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Product Information
Supplemental Worksheets for McKeague's Prealgebra
Matched Problems Worksheets
The Matched Problem Worksheets are available online for each section of the textbook. They can also be purchased separately. You can view these worksheets online by going to MathTV.com and selecting the Videos by Textbooks tab, then selecting your textbook, or by secting the eBooks by xyztextbooks tab, selecting your textbook, then selecting the worksheet view tab.
Flip Your Classroom with MathTV's Matched Problems Worksheets
Each section of our eBook contains a Matched Problems Worksheet. Each problem on these worksheets is similar to the text example with the same number. Simply assign the matched problems worksheets for students to do before they come to class, and your classroom is flipped. And remember, students never need to get stuck on a problem because every example in the book is accompanied by a number of videos for them to watch | 677.169 | 1 |
Thursday, April 28, 2016
Book on Function and Graphs
The second in a series of systematic studies by a celebrated mathematician I. M. Gelfand and colleagues, this volume presents students with a well-illustrated sequence of problems and exercises designed to illuminate the properties of functions and graphs. Since readers do not have the benefit of a blackboard on which a teacher constructs a graph, the authors abandoned the customary use of diagrams in which only the final form of the graph appears; instead, the book's margins feature step-by-step diagrams for the complete construction of each graph.
The first part of the book employs simple functions to analyze the fundamental methods of constructing graphs. | 677.169 | 1 |
Foundation Mathematics for Biosciences provides an accessible and clear introduction to mathematical skills for students of the biosciences. The book chapters cover key topic areas and their associated techniques, thereby presenting the maths in context.
Foundation Mathematics for Biosciences provides an accessible and clear introduction to mathematical skills for students of the biosciences. The book chapters cover key topic areas and their associated techniques, thereby presenting the maths in context.
A student focused pedagogical approach will help students build their confidence, develop their understanding and learn how to apply mathematical techniques within their studies. Students will be able to use the book as a resource to complement their theory-based textbooks and to prepare themselves for practical classes, tutorials and research projects. | 677.169 | 1 |
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Sixth Grade Algebra 2 - Using Properties to Generate Equivalent Expressions teaches students how to use the operation properties: zero, identity, commutative, associative and distributive. Then students can use these properties to find missing variables and numbers. There is a title slide, focus slide, objective, essential question, vocabulary, concept development, step-by-step demonstrations, guided practice, checking for understanding, problem solving with word problem, and a reward slide at the end. For best results, students should have white boards and dry erase markers. You may be interested in the following related powerpoint lessons: | 677.169 | 1 |
New Powerpoint about Communications Systems
How DEMML™ was Invented
Structure of a sample DEMCS™ code number
Now that you are familiar with the basics of what went into the design of the DEMCS™ classification codes, its time to take a look at a specific example. (Please note that this is just an example and not a specific code that is already in use. The specific codes for all the topics have not yet been worked out. There is still quite a bit of work that needs to be done before this goal can be realized.)
LCC section
The first part of the DEMCS™ code is the base LCC classification number. Remember, only the first part of the LCC number is used. The letters in this section are upper-case just like in LCC. Notice that the third piece of this section consists of 3 characters. This is because each character of that piece does not represent a new level in the hierarchical tree within the LCC system. The LCC often assigns a range of numbers to a specific subject in an attempt to make the best use of the limited set of different values that can be expressed in that system. Another point to notice is that 154 represents General Algebra in LCC whereas "QA" represents all of Mathematics. In the final DEMCS™ hierarchical tree of knowledge it is possible that only the "QA" part of the LCC number would be used. Then we would use the tree of all mathematical educational material generated by the math associations to go from there using DEMCS codes. How much of the LCC number is used for each major subject will depend on how much of the tree is or can be defined by the associations for the different academic disciplines.
There is another difference between the way LCC numbers are normally written and how they are used in DEMCS™. LCC numbers are normally written in sections, called "cutters", separated by carriage returns, spaces, or periods. Each of those cutters may actually represent one or more levels in the LCC hierarchical tree. The system is designed so that, once an LCC number is assigned to a book, all one needs to do is sort the numbers alphabetically to find the correct location for the book. There is no reason to clutter up the number by indicating the divisions between each level. In LCC the above number would be written simply as shown at left.
In DEMCS™ each level in the classification tree is also a level in a computer file-system folder structure. This means that the path-name must have slashes in between the parts of the code for each level in the tree. Since we want the DEMCS™ code numbers to exactly parallel the file-system path-name, we will also use the slashes in the code number itself. While this does make the code number longer and a little more difficult to read, it also removes all ambiguity. This also means that people can copy a path-name directly from their file browser, and get the exact code number to paste anywhere they need it. They can also copy a code number and paste it into the address bar of their file browser or web browser and instantly go to the correct part of their personal collection of DEMML™ content or to the correct part of any DEMML™ distribution server.
DEMCS™ Section
Where the LCC system does not provide the necessary detail and granularity to specify an exact, very-specific topic, DEMCS™ picks up the slack. The code for this example is derived from a rather loose interpretation of the "Core Subject Taxonomy for Mathematical Sciences Education" on the "Mathematical Sciences Conference Group on Digital Educational Resources" web site at " As described earlier, the DEMCS™ coding system allows an infinite amount of granularity while allowing infinite growth in depth and breadth of the hierarchical tree of knowledge.
Topic Name
With all these code numbers you may have been wondering how in the world anyone is supposed to know what topics those darn codes actually represent. Just as with any other classification system, it can be pretty difficult to learn all the different codes. But, also just like any other classification system, regular users have no need to learn all the codes. They just look them up and use them. However, with DEMCS™ there is some built in help.
Remember how the actual content files are stored in special folders referred to as "stems" in the tree metaphor? Well, as you can see, those folders have actual human readable names. The first character is always an exclamation point so that the stem folders will sort up at the top of the list. The next two or three characters are the language code as defined by the ISO 639-2 specification. Then a dash followed by the name of the topic in the appropriate language.
Here is a list of similar codes but in different languages:
Q/A/154/9/c/c/!ENG-Polynomial_Functions
Q/A/154/9/c/c/!GER-Polynomische_Funktionen
Q/A/154/9/c/c/!SPA-Funciones_Polinomicas
When looking at an expanded tree of folders it will always be possible to see the name of the topic referred to by a specific code simply by looking at the first few folders directly under it as can be seen in the directory listings below.
All the main science subject and topic folders.
The Mathematics subject folder with additional subject and topic folders for all the major Math subjects. | 677.169 | 1 |
TEKS: Algebra II
111.33 ALGEBRA II (ONE-HALF TO ONE CREDIT) Foundations for
functions: knowledge and skills and performance descriptions.
(2A.1) The student uses properties and attributes of functions and applies functions to problem situations.
(A) identify the mathematical domains and ranges of functions and determine reasonable domain and range values for continuous and discrete situations.
(B) collect and organize data, make and interpret scatter plots, fit the graph of a function to the data, interpret the results, and proceed to model, predict, and make decisions and critical judgements.
(2A.2) The student understands the importance of the skills required to manipulate symbols in order to solve problems and uses the necessary algebraic skills required to simplify algebraic expressions and solve equations and inequalities in problem situations.
(A) use tools including factoring and properties of exponents to simplify expressions and to transform and solve equations.
(B) use complex numbers to describe the solutions of quadratic equations.
(2A.3) The student formulates systems of equations and inequalities from problem situations, uses a variety of methods to solve them, and analyzes the solutions in terms of the situations.
(A) analyze situations and formulate systems of equations in two or more unknowns or inequalities in two unknowns to solve problems.
(B) use algebraic methods, graphs, tables, or matrices, to solve systems of equations or inequalities.
(C) interpret and determine the reasonableness of solutions to systems of equations or inequalities for given contexts.
Algebra and geometry: Knowledge and skills and performance descriptions.
(2A.4) The student connects algebraic and geometric representations of functions.
(B) use the parent function to investigate, describe, and predict the effects of changes in a, h, and k on the graphs of y = a(x - h)2 + k form of a function in applied and purely mathematical situations.
(2A.8) The student formulates equations and inequalities based on quadratic functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.
C) Suppose the graph of the parabola shown in the figure represents a hill. There is a 50-foot tree growing vertically at the top of the hill. Does a spotlight at point P directed along line shine on any part of the tree? Explain your reasoning.
This question is based on the 1996 AB6 AP Calculus question.
(B) analyze and interpret the solutions of quadratic equations using
discriminants and solve quadratic equations using the quadratic formula.
(C) compare and translate between algebraic and graphical solutions of quadratic equations.
To start this activity you will need a stopwatch, a piece of string at least 1.7 meters long, a ruler, and a weight.
1. Tie the weight to the end of your string and then measure off 1.5 meters.
2. Have one person hold the pendulum. Use your stopwatch to time, in seconds, how long it takes the pendulum to complete ten periods. Divide this time by 10 to estimate the time it takes for the pendulum to complete one period.
3. Repeat the process in part 2 several times, each time shortening the length of your string by 15 cm. Continue to collect your data (length of string, time/period).
4. Draw a sketch of the data, the time of a period as a function of the length of the pendulum.
5. If the graph appears linear, write an equation of the regression line that
best models the data. If the graph does not appear to be linear, you will need
to perform a transformation to straighten the data. What model and what transformation
seem most appropriate? Write the equation of this model.
6. Predict t(.9 meters), that is, the time of one period if the length of the pendulum is .9 meters.
7. Predict t(2 meter), that is, the time of one period if the length of the pendulum is 2 meters.
8. Which of the two values t(.9) or t(2) do you feel is more accurate? Explain why.
9. What type of function did you determine was the best model for your data? Explain the process you had to use to re-express your data to be able to write an equation for this model.
This activity introduces the student to data collection, curve fitting, and experimental design—all topics of the AP Statistics curriculum.
Does the weight of the pendulum affect the regression equation? Give each group a different weight and compare the results.
(2A.10) The student formulates equations and inequalities based on rational functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.
(A) use quotients of polynomials to describe the graphs of rational functions, predict the effects of parameter changes, describe limitations on the domains and ranges, and examine asymptotic behavior.
Let f be the function given by f(x)= x / √(x2 - 4)
a. Find the domain of f.
b. Write an equation for each vertical asymptote to the graph of f.
c. Write an equation for each horizontal asymptote to the graph of f.
This question is based on the 1989 AB4 AP Calculus question.
(B) analyze various representations of rational functions with respect to problem situations.
(C) determine the reasonable domain and range values of rational functions, as well as interpret and determine the reasonableness of solutions to rational equations and inequalities.
(D) determine the solutions of rational equations using graphs, tables, and algebraic methods.
(E) determine solutions of rational inequalities using graphs and tables.
(F) analyze a situation modeled by a rational function, formulate an equation or inequality composed of a linear or quadratic function, and solve the problem.
The city of Katy, Texas, wants to enclose a 3000 square foot rectangular region as a park. The city plans to build a brick fence along 3 sides of the park that will cost $25 per linear foot. A wooden fence that will cost $10 per linear foot will enclose the fourth side of the park. Find the minimum cost of the fence.
This relates to the calculus concept of optimization.
(G) use functions to model and make predictions in problem situations, involving direct and inverse variation.
(2A.11) The student formulates equations and inequalities based on exponential and logarithmic functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.
(A) develop the definition of logarithms by exploring and describing the relationship between exponential functions and their inverses.
(B) use the parent functions to investigate, describe, and predict the effects of parameter changes on the graphs of exponential and logarithmic functions, describe limitations on the domains and ranges, and examine asymptotic behavior.
Let f be the function given by f(x) = 2xe2x
Use your graphing calculator to do the following:
a) find all horizontal asymptotes of f(x)
b) locate the absolute minimum value of f
c) determine the domain and range of f
Examine the family of functions defined by y = bxebx where b is a nonzero constant. What do all of these graphs have in common? Why?
This problem is based on the 1998 AB/BC2 AP Calculus exam. This is a good problem to tackle as a class. Every student can be assigned a different value of b.
(C) determine the reasonable domain and range values of exponential and logarithmic functions, as well as interpret and determine the reasonableness of solutions to exponential and logarithmic equations and inequalities. | 677.169 | 1 |
Videos: Intro to Differential Forms (and related topics)
This is (so far) my longest video series, done originally for the end of a multivariable calculus course. Best if you are confident with vector calculus already, but most videos don't presuppose anything further. Some of the later videos assume that you know Maxwell's Equations, including the vector potential. | 677.169 | 1 |
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We've taken one of the most common and versatile hands-on manipulatives and transformed it for use with your classroom SMART Board®! Use our Virtual Algebra Tiles to solve expressions for a given value, integer exploration, multiplying and/or factoring polynomials, solving equations, and more in a new and engaging way. Features 5 virtual screens with teacher tips and printable blackline master worksheets. Software accredited by SMART. CD-ROM.
System Requirements: SMART Notebook™ software version 9.5 or later and Adobe Acrobat Reader version 7 or later for Windows, Mac, or Linux operating systems. If you do not have SMART Notebook™, you can use the web-based SMART Notebook Express™. Simply click on "Open an existing Notebook file" and navigate to your Virtual Manipulatives. | 677.169 | 1 |
The thought of distributions constitutes a vital software within the learn of partial differential equations. This textbook would supply, in a concise, principally self-contained shape, a quick creation to the speculation of distributions and its purposes to partial differential equations, together with computing basic recommendations for the main easy differential operators: the Laplace, warmth, wave, Lam\'e and Schrodinger operators.
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This e-book presents in a concise, but specific approach, the majority of the probabilistic instruments scholar operating towards a sophisticated measure in statistics,probability and different similar components, can be outfitted with. The procedure is classical, averting using mathematical instruments now not worthwhile for engaging in the discussions.
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From the contours of coastlines to the outlines of clouds, and the branching of bushes, fractal shapes are available far and wide in nature. during this Very brief advent, Kenneth Falconer explains the fundamental ideas of fractal geometry, which produced a revolution in our mathematical figuring out of styles within the 20th century, and explores the wide variety of purposes in technological know-how, and in points of economics.
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From what we now have proved partially (1) and Theorem 4. ninety nine we then finish that, within the feel of , (10. five. eight) Upon taking , formulation (10. five. 6) follows, completing the facts of half (3). finally, the declare in (4) is a end result of (3) and the boundedness of the singular indispensable operators on (as obvious via utilising Theorem 4. ninety seven componentwise). □ 10. 6 primary strategies for the Stokes Operator enable and . Then the Stokes operator L S performing on is outlined through (10. 6. 1) In perform, u and p are often called the rate box and the strain functionality, respectively.
