithmetic, Algebra, Geometry, Trigonometry, and Logarithms to the Step-by-Step Solutions of Mechanical Problems, with Formulas Commonly Used in Engineering Practice and a Concise Review of Basic Mathematical Principles.
Browsing through the book reveals an amazing mix of topics, from very elementary stuff about divisibility to rather sophisticated chapters on plane and spatial geometry. Many pages contain elaborate tables of results on trigonometric functions, solving triangles, factoring expressions, and so on. Many specific construction problems are considered too, such as (to choose an example at random) how to find the "radius of a circle tangent to a given circle and to two lines at a given angle." There is a whole section on approximate formulas which includes a rather sophisticated discussion of where such formulas come from and how one might decide whether it is OK to use them. There is a chapter on "gear ratio problems", which turns out to be about continued fractions. At the back, there are dozens of tables giving all sorts of interesting and useful functions (one wonders why, in an age of calculators, one would need tables of common logarithms or trigonometric functions, but there they are).
I find this a fascinating artifact. On the one hand, it can be an excellent source of "real world" problems for those of us who teach elementary mathematics. Many of these problems are quite interesting, and some are quite difficult; in fact, I'd probably have trouble solving some of them on my own. On the other hand, it reflects a perspective on what mathematics is all about that I find deeply alien. This mathematics is about vast collections of apparently unrelated facts that one looks up as needed. (So, for example, there are not only tables indicating how the sines and cosines of complementary and supplementary angles are related, but also similar tables for tangents, cotangents, secants and cosecants!) Here is mathematics as a tool, but perhaps also as less than a science. | 677.169 | 1 |
Inequalities Classwork
PDF (Acrobat) Document File
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PRODUCT DESCRIPTION
This assignment is designed to allow students to practice solving, simplifying, writing and graphing inequalities on a number line BEFORE starting to solve/simplify with negatives (which is usually more of a challenge). There are no negative coefficient/sign-flip problems included. There are multiple types of problem and this allows students choice; they select three problems from each section (I usually assign one extra per section for homework). The choice and variety keep students engaged and the comfort level in completion helps the teacher assess whether the class is ready to move on to working with negatives. This can also be used as an assessment, study guide, homework, as partner work or as an alternate | 677.169 | 1 |
Technical overview
WIRIS editor as a way to input equations. This is a visual and powerful, but easy to use, formulas and equations editor. The editor can be integrated in any platform in a straight forward way; you might get surprised to discover that such integration already exists. See plugins. The editor is developed in JavaScript and we have also ported it to Flash, C/Qt, Java/Swing and .NET.
WIRIS editor as a way to render equations. You will be able to create high quality rendering of formulas suitable both for the Web and for a printed version. The file output formats available are PNG and SWF, with SVG coming soon. The render engine can be used as a Web services SaaS or installed as a Java or .NET library.
WIRIS editor as a way to store equations. WIRIS editor can work both with the MathML standard or LaTeX formats.
WIRIS editor makes formulas accessible. WIRIS editor generates also a textual version of any formula. This feature is available in Spanish and English. Other languages can be implemented on demand.
For example, a formula like can be read as "one half".
WIRIS quizzes as a way to automatically grade students. WIRIS quizzes can be used to improve the computer guided assessment to check that the input answer of a student is mathematically equal to the correct answer. A powerful mathematical engine is used for this purpose. Thus, x+2 is the same as 2+x.
WIRIS quizzes as a way to generate random questions. With WIRIS quizzes you will be able to generate thousands of variants of the same question. You will use the WIRIS quizzes studio tool to build the random values and graphics that you will insert into your own assessment system.
WIRIS quizzes as a way to allow students input formulas in questions. With WIRIS quizzes is feasible that students answers questions with formulas because a custom version of WIRIS editor is used. The editor itself ensures that formulas all well-formed before submitting the questionnaire.
WIRIS quizzes has as minimal impact in your platform. WIRIS quizzes adds a whole set of functionality to your assessment platform while you still remain your original flavor. WIRIS quizzes is a small library available in PHP, Java and .NET. For a quick setup, the library depends on Web services available as SaaS but you can also install all components in your own servers.
WIRIS editorcomes with a WYSIWYG interface to input equations. Once the math formula is created a web-service generates an image to be included in the content. Those images are stored in a cache folder to improve system performance.
UI is available in Javascript, Flash, C/Qt, Java/Swing and .NET.
Available output formats include PNG and SWF.
Render engine can be used as SaaS web services or installed as a Java or .NET library.
Plugins The editor can be integrated in any platform in a straight forward way; you might get surprised to discover that such integration already exists. Integrations are available for PHP, Java and .NET platforms. | 677.169 | 1 |
Mathematical Copyright - Wilfrid Hodges
What do you want from your publisher? This page links to a PDF document on aspects of copyright in mathematical publication, featuring an extensive checklist on what an author and a publisher might expect from each other, and how the law can help or hinder.
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Mathematical Functions - Wolfram Research, Inc.
An encyclopedic collection of information about tens of thousands of mathematical functions. The site details the interrelationships between the special functions of mathematical physics and the elementary functions of mathematical analysis, as well as
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Mathematical Words: Origins and Sources - John Aldrich
"Notes that describe in general terms the origins of the modern vocabulary of mathematics and the sources of information" on which Jeff Miller based his Earliest Uses of Some of the Words of Mathematics. See, in particular, "When and whence for some English
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Maths - Martin John Baker, EuclideanSpace
Originally intended to give enough maths information to allow physical objects to be simulated by a computer program, these pages now cover a broader range of mathematical topics. The pages that get the most hits on the site are those concerned with 3D
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Math Teacher Career Guide - Project 8 Labs LLC
All about careers in the math classroom, for every state in the union: education requirements, pathways to certification, salary and job outlooks, and more. See, in particular, TeacherCertificationDegrees.com's collection of interviews, including Scott
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Math Teacher Life - Jud Soderborg
Select a state from the school directory to browse program and contact information about U.S. colleges and universities that offers teaching certifications, BA, MA, and/or PhD degrees. The reference section includes articles about curricular choices,
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A Matter of Time - Thinkquest 2007
This site examines the concept of time, in both English and Greek, from its suggested beginning to its projected end. It explores and engages the reader with varying views of time from scientific, religious, and cultural perspectives.
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More Complicated Than It Seems - Kate Nonesuch
In this review of the literature of approaches to adult numeracy instruction, Kate Nonesuch asks the question, "How can ABE math instructors apply research findings to their own teaching practice?" Through an extensive literature review and ongoing discussions
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National Science Digital Library (NSDL)
A comprehensive online source for science, technology, engineering and mathematics education. The NSDL mission is to both deepen and extend science literacy through access to materials and methods that reveal the nature of the physical universe and the
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Newton Papers - University of Cambridge
View and download Isaac Netwon's handwritten papers: his own annotated copy of Principia Mathematica; the so-called "Waste Book," a large notebook that he inherited from his stepfather, and which Newton filled with notes and calculations when forced to
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NFL Stats & Research Articles - Roland Beech
In-depth statistical coverage and analysis of the National Football League (NFL). See player stats and ratings by position, and regular season team stats such as drive charts, play call by down, and red zone performance. "Classic" articles include correlation
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Number Gossip - Tanya Khovanova
Searchable database up to the number 10,000. Checks more than 40 fun predefined properties of numbers, and shows many original and unique properties of an input number. See also this math coach's math blog, lectures, and more from her home page.
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Number Of
"You ask, we count": NumberOf.net answers questions that begin "How many ...?" All entries appear in paragraph form that follow a stock template, and link to references. Science entries have enumerated on numbers of breaths per minute, edges on a cylinder,
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OPenn - University of Pennsylvania Libraries
High-resolution archival images of manuscripts from the University of Pennsylvania Libraries and other institutions, along with machine-readable descriptions and technical metadata. Digitized cultural heritage materials on mathematics include "Treatise
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This book is written for mathematics students who have encountered basic complex analysis and want to explore more advanced project and/or research topics. It could be used as (a) a supplement for a standard undergraduate complex analysis course, allowing students in groups or as individuals to explore advanced topics, (b) a project resource for a senior capstone course for mathematics majors, (c) a guide for an advanced student or a small group of students to independently choose and explore an undergraduate research topic, or (d) a portal for the mathematically curious, a hands-on introduction to the beauties of complex analysis. Research topics in the book include complex dynamics, minimal surfaces, fluid flows, harmonic, conformal, and polygonal mappings, and discrete complex analysis via circle packing. The nature of this book is different from many mathematics texts: the focus is on student-driven and technology-enhanced investigation. Interlaced in the reading for each chapter are examples, exercises, explorations, and projects, nearly all linked explicitly with computer applets for visualization and hands-on manipulation. There are more than 15 Java applets that allow students to explore the research topics without the need for purchasing additional software. | 677.169 | 1 |
PDF (Acrobat) Document File
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0.74 MB | 178 pages
PRODUCT DESCRIPTION
Powerpoint with instructional facts, questions and answers with explanations. This PowerPoint will work with Holt Algebra I Common Core Chapter 2. The following topics: Graphing, writing inequalities, solving inequalities by adding or subtracting, solving inequalities by multiplying or dividing, solving 2-step and multi-step inequalities, solving inequalities with variable on both sides, solving compound inequalities and solving absolute-value inequalities | 677.169 | 1 |
Beginning and Intermediate Algebra A Guided Approach, 7th Edition
The new edition of BEGINNING & INTERMEDIATE ALGEBRA is an exciting and innovative revision that takes an already successful text and makes it more compelling for today's instructor and student. The authors have developed a learning plan to help students succeed and transition to the next level in their coursework. Based on their years of experience in developmental education, the accessible approach builds upon the book's known clear writing and engaging style which teaches students to develop problem-solving skills and strategies that they can use in their everyday lives. The authors have developed an acute awareness of students' approach to homework and present a learning plan keyed to Learning Objectives and supported by a comprehensive range of exercise sets that reinforces the material that students have learned setting the stage for their success. | 677.169 | 1 |
Showing 1 to 3 of 4
I recommend anyone skilled in mathematics to take this class because it proposes a challenge. You are able to express all other learned previous mathematics in this course and it can prove to be fun if you enjoy solving equations.
Course highlights:
My highlight of this course was the study of derivative and the use of differentiation. Derivatives are a fundamental tool of calculus and mastering the fundamentals are important. Mastering important things in life are a highlight for me.
I recommend this course to anybody who is looking to challenge themselves. Keep in mind though that with the necessity of covering more material Ms. Labayog will likely put a fairly equal amount of emphasis upon understanding the concepts and preparing for the exam.
Course highlights:
The highlights of taking AP Calculus would be that it requires you to think. By that, I mean it challenges you to think on a higher math level than your use too. In AP Calculus so far, I have learn derivatives. Derivatives of trig functions, exponential and logarithm functions, inverse trig functions, etc.
Hours per week:
6-8 hours
Advice for students:
My advice to future Calculus students would be during class, view the examples seriously and copy them in detail. Also I think its good to find people you can trust and rely on as study partners. Last, but not least ASK QUESTIONS! | 677.169 | 1 |
Hilbert Space by James R. Retherford
Book Description
Professor Retherford's aim in this book is to provide the reader with a virtually self-contained treatment of Hilbert space theory, leading to an elementary proof of the Lidskij trace theorem. He assumes the reader is familiar with only linear algebra and advanced calculus, and develops everything needed to introduce the ideas of compact, self-adjoint, Hilbert-Schmidt and trace class operators. Many exercises and hints are included, and throughout the emphasis is on a user-friendly approach. Advanced undergraduates and graduate students will find that this book presents a unique introduction to operators and Hilbert | 677.169 | 1 |
Designed for an introductory course in analysis or advanced calculus at undergraduate level, this text introduces students to the analysis of functions of a real variable. It provides them with solid training in mathematical thinking and writing and their first real application of the nature and role of mathematical proof. While preserving the presentation of an elementary text, it offers comprehensive coverage of one-variable real analysis. In this edition, a new chapter on sets, functions and countability provides a theoretical background for the rest of the text. There is also a wide selection of exercises with solutions and hints for some at the back of the | 677.169 | 1 |
Systems of Equations Problem Based Learning Hiker Problem
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2.82 MB | 13+ pages
PRODUCT DESCRIPTION
This is a PBL covering systems of equations as its primary focus.
Students will watch a short video (or have a discussion with a local Search and Rescue volunteer) and discuss the actions that led to the situation in the video. Students are given a packet of information and instructions.
Students are tacked with finding the location of a missing hiker in a state park. They are given information from the Park Rangers about contact that the rangers had with the hiker throughout the day, and must interpret this data to create systems of equations that map out the hikers locations throughout the day. Once this is done, they must make reasonable assumptions about the situation given the data in their packet, and determine where the missing hiker is located, how they plan to rescue him, and what method of rescue is best for the location. This project focuses on making student apply math to a real world situation about triangulation of radio signals. Project also leads to concepts of Unit Rates, Interpreting Topographical maps, and Line of Best Fit.
The PBL includes both instructor and student packets, maps, rubrics, sample solution, and electronic resources. It has details for both using the project as a physical turn-in, and for a paperless electronic turn-in.
Please see the sample packet for more information
If there are any issues accessing the online resources, please contact me prior to leaving negative feedback so it can be corrected. Thanks | 677.169 | 1 |
Here is clear, well-organized coverage of the most standard theorems, including isomorphism theorems, transformations and subgroups, direct sums, abelian groups, and more. This undergraduate-level text features more than 500 exercises.
" A group is defined by means of the laws of combinations of its symbols," according to a celebrated dictum of Cayley. And this is probably still as good a one-line explanation as any. The concept of a group is surely one of the central ideas of mathematics. Certainly there are a few branches of that science in which groups are not employed implicitly or explicitly. Nor is the use of groups confined to pure mathematics. Quantum theory, molecular and atomic structure, and crystallography are just a few of the areas of science in which the idea of a group as a measure of symmetry has played an important part. The theory of groups is the oldest branch of modern algebra. Its origins are to be found in the work of Joseph Louis Lagrange (1736-1813), Paulo Ruffini (1765-1822), and Evariste Galois (1811-1832) on the theory of algebraic equations. Their groups consisted of permutations of the variables or of the roots of polynomials, and indeed for much of the nineteenth century all groups were finite permutation groups. Nevertheless many of the fundamental ideas of group theory were introduced by these early workers and their successors, Augustin Louis Cauchy (1789-1857), Ludwig Sylow (1832-1918), Camille Jordan (1838-1922) among others. The concept of an abstract group is clearly recognizable in the work of Arthur Cayley (1821-1895) but it did not really win widespread acceptance until Walther von Dyck (1856-1934) introduced presentations of groups.
"The book is a pleasure to read. There is no question but that it will become, and deserves to be, a widely used textbook and reference." — Bulletin of the American Mathematical Society. Character theory provides a powerful tool for proving theorems about finite groups. In addition to dealing with techniques for applying characters to "pure" group theory, a large part of this book is devoted to the properties of the characters themselves and how these properties reflect and are reflected in the structure of the group. Chapter I consists of ring theoretic preliminaries. Chapters 2 to 6 and 8 contain the basic material of character theory, while Chapter 7 treats an important technique for the application of characters to group theory. Chapter 9 considers irreducible representations over arbitrary fields, leading to a focus on subfields of the complex numbers in Chapter 10. In Chapter 15 the author introduces Brauer's theory of blocks and "modular characters." Remaining chapters deal with more specialized topics, such as the connections between the set of degrees of the irreducible characters and structure of a group. Following each chapter is a selection of carefully thought out problems, including exercises, examples, further results and extensions and variations of theorems in the text. Prerequisites for this book are some basic finite group theory: the Sylow theorems, elementary properties of permutation groups and solvable and nilpotent groups. Also useful would be some familiarity with rings and Galois theory. In short, the contents of a first-year graduate algebra course should be sufficient preparation. | 677.169 | 1 |
This text helps you succeed in finite mathematics and applied calculus by using clear explanations, real-life examples, and up-to-date technology. Real-life applications-such as satellite radio subscriptions, Google's revenue, job outsourcing, and the effects of smoking bans-are drawn from the areas of business and the behavioral, life, and social sciences.
Market-leading APPLIED MATHEMATICS FOR THE MANAGERIAL, LIFE, AND SOCIAL SCIENCES, 5th EDITION, is a traditional text with a slightly modern feel. This new edition incorporates technology in such a way that both traditional and modern practitioners find the support they need to teach effectively | 677.169 | 1 |
Chapter 1. Numbers
In This Chapter
Overview
Most people would say that numbers are the foundation of mathematics. This is quite a modern view, because for most of the past two thousand years, students began with geometry. On the other hand, numbers are certainly the foundation of computers, and a thorough understanding of numbers and how they work is vital to programming.
In this respect, then, the journey begins with a look at the way computers represent numbers and what you can do with numbers using a computer. The goal here is to think about what a number is, especially the distinction between the number and the ...
Find the exact information you need to solve a problem on the fly, or go deeper to master
the technologies and skills you need to succeed | 677.169 | 1 |
Additional Features:Any question too difficult? Ask your question by dropping us a mail! Introduction to Singapore Math:
In the United States, Singapore Math is a teaching method based on the primary textbooks and syllabus from the national curriculum of Singapore.
These textbooks have a consistent and strong emphasis on problem solving, with a focus on in-depth understanding of essential math skills.
Explanations of math concepts are exceptionally clear and simple, so that students can read it easily. | 677.169 | 1 |
Graphmatica2.2.2
Graphmatica is a powerful, easy-to-use, equation plotter with numerical and calculus features. Graph Cartesian functions, relations, and inequalities, plus polar, parametric, and ordinary differential equations. Numerically solve and graphically display tangent lines and integrals. Find critical points, solutions to equations, and intersections between Cartesian functions. In summary, a great tool for students and teachers of anything from high-school algebra through college calculus.
What's New
Fixed domains in some of the demo files to be parseable when the decimal separator is set to ','
Improved rendering of graphs with highly-vertical segments (including any graph that crosses y=0) when using logarithmic graph paper. | 677.169 | 1 |
Product Description
Foundations Of Mathematical Analysis
This book evolved from a one-year Advanced Calculus course that we have given during the last decade. Our audiences have included junior and senior majors and honors students, and, on occasion, gifted sophomores.
The material is logically self-contained; that is, all of our results are proved and are ultimately based on the axioms for the real numbers. We do not use results from other sources, except for a few results from linear algebra which are summarized in a brief appendix. Thus, theoretically, no prerequisites are necessary to understand this material. Realistically, the prerequisite is some mathematical maturity such as one might acquire by taking calculus and, perhaps, linear algebra.
Our intent is to teach students the tools of modern analysis as it relates to further study in mathematics, especially statistics, numerical analysis, differential equations, mathematical analysis, and functional analysis.
It is our belief that the key to a sound foundation for the study of analysis lies in an understanding of the limit concept. Thus, after initial chapters on sets and the real number system, we introduce the limit concept using numerical sequences and series (Chapters IV and V). This is followed by Chapter VI on the limit of a function. We then move to the general setting of metric spaces (Chapter VII). Chapter VIII is a review of differential calculus. Chapter IX gives a detailed introduction to the theory of Riemann-Stieltjes integration. We then turn to the study of sequences and series of functions (Chapters X and XI), Fourier series (Chapter XII), the Riesz representation theorem (Chapter XIII), and the Lebesgue integral (Chapter XIV). The first seven chapters could be used for a one-term course on the Concept of Limit.
Because we believe that an essential part of learning mathematics is doing mathematics, we have included over 750 exercises, some containing several parts, of varying degrees of difficulty. Hints and solutions to selected exercises, indicated by an asterisk, are given at the back of the book.
We would like to thank our colleagues, Dr. Rosalind Reichard, who taught this course from a preliminary version and gave us useful information, and Dr. Keith Rose, who read the manuscript and offered valuable criticism. Thanks also to our many students who studied this material and offered suggestions, and especially Mr. James Africh, who worked nearly every exercise and made many helpful comments. Our thanks also go to the secretarial staff at the University of Victoria, who over the years typed various versions of the manuscript. Of course, we assume joint responsibility for the book's strengths and weaknesses, and we welcome comment. | 677.169 | 1 |
Linear Algebra and Its Applications6467.9521
FREE
Used Very Good(1 Copy):
Very good Legendary independent bookstore online since 1994. Reliable customer service and no-hassle return policy.
About the Book
Linear algebra is relatively easy for students during the early stages of the course, when the material is presented in a familiar, concrete setting. But when abstract concepts are introduced, students often hit a brick wall. Instructors seem to agree that certain concepts (such as linear independence, spanning, subspace, vector space, and linear transformations), are not easily understood, and require time to assimilate. Since they are fundamental to the study of linear algebra, students' understanding of these concepts is vital to their mastery of the subject. David Lay introduces these concepts early in a familiar, concrete "Rn" setting, develops them gradually, and returns to them again and again throughout the text so that when discussed in the abstract, these concepts are more accessible. | 677.169 | 1 |
Math.NET aims to provide a self contained clean framework for symbolic mathematical (Computer Algebra System) and numerical/scientific computations, including a parser and support for linear algebra, complex differential analysis, system solving and more | 677.169 | 1 |
Study & Teaching
e-books in this category
High-level Math for Little Tykes
by Evelyn Raiken Lewis - Smashwords , 2016 This guide advocates for teaching the vocabulary and concepts of high-level math to children in their first years of life. This is the time when the human brain is optimized to learn any language, even the language of mathematics. (547 views)
Primary Mathematics
- Wikibooks , 2012 This book focuses on primary school mathematics for students, whether children or adults. It is assumed that no calculators are used, to encourage mental arithmetic. This course uses as much lay language as possible to also be helpful to parents. (8801 views)
On the Study and Difficulties of Mathematics
by Augustus De Morgan - The Open Court Publishing , 1910 In compiling the following pages, my object has been to notice particularly several points in the principles of algebra and geometry, which have not obtained their due importance in our elementary works on these sciences. (4368 views)
A First Course in Mathematics Concepts for Elementary School Teachers
by Marcel B. Finan - Arkansas Tech University , 2006 Problem-solving is the cornerstone of school mathematics. The techniques discussed in this book should help you to become a better problem solver and should show you how to help others develop their problem-solving skills. (11833 views)
Mathematical Proficiency for All Students
by Deborah Loewenberg Ball - RAND Corporation , 2003 A clear need exists for improvement in mathematics proficiency in US schools. While the federal government have made significant investments toward improving mathematics education, the knowledge base supporting these efforts has generally been weak. (6455 views)
Contemporary Issues in Mathematics Education
by E. A. Gavosto, S. G. Krantz, W. McCallum - Cambridge University Press , 1999 What is the appropriate balance among theory, technique, and applications? What is the role of technology? How do we fulfill the needs of students entering other fields? This volume presents a serious discussion of these educational issues. (7081 views)
Mathematics under the Microscope
by Alexandre V. Borovik - American Mathematical Society , 2008 An unusual book that casts new light on the nature of mathematics. Interesting to maths majors at universities, school teachers of mathematics, graduate students in computer science or mathematics, computer scientists and research mathematicians. (15760 views) | 677.169 | 1 |
Course Descriptions
Declamations
As part of the English program, all students choose, memorize, and declaim before the middle school a selection from a work of literary merit.
humanEnglish 7
The course stresses both grammar and vocabulary as valuable prerequisites for effective writing. Students are introduced to writing and encouraged to view writing as a recursive process involving five stages: prewriting, drafting, revising, editing and proofreading, and publishing/presenting. The class reads and studies various classical literary genres: short stories, plays, novels, and poetry. The students develop a vocabulary of specific literary terms for each genre, as well as vocabulary that enhances speaking and writing.
English 8
Both grammar and vocabulary are essential to effective writing and are, therefore, the foci of this course. The five stages of the writing process are reviewed often as students continue their exploration of the narrative, descriptive, expository, and persuasive modes. Students read a sampling of works from various genres, and students continue to enlarge their vocabulary of literary terms in order to create a foundation with which to discuss the various genres. In addition, students learn the fundamental steps in the research process.
Mathematics 6
The math curriculum is devoted to developing student knowledge and an understanding of mathematics that is rich in connections: connections among core ideas in math, connections between math and its applications in other school subjects, connections between the planned teaching/learning activities and the special aptitudes and interests of middle school students. The content includes the study of number theory, understanding rational numbers, two-dimensional geometry, understanding of fraction operations, two-dimensional measurement, computing with decimals and percentages and probability.
Mathematics 7
In this course, students review and improve arithmetical skills, with an emphasis on operations with fractions and decimals and percentages. Ratios, proportions, and percents are used extensively in problem solving. Students learn fundamental geometric concepts, including similarity, and solve problems involving distance, area, and volume. Variables and patterns are studied extensively, including tables and four-quadrant graphing. Simple equations, integers and rational numbers, order of operations and distributive property are learned.
Pre-Algebra 7 (Honors)
This course is designed for above-average students. It enables the students to move from arithmetic and elementary concepts to algebra. The course emphasizes pre-algebra skills, such as working with variables, equation solving, and problem solving. Other topics covered include pre-geometry (similarity, polygonal shapes, tessellations, graphing of lines) and probability and statistics. Proportional reasoning is emphasized throughout. The course is taught using an integrated approach to the concepts, and cooperative learning is used frequently. All students learn to work with scientific calculators and computer problem solving.
Pre-Algebra 8
Designed to provide a smooth transition from arithmetic to algebra, this course reinforces arithmetic skills while introducing students to algebraic concepts and problems. A substantial amount of geometry is integrated into the arithmetic and algebra. Probability and statistics, equation solving, reading, and problem solving are emphasized throughout, and cooperative learning is used frequently. Students study linear and inverse variations and graphing, work with square roots and the Pythagorean Theorem, and recognize and represent quadratic functions in tables, graphs, words and symbols. Students are introduced to simple quadratic expressions.
Algebra I Honors
This course covers concepts such as equations, inequalities, graphing, informal geometry, data analysis, and matrices. Applications are frequently used to develop topics. Systems, polynomials, and square roots will frequently be related to geometry and be motivated by applications, as well. Technology is used where appropriate.
Science 6
The course is designed to give students foundational and general instruction in a variety of scientific disciplines. A hands-on, lab-oriented approach is used whenever possible to introduce and reinforce the concepts that are covered during the year. Initially, students become familiar with the way that science works and the nature of science. Other major topics covered during the year are (1) earth materials and processes; (2) measurement and conversions; (3) the nature of matter; and (4) waves, sound and light.
Science 7
Seventh graders spend most of the year exploring the main themes of environmental science and ecology by focusing on the planet Earth as a space shared by all living organisms. They study the Earth, ecological interactions, biomes, people in the global ecosystem, energy resources, other resources in the biosphere, and managing human impact. The year concludes with a field habitat study and a survey of the six kingdoms of organisms, which emphasizes invertebrates and vertebrates.
Science 8
Science 8 leads students to a deeper understanding of how science works and of specific information covering various disciplines of science. A hands-on approach is used whenever possible to reinforce concepts in these fields. Topics covered during the year are (1) measurement and conversions; (2) chemistry; (3) motion, forces, and energy; (4) maps and weather; and (5) astronomy.
Health and Wellness
Health and Wellness is a required course for all eighth grade students. Acquiring an understanding and establishment of good health practices and incorporating them into daily life are the key objectives for this semester. Health topics will fall under several various categories: Wellness, Drugs/Alcohol, Life Cycle, Communicable Diseases, First Aid, and Personal Fitness. Issues addressed in-depth will include nutrition, conception and birth, alcohol, steroids, tobacco use, STD's, self-esteem, and stress-management.
French 1A, Spanish 1A, Chinese 1A (8TH GRADE ONLY)
Students are introduced to the language, with vocabulary and basic structures demonstrated in context to encourage communication. Basic vocabulary includes friends and family, shopping, and food 1B, Spanish 1B
Students are introduced to the language, with vocabulary and basic structures demonstrated in context to encourage communication. Basic vocabulary includes health, vacation, and festivals II (8th grade only)
Students at this level acquire a command of the four basic skills of the language. Increased emphasis is placed on the ability to communicate in realistic situations. Cultural readings survey life in the French-speaking world.
French I, Spanish I (8th grade only)
Students are introduced to the language, with vocabulary and basic structures demonstrated in context to encourage communication. The primary objective is to help each student attain an acceptable degree of proficiency in the four skills of listening, speaking, reading, and writing.
Latin I (8th grade only)
This course gives students a solid foundation in Latin grammar and vocabulary, as well as an introduction to Roman civilization and culture. The primary emphasis of the course is to develop reading skills in Latin while learning declensions of nouns, adjectives, and pronouns, and conjugation of verbs in the active voice. Basic spoken Latin is used as a tool for enhancing understanding of the material. Cultural topics include the daily life of a family during the early/middle Empire and early Roman history/mythology.
HumanWorld Geography (7th Grade)
This course is an introduction to the world's physical and cultural geography. The continents of Africa, Europe, Antarctica, Asia, Australia, South America, and North America are studied. Focusing on the basic skills of reading and making maps, the course involves special assignments on various topics being studied. Critical thinking, internet-based research, and current events are stressed. Students acquire broad cultural, social, economic, and political perspectives on countries around the world.
American History (8th Grade)
This course is an introduction to American history from the Age of Discovery to the mid-twentieth century. Particular emphasis is placed upon the period 1776-1876: the American Revolution, the early Federal Period, the Age of Jackson, westward expansion, the Civil War, and Reconstruction. Students learn the impact of key events and figures in the development of the government and society of the United States, and they develop skills in the use of primary and secondary sources, in map reading, in research projects, and in essay writing.
Art 7
In a semester, students study the French impressionists and learn principles of composition that they apply to original drawings and photographs. In clay, students work on basic slab construction projects and throw on the wheel.
Art 8
In this semester course, an art appreciation unit continues to introduce great still life artists (like Georgia O'Keeffe) and prominent portrait artists (from Rembrandt to Chuck Close). Projects in clay incorporate more advanced skills in building slab boxes and throwing pots on the wheel.
Middle School Computer
For one semester each year, 7th and 8th grade students receive a broad-based orientation to computer applications. With increasing practice and sophistication, they work on keyboarding, word processing, spreadsheets, Internet research, and applications involving multiple formats simultaneously. Each year's work quickly reviews and then builds upon the prior year's instruction. Ultimately, students become adept at using Microsoft Word, Excel, and PowerPoint.
Other Middle School Offerings
In addition to the standard courses, Webb's middle school program also includes the following offerings.
Middle School After Lunch Program
Webb's Middle School after Lunch Program is designed to
enrich the personal development of middle school students and encourage
the discovery of new passions. The program allows the students to choose
from the following activities: Art, Choir/Music, Feet-to-Feet, Chinese
Culture Survey, TEAM collaborative strategies, Finance, Quiz Bowl, PE and WILD
(Outer limits).
Emerging Voices Program
Each year, all middle school students choose, memorize, and declaim a selection from a work of literary merit in front of the entire middle school. | 677.169 | 1 |
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Unformatted text preview: Note that Y= Mat rix Binomials I ntroduction This paper will focus on the study of matrix binomials. In mathematics, a matrix ( plural matrices) is a rectangular array of numbers, referred to as elements, consisting of rows and columns. Matrices are similar to vectors but as mentioned before matrices are represented by blocks of number with rows and columns. The matrix illustrated above has 2 rows (horizontal components) and 2 columns (vertical components) and thus have and order of 2 2. In general, a matrix is used to store information, especially in the field of data management, and record data that depends on multiple parameters. Matrix multiplication connects matrices to linear transformations and has led to fractal geometry. When multiplying matrices the rows on the left hand matrix, the first matrix, have to pair up with the columns of the second matrix. For example, 2 4 = 8 4 2 = 8 2 2 = 4 The first step is to take the first row of the first matrix [2 4 2] and pair it with the first column of the second matrix. Each pair is multiplied and then added together. The product achieved would be the element in the first row and first column of the answer. All combinations of rows and columns must be calculated. In case of square matrices, matrices with an equal number of rows and columns, more data can be extracted such as the determinant and inverse matrices. In relation to square matrices, matrix binomials refer to a situation consisting of two matrices of which both orders are 2 2. By applying the matrix binomials to different situations and testing the certain validities and claims general expressions and statements about the different matrix binomials would be reached. In this investigation one of the key focal points is to distinguish as well as relate different matrices in order to arrive at general statements and expressions concerning the matrix binomials. By manipulating matrix binomials through various calculations certain relations would be touched upon and related to the further calculations concerning the matrix binomials dealt with in the investigation. In this paper we will analyze the matrix binomials of X and Y and then its relations. The analysis of the matrices X and Y and all of the other operations will be carried out by algebraic methods. After calculating the matrix binomials of X and Y a general formula or statement would be reached. We will then focus on the matrices A and B, where A= a X and B= b Y. General statement would be reached for A n , B n and (A+B) n . Finally, the relationship on the matrices A and B will be investigated through the matrix M. We will then compare the different results achieved....
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This note was uploaded on 04/11/2010 for the course ENG 1p03 taught by Professor Dr.fleisig during the Spring '10 term at McMaster University. | 677.169 | 1 |
$332Elayn Martin-Gay's developmental math program is motivated by her firm belief that every student can succeed. Martin-Gay's focus on the student shapes her clear, accessible writing, inspires her constant pedagogical invations, and contributes to the popularity and effectiveness of her video resources. This revision of Martin-Gay's series continues her focus on students and what they need to be successful. Note: You are purchasing a standalone product; MyMathLab does t come packaged with this content. MyMathLab is t a self-paced techlogy and should only be purchased when required by an instructor. If you would like to purchase both the physical text and MyMathLab, search for: 0133858251 / 9780133858259 Basic College Mathematics with Early Integers Plus NEW MyMathLab with Pearson eText -- Access Card Package Package consists of: 0133864715 / 9780133864717 Basic College Mathematics with Early Integers 0321431308 / 9780321431301 MyMathLab -- Glue-in Access Card 0321654064 / 9780321654069 MyMathLab Inside Star Sticker Students, if interested in purchasing this title with MyMathLab, ask your instructor for the correct package ISBN and Course ID. Instructors, contact your Pearson representative for more information.
Author Biography
Elayn Martin-Gay has taught mathematics at the University of New Orleans for more than 25 years. Her numerous teaching awards include the local University Alumni Association's Award for Excellence in Teaching, and Outstanding Developmental Educator at University of New Orleans, presented by the Louisiana Association of Developmental Educators. Prior to writing textbooks, Elayn Martin-Gay developed an acclaimed series of lecture videos to support developmental mathematics students. These highly successful videos originally served as the foundation materials for her texts. Today, the videos are specific to each book in her series. She has also created Chapter Test Prep Videos to help students during their most teachable moment -as they prepare for a test-along with Instructor-to-Instructor videos that provide teaching tips, hints, and suggestions for every developmental mathematics course, including basic mathematics, prealgebra, beginning algebra, and intermediate algebra. Elayn is the author of 12 published textbooks and numerous multimedia interactive products, all specializing in developmental mathematics courses. She has also published series in Algebra 1, Algebra 2, and Geometry. She has participated as an author across a broad range of educational materials: textbooks, videos, tutorial software, and courseware. This offers an opportunity for multiple combinations for an integrated teaching and learning package, offering great consistency for the student. | 677.169 | 1 |
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Unformatted text preview: Unit 1. Algebra as the Study of Structures Algebra started in ancient Egypt and Babylon where the preoccupation of early settlers was concentrated to solving linear equations (ax = b), quadratic equations (ax 2 + bx = c) and indeterminate equations (a x 2 +b y 2 = c z 2 ), whereby several unknowns are involved. Of course, the way they wrote their equations and the variables were very much different from how we them now. Interestingly, the ancient Babylonian's solution of the quadratic equations resembled our present method of solving them today. The humble beginnings of Algebra continued a tradition of finding solutions of equations from very specific ones to the more general. This preoccupation spread across the Islamic world and later on to the continental Europe and the Americas over several centuries. Many renowned mathematicians, including Cardano, Ferrari, Abel and Galois, kept themselves busy with the quest for finding solutions of polynomial equations (ax n + bx n-1 + …+ c = 0) in their most general form. Even the philosopher Descartes contributed much to the development of the subject. However, it was during the time of Gauss when the modern phase of Algebra commenced. Rather than deal on the solution of equations, the focus was redirected to the study of the structure of mathematical systems composed of objects that behave in some common manners. From them on, Algebra has been considered as the study of mathematical structures. OUTLINE: 1. Sets, Set Operations and Number Sets: The Basic Objects of Algebra 2. The Real Number System as a Number Field a. Group properties b. Ring properties c. Field properties d. Ordered field properties e. Completely ordered field 3. The Complex Number System as a Number Field a. Group properties b. Ring properties c. Field properties 4. The Ring of Polynomials a. Addition and subtraction b. Multiplication 5. The Field of Algebraic Expressions a. Addition and subtraction b. Multiplication c. Division Unit 1. Algebra as the Study of Structures Section 1 page 2 _____________________________________________________________________________________ 1.1. The Basic Objects of Algebra: Sets, Set Operations and Number Sets The concept of "set" has pervaded almost all of mathematics so that it has become a fundamental concept. Due to this, it becomes impossible to define precisely in terms of more basic concepts. However, our real world experience has provided us with an intuitive knowledge of the notion of a set to rely on. Whenever a group of objects is formed, to our mind, a set is formed. Thus, it is east to accept that a set is simply a collection of objects, real or imagined . The only condition we impose on a collection to become technically a set is that it is possible to determine (in some manner) whether an object belongs to the given collection or not. For example, we may consider the following as sets: a) The set of freshman students of the present class b) The set of students in this class whose last name begins with the letter P...
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This note was uploaded on 05/13/2011 for the course MATH 17 taught by Professor Dikopaalam during the Spring '11 term at University of the Philippines Los Baños. | 677.169 | 1 |
Manvel, TX TrigonometryCameron C.
...Thomas and received an A in the course. Linear Algebra is the study of matrices and their properties. The applications for linear algebra are far reaching whether you want to continue studying advanced algebra or computer science | 677.169 | 1 |
CBSE Class 10 Mathematics Syllabus For SA1 & SA2
Class 10 Mathematics These chapters are quadratic equation , arithematic progression , circles , probability , surface areas and volumes. Total 95 periods are given for CCE first term syllabus.For cce second term syllabus total 100 periods are given .
Mathematics Syllabus For Class 10
CBSE Syllabus For 2015 – 2016 Class 10 Mathematics Mathematics CBSE Syllabus For SA1 & SA2 (2014-2015) was recently introduced by CBSE ,New Delhi this Year . It is available for download in pdf format. For session 2015 schools must follow this syllabus .
Mathematics Class 10 Syllabus 2013 CBSE – Term 1& Term 2
Mathematics MathsMathematics Syllabus Overview
Total Number of Periods for Class 10 Mathematics Syllabus
For session 2015-2016 total 190 periods have been alloted for full maths syllabus . For cce first term 90 period have been given and for cce second term 100 periods have been given . | 677.169 | 1 |
A review of the possibilities and challenges of computer-assisted instruction (CAI), and a brief history of CAI projects at Stanford serve to give the reader the context of the particular program described and analyzed in this book. The 1965-66 arithmetic drill-and-practice program is described, summarizing the curriculum and project operation. An edited version of the daily log of the project operation documents the types of problems encountered in the first application of a new technology in an operational setting. The results of surveys of students, parents, and teachers at the school made after the drill program had been in operation several months are presented and discussed. Previous research on methods of arithmetic teaching is reviewed; the implications of this research for the design and content of the drill program are described. The report presents some models for student performance in considerable detail. A controlled experiment conducted within the drill program is reported. The hardware, programing logic, and programing language developed to handle the program are described and analyzed. Appendixes provide a report on the previous year's program in CAI mathematics and several examples of the set of drills used by students at various grade levels. (JY) | 677.169 | 1 |
The aim of this work is to show how Mathematica and its graphical potentialities can aid students in learning some concepts of rational mechanics through the resolution of exercises in an enjoyable way. The basic idea is that a student can learn in a more stimulating way by manipulating data and observing the results. Students can construct their knowledge step by step, interacting with the notebook, inserting data and waiting for the response. | 677.169 | 1 |
Calculus Area Between Curves GOOGLE Slides Digital Task Cards
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PRODUCT DESCRIPTION
Teach Interactive™ Digital Task Cards GOOGLE® Resource
This lesson is designed for AP Calculus AB, AP Calculus BC, College Calculus 1 and 2. In this 1:1 paperless digital activity students find the area between curves using vertical strips. There are transcendental functions included. There are10 task cards and a digital answer sheet.
Students access the Task Cards through Google Slides® . Paperless and NO PREP for you! I have also included a printable answer sheet and a printable version of the lesson should you need it for differentiation, a bad tech day, or even a sub. There is also a printable answer sheet where students can show work if desired.
New innovative resources which you and your students access through the free Google file sharing system, Google Drive®. Students can interact, edit, and if desired, print files from any computer or tablet. They explore math interactively while using the same technology that permeates their daily lives.
Why should you teach with Teach Interactive™ Google Resources?
✓ Completely paperless, no printing, no lost assignments, and NO PREP for you.
✓ Students work directly on their own pages or work collaboratively - your choice!
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✓ More engaging than pencil and paper
✓ Incorporate technology that students are familiar with into your lessons.
✓ Students can organize their materials in their own Google Drive. Great for Review!
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Please feel free to email me at teachdydx@distancemath.com | 677.169 | 1 |
Visual and interactive way to thorough understanding and mastering Trigonometry without getting wearied on the very first chapter! Java- and web-based math course includes theoretical concepts, hands-on examples featuring animated graphics and live formulas, problem-solving lessons, and customizable real time tests with solutions and evaluations. Topics covered: angles and their measure, trigonometric functions, identities and equations, transformations of trigonometric graphs, inverse trigonometric functions, solving triangles, polar coordinate system, vectors in the plane, complex numbers. The demo version contains selected lessons from the full version, fully functional, all features included.
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An Introduction to the Mathematics of the Special Theory of Relativity
Product Description:
This book offers a presentation of the special theory of relativity that is mathematically rigorous and yet spells out in considerable detail the physical significance of the mathematics. It treats, in addition to the usual menu of topics one is accustomed to finding in introductions to special relativity, a wide variety of results of more contemporary origin. These include Zeeman's characterization of the causal automorphisms of Minkowski spacetime, the Penrose theorem on the apparent shape of a relativistically moving sphere, a detailed introduction to the theory of spinors, a Petrov-type classification of electromagnetic fields in both tensor and spinor form, a topology for Minkowski spacetime whose homeomorphism group is essentially the Lorentz group, and a careful discussion of Dirac's famous Scissors Problem and its relation to the notion of a two-valued representation of the Lorentz group. This second edition includes a new chapter on the de Sitter universe which is intended to serve two purposes. The first is to provide a gentle prologue to the steps one must take to move beyond special relativity and adapt to the presence of gravitational fields that cannot be considered negligible. The second is to understand some of the basic features of a model of the empty universe that differs markedly from Minkowski spacetime, but may be recommended by recent astronomical observations suggesting that the expansion of our own universe is accelerating rather than slowing down. The treatment presumes only a knowledge of linear algebra in the first three chapters, a bit of real analysis in the fourth and, in two appendices, some elementary point-set topology. The first edition of the book received the 1993 CHOICE award for Outstanding Academic Title.Reviews of first edition: "... a valuable contribution to the pedagogical literature which will be enjoyed by all who delight in precise mathematics and physics." (American Mathematical Society, 1993) "Where many physics texts explain physical phenomena by means of mathematical models, here a rigorous and detailed mathematical development is accompanied by precise physical interpretations." (CHOICE, 1993) "... his talent in choosing the most significant results and ordering them within the book can't be denied. The reading of the book is, really, a pleasure." (Dutch Mathematical Society, 1993)
REVIEWS for The Geometry of Minkowski Spacetime | 677.169 | 1 |
Introduction to Metric Measurement. Topical Module for Use in a Mathematics Laboratory Setting.