2. 14) we've got , whereas from the definition of the Fourier rework it's speedy that (3. 2. 15) retaining this in brain and using half (a) in Exercise 2. 22 we receive (3. 2. sixteen) additionally, on account of (3. 2. 14) and the truth that , Lebesgue's ruled convergence theorem offers (3. 2. 17) In summary, (3. 2. 13), (3. 2. 16), and (3. 2. 17), exhibit that every time is such that we've got (3. 2. 18) the place the normalization consistent C is given via (3. 2. 19) As such, (3. 2. eleven) will persist with once we end up that .
1. four) and (4. 1. eight) . end up that during for every and every . trace: Use (3. 2. 27) and Exercise 3. 29. Lemma 4. 27 (Riemann–Lebesgue Lemma). If , then the tempered distribution u f satisfies . evidence. this can be a outcome of Exercise 4. 26 and (3. 1. 3). □ Exercise 4. 28. turn out that for each one has in . trace: Use a density argument in accordance with the formulation from half (c) of Proposition 3. 27, Exercise 4. eleven, Young's inequality (cf. Theorem 13. thirteen) within the specific case whilst p = q = 2, and the truth that the Fourier rework is continuing either on and on .
15 for harmonic capabilities it follows that there exists such that u(x) = c for all . we will subsequent exhibit that bi-harmonic capabilities fulfill inside estimates and are real-analytic. Theorem 7. 26. consider satisfies △ 2 u = zero in . Then u is real-analytic in Ω and there exists a dimensional consistent C ∈ (0,∞) such that (7. four. five) for every x ∈ Ω and every . facts. within the case whilst n = 1 or n ≥ 3, all claims are direct effects of Theorem 6. 26 and Theorem 7. 21. to regard the case n = 2 we will introduce a "dummy" variable.
Three. forty two) From this illustration, (11. three. 41), and (11. three. 31), it truly is transparent that we have got . to accomplish the facts of Step II, there is still to monitor that . Step III. facts of half (3) within the assertion of the concept. To facilitate the dialogue, repair , introduce (11. three. forty three) and outline through environment (11. three. forty four) for every . realize that Q jk is a polynomial of measure 2m + q that vanishes whilst n is extraordinary [since if so the integrand in (11. three. forty three) is odd]. additionally, from our previous research in (11. three. 42), we all know that the indispensable within the right-hand part of (11. | 677.169 | 1 |
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Every Texas Mathematics teacher will love this TEKS checklist. The TEKS are presented in a shortened, user-friendly, printable checklist. The checklist format is designed to help teachers track what TEKS have been taught or as a tool in aligning curriculum. Print only the grade levels you need for vertical alignment. All updated K-12 Mathematics TEKS are included. High School TEKS for Algebra I, Algebra II, Geometry, Precalculus,, Mathematical Models with Applications, Advanced Quantitative Reasoning, Independent Study, Discrete Mathematics for Problem Solving, Statistics, and Algebraic Reasoning are all included. Enjoy! | 677.169 | 1 |
Grade 11 Platinum Maths Study Guide Caps
Grade 11 Platinum Maths Study Guide Caps
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Browse related Subjects ...
Read More "staggered grids" and "edge elements." The main goal of the book is to make the reader aware of different sources of errors in numerical computations, and also to provide the tools for assessing the accuracy of numerical methods and their solutions. To reach this goal, convergence analysis, extrapolation, von Neumann stability analysis, and dispersion analysis are introduced and used frequently throughout the book. Another major goal of the book is to provide students with enough practical understanding of the methods so they are able to write simple programs on their own. To achieve this, the book contains several MATLAB programs and detailed description of practical issues such as assembly of finite element matrices and handling of unstructured meshes. Finally, the book aims at making the students well-aware of the strengths and weaknesses of the different methods, so they can decide which method is best for each problem. In this second edition, extensive computer projects are added as well as new material throughout.Reviews of previous edition: "The well-written monograph is devoted to students at the undergraduate level, but is also useful for practising engineers." (Zentralblatt MATH, 2007)
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Synopses & Reviews
Publisher Comments
This new ADVANTAGE SERIES of C. L. Johnston, Alden T. Willis, and Jeanne Lazaris' INTERMEDIATE ALGEBRA is a traditional, straight-forward, extremely popular book which is noted for its one-step, one-concept-at-a-time approach. All major topics are divided into small sections, each with its own examples and often with its own exercises--an approach that helps students master each section before proceeding to the next one. As part of the ADVANTAGE SERIES, this version will offer all the quality content you've come to expect from Johnston, Willis, and Hughes sold to your students at a significantly lower price.
Synopsis
The main goal of this book is to prepare students for courses in college algebra, statistics, business calculus, pre-calculus, science, or any other subject that has intermediate algebra as a prerequisite.
Synopsis
This traditional, straight-forward, extremely popular book helps students learn algebra concepts-by using a one-step, one-concept-at-a-time approach. All major topics are divided into small sections, each with its own examples and often with its own exercises--an approach that helps students master each section before proceeding on to the next. | 677.169 | 1 |
Pre-Algebra A
What are the basic ways people use algebraic and geometric concepts to be effective in their jobs and careers?
Why Take This Course?
Pre-Algebra bridges the gap between arithmetic and algebra.
What do you want to do when you grow up? In this math course, go on an adventure with Fred (from the Life of Fred series) to find out what career path might be in your future. As Fred explores principles of economics on his own quest to get a summer job, we will apply our mathematical knowledge to build our problem-solving skills. You'll be surprised how much our job search requires us to solidify our foundational algebra and geometry skills, and how relevant and meaningful these skills can be to our everyday lives.
The focus of this course is learning how to use algebra to understand equations and functions with meaningful applications. Students will review numbers and operations, explore patterns of geometry, and continue solving equations with one unknown. They will represent and solve real-world situations with two-variable linear functions, and statistical data analysis. This High School Math course includes an emphasis on having a growth mindset towards math, with an engaging midterm that helps students see the fun and fascinating side of mathematics.
Expedition: Get a Job!
This semester, students will be trying different types of jobs in a series of imaginary "internships," (including logistics, animation, science, or contracting) that provide us with necessary skills to build up our resume. Students will increase their number sense and statistical analysis skills during an internship with NASA. After an internship with a contractor, students will have mastered the Pythagorean Theorem and volumes of 3D objects. Students will continue with internships with an online store and Animation Studios to fine-tune their solving and scaling skills. The Get a Job! expedition allows the students to explore careers while applying math in a meaningful way. Throughout the semester, students will build their resumes and practice presentation skills, preparing for the Summit Project of interviewing for a job.
Course Framework
Unit 1
Unit 2
Unit 3
Unit 4
How is math applied in the scientific world?
Where can we see math in the physical world?
How does algebra represent logistical relationships?
Where's the math in animation?
How is scientific notation used to represent the universe?
What is the Pythagorean Theorem and where does it come from?
What is a solution?
What is a transformation in math?
How do I measure the distance between planets and stars?
How can I use the Pythagorean Theorem to find a missing side of a right triangle?
How can I solve multi-step equations?
How do translations, reflections, rotations, and dilations affect a shape and its coordinates? | 677.169 | 1 |
Ncert 9th Class Guide Of Mathematics
syllabus of cbse class 9 hindi course a 2016 u2013 2017 sa u2012 i
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NCERT Books are very useful for students who want to score good percentage in their Exams. We provide NCERT textbooks and solution for all class 8, class 9, class 10, class 11, class 12. In this post, We provide NCERT Solutions for Class 11 Maths in PDF format with direct download option.Our Website gives students the best NCERT solutions for class 10 math. we provide for all the learners can have a way to Learn mathematics for Class 10th with the unique solution. Students can download NCERT Solutions for class 10 maths chapter 1 in anytime and anywhere. This solution provides you a better and easy […]
NCERT Class 10 maths Books are very important for students who want to get good marks in their exams. In this post, we published NCERT Solutions for class 10 Maths chapter 3. Name of class 10 Maths chapter 3 is Pair of linear equations in two variables. Class 10 Students have faced many problems to solveSSC CHSL exam has been a boon to many people who are seeking for a job right after class 12 for various reasons like supporting their family in financial crisis or to stand on their own. However, the exam is not at all easy to crack and to qualify because the questions and topics that […]
When the applicants get aware of the fact that SSC CHSL exam is scheduled at a particular time then they start preparing for the exam but instead of that, the applicants should prepare for the exam beforehand even before filling up the form. Once they have made up their mind to apply for SSC CHSL or Staff Selection Commission- Combined Higher Secondary Level exam is conducted for students who have passed their class 12 exams so that they can get recruitment into government offices. The examination that is conducted by SSC is the most participated examination in the country. There are 2 phases in which the examination is conducted. […] | 677.169 | 1 |
Algebra 1 Final Exam
This 60 question test works great as a final exam, or practice for a state test. The test covers the following objectives:
-Solve multi-step equations and inequalities.
-Identify properties used while solving an equation or inequality.
-Translate a verbal expression.
-Simplif
About this resource :
Common Core aligned 8th grade math benchmark exam. Two versions of the same 6 page assessment are included, each with 56 questions. The questions on each version are nearly identical, with the exception of different numbers. Each version has TWO questions per
These Algebra 1 Spiral ASSESSMENTS are perfect for weekly math quizzes, quick checks, progress monitoring, and spiral review. These math assessments are 100% editable and are perfectly aligned with my popular
This Common Core aligned Algebra (order of operations and writing simple expressions) Assessment Pack is a complete formative and summative assessment package, ready to use, to assess your students understanding during your instruction of order of operations and writing simple expressions.
This pr
Divisibility rules, or divisibility tests, have a wide range of applications in mathematics (finding factors, determining prime vs. composite, simplifying fractions, probability, etc.), but are often underemphasized in the classroom or not explored in enough detail
This test contains 42 multiple choice questions on topics presented in my Algebra Guided Presentation Notes: Unit 1, which is available here on TPT. This is a PDF file.
This test assesses:
Using Variables
Order of Operations
Evaluating Algebraic Expressions
Classifying Real Numbers
Adding and Su | 677.169 | 1 |
During the last three decades geosciences and geo-engineering were influenced by two essential scenarios: First, the technological progress has changed completely the observational and measurement techniques. Modern high speed computers and satellite based techniques are entering more and more all geodisciplines. Second, there is a growing public concern about the future of our planet, its climate, its environment and about an expected shortage of natural resources. Obviously, both aspects, viz. efficient strategies of protection against threats of a changing Earth and the exceptional situation of getting terrestrial, airborne as well as space borne data of better and better quality explain the strong need of new mathematical structures, tools and methods. Mathematics concerned with geoscientific problems, i.e., Geomathematics, is becoming increasingly important.The `Handbook of Geomathematics' deals with the qualitative and quantitative properties for the current and possible structures of the system Earth. As a central reference work it comprises the following geoscientific fields: (I) observational and measurement key technologies (II) modelling of the system Earth (geosphere, cryosphere, hydrosphere, atmosphere, biosphere) (III) analytic, algebraic and operator-theoretic methods (IV) statistical and stochastic methods (V) computational and numerical analysis methods (VI) historical background and future perspectives.
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Integrated Mathematics IV for Middle and High School Teachers
Code:
MATH644
Credits:
3.0
MATH 644 is the final course in a sequence of four courses that integrates big topics of mathematics. The process of moving through these integrated topics of mathematics enables teachers to deepen their own understanding of math, make connections between the different topics within math, and make connections to what they will teach in their own classrooms. The intention is to simultaneously deepen understanding of mathematics while reminding graduate students of what it feels like to have productive struggle in a math class. The fourth and final integrated course focuses on an in-depth investigation of the branch of mathematics called topology. Prerequisites: MATH 641; MATH 642; MATH 643; Pending Approval of the Curriculum Committee. | 677.169 | 1 |
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In certain programs, all it requires to move an test is note getting, memorization, and recall. However, exceeding within a math class can take a different variety of energy. You can't simply display up for the lecture and view your instructor "talk" about geometry and . You find out it by undertaking: paying attention at school, actively researching, and fixing math difficulties – regardless if your teacher has not assigned you any. In the event you end up having difficulties to carry out effectively inside your math class, then pay a visit to greatest web page for fixing math problems to determine the way you can become a far better math pupil.
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Math courses stick to a organic progression – each one builds on the information you have received and mastered through the prior training course. Should you are finding it difficult to stick to new ideas in class, pull out your previous math notes and review past content to refresh you. Make sure that you satisfy the stipulations ahead of signing up for the class.
Review Notes The Night Just before Class
Loathe whenever a trainer calls on you and you have overlooked how to resolve a particular dilemma? Stay away from this minute by examining your math notes. This will assist you to ascertain which concepts or queries you'd like to go above in class another working day.
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Based on your previous performance this semester, you will be awarded a base line of XP. Note, we will not be using letter grades in this class. Instead you will quest your way through Algebra, earning XP will will help you to achieve higher and higher levels.
Rename the document by clicking on the document title to have your actual name instead of "Your Name"
The quest list will continue to grow.
Please feel free to submit quests I can add to the quest list.
You will NOT have to complete all of the quests. You are able to choose which quests interest you.
Since there will be choices within each unit/module there is a maximum amount of XP you can earn per categorization. Once you max out the amount of points you can earn in a category you will need to complete quests in a different category, even if there are quests you have not completed.
Go to the "My Info" tab down at the bottom. You will want to fill in your personal information into the yellow boxes. Your level will be automatically calculated, do not edit that.
4) Sign Up For Quia
We will be using Quia for some of our Quests, thus you will need an account.
Note: if you are able to complete a Quia activity unsupervised you will not receive credit. You will have to do the quest over again in a supervised location.
Step 2. Now, click the area labeled Students. When the next page appears, enter your username and password if you already have a Quia account. If you do not have an account, click the linkCreate my free account. Fill out the form that appears. Select "Student" as the account type. When you are done, press the Create my account button.
Step 3. You should now be in the Student Zone. Type in the class code MGDK468 in the text field and press the Add class button. Now you're done!
Now that you have registered for your instructor's course, you can view your class web page, take quizzes, view your quiz results, view time spent on Quia activities, and read your instructor's feedback from your Quia account.