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The purpose of this module is to teach the basic metric measures of length, area, volume, capacity, mass, and temperature. It introduces students to metric prefixes, abbreviations, and unit conversions with the system. Illustrative and optional material compares metric measures to our familiar American standard measures. The purposes are accomplished through the use of detailed explanations, experiments, charts, games, and manipulatives. After an introduction which points up the need for a uniform international measurement system, the student proceeds through a series of experiments and worksheets. Most problems are related in some way to a physical model or actual measurement device. (Author/MK) | 677.169 | 1 |
26 September 2013
One of my summer institute participants wrote in the other day with a question that I've been asked in similar
from wyzant.com... this is NOT calculus!
form many, many times...
I discovered this morning that the textbook we have for the course, College Physics [by Serway and Vuille] has calculus-based content for 2D motion. I have resorted to using the textbook I have for general Physics, Physics: Principles and Problems by Glencoe, as an alternative for this section of material. Have any of you run into a similar issue or have any suggestions for other ways to communicate the necessary material at an AP level? I'm just wondering for this particular section, and if I run into a similar issue again down the road with content (since we're teaching algebra-based Physics).
Yeah, this is why I hate the standard-fare textbooks, written by Ph.D. physicists for Ph.D. physicists. It's NOT calculus, even though it looks like it on first glance. My correspondent pointed me to the section describing instantaneous velocity. Serway uses a full page of equations, many of which look exactly alike to the untutored eye,* to make the simplest of conceptual points.
* My eye is tutored, but the 17 or 19 year old reading this text is not. First rule of writing: know your audience.
The page in question uses mathematical notation that says the limit of a distance divided by a time as time goes to zero is the definition of instantaneous velocity. Well, the eleventh grade student came to class angry: "We just started taking limits last week in my calculus class. I've never seen this sort of thing before, and I don't understand it yet. I thought you said we don't need calculus for this class! How am I supposed to understand it?"
First, the general issue about algebra-based physics, calculus, and resources: If students read texts or online information, they will often -- too often -- see mathematical explanations that resemble calculus. See the picture above, which is using five rectangles to approximate the area under a curve. "That's calculus, I know it!" says the novice. Well, it's not. The area of a rectangle is base times height -- that's 6th grade math, not calculus. Even in algebra-based physics, we have to compare the slopes and areas of curved graphs... and you can expect someone to indignantly holler "Calculus!" when you draw the slope of a tangent line. What "algebra-based" means is that we don't ever have to evaluate an integral or derivative of a function to make a numerical calculation or derivation -- it doesn't mean that we never look at curved graphs.
One of our tasks as a teacher of first-year physicists is to help them simplify tough ideas. That means steering them away from poorly-written or misleading sources. That means explaining in words, and minimizing mathematics. A diligent but frustrated student must understand that yeah, the textbook is ridiculously confusing, but that doesn't mean you can get angry -- you simply have to find a different way to understand the topic.
Finally, the specific issue of Serway's presentation of instantaneous velocity: All this math is just telling you that (1.) velocity is distance traveled per second, and (2.) "instantaneous" velocity means the velocity RIGHT NOW. Distance divided by time is, generally, velocity. If you use data over an hour, you get the average velocity for that hour. But if you don't look at an hour, or a second, but at a fraction of a second, then you're looking at instantaneous velocity. Serway is doing his highfalutin' physics professor best to say just that, but in mathematics. I wish he'd speak English.
19 September 2013
On Wednesday, the Google Doodle showed a working Foucault Pendulum simulation. As it happens, my research students are in the opening stages of a deep investigation of the Foucault in preparation for the US Invitational Young Physicists Tournament. We are tasked with building a Foucault, using it to determine our latitude, and then conducting the error analysis to define the precision of the measurement.
What a useful coincidence... I added the question to my research students' quiz: "Determine the latitude portrayed by the Google Doodle."
The equation for the precession per day of a Foucault pendulum is 360 degrees times the sine of the latitude. Solving, then, the latitude is the inverse sine of the precession per day divided by 360 degrees.* We need to find the precession rate from the simulation.
*Explaining the geometry and conceptual physics behind this equation will be part of each research team's presentation at the tournament, of course.
One of my students sent a rather tetchy response, complaining that he'd have to sit there for most of an hour just to watch how long it takes for a peg to be knocked down. Some cursory exploration finds a cheat: look in the lower right corner at the clock face. Click on the clock. A slider appears, allowing you to fast-forward time.*
*A second slider allows you to adjust latitude. I'm doing everything here for the default latitude when I just click on the doodle link.
I set the slider to 12:00, and fast-forwarded until all pegs were knocked down. At 6:25 PM by the clock, the last peg was still standing; at 6:40 PM, the last peg had fallen. This means that the pendulum rotates 180 degrees in somewhere between 18.42 hours and 18.67 hours. Pro-rating this rotation rate, this works out to between 276 and 280 degrees per day.
Now plug into the relevant equation: the latitude of this pendulum is between 40.0 and 40.7 degrees.
Reader help, please: I anticipated that the simulation either (a) used the geo-located latitude of the computer accessing the doodle, or (b) used a default latitude with some special meaning, such as Google's Mountain View, CA headquarters. Oops. I am located at Woodberry Forest, VA, 37 degrees north latitude; Mountain View is also 37 degrees north latitude. Any clue where this Foucault is supposed to be? (Or, alternately, any corrections to my calculations?)
And, if you'd like to participate in our tournament, solve three of these four problems and come to San Jose, CA on Jan. 31, 2014. I'll be happy to help you out with both the physics and the attendance logistics.
12 September 2013
Before I start talking about an awesome simulation, hear the standard disclaimer: Online simulations are in no way a substitute for live quantitative demonstrations.
That said, online simulations, if they're programmed correctly, can be extraordinarily useful: for making quick "measurements," for showing experiments and regimes within an experiment for which you don't have the equipment, for student use at home... As long as you are not trying to replace live equipment with a computer, simulations are wonderful resources.
The Phetinteractive simulation site is one of the traditional favorites of physics teachers. These have been maintained and developed over time by pros. Note that they are free (with donations accepted), and that they require Java.
Today my conceptual class used a laser and a fish tank to make measurements of incident, reflected, and refracted angles. Homework questions will ask qualitatively about which way light bends at various interfaces, about comparing angles, about how these angles change in different situations.
My colleague Alex Tisch whipped out this phet simulation which runs exactly the same way as my in-class live demonstration. It even comes with a protractor that you have to place properly to measure angles. I particularly love the option of a "mystery material" for which you have to use the protractor to figure out the index of refraction.*
* In Regents or AP physics, I'd have students use Snell's law to determine the mystery index of refraction. For conceptual, I could ask students to rank materials by their n, or to compare the material's index of refraction to that of water, say.
I'm not actually using this for any sort of official assignment, at least for now. Rather, I just put a link on the class folder, and offered extra credit to anyone who actually downloads and plays with the simulation tonight. If nothing else, I might use it myself in creating a problem -- a screen shot provides me a diagram from which I can ask virtually anything. Alex did the live demonstration, then used the simulation to make many quick measurements without having to turn out the lights, click erasers to visualize the laser, draw the rays on the glass, etc.
09 September 2013
Folks, I've been asked for years: "Do you have a list of all of the quantitative demonstrations and lab setups that you do?" I've never actually compiled such a list. I just create on the fly, usually. A quantitative demonstration is merely an end-of-chapter problem scaled such that the answer can be tested with available equipment during class. Each year, I look in the equipment closet, set something up, and go with it. I *like* the improvisational elements this approach brings to my classes. Just as I don't want my students to think of laboratory as an object lesson in instruction-following, I don't want to fall into the trap of making physics teaching a strict note-following process, either.
That said, I often want to remember things year-to-year, and I often want to communicate to others what I'm doing. I've never been organized enough to write down details of my demonstrations. I've documented many demos on this blog with a photograph and description; but taking and uploading each photo, and then writing the description, has been a time consuming process.
Today, my colleague Curtis offered an elementary yet elegant observation about documenting his demonstrations. He was frustrated because he didn't remember the experiment that we ran on the first day of conceptual physics last year, even though we had done it in detail last year, even though I described it to him again. However, when I went into my classroom and actually set up the experiment for him, he instantly knew what to do.
This year, then, he took a picture of the setup with his phone; he emailed the picture to himself, and saved it in a file marked "lesson plans."
See, I hate the term "lesson plan." It implies that I should have pages of notes explaining what I'm doing in each portion of my class. Well, I did have such notes the first couple of years I taught. Now, though, I just set up a demo and improvise. I don't need no stinkin' "lesson plan" -- The photo BY ITSELF is sufficient for reminding me what I did last year, for communicating to colleagues, and even perhaps for reminding students about setups. Curtis even suggested using the photo as the basis for a lab quiz: "Here's the setup from yesterday's demonstration. Explain how to use the equipment present to measure angles of incidence and reflection."
My pledge for the next couple of years is to remember to take as many pictures of lab setups as I can. This year I'll work on conceptual; next year will be AP Physics 1. Hopefully I can compile a big file of picture after picture so that when other teachers ask for a list of demonstrations, I can forward these files.
And yes, I am aware that to folks who are more tech savvy and/or about a decade younger than I, this post must sound like "oh, it's good to have a collection of books, but they're especially useful if you take the books down occasionally and read them." :-)
02 September 2013
It's that crazy-arse time of the year, at which point I look at the calendar and say, "Oy, my next day without an obligation is the Wednesday before Thanksgiving." So in honor of the start of school, here are a few quick questions from readers with quick answers.
From Joseph:
Hi Greg. I was examining some of the grading done on the AP as well as how you graded some of your tests. I ... saw that you adjust the multiple choice scores slightly. The example I'm looking at says you multiplied the MC score by 1.304 after rounding then added that to the total FR points for the RAW AP score. Why did you adjust the MC? Does your strategy vary test to test?
Hey, Joseph. Both sections should be weighted to one minute per point. Since on that test I gave 23 questions in 30 minutes, I multiplied the mc score by 30/23 to add to the free response.
From Youri, who has two questions:
1. I can't remember but on the AP do they go by significant figures or by given answer to 3 decimal places?? Can you clarify that for me.
Use 2 or 3 sig figs. Not worth throwing a fit over with the students, though, compared to the other classic battles like using units or describing a solution thoroughly.
2. Do you have any cool demos I can do for kinematics, using a pasco track, carts, I have a fan for the cart, a labquest, a motion detector a force sensor...basically what you told me to get. I want to do a demo but I am not really sure what would be the most appropriate and useful to the kids???
Use the fan cart on the track with the motion detector and do qualitative and quantitative demos. Like, what will the x-t or v-t graph of this motion look like? Can someone make the cart create this graph? What initial velocity will get the cart to stop at the top of this inclined track (given the cart's acceleration)? Or, just what is the cart's acceleration given the v-t graph? All sorts of fun stuff. Choose an end-of-chapter problem, and scale it to a cart on a track.
From Jessica:
Random question. I have a student who is solving force problems with tangents instead of sines and cosines to break forces into components and determine magnitudes of force components. His math works. But I rarely see tangents show up on rubrics. Does it matter? As long as his math is sound? Or will it lose him points to not show force components in sines and cosines?
Hey, Jessica! His approach is fine, as long as the physics is correct. Nonstandard but correct and clear approaches always earn full credit. (As I sometimes say rather cheekily, that's why the College Board hires physicists to grade the exam rather than lawyers. The rubrics are meant to be interpreted intelligently, not inflexibly.)
Good luck to all this year... please email questions as you have them. | 677.169 | 1 |
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This best-selling book provides an accessible introduction to discrete mathematics through an algorithmic approach that focuses on problem- solving techniques. This edition has the techniques of proofs woven into the text as a running theme and each chapter has the problem-solving corner. The text provides complete coverage of: Logic and Proofs; Algorithms; Counting Methods and the Pigeonhole Principle; Recurrence Relations; Graph Theory; Trees; Network Models; Boolean Algebra and Combinatorial Circuits; Automata, Grammars, and Languages; Computational Geometry. For individuals interested in mastering introductory discrete mathematics. | 677.169 | 1 |
EasyConicSections gives students the ability to plot the equations of lines, circles, parabolas,
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books.google.com - This report presents information from three special studies conducted as part of the National Assessment of Educational Progress (NAEP) 1996 mathematics assessment. It is intended primarily for mathematics educators and others concerned with mathematics education, such as curriculum specialists, teachers,... Skills, Mathematics-in-context, and Advanced Skills in Mathematics
This report presents information from three special studies conducted as part of the National Assessment of Educational Progress (NAEP) 1996 mathematics assessment. It is intended primarily for mathematics educators and others concerned with mathematics education, such as curriculum specialists, teachers, and university faculty in schools of education. The three studies reported here were designed to provide greater detail on how students perform on particular types of mathematics questions. Studies include the Estimation Study, the Study of Mathematics-in-Context, and the Study of Students Taking Advanced Courses in Mathematics. The first study was designed to explore students' skills in estimation and was implemented at three grade levels. It concludes that although there has been significant improvement in mathematics performance overall since 1990 at all grade levels, the trend for student performance in estimation over the six years since the inception of the Estimation Study of 1990 is less clear. The second study was designed to assess problem-solving abilities within contexts that allow students to make connections across mathematics content areas. The Advanced study was administered at grades 8 and 12 and was designed to provide students who were taking or had taken advanced courses in mathematics an opportunity to demonstrate their full mathematical proficiency. (Contains 71 tables and figures.) (ASK)
Bibliographic information
Title
Estimation Skills, Mathematics-in-context, and Advanced Skills in Mathematics: Results from Three Studies of the National Assessment of Educational Progress 1996 Mathematics Assessment The Nation's report card | 677.169 | 1 |
The multiple-choice exams from 2003, 2008 and 2012 and all the free-response questions and solutions from past years are available online. The students can easily find them. Starting in 2012 the College Board provided full actual AP Calculus exams, AB and BC, for teachers who had an audit on file to use with their students…
Here are several resources that will help you get started with your review "The AP Calculus Exam: How, not only to Survive, but to Prevail…" – Advice for students on the format of the exam and do's and don'ts for the exam. Print this and share it with your students. Released free-response questions from the College Board.…
Don't panic! It is not time to start reviewing. I try to keep these posts ahead of the typical AP Calculus timeline so you can have time to think them over and include what you want to use from them (if anything). Over the next 6 weeks I will post several times each week. The…
One of the great things – at least I like it – about Taylor series is that they are unique. There is only one Taylor series for any function centered at a given point, What that means is that any way you get it, it's right. Faced with writing the power series for, say, ,…
The seventh in the Graphing Calculator / Technology series Here are some hints for graphing Taylor polynomials using technology. (The illustrations are made using a TI-8x calculator. The ideas are the same on other graphing calculators; the syntax may be slightly different.) Each successive term of a Taylor polynomial consists of all the previous terms…
After my last post, I realized I have never written about the logistic growth model. This is a topic tested on the AP Calculus BC exam (and not on AB). Here is a brief outline of this topic. Logistic growth occurs in situations where the rate of change of a population, y, is proportional to…
The logistic growth model describes situation where the growth of some population is proportional to the number present at any time and the difference between that amount and some limiting value called the "carrying capacity." The standard example is this: a small group of rabbits is placed on an island. The population will grow rapidly…
Our BC friends will soon be starting to teach series. Today, to emphasize that series are all around us, I would like to discuss series that we see every day: numbers. Long ago I was taught that no one has ever seen a "number." Have you ever see a four? What we see are numerals, symbols or…
Density, as an application of integration, has snuck onto the exams. It is specifically not mentioned in the " Curriculum Framework" chapter of the new Course and Exam Description. There is an example (#12 p. 58) in the AB sample exam question section of Course and Exam Description.The first time this topic appeared was in…
The sixth in the Graphing Calculator / Technology Series Both graphing calculators and CAS calculators allow students to evaluate definite integrals. In the sections of the AP Calculus that allow calculator use students are expected to use their calculator to evaluate definite integrals. On the free-response section, students should write the integral on their paper,… | 677.169 | 1 |
Product Description:
This user-friendly workbook improves both student understanding and retention of algebra concepts through a series of activities and guided explorations using the graphing calculator. An ideal supplement for any beginning or intermediate algebra course, EXPLORATIONS IN BEGINNING AND INTERMEDIATE ALGEBRA, THIRD EDITION is a useful tool for integrating technology without sacrificing content. By clearly and succinctly teaching keystrokes, class time is devoted to investigations instead of how to use a graphing calculator. Arranged by topics, this workbook enables the instructor to assign the appropriate Explorations Unit(s) that correlate(s) with the topic under discussion in the classroom. The workbook is not meant to be used in sequential order. Each unit has one or more prerequisite units that are required for student success in working the assigned unit. This allows the use of this ancillary text with any core course textbook. Charts that correlate the concepts from textbook sections with specific Explorations units are available in the Instructor Resources section of the Book Companion Web Site. The Companion Web Site can be accessed at
REVIEWS for Explorations in Beginning and Intermediate Algebra Using the TI-82/83/83 Plus/85/86 | 677.169 | 1 |
Algebra Study Tips
In the past, many visitors have requested general help with algebra. It is
difficult to recommend better methods for studying and for learning because
the best methods vary from person to person. Instead, we have provided
several ideas which can be the foundation to a good study program.
Copy notes or examples your teacher gives you. Consider copying
examples and notes from another student after class if you feel that you learn
better by focusing on the presentation.
Pay attention regardless of whether you are comfortable
with the current topic; your teacher may be showing some special
details which are necessary to do well.
Never cheat on a homework assignment, regardless of how easy or how
complicated the assignment is. Homework is an excellent method of studying
and it is assigned for a reason. It is easy to forget a memorized solution,
but it is much harder to forget a process for finding a solution which you have
applied several times.
Redo problems from tests and homework assignments, particularly
ones that you got wrong or have trouble understanding.
Remember that you must crawl before you can walk. Similarly, you must have a
good handle on the basics of algebra before you can master the advanced
concepts.
Get help from parents. Parent involvement is very important to the success of many
individuals. If you are a parent who has never learned or who does not remember
algebra, try learning the basics with a book, online tutorials, or from your
children. Reviewing the basics will put you at a level of understanding nearer to your
child -- then you can learn advanced concepts alongside each another. | 677.169 | 1 |
MAT 100 FUNDAMENTALS OF MATHEMATICS
An introductory mathematics course including topics basic to the foundations of algebra: rational numbers and integers; equations; ratio, proportion, and percents; and problem solving. Three credit hours. This course is required for and limited to all students who place within the specified range on the placement test. Offered fall and spring semesters.
MAT 110 INTRODUCTION TO ALGEBRA
A study of the structure of algebra, including numbers and their properties, exponents, equations, polynomials, functions, and graphs. Three credit hours. Prerequisites: MAT 100 or placement. Offered fall and spring semesters.
MAT 114 INTERMEDIATE ALGEBRA
Intermediate Algebra assumes proficiency with the techniques of basic algebra. The course includes study of the algebra of functions, rational functions, solving and graphing non-linear functions, inequalities, and the complex number system. Additional topics such as matrices, sequences and series, or conic sections may be covered at the discretion of the instructor. Three credit hours. Prerequisites: MAT 110 or placement. Course may not be taken out of sequence. Offered fall and spring semesters.
MAT 115 PRE-CALCULUS
This course combines pertinent topics from intermediate algebra and trigonometry that are necessary as fundamentals to master subsequent course study in calculus. Three credit hours. Prerequisites: MAT 114 or placement. Course may not be taken out of sequence. Offered fall and spring semesters.
MAT 125 CONCEPTS IN MATHEMATICS I
This is a course in a two semester sequence designed for Elementary Education majors and students seeking a broader understanding of the field of mathematics. Topics covered in this course include problem solving, numeration systems, arithmetic operations, fractions, and elementary number theory. Three credit hours. Prerequisites: Completion of MAT 110 or higher placement. Offered fall/spring semester.
MAT 126 Concepts in Mathematics II
This is a course in a two semester sequence designed for Elementary Education majors and students seeking a broader understanding of the field of mathematics. Topics covered in this course include decimals, ratio and proportional relationships, integers, real numbers, probability, measurement, dimensional analysis, and data analysis. Three credit hours. Prerequisites: Completion of MAT110 or higher placement. Offered spring/fall semester.
MAT 152 COLLEGE GEOMETRY
This course is an introductory study of the structures of geometry. It is designed for Elementary Education majors and students seeking a broader understanding of the area of geometry. Topics covered in this course include two- and three-dimensional geometric shapes, perimeter, area, volume, congruence and similarity, coordinate geometry, and transformations. Three credit hours. Prerequisites: MAT 114 or higher placement. Offered fall semester.
MAT 182 DISCRETE MATHEMATICS
This course is an introduction to non-continuous mathematics. Topics will include Logic, Proof, Matrices, Linear Programming, Counting, and Functions. Three credit hours. Offered spring semester in odd numbered years. Prerequisites: MAT 115 or higher placement.
MAT 216 SURVEY OF INTRODUCTORY CALCULUS AND ITS APPLICATIONS
This course introduces the techniques of differential and integral calculus and illustrates these ideas with practical applications from the social, managerial, and life sciences with special emphasis on business and economics. Three credit hours. Prerequisites: MAT 115 or placement. Course may not be taken out of sequence. Offered fall and spring semesters.