Follow these steps to view your results:
Step 1. Log in to your account. (Remember, go to the Quia Web home page at and click the area labeled Students.)
Step 2. Click on the class name.
5) Turn in a Quest
The Dungeon Master will write an algebra problem on the board.
Use a quarter sheet of paper to write your name on the back.
Write the question on the front and work out the problem showing all work.
Regardless if you get the correct answer, you will turn in quest #3
Go to your Google Drive (
Your Custom "Slay The Algebra Dragon Quest List" should be in the drive.
If you have not already, change the "Copy of YOUR NAME" part to your actual name. First and Last.
In Column A (the yellow column) you will mark down how much XP this quest is worth based on the adjusted XP in column K.
Each time you turn in a quest you will want to write down the adjusted XP amount in the first column (yellow).
If you do NOT receive credit for a quest, you will want to replace the XP with a zero and re-attempt the quest.
Periodically the dungeon master will send you an email with your level in the class. You will want to make sure that your level and XP points match what the dungeon master has for you. If they do not match you will need to work with the dungeon master on reconciling the records.
Click on the Blue Link in column J which says "Click Here to turn in Quest #3"
Fill out the form and submit.
6) Go Forth and Slay the Dragon
Some of the quests you can work on independently. Others will be projects you are doing during class.
Make sure everyday you come to the Daily Algebra to see what in class quests you are suppose to be working on. Once you've completed in class work you can work on quests of your choice.
Hints on how to use the Quest List
In your Google Drive: you will find your personal quest list. It is recommended that you STAR your quest list. This way when you go to your Google Drive it will stick out. Also notice on the left hand side is "Starred" so you can easily find it there.
Also Try making a URL shortener.
Now go to
You will PASTE the URL into the box.
Under that is the option to make a custom alias. This means you can make your own code for how to get back to the link.
It is suggested that you put in something like ACELnameMATH so that your URL is | 677.169 | 1 |
GCSE Mathematics
About the course
This course in studied in Years 10 and 11. Mathematics is an essential tool, used to model and solve problems in engineering and science. In your GCSE Mathematics course you will learn to reason logically and interpret and communicate mathematical information. You will develop skills in and understanding of mathematical methods and concepts, and apply mathematical techniques to solve a variety of problems.
Overview of units
The course content is built around a number of broad subject areas:
Number
Algebra
Ratio, proportion and rates of change
Geometry and measures
Probability and statistics
Entry requirements
There are no entry requirements for starting this course.
Assessment
You will sit three examination papers, each 1 hour and 30 minutes long, in the summer of Year 11. There is no coursework element in this course. Paper 1 is a non-calculator assessment and a calculator is allowed for Paper 2 and Paper 3. You will be graded on the AQA scale from 9 to 1, based on the total marks across all three papers, with 9 the highest grade. Foundation tier grades range from 1 to 5, while higher tier grades range from 4 to 9.
Where you can go next
Mathematics is a way of thinking, teaching you skills that you can use in any career, so mathematicians work in almost every field. GCSE Maths is an essential qualification for higher education, apprenticeships and many employment roles. | 677.169 | 1 |
The following is NOT HOMEWORK unless you miss part or all of the class.
See the main class web page
for ALL homework and due dates.
Tues Nov 28
Discuss
geodesics on the cone.
Mention p. 262 of Oprea on numerical issues for the torus. Mention
p. 269 about the cylinder uncovering, and the application to plastic
wrap production on p. 282. Revisit spacetime via the
Wormhole metric. Revisit
spacetime via the geometry of Minkowski space (Lorentzian/Special Relativity)
and showing that free particles follow straight line geodesics, and
discuss the geometry of general relativity and begin Einstein's field
equations. Hand out review sheet and take questions on the test.
Thur Nov 30 Test 3
Tues Nov 21 Presentations from Thursday wrap up.
Discuss p. 134-136 that the Gauss curvature only depends on the metric, and
why the geodesic equations yield that the geodesic curvature is 0 (p. 230).
Thur Nov 1
Continue with
applications of the first fundamental form
to surface area calculations using the determinant of the metric form for
the sphere, the cone, the strake, and the hyperbolic annulus.
If time remains, begin
the geodesic worksheet:
Christoffel symbols
the geodesic equation, Euler-Lagrange equations, and curvature.
Tues Oct 24
Take questions on test 2.
Continue with the first fundamental form.
Thur Oct 26 Test 2.
Tues Oct 17
Revisit surfaces and regularity. First fundamental form.
Tues Oct 10
Revisit the cylinder and discuss the curvature vector and curves
on the cylinder. Geodesic and normal curvature and the relationship to
geodesics from an intrinsic point of view.
Maple file on geodesic and normal curvatures
adapted from David Henderson.
Discuss the sphere and the helicoid.
Thur Sep 7 Finish strake problem. Discuss the calculation of
curvature when parametrizing by arc length is impractical. Discuss and prove
the formula for curvature for twice-differentiable function of one variable. | 677.169 | 1 |
BOOM! POW! WHAMO! If those words remind you of your 7th Period Class, I... think you need to find someone that can help you. If your kids dig comics and comic-book movies. This might be perfect for them!
Turn your Algebra 2 or Pre-Calculus classroom into Superhero City while teaching the useful sk
This activity bundle is designed for an algebra student who is learning exponential functions for the very first time. The main topics in this bundle include an introduction to exponential functions,
characteristics of exponential functions, graphing exponential functions with transformations, appli
n American culture people have an affinity for launching birds, pheasants and other sorts of fowl at oblivious targets with a sling shot. Where does this fascination come from? Nobody knows. Nonetheless, it makes for an interesting quadratic function application. Are you ready to help out costumed P
As your students try to sneak cell phone usage into your lesson, make them consider the costs associated with international travel!
In this project, you will receive three separate assignments.
In "Cell Phone Comparison" students will become familiar with writing linear equations from cell phone previe
Every minute of relief can count for something. Once medicine enters the blood stream it will soon have its most powerful effect because it has its highest concentration. Over time the concentration reduces and once it reaches a certain level, the medicine will no longer be effective. The concentrat foldable provides an introduction to piecewise and step functions. Students are provided with a total of 8 examples, where they will need to either state the domain given the graph and equations of a piecewise or step function OR create the graph given the equation and domain.
Students should
This packet of scaffolded notes is perf activity will get your students out of their seats and working cooperatively in small groups. They will use their knowledge of graphing functions in order to solve problems.
This is one of my favorite activities to do as a review & as a way to deepen students' understanding of concepts thThis document includes an assessment that can be used as an end of year algebra exam OR it can be used as a practice test for the End of Year PARCC Test (EOY). This was created with the sample EOY test as a model. Another option is to integrate the questions into classwork/homework during the week
I used this flip book as an introduction to Special Functions. It has a cover page, pages for piecewise, step, greatest integer, and absolute value functions, and a page with 3 practice problems. To assemble the book, students should cut on all the dashed lines, stack the pages, and staple a couplBUNDLED for 50% savings!
Three unique small-group activities encourage students to analyze parent functions and their reflections, horizontal shifts, and vertical shifts.
Each activity requires students to match "personality clues" to a variety of equations. All three activities
Spot the mistake!
Eight quadratic and polynomial problems have been solved, but errors have been made. Students must spot the error, and then complete the problem correctly.
Problems include factoring, the quadratic formula, completing the square, graphing, finding the vertex, par
This is the first lesson in an eight-lesson unit on Functions and Graphs for students enrolled in Pre-Calculus Honors.
Students will be able to:
★ Determine whether a relation represents a function
★ Find the value of a function
★ Find the domain of a function
★ Evaluate a functi
This is a fun activity where students can graph linear equations using different colors for each line. The equations are in slope intercept form. Student just need to find the slope and x- and y- intercepts, then graph. This helps student get more comfortable with graphing.
Take a Look!Nothing like a good criminal investigation to liven up math class!
Based off my popular CSI projects, I have created Whodunnits? The Whodunnits plan to focus on single content topics as opposed to units and will focus more on skill building than application. Every day can't be a project day, so Wh
This is a complete lesson plan on graphing exponential functions in the coordinate plane.
This lesson includes an opening activity, minilesson with guided steps through the process, examples, class activities and a worksheet for homework. Answer keys included.
Common Core standards for High Scho
This activity asks students to use a table of values, slope-intercept form, and finding the intercepts. Students should have multiple strategies for graphing linear equations.
This activity can be used as practice or an assessment. It comes with two versions and a rubric. I us
This is a complete lesson plan for a double-period class (or it can be split up for two classes) on the different types of functions and what their graphs look like.
This lesson covers Linear, Quadratic, Exponential, and Absolute Value functions. (Examples of a Cubic Function, Square Root Function
ALGEBRA 1 TEST PREP set 2
Help your students prepare for Algebra 1 state testing with these task cards.
This resource also includes a paper version of the same problems for use as homework, intervention, test, etc.
Task cards are a popular math classroom resource, including test prep!
Teachers lo
This is a quick and fun activity for students to review their knowledge of Slopes and Intercepts of a line. Students in groups have fun cutting out and solving problems relating to slope and x- or y-intercepts of a line. They will chain them together by finding the answer on the top one of the probFun and creative small group activity requires students to think critically about the characteristics of parent functions.
Students match 33 "personality" clues to the equations of six parent functions.
Includes answer key and a whole-class follow-up with full page large graphs--great as wall
This document is 184 pages long and has over 300 questions that can be used as review for the New York State Algebra Regents Exam. The questions are modeled after questions that have been asked on previous Common Core Regents Exams. Included in the file is an answer key, with detailed solutions to t
Students will:
-Identify key features of graphs of quadratic functions.
-Graph quadratic functions in standard form using a table of values.
-Graph quadratic functions from standard form by finding the axis of symmetry, vertex, and y-intercept.
Includes everything you need to teach this lesson in o
This is the second lesson in an eight-lesson unit on Functions and Graphs for students enrolled in Pre-Calculus Honors.
Students will be able to:
★ Find the domain and range of a function
★ Determine intervals on which the function is increasing, decreasing, or constant
★ Determin
This is a complete lesson plan for a double-period class. The lesson introduces a system of equations where one equation is quadratic and the other is linear. Students solve the system by graphing to find the point(s) where the graphs intersect.
There are several activities and examples to give stu
Interpreting FUNCTIONS
ASSESS EVERY STANDARD
Have you tried to find quick assessments for Common Core Algebra?
So have I!
After giving up the search, I made my own.
The result is this packet of ten formative assessments that cover the following standards; F.IFInt1, F.IF1, F.IF2, F.IF3, F.IF4,
There are two versions included in this product. Each version includes a page of graphs and a page with 16 cards with equations on them. The students will match the graph and the corresponding linear equation. The cards with the equations will be cut and there are 16 cards. Each card will be pla
Engage students in this exploration activity introducing the concept of exponential functions! Students will graph and write an exponential function from data, distinguish between linear and exponential functions, and reason quantitatively in the context of a fun real world problem.
Hook students w
Six stations provide practice in finding factors and roots of quadratic equations both a = 1 and a > 1. The stations require critical thinking, and involve working from factors, from roots, and from equations. The stations make a good review activity for solving quadratic equations by factoring
This is a complete lesson plan for a double-period class. The lesson continues from Pt. I with solving a system of equations where one equation is quadratic and the other is linear.
In this lesson, students use technology (graphing calculator) to solve systems. Students will also apply the solution
Included are two complete lesson plans for two double-period classes.
The first lesson introduces a system of equations where one equation is quadratic and the other is linear. Students solve the system by graphing to find the point(s) where the graphs intersect.
The second lesson continues from
Task-Based Learning gets students intrinsically motivated to learn math! No longer do you need to do a song and dance to get kids interested and excited about learning. The tasks included in this unit, followed by solidifying notes and practice activities, will guarantee that students understand t
Set includes 18 different daily warm ups, each with an answer key.
This set of warmups is great for review of the Algebra 1 Common Core standards each day. I have these waiting on the students' desks when they come in, and after a set amount of time we go over the answers together, usually with sev
This easy foldable covers 7 types of functions:
• Linear
• Constant
• Quadratic
• Exponential
• Absolute Value
• Square Root
• Cube Root
In this foldable students are matching the function name to a sample equation and a sample graph. It is a great study tool as well as a quick reference guide for
With Linear Function - Human Graphs you will get students to model graphs of linear functions with their bodies. This activity is designed where students draw, create, tape a coordinate axis and model their function with their bodies through solutions. It is able to be revised given your available | 677.169 | 1 |
Teachers of Primary Grades Teachers of Intermediate
Grades Teachers of Middle School or
Junior High Teachers of General Math or
Basic Math Teachers of Pre-Algebra Teachers of Special
Education Teachers of the
Hearing-Impaired Teachers of the
Visually-Impaired Teachers of Adult Education
Do you want to teach arithmetic in a way that will prepare
your students for algebra?
Do you want to learn how to use manipulatives (Dr. Henry
Borenson's Hands-On Equations®, Henri Picciotto's Algebra Lab Gear®, Eli's
magic and regular peanuts, four-quadrant graphs) to help your students develop
concepts that are essential to algebra?
Do you want to experience a Hands-On Math Lab in action?
Then you want to take the course
HANDS-ON ALGEBRA WORKSHOP
FOR TEACHERS
To receive 3 hours of graduate credit for this course, in-service
or pre-service teachers can pay $100 per credit hour to Webster University in
addition to the $234 tuition to St. Louis Community College at Meramec. The
registration for the Webster University graduate credit can be done in class at
Meramec.
Summer Session 2006 -
June 5 through July 27, 2006
Monday through Thursday
9:00 - 11:00 AM
Note:If you cannot start the course the week
of June 4, since the course is self-paced, you may start during the week of
June 11.Also, if you do not want
to spend all 8 weeks of the summer session taking a course, consider taking it
over two summers (You will pay the community college tuition both
summers.)Please feel free to
discuss various possibilities with the instructor
HANDS-ON ALGEBRA WORKSHOP
FOR TEACHERS
3 credit hours of graduate credit
This course is designed for teachers who want to be
effective in helping students understand algebra rather than merely memorizing
and applying the rules of algebra. It is held in the Hands-On Math Lab at St.
Louis Community College at Meramec where teachers in this course will usually
be working in the Lab along with adult students at the community college who
are seeking to truly understand algebra. Working individually and/or in small
groups on worksheets and problems, participants in this course will use various
math manipulatives (Hands-On Equations®, Algebra Lab Gear®, pegboards, magic
and regular peanuts, four-quadrant rectangular coordinate graphs, etc.) to
experience how students can use manipulatives to explore algebra concepts in
order to gain understanding of solving equations and inequalities, performing
operations on polynomials and graphing in the rectangular coordinate plane.
Students taking this graduate-level course will also participate in six
one-hour educational seminars relating their experiences in the Hands-On Math
Lab to relevant educational literature. In this Hands-On Math Lab course,
participants may proceed at their own pace, but students in this graduate-level
course must attend the six educational seminars which will take place during
the first six weeks of the course.
The instructor for the course may be one of the following
teachers:
Fran Endicott Armstrong has a bachelor's degree in Mathematics
from Fontbonne College and a Ph.D. in Mathematics Education from the University
of Pennsylvania and has over ten years experience teaching math in Grades 5
through 12. Fran has taught Methods of Teaching Mathematics in Elementary School
at Fontbonne College and has taught Pre-Algebra as well as Elementary,
Intermediate and College Algebra in the St. Louis Community College District.
She has given guest presentations to math classes in Grades 1 through 8.Fran is the Coordinator and Lead Mentor of
the Self-Paced Hands-On Math Lab at The Soulard School.
For more information, please contact Fran Armstrong in the
Mathematics Department at St. Louis Community College at Meramec (314-984-7769). | 677.169 | 1 |
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College Algebra and Trigonometry and Precalculus
McGraw-Hill. 1974. 0070428646 For the student who needs help in the sophomore statistics course in business or the social sciences, let me say first, that this site is far people with more advanced problems. By passing the ELM in high school, students won't have to pay additional testing fees and do expensive remedial coursework in college. These Trigonometry Worksheets are a great resource for children in 5th, 6th Grade, 7th Grade, and 8th Grade.
Pages: 930
Publisher: Pearson Higher Education (November 8, 2001)
ISBN: 0321068521
An Elementary Treatise on Trigonometry: With Its Different Applications
Key to Robinson's New Geometry and trigonometry, and conic sections and analytical geometry; With some additional astronomical problems. Designed for teachers and students
Student Solutions Manual
Elements of plane and spherical trigonometry : with the first principles of analytical geometry
Potato. Humorist/songwriter/math professor Tom Lehrer 's song "New Math" pokes fun at this attitude, especially the result of the 1960s attempt to introduce set theory in elementary school Math 121 Trigonometry at Diablo Valley College. "When you understand this animated diagram, you shall understand the sin(x)." Detailed explanations relating the basic trigonometric functions to the right triangle. Check their Point Definitions for Trig Functions page, where a dynamic graph shows the relationships between the unit circle graph and the standard graph and the right triangle definition of the trigonometric functions College Algebra and Trigonometry with MathXL (12-month access) (2nd Edition). Select the author and textbook title below to find the Browser Check and Installation. Setting Up Computer Labs Lab administrators or IT staff can use this page to install components for all MyMathLab courses taught in the lab. Note that it's advisable to check and reinstall components before the beginning of each semester. Tip: If you are setting up a lab for students using several MyMathLab courses, choose the "Administrators" option at the bottom of the list to conveniently access and install components Trigonometry (with CD-ROM, BCA/iLrn(TM) Tutorial, Personal Tutor, and InfoTrac) (Available Titles CengageNOW). And of course, don't miss the Uses of Trigonometry summary. Trigonometry is often referred to as the study of triangles, as, indeed, it is. Yet trigonometry also concerns itself with the relationships between angles in general. Measuring angles is the most fundamental skill of trigonometry. There are two units that are commonly used to measure angles: degrees and radians Trigonometry and Its Applications.
An Elementary Treatise on Trigonometry: With Its Different Applications
Plane Trigonometry 1ed
Student Solutions Manual Algebra and Trigonometry (3rd Edition)
A calculator is not permitted on the first part of the exam, but an online non-graphing calculator is available during the second part of the test Five-Place Logarithmic and Trigonometric Tables. The result is shown with the Text(-command, wich means that the built in >Frac can't be used. This program finds the exact values in trigonometric functions, like square root 2 over 2, square root 3 over 3, and so on. If you enter a value like 60 or pi/3, the program, regardless of what mode you are in, gives you the exact values for sine, cosine, and tangent, assuming that 60 is degrees and pi/3 is radians Seven Place Natural Trigonometrical Functions. Potato Algebra and Trigonometry, Annotated Instructor's Edition. Pioneer Mathematics skilled professionals and vigorous training will surely turn your IIT dream into a reality. Doubt Forum: A virtual teacher with you 24×7. IIT Model test papers: Latest papers of all chapters. IIT Sample test papers: Latest pattern designed Sample papers download College Algebra and Trigonometry and Precalculus pdf. � Chemistry Index � Gift Shop � Harry Potter DVDs, Videos, Books, Audio CDs and Cassettes � Lord of the Rings DVDs, Videos, Books, Audio CDs and Cassettes � Winnie-the-Pooh DVDs, Videos, Books, Audio CDs, Audio Cassettes and Toys � STAR WARS DVDs and VHS Videos The fundamental ideas needed to understand sines and cosines can be put into one graph, the unit circle: Here we have a circle of radius r = 1 (hence "unit circle"), a point (x, y) on that circle, and perpendiculars from the point to the x and y axes Plane and Spherical Trigonometry. In the manga adaptation of Yume Nikki, Madotsuki backs out of the Number World after commenting that she's bad with math A Text-Book On Advanced Algebra and Trigonometry, with Tables. Each triangle has six parts, three sides and three angles. If three of these are known including at least one side, the other three can be calculated using the two laws The Slide Rule As a Check in Trigonometry. It is a comic book of the FoxTrot newspaper comics. You can see it here: I have a copy of it and it is hilarious! Question:hey guys i am in 11 class and i cant understand trigonometry (ch 3 ) in starting of this chapter i found this prity good but somelater i cant understand anything. how can i get interest in trigo now. {its dont funny} Answers:hmmmmm.... serious problem. even i had faced the same bt as soon as u start understanding trigonometry with the help of diagrammatic view and solve problems by keeping a picture like representation of triangles, u will find it much interesting .just try n understand basics of trigno and then work out a lot of problems ,u will surely start loving trigonometry as i had.. College Algebra and Trigonometry 2nd (second) edition. Examples of these, together with a brief classification of the different kinds of regular solids, will be given later. Take a piece of fairly stout paper and fold it in two. Let AB, Fig. 28, be the line of the fold. Let BCDA, BEF A represent the two parts of the paper. These can be regarded as two separate planes. Starting with the two parts folded together, keeping one part fixed the other part can be rotated about AB into the position indicated by ABEF ALGEBRA & TRIGONOMETRY-CUSTOM EDITION FOR MORRISVILLE STATE COLLEGE. | 677.169 | 1 |
's
CONTENTS: This book is conveniently divided up into 9 chapters so that students can focus on one trigonometry skill at a time. Skills include the following:
review of the Pythagorean theorem and relevant properties of triangles;
understanding sine, cosine, and tangent;
special angles and special triangles;
working with the reference angle;
using the unit circle;
working in Quadrants II-IV;
finding secant, cosecant, and cotangent;
finding inverse trig functions;
and converting between degrees and radians.
ANSWERS: Answers to exercises are tabulated at the back of the book. This helps students develop confidence and ensures that students practice correct techniques, rather than practice making mistakes.
This series of math workbooks is geared toward practicing essential math skills. As a physics teacher, Dr. McMullen observed that many students lack fluency in fundamental math skills. In an effort to help students of all ages and levels master basic math skills, he published this series of math workbooks on arithmetic, fractions, algebra, trigonometry, and more. RELATED BOOKS IN THE IMPROVE YOUR MATH FLUENCY SERIES Trigonometry Essentials Practice Workbook with Answers. Practice essential skills, including conversion from degrees to radians, trig functions, special triangles, the reference angle, going beyond Quadrant I, inverse trig functions, the law of sines, the law of cosines, and trig identities. Each chapters begins with a short review, including examples. ISBN: 1477497781.
Learn or Review Trigonometry: Essential Skills. This book provides an introduction or review to the basic ideas, concepts, and skills of trigonometry with explanations and examples. ISBN: 194169103X. Trigonometry Flash Cards: Memorize the values of trig functions (sine, cosine, and tangent) from 0 to 360 degrees. Available on Kindle. ASIN: B0074EWAUS.
Algebra Essentials Practice Workbook with Answers. Practice essential skills like solving for unknowns, factoring, the quadratic formula, and substitution. Each section begins with a short review, including examples. ISBN: 1453661387.
Systems of Equations: Substitution, Simultaneous, Cramer's Rule. Practice solving systems of equations (two equations with two unknowns, or three equations with three unknowns). Includes 2x2 and 3x3 determinants. Each section begins with a short review, including examples. ISBN: 1941691048.
Basic Linear Graphing Skills Practice Workbook. Learn basic coordinate algebra graphing skills, including the four Quadrants, plotting points, finding slope, y-intercept, and the equation for a straight line. Each section begins with a short review, including examples. ISBN: 1941691056.
About the Author:
Chris McMullen is a physics instructor at Northwestern State University of Louisiana. He earned his Ph.D. in phenomenological high-energy physics (particle physics) from Oklahoma State University in 2002. Originally from California, he earned his Master's degree from California State University, Northridge, where his thesis was in the field of electron spin resonance. As a physics teacher, Dr. McMullen observed that many students lack fluency in fundamental math skills. In an effort to help students of all ages and levels master basic math skills, he has published this Improve Your Math Fluency Series of math workbooks on arithmetic, fractions, algebra, and trigonometry1941691038
Book Description Zishka Publishing, United States, 2015. Paperback. Book Condition: New. Large type / large print edition. Language: English . Brand New Book ***** Print on Demand *****. WHAT Zishka Publishing, United States, 2015. Paperback. Book Condition: New. Large type / large print edition. Language: English . Brand New Book ***** Print on Demand *****. chapter1941691038 | 677.169 | 1 |
infocobuild
Discrete Mathematics
Discrete Mathematics. Instructor: Prof. Sourav Chakraborty, Department of Computer Science, Chennai Mathematical Institute. In this course we will cover the basics of discrete mathematics. We will be learning about the different proof techniques and how to use them for solving different kind of problems. We will introduce graphs and see how graphs can be used for modeling of different problems and see how this can help in solving problems. We will learn how to count the number of possibilities that can arise in different situations.
(from nptel.ac.in) | 677.169 | 1 |
Single Variable Calculus (Paper): Chapters 1-12
What's the ideal balance? How can you make sure students get both the computational skills they need and a deep understanding of the significance of what they are learning? With your teaching—supported by Rogawski's Calculus, Second Edition—the most successful new calculus text in 25 years!
Widely adopted in its first edition, Rogawski's
Now Rogawski's's coverage of topics in single variable calculus.
Book Description W. H. Freeman, United States, 2011. Paperback. Book Condition: New. 2nd ed.. Language: English . This book usually ship within 10-15 business days and we will endeavor to dispatch orders quicker than this where possible. Brand New Book. What s the ideal balance? How can you make sure students get both the computational skills they need and a deep understanding of the significance of what they are learning? With your teaching--supported by Rogawski s Calculus, s coverage of topics in single variable calculus. Bookseller Inventory # BTE9781429231893 | 677.169 | 1 |
concepts, computational weaknesses, and computational language issues. If any of these issues plague you then seeking math coursework help online would be best for you.
Number Facts
Insufficient understanding of basic numeric concepts, for instance, the simple addition and subtraction, multiplication tables, is a prevalent issue for math students. Number concepts are fundamental for learning mathematics and are essential for deciphering more complicated topics. If a student cannot grasp a simple division or multiplication, he/she will be easily overwhelmed with even the simplest of math problems. To avoid any complications in your math assignment, it is suggested that you should consider do my coursework help services to assist you.
Computational drawbacks
Students might encounter computational inabilities while preparing their math homework and exams. Instances of computational drawbacks involve writing the incorrect number during division or multiplication, putting down the wrong number when calculating the outcome, or even misinterpreting particular signs and symbols. You need to remember that the professors offer marks for each question on using the right formula, mentioning the accurate calculations and coming up with the correct answer. Students who are prone to making computational errors lose marks on the paper. But this can be avoided; they choose to buy coursework online and maths coursework help.
Learning Difficulties
Learning or developmental disabilities are a common phenomenon among many students, especially in case of understanding mathematics. Students who are affected with a condition called Dyscalculia, for instance, have an issue with learning arithmetic and numbers. They have difficulty in identifying numbers and combining them with amounts, deciphering sequences and even making accurate assumptions. Such students might also have issues with understanding math concepts and processing the requirements of every math problem. For such students, it is advisable to look for coursework experts online.
Attention deficiencies
Students are required to provide their undivided attention while a math class is in progress and also when finishing homework and in exams to excel in math. Students who don't pay attention to the specific details and don't cross-check their work before submitting end up with a mediocre result at the end of the term. Memorizing rather than grasping mathematical concepts also poses difficulties for students, mainly when they are unable to follow the exact steps applied to solve a problem. This is why the students who practice mathematical problems regularly will be more adept at it than those who do not because they only memorize instead of learning to answer the sums methodically.
Being aware of your limitations will help you to work on them to produce better results. | 677.169 | 1 |
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.
Designed to foster understanding and mastery of mathematics in every student
ICE-EM Mathematics Third Edition is designed to develop a strong foundation in mathematics for every student in Years 5 to 10/10A, and now offers a new level of digital support for teaching, learning, assessment and reporting.
Developed by the Australian Mathematical Sciences Institute (AMSI), ICE-EM Mathematics helps students of all abilities to understand and master mathematics beyond the curriculum while building strong foundation skills.
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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.
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Cambridge Senior Mathematics for the Australian Curriculum Reactivation Codes
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.
We're pleased to bring you a number of videos that demonstrate the features of powered by Cambridge HOTmaths products. Each week, we'll highlight a new feature. This week we look at demos interactive widgets and tools
We're pleased to bring you a number of videos that demonstrate the features of powered by Cambridge HOTmaths products. Each week, we'll highlight a new feature. This week we look at widgets and walkthroughs | 677.169 | 1 |
The author demonstrates how to stretch math curricula across disciplines and make students aware that math is related to almost every area of life.