MAT 250 OPERATIONS ANALYSIS AND MODELING
This course is an introduction to the modeling of certain operational features common to business and information systems management. The focus will be on scheduling models, allocation models, queuing models, and inventory models. The models will provide mathematical information which can be used in the decision-making processes needed to solve large-scale problems. Emphasis is on problem formulation and experimentation with "naive" methods of solution; microcomputer software will be used to solve problems representative of the real world. Three credit hours. Prerequisites: Completion of MAT 114 or higher placement; and CIS 115 or CIS 120. Offered spring semester.
MAT 251 CALCULUS I
Calculus I is the first course of a three semester sequence in Calculus, covering differentiation with applications, including transcendental functions. Three hours of lecture and one hour of lab/recitation per week. Three credit hours. Prerequisites: MAT 115 or higher placement. Offered fall semester.
MAT 252 CALCULUS II
Calculus II is the second of a three course sequence in Calculus. The course covers integration, including transcendental functions, methods of integration, sequences, and series with applications. Three hours of lecture and one hour of lab/recitation per week. Three credit hours. Prerequisites: MAT 251 or MAT 216. Offered spring semester. Note: Registration for both the lecture (MAT 252) and the lab (MAT 252L) is required.
MAT 255 THEORY OF NUMBERS
This course is an introduction to the theory of numbers. Topics will include Prime Numbers, Divisibility, Congruences, Powers of an Integer Modulo m, Quadratic Reciprocity, Greater Integer Function, and Diophantine Functions. Three credit hours. Prerequisites: MAT 151 and MAT 182. Offered spring semester in even numbered years.
MAT 261 CALCULUS III
Calculus III extends the concepts of calculus in one variable to the calculus of several variables. Course topics include: vectors in the plane and space; 3-dimensional coordinate system; vector-valued functions; differential geometry; partial differentiation; and multivariable calculus. Three credit hours. Prerequisites: MAT 252. Offered fall semester. Note: Registration for both the lecture (MAT 261) and the lab (MAT 261L) is required.
MAT 298 SPECIAL TOPIC IN MATHEMATICS
Topic to be specified each semester course offered.
MAT 342 ABSTRACT ALGEBRA
The main goal of this course is to expose the student to the abstract concepts of algebra. The topics include sets, relations, mappings, groups, rings, isomorphism, homomorphism, polynomial ring, ideal, vector spaces, and linear independence. Three credit hours. Prerequisites: MAT 260 and MAT 255. Offered fall semester.
MAT 361 DIFFERENTIAL EQUATIONS
A first course in ordinary differential equations from analytic, geometric, numeric, and applied perspectives (including the use of modern computational technology as appropriate). Topics include exact, separable, and linear equations; initial-value and boundary-value problems; system of first-order equations; undetermined coefficients; variation of parameters; and series solutions. Three credit hours. Prerequisites: MAT 261 and 242. Offered spring semester. Note: Registration for both the lecture (MAT 361) and the lab (MAT 361L) is required.
MAT 381 STATISTICS AND PROBABILITY I
This course introduces students to descriptive statistics, elementary probability theory and counting techniques, random variables, probability distributions, normal distributions, confidence intervals and hypothesis testing. The topics of the course will be presented at a level of depth that is appropriate to mathematics majors. Students will also learn to apply technology to problem solving in statistics. Three credit hours. Prerequisites MAT 115 or higher placement. Offered fall semester. Note: Registration for both lecture (MAT 381) and lab (MAT 381L) is required.
MAT 382 STATISTICS AND PROBABILITY II
This course focuses on the process of statistical inference, presenting confidence intervals and hypothesis testing for two populations, chi-square procedures, linear and nonlinear regression, and one-way analysis of variance. The topics of the course will be presented at a level of depth that is appropriate to mathematics majors. Students will also apply technology to problem solving in statistics. Three credit hours. Prerequisites: MAT 381, or MAT 201, minimum of grade B recommended. Offered spring semester. Note: Registration for both lecture (MAT 382) and lab (MAT 382L) is required.
MAT 442 COMPLEX ANALYSIS
This course will expose the students to the useful concepts of complex numbers, complex functions and their applications. The topic includes complex number, complex plane, analytic functions, their derivatives, Cauchy integral theorem, Cauchy-Riemann differential equations, power series, and residues. Three credit hours. Prerequisites: MAT 342 and 421. Offered spring semester as needed. | 677.169 | 1 |
About this product
Description
Description
Written by the best selling author of Discovering Geometry, Patty Paper Geometry contains 12 chapters of guided and open investigations. Open investigations encourage students to explore their own methods of discovery, and guided investigations provide more direction to students. Use Patty Paper Geometry as a supplement to your geometry program or even as a major course of study. Author: Michael Serra, Pages: 262, paperback, Publisher: Playing It Smart, ISBN: 978-1559530723 | 677.169 | 1 |
'Introductory Statistics follows the scope and sequence of a one-semester, introduction to statistics course and is geared...
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'Introductory Statistics follows the scope and sequence of a one-semester, introduction to statistics course and is geared toward students majoring in fields other than math or engineering. This text assumes students have been exposed to intermediate algebra, and it focuses on the applications of statistical knowledge rather than the theory behind it. The foundation of this textbook is Collaborative Statistics, by Barbara Illowsky and Susan Dean, which has been widely adopted. Introductory Statistics includes innovations in art, terminology, and practical applications, all with a goal of increasing relevance and accessibility for students. We strove to make the discipline meaningful and memorable, so that students can draw a working knowledge from it that will enrich their future studies and help them make sense of the world around them. The text also includes Collaborative Exercises, integration with TI-83,83+,84+ Calculators, technology integration problems, and statistics labsNow hosted by Khan Academy, smART History is a free multi-media web-book designed as a dynamic enhancement (or even...
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Now hosted by Khan Academy, smART History is a free multi-media web-book designed as a dynamic enhancement (or even substitute) for the traditional and static art history textbook.According to the site 'We understand the history of humanity through art. From prehistoric depictions of woolly mammoths to contemporary abstraction, artists have addressed their time and place in history and have expressed universal human truths for tens of thousands of years. Learn what made Rome great, how Islamic tile work evolved, why the Renaissance happened, and about the brilliant art being produced today around the globe. Dr. Beth Harris and Dr. Steven Zucker of Smarthistory together with leading art historians, and our museum partners have created hundreds of short engaging conversational videos and articles, making Khan Academy one of the most accessible and extensive resources for the study of the history of art Smart History to your Bookmark Collection or Course ePortfolio
Select this link to close drop down of your Bookmark Collection or Course ePortfolio for material Smart History
Select this link to open drop down to add material SmartThis is a free, online textbook that provides information on dimensions, from longtitude and latitude to the proof of a...
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This is a free, online textbook that provides information on dimensions, from longtitude and latitude to the proof of a theorem of geometry. There are 9 chapters, each 13 minutes long. The book contains a total of 117 minutes of video, but can also be read as an ordinary textbook.The film can be enjoyed by anyone, provided the chapters are well-chosen. There are 9 chapters, each 13 minutes long. Chapters 3-4, 5-6 and 7-8 are double chapters, but apart from that, they are more or less independent of Dimensions (geometry) to your Bookmark Collection or Course ePortfolio
Select this link to close drop down of your Bookmark Collection or Course ePortfolio for material Dimensions (geometry)
Select this link to open drop down to add material Dimensions (geometryMarketing: The Essential Guide to Online Marketing to your Bookmark Collection or Course ePortfolio
Select this link to close drop down of your Bookmark Collection or Course ePortfolio for material eMarketing: The Essential Guide to Online Marketing
Select this link to open drop down to add material eMarketing: The Essential Guide to Online MarketingLiberté, by Gretchen Angelo, is a first-year college French textbook with a true communicative approach.Each chapter is...
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Liber Liberte: A first year French textbook to your Bookmark Collection or Course ePortfolio
Select this link to close drop down of your Bookmark Collection or Course ePortfolio for material Liberte: A first year French textbook
Select this link to open drop down to add material Liberte: A first year French textbook to your Bookmark Collection or Course ePortfolio
The networked environment seems to have successfully released enormous creative energy in domains ranging from software...
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The networked environment seems to have successfully released enormous creative energy in domains ranging from software design to encyclopedia writing. It has come, in many cases, to compete with and outperform traditional proprietary, market-based production. The question we face is whether the basic economics and organizational strategy that have proved so successful in other areas are equally applicable to learning objects and other Wisdom: Peer Production of Educational Materials to your Bookmark Collection or Course ePortfolio
Select this link to close drop down of your Bookmark Collection or Course ePortfolio for material Common Wisdom: Peer Production of Educational Materials
Select this link to open drop down to add material Common Wisdom: Peer Production of | 677.169 | 1 |
Calculus can be an intimidating subject. For many students, even the name sounds intimidating. The truth is that Calculus is based on a few very powerful principles and once you fully understand those principles all of the additional topics naturally follow. Most Calculus textbooks begin the subject with a nauseating discussion of limits and then proceed to the introduction of a derivative which is one of the core topics in CalculusWhat's in the DVD? Simple: Everything that will make you a better rock guitar player! After showing you some perfect warm-up exercises (using both major and minor pentatonic scales as well as chromatics), I'll show you hammer-ons and pull-offs, as well as how to chain scale ideas together | 677.169 | 1 |
Simplifying algebraic expressions
Compressed Zip File
Be sure that you have an application to open this file type before downloading and/or purchasing. How to unzip files.
3.45 MB | 30 pages
PRODUCT DESCRIPTION
This interactive PowerPoint goes through the basics of simplifying algebraic expressions. Students are encouraged to participate in the lesson by using individual white boards to answer questions posed during the PowerPoint or to demonstrate methods to the rest of the class.
The 26 slide PowerPoint deals with:
Parts of an expression
Like and unlike terms
A negative coefficient
.removing brackets to simplify
Two worksheets accompanied by memorandums have also been included.
This PowerPoint is not locked so small variations can be made to suit your students.
If you have any suggestions or queries please do not hesitate to contact me on margauxlangenhoven@gmail.com
You might also be interested in my Equations
Task cards with QR codes | 677.169 | 1 |
PDF (Acrobat) Document File
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4.54 MB | 59 pages
PRODUCT DESCRIPTION
About this resource :
This expressions and equations no prep resource is designed to give your students the opportunity practice skills involving all equations, expressions and inequalities, while making prep easy on you! Included are 30 pages of practice problems. All worksheets align with 6th Grade Common Core Standards | 677.169 | 1 |
New Cambridge Senior Maths resources developed to meet the needs of the Australian Curriculum and its variants in WA, SA, TAS and ACT.
Cambridge Senior Mathematics: Australian Curriculum is an authoritative series for the Australian Curriculum that builds on a proven maths teaching and learning formula while incorporating the content and assessment requirements that characterise senior curricula in WA, SA, TAS and ACT.
Hide Series
Essential Mathematics GOLD for the Australian Curriculum Second Edition
Now offering rich digital resources and a powerful Learning Management System for students who require additional support in mathematics in this innovative series.
Essential Mathematics GOLD for the Australian Curriculum Second Edition
Now offering rich digital resources and a powerful Learning Management System for students who require additional support in mathematics in this innovative series.
This second edition continues to provide a practical interpretation of the Australian Curriculum to help students meet the minimum requirements of the achievement standards. It now combines a proven teaching and learning formula with the seamless integration of a structured student text, rich digital learning resources and a powerful learning management system.
Australia's most respected and comprehensive maths series, now available for the new Victorian Curriculum. Complete and authoritative Victorian Curriculum coverage from an author team you know and trust.
This new Victorian Curriculum edition of the popular series continues to support differentiated learning by offering three different pathways (Foundation, Standard and Advanced) through the exercises to cater for learners of all ability levels. These pathways are indicated in the textbook through detailed working programs subtly embedded in the exercises.
Cambridge Senior Mathematics: VCE builds on a proven teaching and learning formula to support the new AC/VCE Mathematics Study Designs for implementation in 2016. Developed from the popular Cambridge Essential Mathematics VCE series, our authors have unrivalled expertise in writing examples and problems to prepare students for exams, as well as proven experience interpreting the Australian Curriculum and VCE Study Designs for VCE students.
This second edition of the popular series now combines a proven teaching and learning formula with the seamless integration of a structured student text, rich digital learning resources and a powerful learning management system | 677.169 | 1 |
Description
Python Math is powerful mathematics and scientific computing in your pocket, backpack, or purse - no network connection required. It is a full implementation of the Python Programming Language (v2.7.3) with additional modules focused on mathematics and scientific computing.
FEATURES
- Python interpreter runs in your iPhone, iPod Touch, or iPad. No network connection is needed.
- Python Math is a universal app: it works on iPhone, iPod Touch, and iPad
- Most modules of the Python Standard Library are included
- In the Python interpreter, you can clear the screen, restart the interpreter, email the interpreter transcript, print the transcript, and save all your input commands as a script
- Implements raw_input()
- Supports all screen orientations
- If a script named PYTHONSTARTUP.py exists, Python Math will execute it using execfile() upon app launch and upon restarting the interpreter
- Command history lets you recall, edit and enter previously entered commands
- Custom python keyboard with in-app purchase
- Editor and file directory with in-app purchase
- Module numpy is available with in-app purchase
MODULES
Python Math includes most modules from the Python Standard Library. These third party math modules are also included in Python Math:
- SymPy: symbolic mathematics
- mpmath: multiprecision floating-point arithmetic
These modules are available via in-app purchase:
- NumPy: powerful N-dimensional array object, linear algebra, Fourier transform, and random number capabilities
COMMAND HISTORY
The Python Math shell implements command history in three ways:
- Tap the up or down arrow in the lower right of the shell window to recall commands, then edit and submit
- Scroll the shell window up or down to any line you previously entered. Edit the line and press the Go button. The edited line will be submitted to the interpreter just as if you had typed it.
- Command history inspired by tcsh is also available. Enter !! to recall the previous command; !history to display history of commands; !N to recall the Nth command in the history and !-N to recall the Nth command previous to the current command.
IN-APP PURCHASE
- Custom Keyboard: Choose from several Python-specific keyboards displayed above the standard keyboard. Python expressions and statements are easier to type when you don't have to press the shift key twice to get to numbers and symbols used in Python programming. Several keyboard variations are available, selectable in settings (tap menu button in navigation bar and select Store). Try them out and see which is your favorite. You can also disable the custom keyboard by setting the keyboard choice to None.
- Directory and Editor: All your saved scripts and files are displayed in the files directory. You can create new files and delete them. With the text editor, you can edit, save, delete, rename, and run scripts and edit text files.
- Themes: Two themes are included with Python Math. You can get 15 additional themes by purchasing the Themes pack.
- Numpy: From NumPy.org: "NumPy is the fundamental package for scientific computing with Python. It contains among other things, a powerful N-dimensional array object, sophisticated (broadcasting) functions, tools for integrating C/C++ and Fortran code, useful linear algebra, Fourier transform, and random number capabilities. Besides its obvious scientific uses, NumPy can also be used as an efficient multi-dimensional container of generic data. Arbitrary data-types can be defined. This allows NumPy to seamlessly and speedily integrate with a wide variety of databases."
PYTHON.ORG
For more information, documentation, tutorials, downloads for other computers, and even merchandise about Python, go to
Do you know how to install the app?
Download Python | 677.169 | 1 |
MNS205 Intro to Quantitative Methods
Course Description
An examination of advanced algebra techniques in the business setting, including linear systems, polynomials, exponential and logarithmic functions, as well as introduction to probability and statistics. The primary quantitative course required for MNS 407. (Students who have taken college algebra (MTH 215) within the last three years are exempt from this course.)
Learning Outcomes
Construct and solve (algebraically, graphically, and statistically) models for a variety of business problems.
Apply mathematical ideas and express them graphically and numerically.
Solve equations, inequalities, and systems of equations.
Explain and work with polynomials, polynomial functions, rational expressions, quadratic equations and functions. | 677.169 | 1 |
Equation Response Editor
The purpose of this tutorial is to explain how to use the Equation Response Editor tool, and to let you practice using it. You will be using this tool to enter answers that are numbers, expressions, or equations.
Smarter Balanced Assessments
OURMission
The Park Meadows community will provide a safe and orderly environment with expectations of academic success, open communication, development of strong character, and respect for diversity while preparing students for an ever-changing world. | 677.169 | 1 |
Fun Self-Discovery Tools
Continuity
Rating:
Description:
VIDEO NOTES: When I talk about continuity at endpoints you can not see the whole screen, but you get a good view of it right after I finish that section, so copy it down and then rewind and listen. Sorry!
After this video students should be able to ...
1. Determine intervals of continuity, and locations of discontinuities based on a graph.
2. Identify the 5 types of discontinuities and recognize which ones are "removable" | 677.169 | 1 |
7th Grade Math Algebraic Word Problems
PDF (Acrobat) Document File
Be sure that you have an application to open this file type before downloading and/or purchasing.
0.12 MB | 4 pages
PRODUCT DESCRIPTION
This is a worksheet that is made up of previous NYS math assessment questions. The worksheet is all multiple choice questions that ask the students to match algebraic expressions and equations to | 677.169 | 1 |
A math curriculum that focused on real-life problems would still expose students to the abstract tools of mathematics, especially the manipulation of unknown quantities. But there is a world of difference between teaching "pure" math, with no context, and teaching relevant problems that will lead students to appreciate how a mathematical formula models and clarifies real-world situations. The former is how algebra courses currently proceed — introducing the mysterious variable x, which many students struggle to understand. By contrast, a contextual approach, in the style of all working scientists, would introduce formulas using abbreviations for simple quantities — for instance, Einstein's famous equation E=mc2, where E stands for energy, m for mass and c for the speed of light.
Imagine replacing the sequence of algebra, geometry and calculus with a sequence of finance, data and basic engineering. In the finance course, students would learn the exponential function, use formulas in spreadsheets and study the budgets of people, companies and governments. In the data course, students would gather their own data sets and learn how, in fields as diverse as sports and medicine, larger samples give better estimates of averages. In the basic engineering course, students would learn the workings of engines, sound waves, TV signals and computers. Science and math were originally discovered together, and they are best learned together now.
"Learning happens on the fringes of what we already know" David Ausubel.
But then what?
Rarely do we see discussed the benefits of learning "powerful ideas" that are not like our genetic heritage, that require lots of work, that produce not add-ons but qualitative *changes* in the way we think.
Deep thinkers about communications systems such as Innis, Ong and McLuhan have written cogently about the transformational effects of becoming fluent in new ways to represent ideas. Things that are like writing have been particularly powerful precisely because of how they are detached from our built-ins.
And let's put aside that most algebra courses are taught in a ridiculous manner, and prepped worse in earlier grades.
But let's bring front and center the idea that getting fluent in dealing with the abstractions and operations and "making a math when needed" to represent ideas is a major reason to teach it. Another is to be the representation languages for science (which is the relationships between "what's out there" and the representations we can devise to capture meaning).
There's no question that much of math and science co-evolved, but they were not discovered together (the "discoveries" were about 2000 years apart), and real science is quite different and more powerful and important than it seems the authors of the Times piece understand.
I can see major problems with pre-service teacher education. If a student is smart enough to understand finance, data and basic engineering I cannot really see them becoming a lowly underpaid math teacher.
I couldn't help but think that the contexts suggested (especially finance) wouldn't have interested me very much. Would that have turned me off of math? What do we do when the context doesn't work for everyone? It seems like connecting CS to media would be at least somewhat interesting to everyone, but maybe that's making too much of an assumption if I was turned off by all of these math context suggestions. Can't possibly please everyone…hmm…
Any good curriculum ought to connect the concrete to the abstract and then make the abstract concrete. In other words, start with something the student knows and derive an abstract concept out of it. If the student learns it well enough, it will become concrete information which can be used for further connections.
Good teachers ought to be able to do this. The trick is figuring out what piques a student's interest. That's not something easily encapsulated in a one-size-fits-all textbook.
I agree with this. I got the impression that each course was going to fully focus on finance (or data, or whatever), but perhaps I misunderstood. Maybe they just wanted to offer one suggestion of how to ground the context in class.
The "variables" in E=mc^2, and the "unknown variable" in an equation you want solved like 100=x^2 (for finding the length of the side of a say a square garden you want to lay out with area 100) are different mathematical concepts and these concepts are both very important. I agree that teaching how to solve equations for unknown variables purely in the abstract is a very bad thing to do, but, teachers ought to understand and teach, with interesting and applicable motivations, all of the important conceptual contents of mathematics, appropriately chosen and sequenced. Of course, examples of both these particular concepts from math are to be found in any choice of contexts like finance, gardening, multimedia computing and physics.
I think that Alan Kay's response is one aspect of math education reform that does not get enough attention. If have understood many of his other articles and talks, one side of the coin is "How do we make algebra more relevant and natural", but the other equally important side of the coin is that "the fundamental aspect of algebra is that it is not an evolutionary aspect that would naturally evolve out of general thinking".
The ability to conceptualize, analyze and manipulate abstract concepts is a defining part of human civilization.