"synopsis" may belong to another edition of this title.
About the Author:
Hope Martin is an innovative mathematics teacher with over 40 years of experience. Having worked with children in elementary, middle school, and high school, and with teachers in local universities, she is currently a private consultant facilitating workshops across the United States and Canada. Hope, who was born and raised in the Bronx, New York, began her teaching career in Skokie, Illinois and obtained her Masters Degree in Mathematics Education from Northeastern Illinois University. Hope's personal experiences and knowledge of educational learning theories have convinced her that students learn mathematics more effectively when they are active participants and see its relevance to their own lives. | 677.169 | 1 |
Calculus BC
I. FUNCTIONS, GRAPHS, AND LIMITS
Parametric, polar, and vector functions. The analysis of planar curves includes those given in parametric form, polar form, and vector form
SE/TE: 531, 541, 545, 550, 557
II. DERIVATIVES
Applications of derivatives
—Analysis of planar curves given in paremetric form, polar form, and vector form, including velocity and acceleration vectors.
SE/TE: 221, 222, 224–227
—Numerical solution of differential equations using Euler's method
SE/TE: 326, 328, 326, 328, 329
—L'Hôpital's Rule, including its use in determining limits and convergence of improper integrals and series.
SE/TE: 446–448, 450, 451, 461
Computation of derivatives
—Derivatives of parametric, polar, and vector functions
SE/TE: 532, 535, 543, 545, 552
III. INTEGRALS
Applications of integrals. Appropriate integrals are used in a variety of applications to model physical, biological, or economic situations. Although only a sampling of applications can be included in any specific course, students should be able to adapt their knowledge and techniques to solve other similar application problems. Whatever applications are chosen, the emphasis is on using the integral of a rate up an approximating Riemann sum and representing its limit as a definite integral. To provide a common foundation, specific applications should include finding the area of a region (including a region bounded by polar curves), the volume of a solid with known cross sections, the average value of a function, the distance traveled by a particle along a line, and the length of a curve (including a curve given in parametric form.)
IV. POLYNOMIAL APPROXIMATIONS AND SERIES
Concept of series. A series is defined as a sequence of partial sums, and convergence is defined in terms of the limit of the sequence of partial sums. Technology can be used to explore convergence or divergence
SE/TE: 474, 481, 482
Series of constants
—Motivating examples, including decimal expansion
SE/TE: 474, 481, 482
—Geometric series with applications
SE/TE: 482
—The harmonic series
SE/TE: 514, 523
—Alternating series with error bound
SE/TE: 518, 523, 524
—Terms of series as areas of rectangles and their relationship to improper integrals, including the integral test and its use in testing the convergence of p– series. | 677.169 | 1 |
The aim of this course is to introduce, at an elementary level, a set of mathematical and algorithmic ideas rooted in geometry which are important in all branches of the computer science dealing with representations and manipulations of virtual physical objects. Included in this list is computer graphics, computer vision, robotics, computational structural biology, and sensor networks . The emphasis is on algorithms and data structures for modeling the shape and motion of physical objects, and more generally multi-dimensional data. The ideas are also important in other computational domains where geometric ideas play an important role, such as in machine learning, statistical data analysis, and databases. | 677.169 | 1 |
Are Complex Analysis and Complex Variables the same thing?
Is Complex Analysis and Complex Variables the same thing? Is Complex Analysis pure or applied math? Is Complex Variables pure or applied math? What's the prerequisite of Complex Analysis and Complex Variables? Are they useful for the field of computer science?
Both terms are probably referring to the same thing -- complex analysis. The subject can be either theoretical or applied, depending on what the class emphasis is. Complex analysis was developed to solve many physics and engineering problems. It is basic for understanding feedback control systems, ideal fluid flow (irrotational, incompressable), temperature distributions, electrostatic potentials, etc.
I am not aware of any direct applications to computer science. Electrical Engineering will almost certainly require it.
to do complex analysis, you need to understand continuity, integration theory, power series, and some plane topology. Some courses will try to teach all this in the course, but it helps to review your Riemann integration, and not just as antidifferentiation, but as limits of Riemann sums, especially applied to path integrals. It also helps to understand stereographic projection, e.g. lines and circles in the plane and their relation with circles on the sphere. One also usually makes more use of differentials, things like dz, dx, dy than in real calculus. And review your partial derivatives, and green's theorem from advanced calculus. Of course review algebra of complex numbers. | 677.169 | 1 |
I, Lecture 1 - The "Game" of Mathematics
Herb Gross introduces Calculus Revisited II - Functions of Several Variables - and discusses the overarching theme "The Game of Mathematics". A game has objectives, rules, and definitions as well as strategies (logical plans) for meeting the objectives of the game. A mathematical structure is identical with the objective being to model real-world experience. | 677.169 | 1 |
math principles Advice
Showing 1 to 3 of 7
I would recommend this course because it teachers math from the very beginning, which is very good because some people forget, and if you didn't forget it's okay because you will be reviewing old and new things, which will give you more math skills
Course highlights:
We learned basic math and also new math that were different, overall this class is super easy and easy to pass if you do your homework and turn in your work.
Hours per week:
3-5 hours
Advice for students:
To succed this class you have to make sure you get help when you don't understand a topic. Also make sure you turn in your homework and do your homework, and most importantly have a positive attitude
I would recommend this course to others because you review older math lessons and also learn new lessons on it. This class will help you increase your math skills and help you be better at it
Course highlights:
well am still in this class and right now we are basically starting from simple Algebra and moving on from that so that everyone learn what they can and cannot do.
Hours per week:
3-5 hours
Advice for students:
Study, Study and study tests are fairly easy all you have to do is do your part and also if you have any questions make sure you ask teachers, because if you don't ask questions then you will never get it which is not good
Course Term:Fall 2017
Professor:Slither
Course Required?Yes
Course Tags:Great Intro to the SubjectGo to Office HoursA Few Big Assignments
Apr 17, 2017
| Would highly recommend.
Pretty easy, overall.
Course Overview:
It teaches you so much about how to solve problems that might seem hard but breaking the problems down really helped me in the class.
Course highlights:
My highlights were learning all different types of math problems and undertstanding the material and not just writing down the answers.
Hours per week:
0-2 hours
Advice for students:
my tips are work hard and pay attention so you can learn the material better. | 677.169 | 1 |
GeometryNumbers and Geometry is a beautiful and relatively elementary account of a part of mathematics where three main fields—algebra, analysis, and geometry—meet. The aim of this book is to give a broad view of these subjects at the level of calculus, without being a calculus (or a pre-calculus) book." — From the back cover
"This book is designed for a one-quarter or one-semester graduate course on Riemannian geometry. It focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced study of Riemannian manifolds." — From the back cover
"These books are intended to introduce students to algebraic geometry; to give them a sense of the basic objects considered, the questions asked about them, and the sort of answers one can expect to obtain. It thus emphasizes the classical roots of the subject text gives a basic introduction and a unified approach to algebra and geometry. It covers the ideas of complex numbers, scalar and vector products, determinants, linear algebra, group theory, permutation groups, symmetry groups and various aspects of geometry including groups of isometries, rotations, and spherical geometry not a research monograph or a reference book (although research interests of the authors influenced it a lot)—this is a textbook. Its structure is similar to that of a graduate course." — From the Preface (page xi)
"The programmers of video games make heavy use of quaternions, as do the controllers of spacecraft, since in both these disciplines it is necessary to compose rotations with minimal computation. We have eschewed writing of these and other practical applications ..." — From the Preface (page xii)GEOMETRY, TOPOLOGY AND PHYSICS introduces the ideas and techniques of differential geometry and topology at a level suitable for postgraduate students and researchers in these fields." — From the back cover
"Designed for high school students and teachers with an interest in mathematical problem-solving, this volume offers a wealth of nonroutine problems in geometry that stimulate students to explore unfamiliar or little-known aspects of mathematics." — From the back cover | 677.169 | 1 |
Math Notebook Pages
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this file type before downloading and/or purchasing.
957 KB|16 pages
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Product Description
This bundle includes a variety of note pages that can be used during instruction. I have students keep all of their notes in a specific order in a composition book so they can refer to them whenever is necessary.
This includes note pages on the following concepts:
-Order of Operations
-Evaluating Expressions
-Fractions to Decimals
-Rates/Unit Rates
-Simplifying Rational Expressions
-Rational Expressions/Equations
-Slope Intercept Form
-Vertex Form
-Standard Form
-Changing Vertex Form to Standard Form
-Changing Standard Form to Vertex Form
-Piecewise Functions
-Characteristics of Graphs
-Even or Odd Functions | 677.169 | 1 |
Description
About the Book
"MTG's ORIGINAL MASPTERPIECE is a series of collection of books that started their journey as best sellers and continue as a chart-topper generation after generation. Even today these books are considered as a masterpiece among the teachers and students fraternity which is passionate about the subject. The USP of MTG's ORIGINAL MASTERPIECE Series lies in the fact that the work has been reproduced from the Original artifact and remains as true to the original work as possible.This book is a fairly complete elementary text-book on Plane Trigonometry, suitable for inter-college, secondary Schools and the Pass and Honours classes of Universities. In this book Trigonometry is presented in as simple way as it can be. As Trigonometry consists largely of formulae and the applications thereof, a list of the principal formulae which the student should commit to memory are given in the starting. More important formulae are distinguished in the text by changing the formatting attributes. This books starts with an excellent theory in trigonometry from the ground level, starting from measuring the angles. The concepts are explained directly and clearly. The books is divided in to 21 chapters. Each chapter is having basic concepts, preliminary level questions, followed by higher level questions marked by Asterisk. Hence, a selection only should be solved by the student on a first reading. Additionally, during first reading the articles marked with an asterisk should be omitted. Unsolved exercises at the end help in proper revision and checking the grasp on the topic.JEE Aspirants should read this book to have a good grasp on trigonometry which is useful in other topics like coordinate geometry, calculus, vector algebra etc. This book is the most reliable source of trigonometry even today | 677.169 | 1 |
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this file type before downloading and/or purchasing.
2 MB|8 pages
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Product Description
This product has four worksheets about real-life linear functions to be completed with interactive lecturing.
The worksheets are written around the theme of candy in which the idea is to buy two types of candy for a certain amount of money without getting change back.
The students complete a table showing how much of each type of candy can be purchased. The data in the table is later graphed, and there are questions about rate (slope) and a linear equation is developed in the third worksheet.
This series of worksheets was developed to give my Algebra students a real-life meaning to linear functions. | 677.169 | 1 |
Cubic Differentiation
Here, we have a collection of videos, activities and worksheets that are suitable for A Level Maths.
Differentiation - Graph of the derivative of a cubic function
Stationary Points and Nature
An example of finding the stationary points, their nature and sketch the given cubic function | 677.169 | 1 |
Student Solutions Manual to accompany Advanced Engineering Mathematics, 10e. The tenth edition of this bestselling
text includes examples in more detail and more applied exercises; both changes are aimed at making the material more relevant and accessible to readers. Kreyszig ...
This is a Student Solutions Manual for Introductory Statistics, 9th Edition. Introductory Statistics, 9th Edition
is written for a one or two semester first course in applied statistics and is intended for students who do not have a strong background ...
Introductory Statistics, 8th Edition is written for a one or two semester first course in
applied statistics and is intended for students who do not have a strong background in mathematics. The only prerequisite is knowledge of elementary algebra. Introductory ...
Practical Business Statistics, Sixth Edition, is a conceptual, realistic, andmatter-of-fact approach to managerial statistics that
carefully maintains–butdoes not overemphasize–mathematical correctness. The book offers a deepunderstanding of how to learn from data and how to deal with uncertainty ...
STATISTICS: THE EXPLORATION AND ANALYSIS OF DATA, 7th Edition introduces you to the study of
statistics and data analysis by using real data and attention-grabbing examples. The authors guide you through an intuition-based learning process that stresses interpretation and communication ...
WITH MODELING APPLICATIONS, 10th Edition INSTRUCTOR DESCRIPTION: This manual contains fully worked-out solutions to all
of the odd-numbered exercises in the text, giving students a way to check their answers and ensure that they took the correct steps to arrive ...
Prepare for exams and succeed in your mathematics course with this comprehensive solutions manual! Featuring
worked out-solutions to the problems in TOPICS IN CONTEMPORARY MATHEMATICS, 10th Edition, this manual shows you how to approach and solve problems using the same ...
This handy supplement shows students how to come to the answers shown in the back
of the text. It includes solutions to all of the odd numbered exercises. The text itself:In this second edition, master expositor Sheldon Ross has produced ... | 677.169 | 1 |
Got another child ready for geometry? Need a new set of worktexts, but not a new teacher's guide? Then get the LIFEPAC Geometry 10-Unit Set! These ten easy-to-use worktexts will give your student a full year of step-by-step lessons. Included in each worktext are concept reviews, self tests, and a removable teacher-administered test.
Ready to start teaching your tenth grader math? Get your student started in the study of geometry with the LIFEPAC Geometry Unit 1 Worktext! Geometric terms and the foundational principles of postulates and theorems are all explained in this clear, easy-to-understand worktext. Tests are included.
Logic, reasoning, and two-column and paragraph proofs are at the focus of the LIFEPAC Geometry Unit 2 Worktext! This consumable worktext offers easy-to-understand explanations and step-by-step instructions that will give your student the confidence that he needs to learn these geometric concepts! Tests are included.
Want to shape up your teen's knowledge of geometry angles? Not sure how to approach teaching this highschool-level math topic? Then get the LIFEPAC Geometry Unit 3 Worktext! This step-by-step, consumable worktext covers angles and parallels with helpful diagrams and easy-to-follow instructions. Tests are included.
Are you dreading each day's geometry lesson and thinking there's got to be a better way to help your tenth grader learn congruency? Then you need to check out the LIFEPAC Geometry Unit 4 Worktext! This consumable worktext's self-paced, easy-to-understand lessons will clearly explain this upper-level math topic to your teen! Tests are included.
What makes two polygons similar is answered in the LIFEPAC Geometry Unit 5 Worktext! This easy-to-follow, consumable worktext comes with helpful diagrams and clear lessons that show your teenager that geometry isn't so hard after all! Similar polygons, triangles, and right-angle geometry are all explained. Tests are included.
Stop going in circles with your student and put him on the right track with the LIFEPAC Geometry Unit 6 Worktext! This consumable worktext covers curved lines of circles, spheres, and other important geometrical shapes with easy-to-understand text and helpful instructions. Tests are included.
Continue building a solid understanding of geometry with the LIFEPAC Geometry Unit 7 Worktext! This homeschool worktext covers the geometrical concepts of construction and locus with easy-to-understand text and helpful illustrations that will keep you and your child interested and involved. Tests are included.
Want to teach your teen how to find area and volume? Not sure how to explain formulas clearly? Just get the LIFEPAC 10th Geometry Unit 8 Worktext! This slim, consumable worktext is packed with step-by-step lessons that cover how to find area of polygons, circles, and the surface area and volume of solid shapes! Tests are included.
Keep your tenth grader involved and excited about geometry to the very end with the LIFEPAC Geometry Unit 10 Worktext! This colorful, interesting worktext serves as a comprehensive review of the entire year. Topics reviewed include proofs, angles, area and volume, polygons, circles, and more. Tests are included.
Are you and your teen getting ready for geometry? Are you thinking you're going to need a good resource to get you through the year? Order the LIFEPAC Geometry Teacher's Guide! This convenient and comprehensive guide has everything you need for success. Included are answer keys for lessons and tests in Units 1-10. | 677.169 | 1 |
MATH6038: Week 2*Week 2*
After introductions, we looked at systems of linear equations and introduced the idea of writing them in augmented matrix form and simplifying using Gaussian Elimination. We will discuss how to determine if the linear system has a unique, infinite or no solution.
Week 3*
We will probably just do more examples of solving linear systems.
Maple Labs
Due to the large number of students attending the module MATH6038 Mathematics for Science 2.2, we will have to introduce a lab split starting this week, on Wednesday 17 February.
The following is the proposed schedule for Weeks 3, 5, 1*, 7, 9, 11:
Group 1 – Starts at 18:00 and Finishes at 20:50:
Wednesdays 18:00-19:05 – Maple Lab in room C219
Wednesdays 19:15-20.55 – Theory class in room C212
Group 2 – Starts at 19:15 and Finishes at 22:00:
Wednesdays 19:15-20.55 – Theory class in room C212
Wednesdays 20:55-22:00 – Maple Lab in room C214
Test 1
Test 1 will take place 6 April in Week 8.
Independent Learning: Exercises
You are supposed to be working outside of class and I am supposed to help you with this. Working outside of class means doing the exercises in the notes. Any work that is handed up will be corrected by me. Also you can ask me a question here on this site and I will answer it ASAP.
Questions you can do include (question 2 shouldn't be there):
P.20 Q. 1, 5, 6, 7. Harder questions are 8 and 9.
Student Resources
Please see the Student Resources tab on the top of this page for information on the Academic Learning Centre, etc.. | 677.169 | 1 |
Middle School Math Curriculum
ROOM 206 - Ms. Monika Klokocki
MATH The sixth grade program uses the Saxon Course 1 text. This program is both sequential and incremental in developing math concepts. Major strands include: relating math to real life situations; performing basic operations with whole numbers, fractions, decimals, and integers; working with open equations; using estimation and mental math skills; developing math terminology and introducing algebraic and geometry concepts.
The seventh and eighth grade programs use the Glencoe Algebra 1 and Algebra 1 (2012) texts. The series is designed to prepare the students for middle school school mathematics. Major strands include: reviewing and reinforcing concepts taught in prior grades; translating word problems into equations; becoming familiar with calculator usage; developing algebraic concepts and methods; simplifying polynomials; identifying and using mathematical properties; graphing equations on the coordinate plane and simplifying expressions and equations.
The Staff
Miss Klokocki is a graduate of Northeastern Illinois University. She earned her Bachelor of Arts degree in Elementary and Middle Level Education, with a minor in Math & Science Concepts, which includes endorsements in all four core subjects, plus English as a Second Language(ESL). She is a native born Polish speaker. She welcomes any student to challenge and best her in Lord of the Rings and Hobbit trivia. This is her 3rd year at St. Al's. | 677.169 | 1 |
"Partial Differential Equations for Engineers and Scientists" presents various well known mathematical techniques such as variable of separable method, integral transform techniques and Green's R&D organisations would find the book to be most useful. | 677.169 | 1 |
この図書・雑誌をさがす
注記
Includes bibliographical references (p. [239]-240) and indexes
内容説明・目次
巻冊次
: softcover ISBN 9783764367923
内容説明
In algebra, an entity is called linear if it can be expressed in terms of addition, and multiplication by a scalar; a linear expression is a sum of scalar multiples of the entities under consideration. Also, an operation is called linear if it preserves addition, and multiplication by a scalar. For example, if A and Bare 2 x 2 real matrices, v is a (row) vector in the real plane, and c is a real number, then v(A + B) = vA + vB and (cv)A = c(vA), that is, the process of applying a matrix to a vector is linear. Linear Algebra is the study of properties and systems which preserve these two operations, and the following pages present the basic theory and results of this important branch of pure mathematics. There are many books on linear algebra in the bookshops and libraries of the world, so why write another? A number of excellent texts were written about fifty years ago (see the bibliography); in the intervening period the 'style' of math- ematical presentation has changed. Also, some of the more modern texts have concentrated on applications both inside and outside mathematics. There is noth- ing wrong with this approach; these books serve a very useful purpose. But linear algebra contains some fine pure mathematics and so a modern text taking the pure mathematician's viewpoint was thought to be worthwhile.
Linear algebra is one of the most important branches of mathematics - important because of its many applications to other areas of mathematics, and important because it contains a wealth of ideas and results which are basic to pure mathematics. This book gives an introduction to linear algebra, and develops and proves its fundamental properties and theorems taking a pure mathematical approach - linear algebra contains some fine pure mathematics. Its main topics include: vector spaces and algebras, dimension, linear maps, direct sums, and (briefly) exact sequences; matrices and their connections with linear maps, determinants (properties proved using some elementary group theory), and linear equations; Cayley-Hamilton and Jordan theorems leading to the spectrum of a linear map - this provides a geometric-type description of these maps; Hermitian and inner product spaces introducing some metric properties (distance, perpendicularity etc.) into the theory, also unitary and orthogonal maps and matrices; applications to finite fields, mathematical coding theory, finite matrix groups, the geometry of quadratic forms, quaternions and Cayley numbers, and some basic group representation theory; and, a large number of examples, exercises and problems are provided.
It gives answers and/or sketch solutions to all of the problems in an appendix -some of these are theoretical and some numerical, both types are important. No particular computer algebra package is discussed but a number of the exercises are intended to be solved using one of these packages chosen by the reader. The approach is pure-mathematical, and the intended readership is undergraduate mathematicians, also anyone who requires a more than basic understanding of the subject. This book will be most useful for a 'second course' in linear algebra, that is for students that have seen some elementary matrix algebra. But as all terms are defined from scratch, this book can be used for a 'first course' for more advanced students. | 677.169 | 1 |
Explorations in College Algebra, 5th Edition is designed to make algebra interesting and relevant to the student. The text adopts a problem-solving approach that motivates readers goal of Explorations in College Algebra, 5th Edition is to prepare students for future advanced mathematics or other quantitatively based courses, while encouraging them to appreciate and use the power of algebra in answering questions about the world around us. Access to WileyPLUS sold separately. This book usually ship within 10-15 business days and we will endeavor to dispatch orders quicker than this where possible. BZV9780470917619 | 677.169 | 1 |
Hello people ! I need some urgent help! I have had many problems with math lately. I mostly have difficulties with ti-84 quadratic program. I don't understand it at all, no matter how much I try. I would be very glad if anyone would give me some help on this matter .
It seems like you are not the only one encountering this problem. A friend of mine was in the same situation last month. That is when he came across this program known as Algebrator. It is by far the best and cheapest piece of software that can help you with problems on ti-84 quadratic program. It won't just solve problems but also give a step by step explanation of how it arrived at that solution.
Even I've been through that phase when I was trying to figure out a solution to certain type of questions pertaining to trinomials and scientific notation. But then I found this piece of software and it was almost like I found a magic wand. In the blink of an eye it would solve even the most difficult questions for you. And the fact that it gives a detailed and elaborate explanation makes it even more useful . It's a must buy for every math student.
Wow, that's amazing news ! I was so afraid but now I am quite thrilled that I will be able to improve upon my grades! Thank you for the info guys! So then I just have to get the software and do my homework for tomorrow. Where can I find out more about it and buy it?
Algebrator is a user friendly product and is certainly worth a try. You will also find many interesting stuff there. I use it as reference software for my math problems and can swear that it has made learning math much more enjoyable. | 677.169 | 1 |
Hi, I am a freshman in high school and I am having trouble with my homework. One of my problems is dealing with algebra word problems for 5th grade; can anyone help me understand what it is all about? I need to complete this asap. Thanks for helping.
The best way to get this done is using Algebrator . This software provides a very fast and easy to learn technique of doing math problems. You will definitely start liking math once you use and see how simple it is. I remember how I used to have a tough time with my Basic Math class and now with the help of Algebrator, learning is so much fun. I am sure you will get help with algebra word problems for 5th grade problems here.
Algebrator is the perfect math tool to help you with projects. It covers everything you need to be familiar with in exponential equations in an easy and comprehensive manner . algebra had never been easy for me to grasp but this software made it very easy to comprehend . The logical and step-by–step approach to problem solving is really a boon and soon you will discover that you love solving problems.
I am a regular user of Algebrator. It not only helps me finish my assignments faster, the detailed explanations given makes understanding the concepts easier. I strongly suggest using it to help improve problem solving skills. | 677.169 | 1 |
What a fantastic question, but also a fantastic course that you may be considering.
Firstly, i'd like to say that your question is slightly controversial. This is because it may vary from each University, but of course there will be a mimimum amount required. As it is based off complex calculations it is recommended that you have a strong capability in maths to make the course easier to cope with.
Yes, maths is prerequisite and indicator that you can think logically and develop your ability to do this. This is why CS courses require excellent maths score as an indicator of aptitude. Problem solving is logical reasoning. If you cannot solve problems then you are useless unfortunately.
In first year you had a specifically pure maths module that was a mix of a A level math with further maths. Complex numbers, calculus and that sort of thing. With other modules generally just requiring a good basis in GCSE arithmetic and set theory.
Second year the maths becomes more applied. Where you learn maths specifically for CS. Like how to solve problems in uniform ways that a computer could. Like Gaussian elimination where you solve an arbitrary amount simultaneous equations using a set algorithm along with a crap ton of vector math (matrices, intersecting planes with lines/other planes), advanced number set theory, probability and a whole bunch of theorems proving various things (e.g. Proving there are uncomputable numbers and cardinality of infinite sets .etc). The other modules become more dependant on math, requiring again a solid basis in set theory, it's notations along with languages and grammars (For models of computation and compiler theory) and lambda calculus for functional programming.
The specifically maths based modules are pretty intense but the others just require a good basis of math to describe algorithms.
(Original post by RichE)
That can probably only be answered by someone at the uni. Is there an enquiry line/admissions person you can write to?
As you've posted that you're quite taken with Kingston, then you might also consider what your options might be if CS does turn out to be too mathematical once there - is it easy enough to change to an IT or Software Engineering course for example that would be less mathematical?
(Original post by tonyhawken)Just so people are aware - I have programming experience, and can (to an extent) think logically, however my maths skills are very poor (I have dyscalcula so for example 12 to me looks like 21 which gives me all sorts of problems). At least I know Kingston doesn't have too much maths in it's modules, and the modules that have maths aren't too in-depth correct?
While we're on the topic, does anyone know where I could study more programming and less of the other stuff which is highly maths related? | 677.169 | 1 |
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Math 101: PACE Mathematical Foundations MOOC
Starts July 17, 2017 (continuous enrollment)
The PACE Mathematical Foundations MOOC is an online course designed to enhance your mathematics skills
in the areas of Algebra, Geometry, Number Theory, Probability and Statistics. This MOOC, offered by
the School of Professional and Career Education (PACE), is designed to help develop the skills needed
to be successful in college-level mathematics. Other aspects of the Math MOOC include access to instructional
videos and discussion forums with other MOOC participants. This free course does not carry credits and
will not be recorded on a Barry University transcript.
Course Learning Objectives
This course is a review of basic mathematics skills. The learning objectives of this course include
the ability to successfully complete the following with 70% accuracy:
Operations on the Real Number line, including absolute value
Addition, subtraction, multiplication and division of Real Numbers
Problems involving Natural Number factors
Operations involving exponents and square roots
Simplification of mathematical expressions and solutions to linear equations
Introductory geometric problems
Introductory statistical problems
Elementary probability questions
The course is designed to gauge the learner's mastery of mathematics. The student may simply elect to
test their mathematical skills by taking the pre-test. For the learner who continues in the course,
there are eight modules, with each of them providing demonstrations and self-assessment activities.
The course is concluded with a multiple-choice final exam. Successful completion of the pre-test or
the final exam will result in a certificate of completion for the student.
PACE Students
The certificate will be accepted in the School of Professional And Career Education (PACE) at Barry
University as satisfactory completion of the PACE Mathematics Skills Placement Assessment. Students
should present a copy of their certificate of completion to their PACE advisor as soon as it is issued
or at the time of application.
School of Professional And Career Education
Carol Warner, Ph.D.
Associate Professor of Mathematics
Dr. Carol Warner is the Mathematics Coordinator for PACE and Associate Professor of Mathematics. She
also serves as the Alpha Chi Honor Society moderator. She joined Barry in 2009, after 17 years with
the University of Arkansas system, where she was very active. She helped change the climate of her campus
through years of innovative statistical student surveys. She chaired many faculty committees, sponsored
numerous student organizations – including the Organization of Adult and Returning Students, and won
the Master Teacher of the Year award in 2006. Warner has been involved in community service on every
level. She was a volunteer for Habitat for Humanity, the United Way, Meals on Wheels, Girl Scouts, the
Adolescent Pregnancy Clinic, Project Compassion, the American Cancer Society, the Chamber of Commerce
and the Red Cross. She was a founding board member of the Single Parent Scholarship program, designed
websites for local non-profits, helped coordinate the community arts festival, provided guided tours
of historical homes, and was an invited motivational speaker for the Women's Crisis Center. Warner is
currently a sustaining member of the Junior League of the Palm Beaches, and volunteers at the Kravis
Center and at the Peggy Adams Animal Rescue League. A Phi Beta Kappa and recipient of the Fulbright
Senior Scholar award, Warner earned her doctorate in 2005. Her area of expertise is math anxiety and
factors influencing the success of mathematics students.