[…] "passion" and includes "design projects for Freshmen." Sounds to me that contextualized computing education, which includes efforts like Media Computation and robotics, is the kind of thing they're […] | 677.169 | 1 |
Summary and Info
Problem-Solving Strategies is a unique collection of competition problems from over twenty major national and international mathematical competitions for high school students. The discussion of problem-solving strategies is extensive. It is written for trainers and participants of contests of all levels up to the highest level: IMO, Tournament of the Towns, and the noncalculus parts of the Putnam competition. It will appeal to high school teachers conducting a mathematics club who need a range of simple to complex problems and to those instructors wishing to pose a "problem of the week," "problem of the month," and "research problem of the year" to their students, thus bringing a creative atmosphere into their classrooms with continuous discussions of mathematical problems. This volume is a must-have for instructors wishing to enrich their teaching with some interesting nonroutine problems and for individuals who are just interested in solving difficult and challenging problems. | 677.169 | 1 |
Synopsis
This bundle edition contains a Revision Workbook and digital ActiveBook for use online. A code to access the online edition is contained within the bundle. For the classroom and independent study,this Workbook is for those students studying on the higher tiers for Edexcel GCSE Mathematics A. * The Revision Workbooks provide plenty of practice in 3 speeds: guided questions, unguided questions and practice exam papers * Revision resources that are priced to meet both your budget and your students * ResultsPlus data delivers insightful exam experience and guidance on the common pitfalls and misconceptions. * The one topic-per-page format provides hassle-free revision for students with no lengthy set-up time and no complex confusing revision concepts. * Target grades on the page allow students to progress at a speed that is right for them | 677.169 | 1 |
5
Students who successfully complete this course will be able to: – Describe why and how computers are used in different disciplines. – Use computers to analyze errors and finding the solutions. – Find solutions for differential equations. – Approximate integrals scientific computing CS 580
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Problem is well-posed if solution -exists -is unique -depends continuously on problem data Otherwise, problem is ill-posed Even if problem is well posed, solution may still be sensitive to input data Computational algorithm should not make sensitivity worse scientific computing CS 580
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Scientific, Symbolic and Graphical Computation Scientific, Symbolic and Graphical Computation each area of specialisation has evolved its own methodologies and techniques that best fit the structure ''of their problems. In reality, the " chunks" are not particularly well-defined; the problems of these specialities overlap on the one hand, but there may be gaps among them on the other. - Somewhere among these specialistions sits computer science. Our discipline is itself broadly based in the sciences, humanities, engineering and mathematics. scientific computing CS 580
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We view the solution to large problems, both abstractly and conceretely, as a system of small solution that co-oprate through well-defined interfaces. --We are among the engineers when we construct large software systems -We are among mathematicians when we prove properties of our systems. Computers and computation have effected almost every facet of human activity. Traditionally, the branch of computer science and mathematics most concerned with this activity is called numerical analysis. scientific computing CS 580 Scientific, Symbolic and Graphical Computation
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Modern numerical analysis is closely allied with scientific.Computation This term is generally used to denote a huge area of research and application involving the numerical solution of problems in the physical sciences. The solutions to these problems typically involve the numerical solution of linear, non linear or differential equations and integration. Scientific, Symbolic and Graphical Computation scientific computing CS 580 | 677.169 | 1 |
Mathematics
The Valor Math Program offers a differentiated mathematics instruction that engages students in interactive experiences supported by the use of manipulatives, models, textbooks, and technology. Students will move from the concrete foundational stage, to the investigative stage and finally to the project-based stage of contextual application. Frequent and ongoing assessment, in a variety of forms, guides the instructional decisions made by teachers. Assessments include the opportunities for demonstrating mastery and high level thinking.
Mathematics Department Courses
ELE 115: Math Lab Elective I Freshman
Term: YearCredit: 1.0
Prerequisites: Teacher recommendation
Notes: This is a Pass/Fail course.
ELE 116: Math Lab Elective II Sophomore
Term: YearCredit: 1.0
Prerequisites: Teacher recommendation
Notes: This is a Pass/Fail course.
ELE 117: Math Lab Elective III Junior
Term: YearCredit: 1.0
Prerequisites: Teacher recommendation
Notes: This is a Pass/Fail course.
MAT 110: Algebra I
Students will be exposed to the fundamentals of algebra. Topics include operations with real numbers and variable expressions, including exponential expressions, solving and graphing linear equations, inequalities, and systems, factoring polynomials, solving and graphing quadratic equations, and simplifying expressions. Algebra I stresses a systematic approach to problem solving and critical thinking.
Grade: Freshman
Term: YearCredit: 1.0
Prerequisites: Pre-Algebra
Notes: Students are required to have a TI-84 calculator.
MAT 120 HON: Honors Algebra I
Honors Algebra I covers an accelerated Algebra I curriculum with an emphasis in higher level critical thinking skills. Topics include operations with real numbers and variable expressions, including exponential expressions, solving and graphing linear equations, inequalities, and systems, factoring polynomials, solving and graphing quadratic equations, and simplifying expressions. The course includes assignments, applications, and exams at a greater depth and difficulty level.
MAT 210: Geometry
Geometry is a study of geometric figures in two and three dimensions. It is designed to increase students' understanding of spatial relations. Emphasis is also placed upon applying algebra to geometric problem solving, including trigonometry, and applying the basic terminology and concepts of geometry in a logical and organized manner, including formal proofs.
MAT 220 HON: Honors Geometry
Honors Geometry is a study of geometric figures in two and three dimensions. It is designed to increase students' understanding of spatial relations. Emphasis is also placed on applying algebra to geometric problem solving, including trigonometry, and applying the basic terminology and concepts of geometry in a logical and organized manner, including formal proofs. Honors Geometry covers an accelerated Geometry curriculum with an emphasis in higher-level critical thinking skills. The course includes assignments, applications and exams at a greater depth and difficulty level.
MAT 310: Algebra II/Trigonometry
Algebra II/Trigonometry expands on the topics and concepts of Algebra I. New topics include polynomial, exponential, logarithmic and trigonometric functions, matrices, probability and statistics, and conic sections. Students develop problem-solving skills and are challenged to think critically in preparation for advanced mathematical study in upper level courses. Completion of this course provides a strong foundation for ACT and SAT preparation. In addition to numerical, algebraic and graphical analysis using graphing calculator technology, emphasis is also placed on written expression in the form of algebraic communication that documents a logical thought process and support for a correct response.
MAT 320 HON: Honors Algebra II/Trigonometry
Honors Algebra II/Trigonometry covers an accelerated Algebra II/Trigonometry curriculum with a focus on higher-level critical thinking skills, emphasizing application of concepts. Due to the level of rigor, students beginning this course are expected to be proficient in the mathematic content of Algebra I and Geometry. Students will be given the opportunity to learn some basic programming on a graphing calculator that can assist and support learning. The course includes assignments, applications and exams at a greater depth and difficulty level.
Grade: Freshman, Sophomore, Junior
Term: YearCredit: 1.0
Prerequisites: Grade of 93% or better in Geometry or Grade of 83% or better in Honors Geometry, teacher recommendation is required; Entrance examination required for incoming 9th graders
Notes: Student is required to have a TI-83 or TI-84 calculator.
MAT 400: College Algebra
College Algebra expands on the topics and concepts of Algebra 2 with the focus of going deeper with fewer topics in an effort secure mastery of all algebra topics. This course combines traditional instruction with online learning and practice, and topical projects designed to broaden students understanding of the each concept. Students in this course will be required to pass a gateway exam each semester to ensure mastery of each topic. Course topics include identifying, solving and graphing algebraic functions of all forms, solving systems of equations and inequalities, mathematical modeling, polynomial manipulation, rational functions, conic sections, trigonometric functions, matrices and determinants.
Grade: Sophomore, Junior, Senior
Term: YearCredit: 1.0
Prerequisites: Completion of Algebra 1, Geometry, and Algebra II
Notes: Student is required to have a TI-84 calculator.
MAT 410: Pre-Calculus
Pre-Calculus extends the concepts covered in Algebra 2/Trigonometry, and strengthens students' understanding of the elementary functions and mathematical reasoning. New topics include expanded study of the trigonometric functions, vectors, sequences and series, and probability. The calculus ideas of limits and slopes of curves are introduced in preparation for the study of calculus.
Grade: Sophomore, Junior, Senior
Term: YearCredit: 1.0
Prerequisites: Grade of 83% or better in Algebra II or by teacher recommendation
Notes: Students are required to have a TI-84 calculator.
MAT 420 DC: DC Pre-Calculus
DC (Dual Credit) Pre-Calculus covers an accelerated Pre-Calculus curriculum with a focus on higher-level critical thinking skills, emphasizing application of concepts and derivation of theorems. Additional topics include parametric equations, polar coordinates, inductive proof and a formal introduction to calculus. The course includes assignments, applications and exams at a greater depth and difficulty level.
Grade: Sophomore, Junior, Senior
Term: YearCredit: 1.0
Prerequisites: Grade of 93% or better in Algebra II, or Grade of 83% or better in Honors Algebra II, or by teacher reccommendation
Notes: Students are required to have a TI-84 calculator.
MAT 430: Probability and Statistics
Probability and Statistics is designed to familiarize the student with the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Emphasis is placed on exploring data, planning a study, analyzing, and communicating results.
Grade: Senior
Term: YearCredit: 1.0
Prerequisites: Grade of 73% or better in Algebra II, or competion of Pre-Calc, or by teacher recommendation
Notes: Students are required to have a TI-84 calculator.
MAT 510: AP Statistics
In preparation for the AP Statistics exam, this course introduces students to the major concepts and tools for collecting, analyzing and drawing conclusions from data. Students are exposed to four broad conceptual themes: exploring data, planning and conducting a study, anticipating patterns in population data, and statistical Inference. The course makes use of key mathematical concepts taught in algebra with a broader emphasis on clearly defining questions to be investigated, gathering and organizing data, producing informative graphical and numerical summaries, modeling relationships, making decisions while accounting for uncertainty in the data, and clearly communicating results in the context of a study. Students learn to synthesize their mathematics acumen with critical thinking and writing skills to create a framework for evaluating and supporting hypotheses in most disciplines.
Grade: Junior, Senior
Term: YearCredit: 1.0
Prerequisites: Completion of Pre-Calculus and teacher recommendation
Notes: Students are required to have a TI-84 calculator.
MAT 520: AP Calculus A/B
Grade: Sophomore, Junior, Senior
Term: YearCredit: 1.0
Prerequisites: Completion of Pre-Calculus and teacher recommendation.
Notes: Students are required to have a TI-84 calculator.
MAT 530: AP Calculus B/C | 677.169 | 1 |
Eminent mathematician/teacher approaches algebraic number theory from historical standpoint. Demonstrates how concepts, definitions, and theories have evolved during last two centuries. Features over 200 problems and specific theorems. Includes numerous graphs and tables. more...
An engaging treatment of an 800-year-old problem explores the occurrence of Fibonacci numbers in number theory, continued fractions, and geometry. Its entertaining style will appeal to recreational readers and students alike. more...
Unusually clear and interesting classic covers real numbers and sequences, foundations of the theory of infinite series and development of the theory (series of valuable terms, Euler's summation formula, asymptotic expansions, other topics). Includes exercises. more...
This text covers the basics of algebraic number theory, including divisibility theory in principal ideal domains, the unit theorem, finiteness of the class number, and Hilbert ramification theory. 1970 edition. more...
About This Book This book will help high school math students at all learning levels understand basic mathematics. Students will develop the skills, confidence, and knowledge they need to succeed on high school math exams with emphasis on passing high school graduation exams. More than 20 easy-to-follow lessons... more... | 677.169 | 1 |
Circuit Training - Solving Quadratics by Factoring
PDF (Acrobat) Document File
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0.4 MB | 2 pages
PRODUCT DESCRIPTION
Your students will stay engaged as they work to solve these 12 quadratic equations by factoring (no calculator use is expected). The problems are progressive in nature so it is great for guided notes, cooperative work, differentiated instruction, and much more! To prevent students from working backwards from the answers, to advance in the circuit, students must hunt for either " the sum of their solutions " , " the larger solution" , "the smaller solution" or the "product of the solution " (as I have specified). The answers are included in the circuit, the only preparation the teacher needs to do is work the circuit ahead of the students to understand the progression | 677.169 | 1 |
Sequences Review
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0.11 MB | 4 pages
PRODUCT DESCRIPTION
This worksheet covers all topics associated with arithmetic and geometric sequences, as taught in Algebra 2 and Precalculus.
Problems include finding the number of terms in a sequence, finding a given term in a sequence, recognizing a pattern as a sequence, finding the arithmetic mean and geometric mean, and word problems involving sequences.
Series are not covered in this review.
This is appropriate for Algebra 2 or Precalculus, though it could also be used as a review of sequences for a Calculus | 677.169 | 1 |
About this product
Description
Description
This course companion specifically supports the core maths skills A Level and post-16 Physics students need for exam success. It has been mapped to the requirements of the new 2015 A Level specs with new material ensuring complete coverage of the new specs. Written by senior examiners, this full-colour course companion is designed to help you understand how and why mathematical formulae work in physics and it gives you the techniques you need to effectively answer the range of exam questions. // You are helped throughout the book with numerous test yourself questions providing plenty of practice to recap on what you have learnt. // Data exercises practise techniques to handle data and plot results. // Quickfire quizzes quickly reinforce skills and understanding as a topic progresses. // Pointers provide hints for refining exam technique and avoiding common mistakes. // GCSE Mathematics techniques are recapped to make sure they are fully understood so matter how confident you feel with your maths, this book covers your needs. // The book supports and is mapped to A Level Physics courses from AQA, Pearson, OCR, WJEC, CCEA, the International Baccalaureate and the Cambridge Pre-U.It is also appropriate for the CIE Pre U, the IB and Oxford University Physics Aptitude Test.
Author Biography
Gareth Kelly is an experienced teacher who has been involved with A Level and GCSE Physics and Electronics for a major awarding body for many years. Nigel Wood is an experienced Chief Examiner in A Level Physics for a major awarding body, and was formerly Head of Physics at Dulwich College, London. | 677.169 | 1 |
9780077452155
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Summary
Calculus for Business, Economics, and the Social and Life Sciences, Brief Editionintroduces calculus in real-world contexts and provides a sound, intuitive understanding of the basic concepts students need as they pursue careers in business, the life sciences, and the social sciences. Students achieve success using this text as a result of the authors' applied and real-world orientation to concepts, problem-solving approach, straightforward and concise writing style, and comprehensive exercise sets. More than 100,000 students worldwide have studied from this text! .
Table of Contents
Chapter 1: Functions, Graphs, and Limits
1.1 Functions
1.2 The Graph of a Function
1.3 Linear Functions
1.4 Functional Models
1.5 Limits
1.6 One-Sided Limits and Continuity
Chapter 2: Differentiation: Basic Concepts
2.1 The Derivative
2.2 Techniques of Differentiation
2.3 Product and Quotient Rules; Higher-Order Derivatives
2.4 The Chain Rule
2.5 Marginal Analysis and Approximations Using Increments
2.6 Implicit Differentiation and Related Rates
Chapter 3: Additional Applications of the Derivative
3.1 Increasing and Decreasing Functions; Relative Extrema
3.2 Concavity and Points of Inflection
3.3 Curve Sketching
3.4 Optimization; Elasticity of Demand
3.5 Additional Applied Optimization
Chapter 4: Exponential and Logarithmic Functions
4.1 Exponential Functions: Continuous Compounding
4.2 Logarithmic Functions
4.3 Differentiation of Exponential and Logarithmic Functions
4.4 Applications; Exponential Models
Chapter 5: Integration
5.1 Antidifferentiation: The Indefinite Integral
5.2 Integration by Substitution
5.3 The Definite Integral and the Fundamental Theorem of Calculus
5.4 Applying Definite Integration: Area Between Curves and Average Value | 677.169 | 1 |
If you are an undergraduate you are better off focusing on real mathematics rather than more contrived competition math. No one really cares about math olympiads after High School. I suggest you spend your time learning Analysis and Algebra from good sources and solving problems from textbooks rather than High School competition math resources.
Hoffman and Kunze's "Linear Algebra" is a great text for linear algebra. Very informative, lots of detail, explanation, and examples. As a bonus, a lot of the problems are surprisingly difficult and require a similar amount of and depth of thought as you can expect in the putnam. As a deficit, there is no solution manual to help you when/if you get stuck.
At this point you should have a very solid set of approaches towards most problems (except Putnam analysis problems, maybe), and probably you will be weakest at writing formal, well-argued proofs. Actually posting your solutions to the problems you do on the AOPS forums helped me a ton, people will usually be able to spot and point out where you made any flaws or leaps in your logic that would need to be cleared up. To work on that, you should be taking very rigorous proof-based classes in college (basically anything past calc and intro group theory), take a putnam class if your college offers one (working with other people and seeing how others approach a problem is incredibly helpful), work through andreescu's Putnam book (and don't be discouraged by how beautiful some of those proofs are).
It becomes hard to self-evaluate sometimes and it helps to have someone stronger than you critique your proofs -- this is why I recommend trying to take more rigorous math classes as soon as you can because you will gain a lot of mathematical maturity just from your professor's critiquing your homework/exams. It's hard to find any one comprehensive source of problems at this point -- old putnam exams and olympiads from eastern european countries are your best bet, and there are quite a few subforums on AOPS that are dedicated to these foreign competitions and will help you there.
This got me from being a relatively average math team member in 9th grade to scoring 50+ on Putnam a few times by the time I graduated college. | 677.169 | 1 |
Summary
It would be difficult to write a book on multivariate analysis without the compact notation provided by matrix algebra. This chapter introduces all the matrix algebra needed to read the book. A few proofs are given where they seemed instructive, and most techniques are illustrated numerically. A large problem set provides additional numerical illustrations and practice in algebraic manipulations.
The level of presentation does not assume that the reader has had previous exposure to matrix notation, although it would be helpful. Those without prior familiarity with matrices would need to work most of the problems in order to be comfortable with the notation used in the book. | 677.169 | 1 |
The teacher's guide and collection of transparency masters are designed for use in teaching adult basic education (ABE) students how to read and interpret graphs and charts. Covered in the individual lessons of the instructional unit are the reading and interpretation of charts as well as picture, line, bar, and circle graphs. Each unit contains a detailed lesson plan that includes instructions for presenting the vocabulary and mathematical concepts addressed in three separate graphs or charts, a student worksheet along with instructions for its presentation, and an answer key for the worksheet. Throughout the instructional unit, graphs and charts are presented that deal with such relevant topics as taxes, alcohol intake, jobs, earnings, population growth, government spending, clothing sizes, and comparison shopping for computers and checking accounts. The transparency masters include a series of picture, bar, line, and circle graphs and charts dealing with such topics as the number of farms in the United States, the effects of alcohol on the body, tax exemptions, oil consumption, jobs in Washington State, the distribution of earnings in the United States, monthly rainfall, the prison population, household income, government income, government spending, sizes of sweat pants, a comparison of computers, and budget deficits. A brief discussion of procedures for displaying transparency masters and suggestions for presenting these particular transparency masters are provided. (MN) | 677.169 | 1 |
College Algebra and Trigonometry: A Unit Circle Approach (5th Edition)
Author:Mark Dugopolski
ISBN 13:9780321644770
ISBN 10:321644778
Edition:5
Publisher:Pearson
Publication Date:2010-01-15
Format:Hardcover
Pages:992
List Price:$225.33
 
 
Dugopolski's College Algebra and Trigonometry: A Unit Circle Approach, Fifth Edition gives students the essential strategies to help them develop the comprehension and confidence they need to be successful in this course. Students will find enoughcarefully placed learning aids and review tools to help them do the math without getting distracted from their objectives. Regardless of their goals beyond the course, all students will benefit from Dugopolski's emphasis on problem solving and critical thinking, which is enhanced by the addition of nearly 1,000 exercises in this edition.
Booknews
After reviewing briefly the history of the discovery and use of mineral in New Mexico, lists minerals alphabetically from acanthite, an important silver ore, to zircon, usually found microscopically in ancient and modern sediments. The articles describe the appearance, give its chemical makeup, record its place of occurrence, and refer to information sources. The back matter includes an annotated list of the state's 172 mining districts, a list of counties with the minerals found in them, and an extensive and updated bibliography. Very thoroughly cross- referenced. No index. Previously published in 1944 and 1959. Annotation c. Book News, Inc., Portland, OR (booknews.com) | 677.169 | 1 |
6284 Calc
By Amit Kalra
Description
6284 Calc is a tool for students to do their math work without having to memorize hundreds of formulas throughout math or science!
Use 6284 Calc when you're stuck on a math/science problem, forget a formula, or just don't feel like doing you homework because you're too cool for school! (most likely the case)
Not a student? That's cool! Use the Daily Life Math section for real life situations like shopping, giving tips, investments, and interest! (Extremely helpful during the holidays!) There's also an Extra section that contains unique stuff!
What's New in Version 1.0.11
HELLO???? ARE YOU EVEN READING THIS?
Probably not, but here's some REALLY REALLY DOPE stuff we just added!
— Physics Steps! — Displacement Steps! — Equation of Motions (1,2,3) Steps! — Elastic Steps! — Inelastic Steps! — Momentum Impulse Steps! — Potential Energy Steps! — "Bug Fixes!" — Nah, but really. We fixed the removed ads part! — We added a new sharing feature so you can share 6284 Calc with your friends! How bow dah? — UI Improvements! — Haptic Feedback for iPhone 7 & iPhone 7 Plus when you generate answer & all over the app! — iMessage app has been redone, so now when you're texting your homies math stuff and need some symbols, you can use the iMessage version of the app! — And of course, the most important thing : Our app now has an emoji next to it on the home screen!
PLEASE GIVE US FEEDBACK : Have any requests? You have a couple of ways to get in touch with me : Twitter : @amitnkalra Instagram : @amitnkalra Snapchat : @amitnkalra <— Recommended Facebook : @amitnkalra
By the way, if you <3 6284 Calc make sure you drop an awesome rating for us! It really helps out! | 677.169 | 1 |
Product Overview
Includes 40 competencies/skills found on the MTEL Middle School Mathematics-Science test and 271 sample-test questions. This guide, aligned specifically to standards prescribed by the Massachusetts Department of Education, covers the sub-areas of Number Sense and Operations; Patterns, Relations, and Algebra; Geometry and Measurement; Data Analysis, Statistics, and Probability; Trigonometry, Calculus, and Discrete Mathematics; History, Philosophy, and Methodology of Science; Chemistry; Physics; Biology; Earth and Space Science; Integration of Knowledge and Understanding of Mathematics; and Integration of Knowledge and Understanding of Science. | 677.169 | 1 |
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Chapter Objectives Study Skills for Success in Mathematics Problem Solving Fractions The Real Number System Inequalities Addition of Real Numbers Subtraction of Real Numbers Multiplication & Division of Real Numbers Exponents, Parentheses, and the Order of Operations Properties of the Real Number System
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Copies of the Slides I have printed out the first set of slides, using the "handout" option in PowerPoint. From now on, if you want them you can print them yourself. They will be on my website faculty.mccneb.edu/jcallaghan NOTE: no www in front On the left side of the page, click on 0910. There will be a list of sections listed, click on the section(s) desired and have them printed out.