Rationale for the MOOC
NOTE: This course is non-credit and cannot be used to satisfy requirements in any curriculum at Barry
University.
The principal trouble for math-averse students is that success in certain mathematical courses -- college
math and statistics in particular -- is often necessary for continued education at the post-secondary
level. Put simply, students who have a hard time doing math may also have a hard time continuing to
the upper division and completing their degree requirements.
Developmental math classes are available for students who struggle with the pace or methodology of conventional
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While open to anyone interested in refreshing math skills, this course is designed primarily for new
or current college students, particularly those who have not completed their college math requirement.
It will provide math refresher materials covering a wide range of mathematical concepts.
New college students, or current students with expired math prerequisites, are typically placed in college
math courses based on placement exam scores. Students often take these placement exams with minimal
preparation or after a long break since their last math class. The study materials in the course, and
the tips for success, will help students prepare for placement exams. Higher scores mean fewer required
math courses in college. | 677.169 | 1 |
4 Preface Here are my online notes for my Algebra course that I teach here at Lamar University, although I have to admit that it s been years since I last taught this course. At this point in my career I mostly teach Calculus and Differential Equations. Despite the fact that these are my class notes, they should be accessible to anyone wanting to learn Algebra or needing a refresher for algebra. I ve tried to make the notes as self contained as possible and do not reference any book. However, they do assume that you ve had some exposure to the basics of algebra at some point prior to this. While there is some review of exponents, factoring and graphing it is assumed that not a lot of review will be needed to remind you how these topics work. Here are a couple of warnings to my students who may be here to get a copy of what happened on a day that you missed.. Because I wanted to make this a fairly complete set of notes for anyone wanting to learn algebra I have included some material that I do not usually have time to cover in class and because this changes from semester to semester it is not noted here. You will need to find one of your fellow class mates to see if there is something in these notes that wasn t covered in class.. Because I want these notes to provide some more examples for you to read through, I don t always work the same problems in class as those given in the notes. Likewise, even if I do work some of the problems in here I may work fewer problems in class than are presented here. 3. Sometimes questions in class will lead down paths that are not covered here. I try to anticipate as many of the questions as possible in writing these up, but the reality is that I can t anticipate all the questions. Sometimes a very good question gets asked in class that leads to insights that I ve not included here. You should always talk to someone who was in class on the day you missed and compare these notes to their notes and see what the differences are. 4. This is somewhat related to the previous three items, but is important enough to merit its own item. THESE NOTES ARE NOT A SUBSTITUTE FOR ATTENDING CLASS!! Using these notes as a substitute for class is liable to get you in trouble. As already noted not everything in these notes is covered in class and often material or insights not in these notes is covered in class. 007 Paul Dawkins iii
5 Outline Here is a listing of all the material that is currently available in these notes. Preliminaries Solving Equations and Inequalities Solutions and Solution Sets We introduce some of the basic notation and ideas involved in solving in this section. Linear Equations In this section we will solve linear equations, including equations with rational expressions. Applications of Linear Equations We will take a quick look at applications of linear equations in this section. Equations With More Than One Variable Here we will look at solving equations with more than one variable in them. Quadratic Equations, Part I In this section we will start looking at solving quadratic equations. We will look at factoring and the square root property in this section. Quadratic Equations, Part II We will finish up solving quadratic equations in this section. We will look at completing the square and quadratic formula in this section. Quadratic Equations : A Summary We ll give a procedure for determining which method to use in solving quadratic equations in this section. We will also take a quick look at the discriminant. Applications of Quadratic Equations Here we will revisit some of the applications we saw in the linear application section, only this time they will involve solving a quadratic equation. Equations Reducible to Quadratic Form In this section we will solve equations that can be reduced to quadratic in form. Equations with Radicals Here we will solve equations with square roots in them. 007 Paul Dawkins iv
6 Linear Inequalities We will start solving inequalities in this section by looking at linear inequalities. Polynomial Inequalities In this section we will look at solving inequalities that contain polynomials. Rational Inequalities Here we will solve inequalities involving rational expressions. Absolute Value Equations We will officially define absolute value in this section and solve equations that contain absolute value. Absolute Value Inequalities We will solve inequalities that involve absolute value in this section. Graphing and Functions Graphing In this section we will introduce the Cartesian coordinate system and most of the basics of graphing equations. Lines Here we will review the main ideas from the study of lines including slope and the special forms of the equation of a line. Circles We will look at the equation of a circle and graphing circles in this section. The Definition of a Function We will discuss the definition of a function in this section. We will also introduce the idea of function evaluation. Graphing Functions In this section we will look at the basics of graphing functions. We will also graph some piecewise functions in this section. Combining functions Here we will look at basic arithmetic involving functions as well as function composition. Inverse Functions We will define and find inverse functions in this section. Common Graphs Lines, Circles and Piecewise Functions This section is here only to acknowledge that we ve already talked about graphing these in a previous chapter. Parabolas We ll be graphing parabolas in this section. Ellipses In this section we will graph ellipses. Hyperbolas Here we will be graphing hyperbolas. Miscellaneous Functions In this section we will graph a couple of common functions that don t really take all that much work to so. We ll be looking at the constant function, square root, absolute value and a simple cubic function. Transformations We will be looking at shifts and reflections of graphs in this section. Collectively these are often called transformations. Symmetry We will briefly discuss the topic of symmetry in this section. Rational Functions In this section we will graph some rational functions. We will also be taking a look at vertical and horizontal asymptotes. Polynomial Functions Dividing Polynomials We ll review some of the basics of dividing polynomials in this section. Zeroes/Roots of Polynomials In this section we ll define just what zeroes/roots of polynomials are and give some of the more important facts concerning them. Graphing Polynomials Here we will give a process that will allow us to get a rough sketch of some polynomials. Finding Zeroes of Polynomials We ll look at a process that will allow us to find some of the zeroes of a polynomial and in special cases all of the zeroes. Partial Fractions In this section we will take a look at the process of partial fractions and finding the partial fraction decomposition of a rational expression. 007 Paul Dawkins v
7 Exponential and Logarithm Functions Exponential Functions In this section we will introduce exponential functions. We will be taking a look at some of the properties of exponential functions. Logarithm Functions Here we will introduce logarithm functions. We be looking at how to evaluate logarithms as well as the properties of logarithms. Solving Exponential Equations We will be solving equations that contain exponentials in this section. Solving Logarithm Equations Here we will solve equations that contain logarithms. Applications In this section we will look at a couple of applications of exponential functions and an application of logarithms. Systems of Equations Linear Systems with Two Variables In this section we will use systems of two equations and two variables to introduce two of the main methods for solving systems of equations. Linear Systems with Three Variables Here we will work a quick example to show how to use the methods to solve systems of three equations with three variables. Augmented Matrices We will look at the third main method for solving systems in this section. We will look at systems of two equations and systems of three equations. More on the Augmented Matrix In this section we will take a look at some special cases to the solutions to systems and how to identify them using the augmented matrix method. Nonlinear Systems We will take a quick look at solving nonlinear systems of equations in this section. 007 Paul Dawkins vi
8 Preliminaries Introduction The purpose of this chapter is to review several topics that will arise time and again throughout this material. Many of the topics here are so important to an Algebra class that if you don t have a good working grasp of them you will find it very difficult to successfully complete the course. Also, it is assumed that you ve seen the topics in this chapter somewhere prior to this class and so this chapter should be mostly a review for you. However, since most of these topics are so important to an Algebra class we will make sure that you do understand them by doing a quick review of them here. Exponents and polynomials are integral parts of any Algebra class. If you do not remember the basic exponent rules and how to work with polynomials you will find it very difficult, if not impossible, to pass an Algebra class. This is especially true with factoring polynomials. There are more than a few sections in an Algebra course where the ability to factor is absolutely essential to being able to do the work in those sections. In fact, in many of these sections factoring will be the first step taken. It is important that you leave this chapter with a good understanding of this material! If you don t understand this material you will find it difficult to get through the remaining chapters. Here is a brief listing of the material covered in this chapter. 007 Paul Dawkins
9 Integer Exponents We will start off this chapter by looking at integer exponents. In fact, we will initially assume that the exponents are positive as well. We will look at zero and negative exponents in a bit. Let s first recall the definition of exponentiation with positive integer exponents. If a is any number and n is a positive integer then, n a = a a a a So, for example, n times 5 3 = = 43 We should also use this opportunity to remind ourselves about parenthesis and conventions that we have in regards to exponentiation and parenthesis. This will be particularly important when dealing with negative numbers. Consider the following two cases. 4 4 and These will have different values once we evaluate them. When performing exponentiation remember that it is only the quantity that is immediately to the left of the exponent that gets the power. In the first case there is a parenthesis immediately to the left so that means that everything in the parenthesis gets the power. So, in this case we get, 4 = = 6 In the second case however, the is immediately to the left of the exponent and so it is only the that gets the power. The minus sign will stay out in front and will NOT get the power. In this case we have the following, 4 4 = = = 6= 6 We put in some extra parenthesis to help illustrate this case. In general they aren t included and we would write instead, 4 = = 6 The point of this discussion is to make sure that you pay attention to parenthesis. They are important and ignoring parenthesis or putting in a set of parenthesis where they don t belong can completely change the answer to a problem. Be careful. Also, this warning about parenthesis is not just intended for exponents. We will need to be careful with parenthesis throughout this course. Now, let s take care of zero exponents and negative integer exponents. In the case of zero exponents we have, 0 a = provided a 0 0 Notice that it is required that a not be zero. This is important since 0 is not defined. Here is a quick example of this property. ( 68) 0 = 007 Paul Dawkins
10 We have the following definition for negative exponents. If a is any non-zero number and n is a positive integer (yes, positive) then, n a = n a Can you see why we required that a not be zero? Remember that division by zero is not defined and if we had allowed a to be zero we would have gotten division by zero. Here are a couple of quick examples for this definition, 3 5 = = ( 4) = = = Here are some of the main properties of integer exponents. Accompanying each property will be a quick example to illustrate its use. We will be looking at more complicated examples after the properties. Properties n m n m. aa = a + Example : a a = a = a a n. m nm 7 3 ( 7)( 3) = a Example : ( a ) = a = a n m n a a 3. =, a 0 m a m n a Example : 4 a 4 7 = a = a a 4 a = = = a 4 7 a a a 7 4. n n n ab = a b Example : ab = a b n n a a 5. =, b 0 n b b Example : 8 8 a a = b b 8 6. n n n a b b = = b a a n Example : a b b = = b a a 0 7. ( ab) n = Example : n ( ab) ( ab) 0 = ( ab) n a n a = Example : a b n b a m = Example : m n = a a b a b a 6 7 = Paul Dawkins 3
11 ab 0. k ( ) = a b Example : ( ab ) = a b = a b n m nk mk n k a m = b a b nk mk Example : 6 6 a a a = ( 5) = b b b 5 0 Notice that there are two possible forms for the third property. Which form you use is usually dependent upon the form you want the answer to be in. Note as well that many of these properties were given with only two terms/factors but they can be extended out to as many terms/factors as we need. For example, property 4 can be extended as follows. n n n n n abcd = a b c d We only used four factors here, but hopefully you get the point. Property 4 (and most of the other properties) can be extended out to meet the number of factors that we have in a given problem. There are several common mistakes that students make with these properties the first time they see them. Let s take a look at a couple of them. Consider the following case. Correct : a ab = a = b b Incorrect : ab ab In this case only the b gets the exponent since it is immediately off to the left of the exponent and so only this term moves to the denominator. Do NOT carry the a down to the denominator with the b. Contrast this with the following case. ( ab) = ( ab) In this case the exponent is on the set of parenthesis and so we can just use property 7 on it and so both the a and the b move down to the denominator. Again, note the importance of parenthesis and how they can change an answer! Here is another common mistake. a Correct : = = a a 3 5 Incorrect : 3a 5 3a In this case the exponent is only on the a and so to use property 8 on this we would have to break up the fraction as shown and then use property 8 only on the second term. To bring the 3 up with the a we would have needed the following Paul Dawkins 4
12 ( 3 ) = 5 a ( 3a) 5 Once again, notice this common mistake comes down to being careful with parenthesis. This will be a constant refrain throughout these notes. We must always be careful with parenthesis. Misusing them can lead to incorrect answers. Let s take a look at some more complicated examples now. Example Simplify each of the following and write the answers with only positive exponents. 4 5 (a) ( 4x y ) 3 [Solution] (b) ( 0z y ) (c) [Solution] n m 4 3 7m n 5x y 4 (d) 3y 5 z (e) z x zy [Solution] 5 9 [Solution] x 6 [Solution] 3 8 4ab (f) 5 [Solution] 6a b Solution Note that when we say simplify in the problem statement we mean that we will need to use all the properties that we can to get the answer into the required form. Also, a simplified answer will have as few terms as possible and each term should have no more than a single exponent on it. There are many different paths that we can take to get to the final answer for each of these. In the end the answer will be the same regardless of the path that you used to get the answer. All that this means for you is that as long as you used the properties you can take the path that you find the easiest. The path that others find to be the easiest may not be the path that you find to be the easiest. That is okay. Also, we won t put quite as much detail in using some of these properties as we did in the examples given with each property. For instance, we won t show the actual multiplications anymore, we will just give the result of the multiplication. 4x y For this one we will use property 0 first. 4x y = 4 x y 4 5 (a) Don t forget to put the exponent on the constant in this problem. That is one of the more common mistakes that students make with these simplification problems. 007 Paul Dawkins 5