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Study Skills for Success in Mathematics Section 1.1 (2)
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Section Objectives (2) Understand the goals of this text Learn proper study skills Prepare for and take exams Learn to manage time Purchase a calculator Wait for Math 1310
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IMPORTANT The prime purpose of this section is to make you more comfortable with math by giving you hints on how to learn the proper skills to prepare for class, how to study math, how to manage your time, and how to psych yourself that math is not beyond your comprehension. Just try to keep an open mind and don't be afraid to ask questions during or after class.
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1.1 Understand the Text Goals (2) Review traditional algebraic topics Prepare for advanced topics Build your comfort zone for math Apply and improve your reasoning skills Realize that math skills are used in real-life Learn to translate real-life problems into math equations and be able to solve them
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1.2 Learn Proper Study Skills (3) We start at the basics. Just because you can quickly answer some initial real-life problems almost like magic (e.g. cost for a couple of Whoppers and a large drink), learn to do it systematically. Learn how to write down (legibly) what you know, what you need to know, and how you can get what you need. That is true on tests as well as real-life.
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Have a Positive Attitude Or at least a neutral attitude. If you tell yourself that you can't do anything, it will make it really make it exceptionally hard to accomplish it. Think of things you "couldn't" do, but you can now. Maybe, using Windows Vista, driving a motorcycle, using wood tools, flirting with gals/guys, being assertive with your boss. Anything, within reason, is possible. Even math.
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Prepare for Class - 1 A building will easily fall down if it is built on a weak foundation. Math is just like a building. Being able to use the basics is the foundation. The way to learn the basics are to do the homework. Skimping on the homework weakens your foundation. Review the homework you did earlier in the chapter. It will help you, if you legibly and logically wrote the work for the assignment and kept it.
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Prepare for Class - 2 There are assignments that will be assigned at the end of each section. There will also be exercises identified with "TURNIN" that will be handed in at the beginning of the class after the section was covered. These will be evaluated by the teacher to assist you with your problem areas. The TURNIN assignments will count 10% of your test grade.
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Attend Class - 1 Use your eyes and ears to try and understand what your instructor is trying to impart to you. Feel free to ask the instructor questions when things aren't clear. There is no such thing as a dumb question. If a topic is bothering you, you'll worry about it and miss the next six topics. Write down things that are of value. You can't remember everything.
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Attend Class - 2 Guess what, you can't do the previous if you are not in class. If you are unable to attend, e-mail me at jcallaghan@mccneb.edu and explain why you can't attend.jcallaghan@mccneb.edu In a class that meets weekly, more than 2 unexcused absences will lower your grade. In a class that meets twice a week, more than 3 unexcused absences will lower your grade.
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Attend Class - 3 On tests, it is strictly you. But it is good to have a study buddy. You can work together on homework. That does not mean, one does all the work and the other{s) copy. They are also useful for getting missed notes. I will try and keep up creating my notes as slide shows and making them available on my web page faculty.mccneb.edu/jcallaghan (click on 0920 on left side) for as long as I can.
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Read the Text – 1 There is not enough time for the instructor to cover the whole text. Of course you need the text for the exercises. After the lecture on a section, read the text for it. A couple of areas that are helpful are "Avoiding Common Errors" and "Helpful Hints". The text also has the answers for the odd number exercises and all chapter review problems and end of chapter tests.
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Read the Text - 2 Did you think the text was expensive? Frankly I did. Thank goodness, the same text is used for Math 0910. In 0910, we cover most of Chapter 1, all of Chapters 2, 3, 4, and 5, and the first part of Chapter 9. There is a Student Solution Manual for your text (ISBN 0321568516). It has all the odd numbered exercises and the all the tests worked.
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DO THE HOMEWORK It can't be emphasized that almost everyone learns by doing. Watching me do exercises helps, but you must work problems to learn the methodology. Don't just write a few numbers haphazardly on the paper. Identify the problem number and be logical, complete, and NEAT. That is what I am going to look for on your TURNIN homework. You have to discipline yourself to do that.
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Study for Class It is best to set up a fixed time to study. Before you start, have everything set up – pencils, book, paper, etc. Anticipate that you will have about two hours homework for every hour of class. Review your notes and text. For areas that you don't understand, be ready to ask questions the next class. I will normally arrive early before class and stay after class for any topics you need discussed.
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1.3 Prepare for and Take Exams (5) In real life you are continually "graded" by your boss, unless you are your own boss and you probably grade yourself even more harshly. They measure how many widgets you assemble, how many lines of code you create, how many square feet of yards you mowed. In class we have tests. It is as objective a form of determining if you have learned the material. It is not perfect.
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Methods to Help You Prepare for Exams Reread you class notes Review your assignments Study formulas, definitions, and methods used Reread "Avoiding Mistakes" /"Helpful Hints Read summary at the end of the chapter Rework exercises at end of chapter ( TURNIN ) Take the end of chapter practice test Ask your instructor about any areas that you do not feel confident
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Test Rules NO CALCULATORS Turn your cell phones off. If you think that you may get an emergency call, give me your phone and I'll answer. Put all books and notebooks away. If you tear sheets from your notebook for worksheets, tear them out before the test. Keep your eyes on your own test If you have questions of the meaning of it, get my attention and ask me. Turn in all your worksheets. Insure they are legible and have the problem number identified.
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Taking a Test - 1 Write any formulas you'll need on scratch paper Peruse test quickly and guess how long it will take Read test directions carefully Work "easy" questions first, return later for others Attempt each problem. No partial credit for nothing Work carefully step by step – watch signs Identify problem number and be legible If you have time, check your work Don't worry if others finish first, worry about you
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Taking a Test - 2 I know you will be tense when you come in to take a test. Try and relax. Take several deep breathes and shake your shoulders and hands If you have prepared for the test, you will do much better. Don't panic if you come to a problem that scares the shit out of you. Work around it, trying it later may remember the concept required. Check your work to see if your answer is reasonable. Never leave a question completely blank - TRY.
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1.4 Learn to Manage Time (6) Schedule when you will do your homework Be organized, get everything together first Bookmark your text, notes, homework at the end of your session Try to treat your education as top priority Try to take only the number of classes you can handle with your other responsibilities
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Supplements As stated earlier, if you are weak, get the Student Solution Manual. Check on line at half.com, alibris.com, amazon.com (used books) or any other on-line used book store. Just make sure you get the right text. Use the additional resources you obtained with your book package if there were any. There is a web site on the net that can help you work algebra.
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Seek Help I don't have an office; therefore, no office hours. I try to arrive early before each class and I will stay after class as long as anyone has questions. There are Math Help Centers on the South, Fort Omaha, Sarpy, and Elkhorn campuses where you can also get help. Hours and locations can be found at You can also get a tutor.
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Calculators As most other 09xx teachers, I do not allow you to use calculators on tests. I suggest you not get in the habit of using one on your homework either. Unless you are going to become an engineer or a scientist, I suggest that when buy a calculator in the future, you get a scientific computer which is solar powered ($10-$15). A scientific calculator has LOG and SIN keys.
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Section Objectives (2) Understand the goals of this text Learn proper study skills Prepare for and take exams Learn to manage time Purchase a calculator Wait for Math 1310 | 677.169 | 1 |
What is This Course All About?
The world is changing faster and faster. An education must prepare a student to ask and explore questions in contexts that do not yet exist. That is, we need individuals capable of tackling problems they have never encountered and to ask questions no one has yet thought of.
The focus of this course is on reasoning and communication through problem solving and written mathematical arguments in order to provide students with more experience and training early in their university studies. The goal is for the students to work on interesting yet challenging multi-step problems that require almost zero background knowledge. The hope is that students will develop (or at least move in the direction of) the habits of mind of a mathematician. The problem solving of the type in this course is a fundamental component of mathematics that receives little focused attention elsewhere in our program. There will be an explicit focus on students asking questions and developing conjectures.
In addition to helping students develop procedural fluency and conceptual understanding, we must prepare them to ask and explore new questions after they leave our classrooms—a skill that we call mathematical inquiry. | 677.169 | 1 |
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Mathematician here. Mathematics major is great if you aren't sure what specifically you want to do later on, but you know it's going to be something rigorous and technical. It's a lot easier to teach a mathematician programming than to teach mathematics to a programmer, for example.
As for what helps to study math at college level: read your textbook. Actually read it, whatever section you are studying, all the way through. Carefully. Don't just flip to find worked examples, really follow the explanations and the motivations. Read before coming to class. The class lecture should never be your first time seeing the material.
Check out other presentations of the same material: online courses, other textbooks, wikipedia entries.
Kudos for reflecting on how the structure of actuarial exams is helping you engage with mathematics, and best of luck on the exams!
Regarding your ideas about applying the approach you see in actuarial exams to math education, I have a few thoughts.
Firstly, it's important to not confuse assessment with learning process, though at best assessment also contributes to learning. Situational problems (aka word problems) are already highly incorporated into assessment at all levels of math education, where appropriate. (Not all interesting mathematics lends itself to situational problems. For example, what is sqrt(-1) raised to the power of sqrt(-1)? Wouldn't you like to know?)
Secondly, you are right in identifying that a lot of situational problems that students see in their math classes are contrived and uninteresting. Unfortunately, the situation you proposed is like that as well. It is very difficult to start with a mathematical equation that you want students to solve, and work backwards to come up with a scenario that is both realistic and engaging.
I would go beyond that and say that part of the reason these word problems fail at being interesting is that they leave no leeway for alternative models, and thus serve merely as decoder games where the student's goal is to figure out what the right equation is.
So let's try to come up with a scenario where you need to use fourth-grade math in general and fractions in particular, but let's start with an actual problem rather than an equation.
For example: You are going to a birthday party, and you know that some of the guests are keeping track of the number of calories they eat. Since you are bringing cupcakes you have made, it would be nice if you can estimate the number of calories in each cupcake. Here's the recipe that you used for making the batch (...), and your batch resulted in 12 cupcakes. Here's what you know about the calorie count of each ingredient in your batch (...).
That would be great on so many levels! Adjunct professors are contractors, and in many other occupations contractors get paid more than salaried employees. Partly this is because the company doesn't give them benefits, and partly the company is paying a premium on staffing flexibility.
Well, that certainly describes adjunct professors as well!
I am trying to more fully understand your objections. Let me try to paraphrase them, and see if I got them right: You object to my use of basic ideas from introductory-level economics (supply and demand, personal utility) to examine this question. Firstly, you object that the economic notions I use are too simple to shed any light on the issue. Secondly, you are concerned that by referencing economic theory or using economic terms, I am passing judgement about the system in general and individuals in particular.
If I am mistaken in summarizing your main objectives, please correct me. In the meantime, let me proceed with addressing what I think are your main objections.
Regarding using simple ideas from introductory-level economics: You are correct that they fail to model the complexities of what's going on. Nevertheless, I find that trying to apply simple notions to complex ideas is a way to begin to understand the system at first pass. Then, we can talk about what doesn't get accounted for, as you have done in response to my posts by calling my attention to indifference curves and assymetric information.
Regarding passing judgement: I am deriding adjuncts for making poor economic choices, I am pointing out that their choices are rational. And just because I am willing to analyze the system from a basic-level economic perspective, that doesn't mean that I consider the system fair. In fact, I am trying to isolate what exactly makes it unfair.
I am sorry that it pisses you off when people on the internet use their less-advanced knowledge of economic theories and terms to examine what is without question an economic issue.
More importantly, really, is "go work on other people's unearned biases against you if you want to be successful, idiot" your argument that the system isn't biased?
Birmingham's claim wasn't that the system is biased, but that it is exploitative. I am trying to identify which components of the system are indeed exploitative--that is, the ones that ensure that the adjuncts have no other reasonable choice but to continue adjuncting--and which are more the result of a limited supply of highly desirable positions, or the fact that a lot of people find college teaching highly rewarding.
My argument is that Birmingham is wrong in claiming that graduating more English PhDs than there are academic tenure-track positions is exploitative. As long as there are reasonable alternatives to working in academia, or as long as the facts regarding employment in academia are made explicitly clear to potential students, the students themselves choose whether to go through the program. I also think that Birmingham is wrong when he identifies as a sign of exploitation the fact that so many PhDs go on to take adjunct positions. As long as PhDs have reasonable alternatives outside of the academia and are aware of them, they choose to take on those contracts.
Instead, I argue that if graduate students and PhDs are not aware about career opportunities outside the academia and how they can make the skills earned during their education attractive to potential employers, than that is indeed exploitative. Moreover, that problem is something that graduate programs can address directly.
Using an MBA as an example of a degree that confers hard skills and knowledge is perhaps the funniest thing I heard this week, and I spent all week at a conference. Congrats.
I am glad to have provided you with what sounds like a much needed respite.
Let's start with saying that, empirically, firm behavior doesn't bear this theory out because PhDs, not just in English but in all fields that need to look for work outside of their narrow PhD skillset, are categorized as overqualified by employers.
That is an excellent observation. PhDs who go on to work outside of academia usually need to convince their potential employers that they are really committed to transitioning fully to the corporate environment. Part of the concern of hiring someone who is "overqualified" is that they may not work like the rest of us to fit in within the corporate culture, and are not as committed to stay.
Still, it's an obstacle that can be overcome.
On a broader note, whilst the soft skills one develops (or should develop) in academia are impressive, the hard ones... aren't so transferable unless you take the extra effort to learn the same in the context of some industry.
One thing that a Ph.D. signals to a potential employer is that you do have the skills and the perseverance to learn a challenging subject deeply, to the level of an expert. It should be a given that, when you get hired outside of academia, that you intend to develop a similar level of expertise in whatever field you are now working. That's why I respectfully disagree with your statement that:
The downside to being highly specialized is that you become unqualified for a lot of things outside of your specialization.
If the position you are applying for is the kind where most relevant training happens on the job, and doesn't require prior formal education in hard skills and knowledge (e.g., bachelors in Biology, MBA), then a Ph.D. is indeed more prepared for that job if they are fully committed to it.
You're saying that someone who spent 10 years studying at the PhD level should get a job as an HR rep and that's a fair deal that reflects their skill level.
Yes, that's exactly what I am saying. If the alternative is, as Birmingham describes it, near-poverty-level adjuncting in disrespectful conditions, with very little chance for advancement, then another job with better pay is indeed preferable.
I want to point out that for most people, their jobs are not the source of fulfillment and intellectual stimulation. Most people work because they have to, and find fulfillment in activities outside of work.
I agree with your observation, and that is why I describe (c) as a failure of graduate programs to provide their students with necessary information and perspective on the value of their skills outside of academia.
In many US universities, the graduate programs are not just overseen by the professors of a specific department, but also by an umbrella college that includes multiple disciplines (e.g., College of Arts and Sciences). Even if the professors in the English department don't know jack shit about work outside of the academia, someone within the umbrella college does. In my graduate program, we had all kinds of employment-related workshops for graduate students from all kinds of disciplines, and they overwhelmingly focused on the advanced skills that all graduate students develop which are valuable in the job market, and how to high-light the value of those skills for potential employers.
You are getting a lot of flack, but you raise a lot of valid points from basic economic theory. I would like to add a few observations to that effect as well.
Birmingham assumes that the only profession that a Ph.D. graduate in English is qualified for is as a university professor. That is simply false: people with Ph.D. in English are articulate both orally and in writing, are experienced in various forms of research methodologies, know how to take apart a claim and how to construct an airtight argument... In other words, these are the people with loads of valuable skills that ought to make them competitive in the general white-collar job market.
If so many English Ph.D. graduates choose to forego opportunities in the general white-collar job market, and instead take on the poorly-paid adjunct contracts, it could be because of some of the following:
(a) They consider teaching a university class more rewarding, compared to other white-collar jobs;
(b) They consider full-time university professor position as something sufficiently worthwhile to shoot for, despite the uncertainty of obtaining such a position;
(c) They don't realize the value of their skills on the general job market.
If (c) is the common case, that indicates that the graduate programs are indeed failing their students by not making clear the range of career opportunities for which the skills the students develop in the graduate program are valuable.
However, if the graduates of Ph.D. programs are aware of the value of their skills in the general job market, then if they take on adjunct contracts due to reasons (a) or (b), they could be making reasonable economic choices based on values other than monetary.
I also wish to address the comment for which you received so much flack:
Lastly, I can't help but feel a little bit of antagonism towards adjuncts- imagine if you worked your whole life to get a highly competitive job, and someone out there was willing to do your it for 25% of the pay you receive. Adjuncting was never meant to be a full time job, and the fact that people are willing to do it for so little drives down salaries for tenure track professors (who also have research and service requirements).
Speaking from the theory of labor economics, you are absolutely correct that having a large pool of people who are willing to do a key part of the job of full-time professors for far less money drives down the pay and the demand for full-time professors. I wouldn't blame the adjuncts themselves for this system; they may be making reasonable economic choices for themselves.
Rather, this is exactly the sort of situation where the solution is to unionize.
the techniques required to perform this sort of gene editing have passed crucial milestones.
The advent of a powerful gene-editing tool called Crispr-Cas9 allows researchers to snip, insert and delete genetic material with increasing precision.
Which raises all kinds of interesting ethical questions. For example, if there is a safe procedure to make a future baby stronger, and the parents are willing to do it and are able to afford it, why prohibit that (as the current report does)?
The new report called for prohibiting any alterations resembling "enhancement", including "off label" applications. Under the guidelines, a genetic technique aimed at strengthening the muscles of patients with Duchenne muscular dystrophy, for instance, could not be used to make healthy people stronger.
This is a great opportunity for you to learn how to learn mathematics. Talk to your professors about effective learning strategies for math specifically, apply those strategies and see how they work.
When it comes to mathematics, everyone has a level at which they have to struggle to progress. Everyone. I am a mathematician, and I have found my struggling level in graduate school. One colleague of mine seemed to sail through graduate school, but she found her struggling level in subjects that she researches.
Most of your future students will find their struggling level during their school years. For many people, in fact, fractions are their struggling level. So if you want to teach math, you will be working with students who are struggling with learning mathematics, and you need to know how to encourage them to struggle successfully.
By the way, I have noticed that a lot of students don't take the time to really read their mathematics textbooks. If this applies to you--read your textbook!
Thanks for putting together the international comparisons, they help put things in perspective.
Fraser has interesting ideas, but is in need of fact checking. For example (my boldface):
Never mind that the reality that underlies the new ideal is depressed wage levels, decreased job security, declining living standards, a steep rise in the number of hours worked for wages per household, exacerbation of the double shift – now often a triple or quadruple shift – and a rise in poverty, increasingly concentrated in female-headed households.
Thank you for explaining your point. That is a reasonable stance to take. I especially agree about the point about the culture war, though I don't consider that insisting on due process for non-citizens is part of the culture war.
It's also reasonable to adopt the strategy that ACLU has regarding infractions by US government of civil liberties without due process (and that the NRA has regarding infringements of Second Amendment): make any such infraction expensive by sending in the lawyers or organizing political opposition. Such strategy is has two advantages: first, it makes such infractions expensive, thus keeping them rarer than otherwise; second, it gets lots of publicity for the organization, which increases its political clout and fundraising capability (which in turn increase their ability to make infractions expensive).
"Civil liberties" are not synonymous with "citizenship". Civil liberties are rights of persons that the government cannot infringe without due process. For example, the executive order on immediate blanket prohibition of all persons from the seven Muslim-majority countries to enter US is being contested on precisely on the grounds that it violates due process for those persons who have already obtained visas.
By the way, I am trying to figure out the point you are trying to make, and I find it a bit challenging because of your use of jargon. Also, I think your argument depends on you making some assumptions about me that are unwarranted. Would you please restate your point?
Where you got your undergraduate degree in a fast-changing field like Computer Science, and especially where you studied your introductory courses, is immaterial. The exception to that is if you get your degree at a university with a top Comp Sci department, because these schools attract recruiters from major employers, and have easier time placing their students in top graduate programs. Even then, you need to show that you have gone beyond your classes.
So do yourself a favor and choose the cheapest option. If Amsterdam is free, go there. Better yet, study the basics in online classes and test out of those intro classes, get to the good stuff as soon as you can. If you want to transfer to a top US school in two years, you can do that from Amsterdam.
In my experience with US community colleges, technical courses like Computer Science, math and engineering vary greatly in quality and usually don't offer more material than what's currently available for free online.
Stop firing indiscriminately and pick a target. You don't like an EO? Focus on finding a specific flaw or loophole in it.
That is exactly what the International Refugee Assistance Program (and the ACLU, and the National Rifle Association in many cases) does. They work on specific cases, affecting rights and liberties of specific people who otherwise would not have legal representation, where the government's actions are contrary to the laws already in place. They use the legal system already in place to reverse or ameliorate those cases.
The original post discusses specifically how the International Refugee Assistance Program goes about this, and how useful it is to support such organizations.
So I am trying to understand the context which pertains to your comments. It sounds like you are making the argument that the general, unfocused protests are unhelpful and may even be hurtful, while narrowly focused actions through legal and political systems are more effective. If this is your argument, you and I are in complete agreement. If this is not your argument, I would appreciate it if you make it more clear, especially how it relates to the original post.
My objective is to preserve civil liberties--in particular, those civil liberties that pertain to me and mine. Supporting an effort against any infraction of existing civil liberties is a very effective method towards that objective. Such infractions tend to happen on the edges, at the extreme cases, which doesn't describe me and mine, but reacting to the extreme cases and preventing those infractions ensures that my civil liberties will not be tested.
If you solve one of the open problems, Bob and Ellen Kaplan who run the Boston Math Circle would be very excited to hear from you. As would I. Their contact info is on the website, and you are welcome to PM me.
In general, there are several ways you can turn your work to concrete advantage. You can approach a math teacher at your school, or a college math professor, and ask if they can meet with you to discuss your work. Even if none if your solutions are new to the mathematical community (and thus publishable), they will still write you a recommendation letter for college admission that speaks to your interest and initiative.
They are also likely to get you in touch with others who are interested in exploring mathematics outside of class. Mathematics really is very social, and these connections matter, though they may be tricky to find.
There are plenty of open problems in mathematics that don't require courses traditionally taught in undergraduate level. For example, check out this collection of open problems from the Boston Math Circle. They are accessible to people who with middle-school or high-school background, meaning that such a person has the tools to understand the problem and to start exploring it, possibly coming up with a solution (we don't know, that's why it's an open problem--nobody has solved it yet).
On a more general note, I recommend looking for a Math Circle program near you. Math Circles are very varied in their approach: some are more into cooperative tackling of deep math problems, some are more into competitions, others are all about exposure to interesting maths. It all depends on the interests and the personality of the mathematician leading the Math Circle. The only constant is that they are organized and ran by someone who is really into math and who is excited about sharing it.
STEM researchers are not interchangeable. Asking whether this graduate student can be replaced by an American is like asking whether Einstein or Ramanujan could have been replaced by an American. At that level, the insights and talents of an individual matter.
There is no shortage of support for qualified US graduate students. Because some of the grants can only be used for domestic students, US STEM departments are keen to recruit qualified US residents.
I am a mathematician, and I am not in algebraic geometry (combinatorics and statistics). I am not convinced that algebraic geometry is over-represented. Some of us just like words with animals more than math puns.
But if I did have a username to signal my tribal affiliation, what would it be? | 677.169 | 1 |
Simplifying radical expressions. Analyzing general radical functions and horizontal translations. Using the conjugate to simplify radical expressions. Utilizing a fractional exponent to represent a radical expression. Using the fundamental theorem of arithmetic to reduce numbers underneath a radical (a radical expression)."
"Since the student has a test tomorrow, we focused on reviewing for the exam. In particular, we looked at unit rates and how to simplify ratios. Then, we looked at scaling, and we went over basic conversions (ex. feet to yards, ounces to pounds) and how to solve problems involving ratios. She was very positive throughout the session, and even though she admitted to me that Math isn't her favorite subject, she has very strong computational skills. I was impressed at how, once she knew what the question was asking, she was able to solve problems quickly and correctly. I am excited to hear how she does on her test! I am sure she will do a great job."
"Solving equations with two unknown require basic knowledge, such as solving equations with one unknown and the result of a negative number multiplied by another negative number. I went through many basics so the student can understand his current topics. I left practice problems for the student. The student needs a lot of practice and assistance in order to catch up. We will continue to work on this next session."
"Starting with chapter 1 to chapter 2.6, we went over step functions, absolute values (graphing and solving equations), piecewise functions, and some word problems. While the student remembers the previous math problems, she is hesitant with some simpler equations and just needs a little practice to gain confidence before finals. She is sticking with old habits that have worked in the past. I will send some practice multiple-choice questions her way as extra practice and review."
"Student 1 and I began her review for her final in AP Statistics. We worked on free response questions. We went over probability, including the difference between geometric and binomial and how to use the different equations for standard deviation and mean. We also went over how to find expected probability and standard deviation for standard probability. Lastly, we went over least squares regression lines and the formula for finding LSRL.
Going over the old material was beneficial for the student. She didn't really remember the older material at first, but after talking about it, she picked it right back up. As long as she finishes the review and does extra practice of the material she does not know as well, she will do just fine on the final."
"Student 1 and I covered test material to help him prepare for the SAT. We practiced a variety of skills: Geometry, data, and Algebra. He is solid regarding material at his grade level. Most of the material is upper-middle school material. With Student 2, we went over her homework and building her confidence." | 677.169 | 1 |
Solving Equations Using Factoring Spring 2013
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After teaching my algebra 1 students to factor, I like for them to apply their skills of factoring to solving equations using factoring. Instead of lecturing them and then having a few minutes left at the end of the period, I instead give them a "mini-lesson" of about 10 minutes length at the start of class, during which they generally don't take notes, but simply focus on the concept.
Instead of a lecture, I hand out this worksheet, which has an example for them. They then have the bulk of the period to work on the problems in class | 677.169 | 1 |
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Unformatted text preview: Chapter 1. Matrices, determinants, system of linear equa- tions 1.1. Matrix Arithmetic and Operations This section is devoted to developing the arithmetic of matrices. We will see some of the differences between arithmetic of real numbers and matrices. Definition 1.1 Let m , n be positive integers. An m × n matrix A is an array of real numbers A = a 11 a 12 ··· a 1 n a 21 a 22 ··· a 2 n . . . . . . . . . . . . a m 1 a m 2 ··· a mn where a ij ∈ R is the ( i, j )-th entry of A . We shall write A = ( a ij ) 1 ≤ i ≤ m ;1 ≤ j ≤ n for short, or A = ( a ij ) if the size of A is understood. Denote by M m × n ( R ) the set of all m × n matrices with real entries. Matrices of the shape m × 1 are called column vectors , whereas matrices of the shape 1 × n are called row vectors . Note that the integer m need not be equal to n . In the case of m = n , we have a n × n matrix, and it is called a square matrix of order n . Denote by M n ( R ) the set of all square matrices of order n with real entries. The following are some examples of matrices: A = a 11 a 12 a 13 a 14 a 21 a 22 a 23 a 24 ! , B = 1 9 2 7 5- 3- 5 8 4 , C = 4- 6 5 1 Matrix A is a general 2 × 4 matrix with entries a ij ∈ R where 1 ≤ i ≤ 2 and 1 ≤ j ≤ 4 . Matrix B is a square matrix of order 3 , and C is a 4 × 1 matrix (column vector). Example 1.2 A zero matrix m × n ∈ M m × n ( R ) (or just if the size is understood) is a matrix with all its entries equal to zero, i.e. a ij = 0 for 1 ≤ i ≤ m and 1 ≤ j ≤ n . Another special matrix is the n × n identity matrix whose entries δ ij are the Kronecker delta : δ ij = 1 if i = j ; if i 6 = j, for 1 ≤ i, j ≤ n , i.e. the diagonal entries are all one while the off-diagonal entries are all zero. Often the identity matrices are denoted by I n . As you will see later, the zero and identity matrices play a similar role as 0 and 1 in the arithmetic of real numbers. 2 Definition 1.3 If A, B ∈ M m × n ( R ) then we say that A = B provided corresponding entries from each matrix are equal, that is, A = B provided a ij = b ij for all i and j . Matrices of different sizes cannot be equal. Now we define addition and subtraction of matrices: Definition 1.4 Let A, B ∈ M m × n ( R ) , with A = ( a ij ) and B = ( b ij ) . Then the sum and the difference of A and B , written as A + B and A- B , are also m × n matrices with entries given by a ij + b ij and a ij- b ij respectively. Matrices of different sizes cannot be added or subtracted. Next we proceed to multiplication involving matrices. Note that we can define two kinds of multiplication, namely scalar multiplication and matrix multiplication. We first look at scalar multiplication: Definition 1.5 Let A = ( a ij ) m × n ∈ M m × n ( R ) . For any λ ∈ R , the scalar multiple of A by λ is defined by λA = ( λa ij ) m × n . In particular,....
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Lectures on Finite Fields and Galois Rings
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This is a textbook for graduate and upper level undergraduate students in mathematics, computer science, communication engineering and other fields. The explicit construction of finite fields and the computation in finite fields are emphasised. In particular, the construction of irreducible polynomials and the normal basis of finite fields are included. The essentials of Galois rings are also presented. This invaluable book has been written in a friendly style, so that lecturers can easily use it as a text and students can use it for self-study. A great number of exercises have been incorporated. | 677.169 | 1 |
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Monday, February 20, 2017
We'll review planes (12.1) by working several examples. Then we'll turn to the more interesting quadric surfaces. We've played with several of these, including spheres, circular cylinders and cones.
As you read through section 12.1 look at the images of the surfaces. Pay attention to the curves drawn on those surfaces. These space curves are called traces, and they represent intersections between planes and the surfaces themselves. The traces help our brains interpret the images as curvy 2-dim objects living in $\mathbb{R}^3$.
Our main objective is to describe the traces with Cartesian equations and then interpret those traces as lines, circles, parabolas or hyperbolas. This is how we match a particular quadric equation with its graph. This is how we visualize surfaces.
Friday, February 17, 2017
We'll review the main points about differentiating and integrating vector functions by working a few examples (11.6, 11.7).
But then we have to jump into chapter 12. Before long you will be finding partial derivatives and working with the multivariable version of the chain rule. We'll start by talking about planes (12.1). I'll show how to assemble a plane equation from a point and a normal vector. Some of our examples will involve cross products and lines.
Exam one began at 5:15 pm on Thursday, February 16. The exam covers only sections 11.1-11.5. No electronic devices are allowed at the exam.
We will provide you with this equation sheet. Some facts are not on the equation sheet. You need to know how to measure distance between points in $\mathbb{R}^3$, the sphere equation, and how to compute the dot and cross products. You should also know the cosine and sine of common angles like $0$, $\pi/6$, $\pi/4$, $\pi/3$, $\pi/2$, $\pi$, and $2\pi$ radians.
This exam is your opportunity to demonstrate to us that you understand the material. Be sure to read each question carefully, and draw sketches where appropriate. We expect complete solutions and correct notation. Be careful with the T/F questions; think, don't react.
Your exam room is a function of the first four letters of your last name.
Aaaa through Hanc, go to CR 302
Hans through Pont, go to CR 306
Post through Zzzz, go to CR 310
We are sharing the rooms with Calculus I and II students. Make sure you are not sitting next to another Calculus III student.
To practice for the exam, use the problems from MyMathLab, discussion, and the mock exams and examples from the text. If you don't understand something ask questions at your discussion section and during our office hours.
Monday, February 6, 2017
After doing one more cross product example, we'll write parametrized equations for lines in $\mathbb{R}^3$ (11.5). We'll figure out how to tell if a particular point is on the line, and we'll project the line onto one of the coordinate planes and figure out how to describe the projected line with parametric and Cartesian equations. If there is time, we'll try to decide if two specified lines are parallel, intersecting, or skew (not parallel, not intersecting).
Sunday, February 5, 2017
Friday, February 3, 2017
We'll wrap up the dot product and look at the cross product (11.4). We'll use cross products to determine the area of parallelograms and triangles in $\mathbb{R}^3$. You'll play with additional examples in discussion next week.
Wednesday, February 1, 2017
I'll do two examples involving the dot product (11.3). We'll calculate the work done by a constant force acting on a mass that is moving through $\mathbb{R}^3$, and we'll compute the flux of a force across a line segment in $\mathbb{R}^2$. Then, we'll define the cross product (11.4) and look at some of its properties.
Monday, January 30, 2017
We'll do a little vector arithmetic using basis vectors (11.1, 11.2) and, also, look at some applications of the dot product (11.3). This video shows how to use vector triangles to locate the centroid of a triangle.
Wednesday, January 25, 2017
We'll finish Monday's discussion by looking at simple surfaces (planes, cylinders and spheres) in $\mathbb{R}^3$. Then we will move on to vectors and vector arithmetic in sections 11.1 and 11.2. Basic quantities such as position, velocity, acceleration, and force are represented by vectors. We will add vectors and also scale vectors. We'll talk about basis vectors and see how to express a general vector in terms of the basis vectors.
We'll talk about some common objects (points, curves and surfaces) and the spaces ($\mathbb{R}$, $\mathbb{R}^2$, and $\mathbb{R}^3$) they live in. Our goal is to figure out how many Cartesian equations are required to describe the different objects in the different spaces. Also, we'll talk about how to measure distances between pairs of points in the various spaces.
Sunday, January 22, 2017
Office hours are an important part of the course; if you are not using them you are not fully participating in the course.
My official office hours are M, W, and F from 3:10 - 5:00 pm, or by appointment. I'll post office hours for the discussion leaders (Bang and Andrew) as soon as possible. Keep checking the link at the top of this page. | 677.169 | 1 |
Description: Published by OpenStax College, Precalculus is intended for college-level precalculus students. Since precalculus courses vary from one institution to the next, we have attempted to meet the needs of as broad an audience as possible, including all of the content that might be covered in any particular course. The result is a comprehensive book that covers more ground than an instructor could likely cover in a typical one- or two-semester course; but instructors should find, almost without fail, ...[more]
Description: Published by OpenStax College, Principles of Macroeconomics covers the scope and sequence for a one-semester economics course. The text also includes many current examples, including: the housing bubble and housing crisis, Zimbabwe's hyperinflation, global unemployment, and the appointment of the United States' first female Federal Reserve chair, Janet Yellen. The pedagogical choices, chapter arrangements, and learning objective fulfillment were developed and vetted with feedback from educators...[more]
Description: Published by OpenStax College, Principles of Economics covers the scope and sequence for a two-semester principles of economics course. The text also includes many current examples, including; discussions on the great recession, the controversy among economists over the Affordable Care Act (Obamacare), the recent government shutdown, and the appointment of the United States' first female Federal Reserve chair, Janet Yellen. The pedagogical choices, chapter arrangements, and learning objective f...[more]
Description: Precalculus is an introductory text. The material is presented at a level intended to prepare students for Calculus while also giving them relevant mathematical skills that can be used in other classes. The authors describe their approach as "Functions First," believing introducing functions first will help students understand new concepts more completely. Each section includes homework exercises, and the answers to most computational questions are included in the text (discussion questions a...[more]
Description: Prealgebra is designed to meet scope and sequence requirements for a one-semester prealgebra course. The text introduces the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles. Each topic builds upon previously developed material to demonstrate the cohesiveness and structure of mathematics. Prealgebra follows a nontraditional approach in its presentation of content. The beginning, in particular, is presented as a sequence of small...[more]
Description: The book examines the underlying principles that guide effective teaching in an age when everyone,and in particular the students we are teaching, are using technology. A framework for making decisions about your teaching is provided, while understanding that every subject is different, and every instructor has something unique and special to bring to their teaching.
The book enables teachers and instructors to help students develop the knowledge and skills they will need in a digital age: not...[more]
Description: The author designed this book for students and professionals who want to understand and apply basic meteorological concepts, but who don't need to derive equations. To make this book accessible to more people, the author converted the equations into algebra. With algebraic approximations to the atmosphere, you can see the physical meaning of each term and you can plug in numbers to get usable answers. No previous knowledge of meteorology is needed — the book starts from the ...[more]
Description: Physical Geology is a comprehensive introductory text on the physical aspects of geology, including rocks and minerals, plate tectonics, earthquakes, volcanoes, glaciation, groundwater, streams, coasts, mass wasting, climate change, planetary geology and much more. It has a strong emphasis on examples from western Canada, especially British Columbia, and also includes a chapter devoted to the geological history of western Canada. The book is a collaboration of faculty from Earth Science depar...[more]
Description: Microbiology covers the scope and sequence requirements for a single-semester microbiology course for non-majors. The book presents the core concepts of microbiology with a focus on applications for careers in allied health. The pedagogical features of the text make the material interesting and accessible while maintaining the career-application focus and scientific rigor inherent in the subject matter. Microbiology's art program enhances students' understanding of concepts through clear and ef...[more] | 677.169 | 1 |
UNIVERSITY ENTRANCE EXAMINATION MATHEMATICS ( 'A' level equivalent) Duration : 2 hours Please read the follow instructions carefully. 1. This examination has TWO (2) sections – A and B, and comprises THIRTEEN ( 13 ) printed pages. 2. Attempt all sections. 3. Answer all questions in section A. Indicate your answers on the answer paper provided. Each question carries 2 marks. Marks will not be deducted for wrong answers. 4. Answer FOUR (4) questions from section B with not more than THREE (3) from any one option. Write your answers on the answer paper provided. Begin each question with a fresh sheet of paper. Write the question number clearly Each question carries 15 marks. 5. A non-programmable scientific calculator may be used. However, candidates should lay out systematically the various steps in the calculation. 6. At the end of the examination, attach the cover paper on top of your answer script. Complete the information required on the cover page and tie the papers together with the string provided. 7. Do not take any paper, including the question paper and unused answer paper, out of the examination hall....
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An Introduction to Abstract Analysis (Chapman Hall/CRC Mathematics Series 3)
Description
Abstract analysis, and particularly the language of normed linear spaces, now lies at the heart of a major portion of modern mathematics. Unfortunately, it is also a subject which students seem to find quite challenging and difficult. This book presumes that the student has had a first course in mathematical analysis or advanced calculus, but it does not presume the student has achieved mastery of such a course. Accordingly, a gentle introduction to the basic notions of convergence of sequences, continuity of functions, open and closed set, compactness, completeness and separability is given. The pace in the early chapters does not presume in any way that the readers have at their fingertips the techniques provided by an introductory course. Instead, considerable care is taken to introduce and use the basic methods of proof in a slow and explicit fashion. As the chapters progress, the pace does quicken and later chapters on differentiation, linear mappings, integration and the implicit function theorem delve quite deeply into interesting mathematical areas. There are many exercises and many examples of applications of the theory to diverse areas of mathematics.
Some of these applications take considerable space and time to develop, and make interesting reading in their own right. The treatment of the subject is deliberately not a comprehensive one. The aim is to convince the undergraduate reader that analysis is a stimulating, useful, powerful and comprehensible tool in modern mathematics. This book will whet the readers' appetite, not overwhelm them with material. | 677.169 | 1 |
Math141OutlineFinal - MATH 141: PRECALCULUS FINAL: SYSTEMS...
MATH 141: PRECALCULUS FINAL: SYSTEMS AND MATRICES (CHAPTERS 7 AND 8), DISCRETE MATH (CHAPTER 9), AND CONICS AND POLAR EQUATIONS (CHAPTER 10) DISCLAIMER: This may or may not be a comprehensive list, but it's a very good start! Know all aspects of these topics; I may go beyond listed subtopics. CHAPTER 7: SYSTEMS Solving Linear and Nonlinear Systems of Equations using: (7.1, 7.2) Substitution Method Addition / Elimination Method Graphical Method (the idea) Some Issues: (7.1, 7.2) Real solutions of systems correspond to intersection points. Consistent and Inconsistent Systems Systems of Linear Equations can have 0, 1, or infinitely many solutions. Write all coordinates of a solution in the appropriate order. Partial Fractions and Systems (7.4) Use Long Division when necessary Forms based on the factored form of the denominator Finding the Unknowns using "Plugging In" and "Matching Coefficients" CHAPTER 8: MATRICES Size Gaussian Elimination (with Back-Substitution) and Gauss-Jordan Elimination (8.1)
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Certificate in Maths Refresher Online Course
Wichtige informationen
Kurs
Online
Wann: Freie Auswahl
Beschreibung
Learn How to Use Math to your Advantage Math isn't about plugging numbers into formulas. It's about knowing enough to make the numbers and formulas work for you. Math can be incredibly useful - but only if you understand how and when to apply it in your everyday life. This Certificate in Maths how calculators work, and then you'll discover how best to get a handle on your income and expenses. You'll be able to check your paystub, invoices, and bank statements for errors and overcharges, and you'll become more skilled at handling money and comparing investment opportunities. You'll learn how to calculate percentages, including the proper amount to pay in tips, commissions, taxes, and discounts. You'll find out how to calculate interest rates and you'll develop a better understanding of mortgages, credit cards, and other types of loans. You'll discover a handy method for converting one type of measurement to another, and you'll be able to calculate areas correctly so you don't overspend on your next home improvement project. You'll become adept at interpreting graphs, calculating the probability that something will (or won't) happen, and understanding the statistics embedded in test results, polls, and even news storiesLoans
Credit
Statistics
Maths
Financial
Insurance
Financial Training
Probability
Themenkreis
There are 12 units of study
Integers and Other Mathematic Equations In this lesson, we're going to revive some childhood memories about math by reviewing some basic number properties. You'll learn about integers, exponents, roots, and multiple-step problems. Doing these types of problems just for practice can be tedious, but you're going to take what you learn and put it to use in every other lesson in this course. Once we've talked about the mechanics of doing these problems by hand, you'll learn how to put them into the calculator. I believe that once you know how to do the math, you should use every tool and shortcut you know to make math easier. I'm also going to show you a few interesting things that you may not know about how calculators work.
Percents in Retail Whether it's discounts, taxes, or a tip, most of us deal with percentages every day. In this lesson, you'll learn about the percents you'll find in retail from both a consumer and a managerial perspective. We'll go over discounts, sales prices, and sales tax. And last but not least, we'll talk about tipping, markup, and handling money in the retail work environment.
Income, Deductions, and Expenses Today, we'll be talking about income. Are you paid hourly, are you a salaried employee, do you receive a commission, or some combination of these? In this lesson, you'll learn how to calculate your paycheck no matter how you're paid. But wages don't stop there. You also have to pay taxes to the government, and you may choose to pay for insurance and save for retirement. All these deductions have to be calculated before a paycheck is written. Once you receive your check, you need to know how you spend your money. In the last part of the lesson, you'll learn how to find out where your money goes once you have it.
Opening and Balancing a Checking Account Now that you have your paycheck, you need somewhere to put it. It's time to talk about financial institutions; banks, credit unions, and savings and loans. In today's lesson, you'll discover what to look for in an institution and what questions to ask about checking, savings, and other accounts. Plus, we'll look at ways to keep a check register in order and how to balance a bank statement.
Earning Interest Investing is an ominous word for most of us. Financial professionals can sound like they're speaking a foreign language. Today, we're going to unravel some of this terminology and the math that goes with it. You'll learn the basics of earning interest and find out what questions to ask the professionals. I'm also going to walk you through the features and terminology of several types of interest earning investments; bonds, certificates of deposit, and money market accounts.
Paying Interest As you probably know, you can't just earn interest—you also have to pay interest. Credit cards and loans cost you money in interest and fees. Do you know why it's so difficult to pay off a credit card over time? Not knowing the answer to this question has caused financial heartache for many. In this lesson, we'll study what happens when you pay only the minimum balance on a credit card each month. And then you'll see what happens when you pay as little as $10 or $20 extra each month. I think you'll be shocked and amazed at the money you can save.
Mortgage Math Interested in buying a home, but not sure where to start? There are realtors, attorneys, and loan officers to get you through this process. But I never feel comfortable signing documents unless I understand at least some of the terminology and math. That's our goal in this lesson. We'll explore the different aspects of a mortgage payment (principle, interest, taxes, and insurance or PITI) and the amount of money you'll need up front.
Ratios This lesson is a student favorite. You'll find out that you can solve most problems you come across, including conversions, with some sort of ratio. I like to call ratios "fractions with a purpose." Many students find the thought of fractions disconcerting, but I'm going to give you step-by-step instructions for setting up ratios and then proportions. And after today's lesson, you'll be able to convert even the most complicated measurements.
Measurement Enter the world of geometry, or at least the practical side of it. In this lesson, you'll learn how to calculate area in different units of measurement and how to convert between them. This will let you figure out how much carpet, paint, or tile you need for those home projects. You don't do your own projects? You'll still want to be able to check your contractor's measurements and calculations. You'll also learn a little about metrics, and I'll teach you a very simple conversion method.
Probability You'll learn all about probability in this lesson. It's used in the gaming industry, in forecasting weather, and in determining insurance rates. How does the insurance industry know there's a 10% chance I'll be in an accident? Or how does a casino predict a 3% chance I'll win at blackjack? You have to know which numbers to divide and how to find them. I'm here to guide you through this fascinating topic.
Statistics Our society is bombarded with information and statistics all day, every day. We're going to start this lesson by discussing statistical data and how it's chosen. Next, I'll teach you about the four most commonly used statistical measures: mean, median, mode, and range. We'll calculate a few of these measures and discuss what each means, individually and as a group. Last, we'll discuss standardized test scores. If you've ever taken a standardized test, you've probably received a very confusing report with lots of statistical terminology and not much explanation. In this lesson, you'll learn how to read and interpret a test score report with confidence.
Statistical Graphs A great way to understand all those statistics you learned about in Lesson 11 is to put them on a graph. Graphs can help you look at the big picture by summarizing information. Just as there are different types of information and relationships, there are different types of graphs. Each one is best suited for displaying a particular type of information or relationship. So in this, our final lesson, we'll talk about the best use of each type of graph and how to read each one | 677.169 | 1 |
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Math Student's Civil Rights
I have the right to learn Math (Math is learnable like other subjects)
I have a right to make mistakes, erase then, and try again (Failure points to what I have not learned yet)
I have the right to ask for help (asking for help is a great decision)
I have the right to ask questions when I don't understand (understanding is the primary goal)
I have the right to ask questions until I understand (perseverance is priceless)
I have the right to receive help and not feel stupid for receiving it (asking for help is natural)
I have the right to not like some math concepts or disciplines (i.e. trigonometry, statistics, differential equations, etc.)
I have the right to define success as learning no matter how I feel about Math or supporters
I have the right to reduce negative self-talk & feelings
I have the right to be treated as a person capable of learning
I have the right to assess a helper's ability to...
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This week's Math Journey builds on the material in
The Function Machine. If you have not yet read that journey, I suggest you do so now.
In The Function Machine we discussed why graphing a function is possible at all on a conceptual level – essentially, since every x value of a function has a corresponding y value, we can plot those corresponding values as an ordered pair on a coordinate plane. Plot enough pairs and a pattern begins to emerge; we join the points into a continuous line as an indication that there are actually an infinite number of pairs when you account for all real numbers as possible x values.
But plotting point after point is a tedious and time-consuming process. Wouldn't it be great if there was a quick way to tell what the graph was going to look like, and to be able to sketch it after plotting just a few carefully-chosen points?
Well, there is! Mathematicians look for an assortment of clues that help to determine the shape of a function's...
read more | 677.169 | 1 |
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Other answers:
Calculus is tough to explain in a mathematical sense. My first thought was that it is the study of motion and how objects move, but that is mechanical rather than mathematical. It involves derivatives and integrals and is used in a large part of mathematics.
Calculus is the study of change, with the basic focus being on
Rate of change
Accumulation
pic...
In both of these branches (Differential and Integral), the concepts learned in algebra and geometry are extended using the idea of limits. Limits allow us to study what happens when points on a graph get closer and closer together until their distance is infinitesimally small (almost zero). Once the idea of limits is applied to our Calculus problem, the techniques used in algebra and geometry can be implemented. | 677.169 | 1 |
An imaginative introduction to number theory, this unique approach employs a pair of fictional characters, Ant and Gnam. Ant leads Gnam through a variety of theories, and together, they put the theories into action?applying linear diophantine equations to football scoring, using a black-magic device to simplify problems in modular structures, and... more...
Classic two-part work now available in a single volume assumes no prior theoretical knowledge on reader's part and develops the subject fully. Volume I is a suitable first course text for advanced undergraduate and beginning graduate students. Volume II requires a much higher level of mathematical maturity, including a working knowledge of the theory... more...
Basic treatment, incorporating language of abstract algebra and a history of the discipline. Unique factorization and the GCD, quadratic residues, sums of squares, much more. Numerous problems. Bibliography. 1977 edition. more...
An advanced monograph on Galois representation theory by one of the world's leading algebraists, this volume is directed at mathematics students who have completed a graduate course in introductory algebraic topology. Topics include abelian and nonabelian cohomology of groups, characteristic classes of forms and algebras, explicit Brauer induction... | 677.169 | 1 |
Course Summary
If you use the Big Ideas Math: A Common Core Curriculum 7th grade textbook in class, this course is a great resource to supplement your studies. The course covers the same important 7th grade math concepts found in the book, but uses short videos that make the math lessons easier to understand and more fun to learn.
Who's it for?
Anyone enrolled in a class using the Big Ideas Math: A Common Core Curriculum textbook should consider this companion course. You will learn the material faster, retain it longer and earn a better grade.
How it works:
Identify the chapter in your Big Ideas Math: A Common Core Curriculum textbook with which you need help | 677.169 | 1 |
Intermediate Mathematics B
Course Overview
Intermediate Mathematics B is the second of a three-year middle school math sequence that prepares students for success in high school algebra. The course begins by developing an understanding of operations with rational numbers, which is applied to working with algebraic expressions and linear equations. This course also helps students develop understanding of proportional relationships and the use of these relationships to solve problems. Geometry topics focus on constructions of two-dimensional figures; properties of circles; scale factors; and problems involving area, surface area, and volume. Finally, students use the tools of probability and statistics to solve basic probability problems and to make inferences based on population samples. This course aligns to national standards and is designed to focus on critical skills and knowledge needed for success in further mathematical studies, including high school algebra. | 677.169 | 1 |
books.google.com - Through... Engineering Mathematics
Advanced Engineering Mathematics
Through throughout to improve the clear flow of ideas. The computer plays a more prominent role than ever in generating computer graphics used to display concepts. And problem sets incorporate the use of such leading software packages as MAPLE. Computational assistance, exercises and projects have been included to encourage students to make use of these computational tools. The content is organized into eight-parts and covers a wide spectrum of topics including Ordinary Differential Equations, Vectors and Linear Algebra, Systems of Differential Equations, Vector Analysis, Fourier Analysis, Orthogonal Expansions, and Wavelets, Special Functions, Partial Differential Equations, Complex Analysis, and Historical Notes. | 677.169 | 1 |
Presentation (Powerpoint) File
Be sure that you have an application to open this file type before downloading and/or purchasing.
1.21 MB | 31 pages
PRODUCT DESCRIPTION
Limits at Infinity PowerPoint Lesson
This lesson is designed for Calculus 1 or AP Calculus. Students will learn to find the limits of various functions as x approaches infinity. Determining these limits will help students find the horizontal asymptotes of a function and to determine end behavior, necessary for curve sketching. The limits in this PowerPoint can all be found without L'Hopital's rule, but the rule does apply to many of the problems and if your course/curriculum includes L'Hopital in this unit, you can augment the lesson.
There are 30 slides with 23 fully animated step-by-step problems including two applications. Many have matching illustrated graphs. This PowerPoint is 2003 and up compatible. The PowerPoint is editable, but your license is to edit the design features only. Please read the license carefully.
• Look for the green star next to my store logo and click it to become a follower. Tahdah! You will now receive email updates about sales and all the new products expertly designed to help you teach and save you | 677.169 | 1 |
Title:
Polynomials and Rational Functions URL: Description: This a WebQuest designed to help students learn and understand Polynomials and how to evaluate the fundamental operations, together with Rational functions, this WebQuest is filled of sujects accessed through hyperlinks to different websites and are filled with different exercises and games to help the students learn more and practice solving Polynomials Keywords: Mathematics, Algebra, Polynomials, Synthetic Division, Remainder Theorem, and Rational Functions Published: Yes |
Featured: Yes Author(s): Ibrahim Giem Novenario | 677.169 | 1 |
Books Download Free
Excursions in Modern Mathematics (8th Edition)
Donwload Excursions in Modern Mathematics (8th Edition) book by also, you can download unlimited books ,only here for free.
NOTE: This book DOES NOT include an Access Code
Excursions in Modern Mathematics introduces you to the power of math by exploring applications like social choice and management science, showing that math is more than a set of formulas. Ideal for an applied liberal arts math course, Tannenbaum's text is known for its clear, accessible writing style and its unique exercise sets that build in complexity from basic to more challenging. The Eighth Edition offers…
Description :
Books a la Carte are unbound, three-hole-punch versions of the textbook. This lower cost option is easy to transport and comes with same access code or media that would be packaged with the bound book...This lively and accessible exploration of the nature of mathematics examines the role of the mathematician as well as the four major branches: number theory, algebra, geometry, and analysis.... | 677.169 | 1 |
Calculus Straight Line Motion Task Cards (with optional QR Codes)
PDF (Acrobat) Document File
Be sure that you have an application to open this file type before downloading and/or purchasing.
4.67 MB | 12 task cards and 1 record sheet pages
PRODUCT DESCRIPTION
This is a set of 12 task cards that students can use to practice working problems that involve straight line motion. (Assume all questions are in terms of meters and seconds). The QR Code answers are included on a separate sheet that can be posted somewhere in the classroom. Students can get up and check them as they finish a question. I have also included the answers for the teacher on a separate sheet so these cards can be used without needing to use the QR Codes.
A worksheet that students can use to show their work and record their answers to the task cards is also included.
I have also included the same 12 problems that are on the task cards in worksheet format. I use this worksheet if there were any students that were absent. Please note these are the same 12 problems that are on the task cards – just in a different format. (There are no QR codes on this worksheet).
QR Codes are codes that can embed text, video, or website addresses. In this activity, students can scan the code to check to see if their answers are correct. Some of the codes in this activity do lead to a website so students can see their answers in correct mathematical notation, so students do need to be connected to the internet to complete this activity | 677.169 | 1 |
College Algebra with Modeling and Visualization GaryMore...
Gary on conceptual understanding helps students make connections between the concepts and as a result, students see the bigger picture of math and are prepared for future courses. Introduction to Functions and Graphs; Linear Functions and Equations; Quadratic Functions and Equations; More Nonlinear Functions and Equations; Exponential and Logarithmic Functions; Trigonometric Functions; Trigonometric Identities and Equations; Further Topics in Trigonometry; Systems of Equations and Inequalities; Conic Sections; Further Topics in Algebra For all readers interested in college algebra | 677.169 | 1 |
Algebraic function
In mathematics, an algebraic function is informally a function that satisfies a polynomial equation whose coefficients are themselves polynomials with rational coefficients. For example, an algebraic function in one variable x is a solution y for an equation where the coefficients ai(x) are polynomial functions of x with rational coefficients. A function which is not algebraic is called a transcendental function.
more from Wikipedia
Mathematical optimization
In mathematics, computer science, or management science, mathematical optimization (alternatively, optimization or mathematical programming) refers to the selection of a best element from some set of available alternatives. In the simplest case, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function | 677.169 | 1 |
Algebra Through Modeling
This module is designed to familiarize teachers with a new and very innovative advanced algebra course. This course presents algebra from the perspective of modeling and data analysis using the basic algebraic functions and a graphing calculator with data analysis capabilities such as those of any of the TI-83/84 family of graphing calculators including the TI-83, 83+, 83+ Silver Edition, 84+, and 84+ Silver Edition. This new approach will be useful in high school and college for students who have completed two years of algebra but are not ready for precalculus. It reviews algebra without repeating earlier course work, and it clearly demonstrates the importance of algebra to the solution of real world problems. Credit: 1 grad. sem. hr.
Common Core Standardsfor Mathemtical Practice that are emphasized include:
2. Reason abstractly and quantitatively.
4. Model with mathematics.
5. Use appropriate tools strategically.
7. Look for and make use of structure.
Algebra through Modeling with the TI-83 family of Graphing Calculators was written by Tony Peressini and John Luker of the University of Illinois during November 1996. It was revised by Peressini and Luker during November 1997 and by Peressini and Tom Anderson in November 2003 and June 2005.
Check out some sample projects for this module in the MTL Classroom Projects to the right. | 677.169 | 1 |
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Unformatted text preview: Maple for Math Majors Roger Kraft Department of Mathematics, Computer Science, and Statistics Purdue University Calumet roger@purduecal.edu 2. Variables, Assignment, and Equations 2.1. Introduction In this worksheet we look at how Maple treats variables and at Maple's rules for how variables can be named. We also look at how variables are given values with the assignment operator, and we compare Maple's use of the assignment operator and the equal sign with the standard mathematical use of the equal sign in equations. > 2.2. Assigned and unassigned variables Every variable in Maple will have one of two states; either it is an assigned variable, or it is an unassigned variable. Assigned variables are names for some value. In other words, an assigned variable is a name that represents something. An assigned variable can represent almost anything, a number, an expression, a function, an equation, a graph, a solution, a list of things, another variable, etc. Assigned variables are sometimes called "programming variables" because they act, more or less, like the variables in traditional programming languages. Assigned variables are also sometimes referred to as a "label for a result" or simply as "labels". Unassigned variables are names that do not yet represent a particular value. Unassigned variables are sometimes called "free variables", because they are free to take on any value. They are also sometimes called "unknowns" because they do not have a value. Other terms used as synonyms for "unassigned variables" are, mathematical variables, mathematical symbols, mathematical unknowns, algebraic unknowns, and indeterminates. All variables begin their life in Maple as unassigned variables. To change an unassigned variable to an assigned one, we use the assignment operator , which is a colon followed by an equal sign (i.e. := ). A Maple command with an assignment operator in it is called an assignment statement . Here are some examples of assigned and unassigned variables. Until you give the variable x a value, x is an unassigned variable. We sometimes say that an unassigned variable represents itself. > x; Let us change x into an assigned variable. > x := 3; Now x represents the integer 3. (Sometimes we will say "the value of x is 3". Other times we might say " x is a name for 3", or " x refers to 3", or " x has the value 3", or " x is a label for 3", or "3 is assigned to x ".) > x; Here is how we change x back into an unassigned variable. We assign to x a right quoted copy of x . (Right quotes are the single quotes found on the right hand side of the keyboard.) > x := 'x'; # Those are both right quotes. Now x represents itself again (or, we can say that x no longer has a value)....
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This note was uploaded on 02/11/2012 for the course MTH 141, 142, taught by Professor Mcallister during the Spring '08 term at SUNY Empire State. | 677.169 | 1 |
International Journal of Mathematical Education in Science and Technology, v45 n4 p528-551 2014
This paper deals with the modern development of matrices, linear transformations, quadratic forms and their applications to geometry and mechanics, eigenvalues, eigenvectors and characteristic equations with applications. Included are the representations of real and complex numbers, and quaternions by matrices, and isomorphism in order to show that matrices form a ring in abstract algebra. Some special matrices, including Hilbert's matrix, Toeplitz's matrix, Pauli's and Dirac's matrices in quantum mechanics, and Einstein's Pythagorean formula are discussed to illustrate diverse applications of matrix algebra. Included also is a modern piece of information that puts mathematics, science and mathematics education professionals at the forefront of advanced study and research on linear algebra and its applications. | 677.169 | 1 |
Most Recent Documents for L'Amoreaux Collegiate Institute
Example
Solution
11.6 Present Value of an Annuity
In your earlier work, you found the present value of an amount. This skill
can be applied to nd the present value of an annuity. For example:
You win a lottery of $50 000. You do not want to spend it all
7.1
Arithmetic Sequences
YOU WILL NEED
GOAL
linking cubes
graphing calculator or graph
Recognize the characteristics of arithmetic sequences, and
express the general terms in a variety of ways.
paper
spreadsheet software
INVESTIGATE the Math
Chris used
year at 9% per annum compounded annually. How much will she have saved
at the end of the 5th year? To solve the problem, you can interpret the
information visually. Draw a time line.
Now 1 year 2 years 3 years 4 years 5 years
.45 = IUUO
. ,A t
95 comp
Geometric Series
Geometric Series is the addition of all the terms in the geometric sequence. Hence,
a + ar + ar2 + ar3 +.+arn-1 = Sn
Sn means the sum
There are two quick formulas for us to find the sum of the geometric sequence.
When r >1, we use this f
PRESENT VALUE OF AN
ANNUITY
THE POWER OF AN ANNUITY
REVIEWING FUTURE VALUE OF AN
ANNUITY
Used when you want to find the future value of an
amount of money
Money will be compounded
Formula: =
[ 1+ 1]
IMPORTANT INFORMATION ABOUT
COMPOUNDING
Compounding
UNIT 2 - FUNCTIONS
DOMAIN AND RANGE
We will constantly be coming back to
domain and range, make sure you
understand this well
Domain the set of x-values of a
function (input)
Range- the set of y-values of a function
(output)
There are different ways to
Arithmetic Series
Arithmetic Series is the addition of all the terms in the arithmetic sequence. Hence,
a + (a+d) + (a+2d)+ (a+3d)+.+ *a + d(n-1)] = Sn
Sn means the sum
For example: 2 +4 +6 +8 = 20 = Sn
There is two formula that gives you the sum very qu
1.2
Function Notation
YOU WILL NEED
GOAL
graphing calculator
Use function notation to represent linear and quadratic functions.
LEARN ABOUT the Math
The deepest mine in the world, East Rand mine in South Africa,
reaches 3585 m into Earths crust. Another
7.5
YOU WILL NEED
linking cubes
Arithmetic Series
GOAL
Calculate the sum of the terms of an arithmetic sequence.
INVESTIGATE the Math
Marian goes to a party where there are 23 people present, including her. Each
person shakes hands with every other perso
PASCALS TRIANGLE
The Pascals triangle a triangular array of numbers in
which those at the ends of the rows are 1 and each of
the others is the sum of the nearest two numbers in the
row above.
In row 1, 1+1 becomes 2 underneath in row 2. In row 2,
1+2 beco
7.6
YOU WILL NEED
spreadsheet software
Geometric Series
GOAL
Calculate the sum of the terms of a geometric sequence.
INVESTIGATE the Math
An ancestor tree is a family tree that shows only the parents in each generation.
John started to draw his ancestor
1.4
Determining the Domain
and Range of a Function
YOU WILL NEED
GOAL
Use tables, graphs, and equations to find domains and ranges
of functions.
graph paper
graphing calculator
LEARN ABOUT the Math
The CN Tower in Toronto has a lookout level that is 346
1.1
YOU WILL NEED
graphing calculator or
graph paper
Relations and Functions
GOAL
Recognize functions in various representations.
INVESTIGATE the Math
Ang recorded the heights and shoe sizes of students in his class.
Shoe Size
?
Tech
Support
For help dra
UNIT 2 - FUNCTION
INVERSE FUNCTION
An inverse of a linear function is the reverse of an
original function. It means that the x-values and yvalues are switched. The y-values of the original
function becomes the x-values of its inverse
function, and the x-v
SIMPLE INTEREST
SIMPLE INTEREST
Simple Interest is similar to Arithmetic sequences
You start with an original amount, P = Principal (a value)
The first amount is then added to the interest earned in that
corresponding year (d - common difference)
Simp
7.2
Geometric Sequences
YOU WILL NEED
GOAL
graphing calculator
graph paper
Recognize the characteristics of geometric sequences and express the
general terms in a variety of ways.
INVESTIGATE the Math
A local conservation group set up a challenge to get
AMOUNT OF AN ANNUITY
FUTURE VALUE
HUMOUR FOR THE DAY
A motorist, driving in the countryside, hit and killed a calf
that was crossing the road.
The driver went to the owner of the calf and explained
what had happened. He then asked what the animal was
wort
SIMPLIFYING RADICALS
WE SAY THAT A SQUARE ROOT RADICAL is simplified, or in its simplest
form, when the radicand has no square factors.
A radical is also in simplest form when the radicand is not a
fraction.
Example 1. Square factors are when you can take
UNIT 2: FUNCTIONS
FUNCTIONS AND RELATIONS
A Relation is a correspondence between two
variables(x,y). Basically, you can think of it as a set
of points that has some sort of relationship.
A Function is a relation such that for each x-value,
there is exactl | 677.169 | 1 |
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