13 At this point we need to evaluate the first term and eliminate the negative exponent on the second term. The evaluation of the first term isn t too bad and all we need to do to eliminate the negative exponent on the second term is use the definition we gave for negative exponents y ( 4x y ) = 64 y = x x We further simplified our answer by combining everything up into a single fraction. This should always be done. The middle step in this part is usually skipped. All the definition of negative exponents tells us to do is move the term to the denominator and drop the minus sign in the exponent. So, from this point on, that is what we will do without writing in the middle step (b) ( 0z y ) zy In this case we will first use property 0 on both terms and then we will combine the terms using property. Finally, we will eliminate the negative exponents using the definition of negative exponents ( 0z y ) ( z y) = ( 0) z y z y = 00z y = 3 z y There are a couple of things to be careful with in this problem. First, when using the property 0 on the first term, make sure that you square the -0 and not just the 0 (i.e. don t forget the minus sign ). Second, in the final step, the 00 stays in the numerator since there is no negative exponent on it. The exponent of - is only on the z and so only the z moves to the denominator. (c) n m 4 3 7m n This one isn t too bad. We will use the definition of negative exponents to move all terms with negative exponents in them to the denominator. Also, property 8 simply says that if there is a term with a negative exponent in the denominator then we will just move it to the numerator and drop the minus sign. So, let s take care of the negative exponents first. 4 3 n m mnm = 4 3 7m n 7n Now simplify. We will use property to combine the m s in the numerator. We will use property 3 to combine the n s and since we are looking for positive exponents we will use the first form of this property since that will put a positive exponent up in the numerator. 5 n m mn = 4 3 7m n 7 Again, the 7 will stay in the denominator since there isn t a negative exponent on it. It will NOT 007 Paul Dawkins 6
14 move up to the numerator with the m. Do not get excited if all the terms move up to the numerator or if all the terms move down to the denominator. That will happen on occasion. 5x 3y y (d) x This example is similar to the previous one except there is a little more going on with this one. The first step will be to again, get rid of the negative exponents as we did in the previous example. Any terms in the numerator with negative exponents will get moved to the denominator and we ll drop the minus sign in the exponent. Likewise, any terms in the denominator with negative exponents will move to the numerator and we ll drop the minus sign in the exponent. Notice this time, unlike the previous part, there is a term with a set of parenthesis in the denominator. Because of the parenthesis that whole term, including the 3, will move to the numerator. Here is the work for this part. ( 3y ) ( y ) 5x y y 45y = = = x xy x xy x x z (e) z x There are several first steps that we can take with this one. The first step that we re pretty much always going to take with these kinds of problems is to first simplify the fraction inside the parenthesis as much as possible. After we do that we will use property 5 to deal with the exponent that is on the parenthesis z zx x x = 5 = 3 = 8 z x z z z In this case we used the second form of property 3 to simplify the z s since this put a positive exponent in the denominator. Also note that we almost never write an exponent of. When we have exponents of we will drop them ab (f) 5 6a b This one is very similar to the previous part. The main difference is negative on the outer exponent. We will deal with that once we ve simplified the fraction inside the parenthesis ab 4aa 4a 5 = 8 = 9 6a b bb b Now at this point we can use property 6 to deal with the exponent on the parenthesis. Doing this gives us, 007 Paul Dawkins 7
15 ab b b = = 6a b 4a 6a Before leaving this section we need to talk briefly about the requirement of positive only exponents in the above set of examples. This was done only so there would be a consistent final answer. In many cases negative exponents are okay and in some cases they are required. In fact, if you are on a track that will take you into calculus there are a fair number of problems in a calculus class in which negative exponents are the preferred, if not required, form. 007 Paul Dawkins 8
16 Rational Exponents Now that we have looked at integer exponents we need to start looking at more complicated exponents. In this section we are going to be looking at rational exponents. That is exponents in the form m n b where both m and n are integers. We will start simple by looking at the following special case, n b where n is an integer. Once we have this figured out the more general case given above will actually be pretty easy to deal with. Let s first define just what we mean by exponents of this form. n n a= b is equivalent to a = b n In other words, when evaluating b we are really asking what number (in this case a) did we n raise to the n to get b. Often b is called the n th root of b. Let s do a couple of evaluations. Example Evaluate each of the following. (a) (b) (c) 5 [Solution] 5 3 [Solution] 4 8 [Solution] (d) ( 8) 3 [Solution] (e) ( 6) 4 [Solution] (f) 6 4 [Solution] Solution When doing these evaluations we will do actually not do them directly. When first confronted with these kinds of evaluations doing them directly is often very difficult. In order to evaluate these we will remember the equivalence given in the definition and use that instead. We will work the first one in detail and then not put as much detail into the rest of the problems. 5 (a) So, here is what we are asking in this problem. 5 =? 007 Paul Dawkins 9
17 Using the equivalence from the definition we can rewrite this as,? = 5 So, all that we are really asking here is what number did we square to get 5. In this case that is (hopefully) easy to get. We square 5 to get 5. Therefore, 5 = (b) So what we are asking here is what number did we raise to the 5 th power to get 3? = because = (c) What number did we raise to the 4 th power to get 8? = 3 because 3 = 8 (d) ( 8) 3 We need to be a little careful with minus signs here, but other than that it works the same way as the previous parts. What number did we raise to the 3 rd power (i.e. cube) to get -8? (e) ( 6) = because = 8 3 This part does not have an answer. It is here to make a point. In this case we are asking what number do we raise to the 4 th power to get -6. However, we also know that raising any number (positive or negative) to an even power will be positive. In other words, there is no real number that we can raise to the 4 th power to get -6. Note that this is different from the previous part. If we raise a negative number to an odd power we will get a negative number so we could do the evaluation in the previous part. As this part has shown, we can t always do these evaluations. (f) 6 4 Again, this part is here to make a point more than anything. Unlike the previous part this one has an answer. Recall from the previous section that if there aren t any parentheses then only the part immediately to the left of the exponent gets the exponent. So, this part is really asking us to evaluate the following term. 007 Paul Dawkins 0
18 4 4 6 = 6 So, we need to determine what number raised to the 4 th power will give us 6. This is and so in this case the answer is, = 6 = = As the last two parts of the previous example has once again shown, we really need to be careful with parenthesis. In this case parenthesis makes the difference between being able to get an answer or not. Also, don t be worried if you didn t know some of these powers off the top of your head. They are usually fairly simple to determine if you don t know them right away. For instance in the part b we needed to determine what number raised to the 5 will give 3. If you can t see the power right off the top of your head simply start taking powers until you find the correct one. In other words compute, 3, 4 until you reach the correct value. Of course in this case we wouldn t need to go past the first computation. The next thing that we should acknowledge is that all of the properties for exponents that we gave in the previous section are still valid for all rational exponents. This includes the more general rational exponent that we haven t looked at yet. Now that we know that the properties are still valid we can see how to deal with the more general rational exponent. There are in fact two different ways of dealing with them as we ll see. Both methods involve using property from the previous section. For reference purposes this property is, n nm a = a m So, let s see how to deal with a general rational exponent. We will first rewrite the exponent as follows. b m n = b In other words we can think of the exponent as a product of two numbers. Now we will use the exponent property shown above. However, we will be using it in the opposite direction than what we did in the previous section. Also, there are two ways to do it. Here they are, n ( m) m m m n n n n m b = b OR b = b Using either of these forms we can now evaluate some more complicated expressions 007 Paul Dawkins
19 Example Evaluate each of the following. 3 (a) 8 [Solution] (b) [Solution] (c) [Solution] 3 Solution We can use either form to do the evaluations. However, it is usually more convenient to use the first form as we will see. 3 8 (a) Let s use both forms here since neither one is too bad in this case. Let s take a look at the first form = 8 = = 4 8 = because = 8 Now, let s take a look at the second form = 8 = 64 = 4 64 = 4 because 4 = 64 So, we get the same answer regardless of the form. Notice however that when we used the second form we ended up taking the 3 rd root of a much larger number which can cause problems on occasion. 3 4 (b) 65 Again, let s use both forms to compute this one = 65 = ( 5) = 5 65 = 5 because 5 = = 65 = = 5 because 5 = As this part has shown the second form can be quite difficult to use in computations. The root in this case was not an obvious root and not particularly easy to get if you didn t know it right off the top of your head (c) 3 In this case we ll only use the first form. However, before doing that we ll need to first use property 5 of our exponent properties to get the exponent onto the numerator and denominator. 007 Paul Dawkins
20 ( 3) 8 = = = = We can also do some of the simplification type problems with rational exponents that we saw in the previous section. Example 3 Simplify each of the following and write the answers with only positive exponents. w (a) 6v [Solution] (b) xy [Solution] 3 x y Solution (a) For this problem we will first move the exponent into the parenthesis then we will eliminate the negative exponent as we did in the previous section. We will then move the term to the denominator and drop the minus sign. w v 4 w = = v vw 8 8 (b) In this case we will first simplify the expression inside the parenthesis = = = x y 3 3 xy xx y x y x y y Don t worry if, after simplification, we don t have a fraction anymore. That will happen on occasion. Now we will eliminate the negative in the exponent using property 7 and then we ll use property 4 to finish the problem up. 7 3 xy = = x y x y x y Paul Dawkins 3
21 We will leave this section with a warning about a common mistake that students make in regards to negative exponents and rational exponents. Be careful not to confuse the two as they are totally separate topics. In other words, and NOT b b n n = n b b n This is a very common mistake when students first learn exponent rules. 007 Paul Dawkins 4
22 Real Exponents This is a fairly short section. It s only real purpose is to acknowledge that the exponent properties we listed in the first section work for any exponent. We ve already used them on integer and rational exponents but we aren t actually restricted to these kinds of exponents. The properties will work for any exponent that we want to use. Example Simplify each of the following and write the answers with only positive exponents (a) ( x y z ) xy (b).7 x Solution We will not put as much detail into these as we have in the previous sections. By this point it is assumed that you re starting to get a good handle on the exponent rules. (a) (b) x x y z = x y z = y 4. z xy xx x y y = = = = x y y x x Note that we won t be doing anything like this in the remainder of this course. This section is here only to acknowledge that these rules will work for any kind of exponent that we might need to work with. 007 Paul Dawkins 5
23 Radicals We ll open this section with the definition of the radical. If n is a positive integer that is greater than and a is a real number then, n n a = a where n is called the index, a is called the radicand, and the symbol is called the radical. The left side of this equation is often called the radical form and the right side is often called the exponent form. From this definition we can see that a radical is simply another notation for the first rational exponent that we looked at in the rational exponents section. Note as well that the index is required in these to make sure that we correctly evaluate the radical. There is one exception to this rule and that is square root. For square roots we have, a = a In other words, for square roots we typically drop the index. Let s do a couple of examples to familiarize us with this new notation. Example Write each of the following radicals in exponent form. (a) 4 6 (b) 0 8x (c) Solution (a) x = 6 8x = 8x + y 0 (b) 0 x + y = x + y (c) As seen in the last two parts of this example we need to be careful with parenthesis. When we convert to exponent form and the radicand consists of more than one term then we need to enclose the whole radicand in parenthesis as we did with these two parts. To see why this is consider the following, 0 8x From our discussion of exponents in the previous sections we know that only the term immediately to the left of the exponent actually gets the exponent. Therefore, the radical form of this is, x = 8 x 8x So, we once again see that parenthesis are very important in this class. Be careful with them. 007 Paul Dawkins 6
24 Since we know how to evaluate rational exponents we also know how to evaluate radicals as the following set of examples shows. Example Evaluate each of the following. (a) 6 and 4 6 [Solution] (b) 5 43 [Solution] (c) 4 96 [Solution] (d) 3 5 [Solution] (e) 4 6 [Solution] Solution To evaluate these we will first convert them to exponent form and then evaluate that since we already know how to do that. (a) These are together to make a point about the importance of the index in this notation. Let s take a look at both of these. 6 = 6 = 4 because 4 = = 6 = because = 6 So, the index is important. Different indexes will give different evaluations so make sure that you don t drop the index unless it is a (and hence we re using square roots). (b) (c) = 43 = 3 5 because 3 = = 96 = 6 4 because 6 = 96 5 = 5 = 5 because 5 = 5 3 (d) 3 6 = 6 4 (e) 4 As we saw in the integer exponent section this does not have a real answer and so we can t evaluate the radical of a negative number if the index is even. Note however that we can evaluate the radical of a negative number if the index is odd as the previous part shows. Let s briefly discuss the answer to the first part in the above example. In this part we made the claim that 6 = 4 because 3 4 = 6. However, 4 isn t the only number that we can square to get 6. We also have ( 4) = 6. So, why didn t we use -4 instead? There is a general rule about evaluating square roots (or more generally radicals with even indexes). When evaluating square roots we ALWAYS take the positive answer. If we want the negative answer we will do the following. 007 Paul Dawkins 7
25 6 = 4 This may not seem to be all that important, but in later topics this can be very important. Following this convention means that we will always get predictable values when evaluating roots. Note that we don t have a similar rule for radicals with odd indexes such as the cube root in part (d) above. This is because there will never be more than one possible answer for a radical with an odd index. We can also write the general rational exponent in terms of radicals as follows. m m m m n n n n m n m a = a ( a) OR a n = = ( a ) = a We now need to talk about some properties of radicals. Properties If n is a positive integer greater than and both a and b are positive real numbers then,.. 3. n n a = a n n n ab = a b n a a n = n b b Note that on occasion we can allow a or b to be negative and still have these properties work. When we run across those situations we will acknowledge them. However, for the remainder of this section we will assume that a and b must be positive. Also note that while we can break up products and quotients under a radical we can t do the same thing for sums or differences. In other words, n n n n n n a+ b a + b AND a b a b If you aren t sure that you believe this consider the following quick number example. 5 = 5 = = 3+ 4 = 7 If we break up the root into the sum of the two pieces we clearly get different answers! So, be careful to not make this very common mistake! We are going to be simplifying radicals shortly so we should next define simplified radical form. A radical is said to be in simplified radical form (or just simplified form) if each of the following are true.. All exponents in the radicand must be less than the index.. Any exponents in the radicand can have no factors in common with the index. 3. No fractions appear under a radical. 4. No radicals appear in the denominator of a fraction. 007 Paul Dawkins 8
26 In our first set of simplification examples we will only look at the first two. We will need to do a little more work before we can deal with the last two. Example 3 Simplify each of the following. Assume that x, y, and z are positive. Solution (a) 7 y (a) 7 y [Solution] (b) 9 x 6 [Solution] (c) (d) (e) 6 8x y [Solution] x yz [Solution] x yz [Solution] (f) 3 9x 3 6x [Solution] In this case the exponent (7) is larger than the index () and so the first rule for simplification is violated. To fix this we will use the first and second properties of radicals above. So, let s note that we can write the radicand as follows. y 7 = yy 6 = ( y 3 ) y So, we ve got the radicand written as a perfect square times a term whose exponent is smaller than the index. The radical then becomes, y 7 = y 3 y Now use the second property of radicals to break up the radical and then use the first property of radicals on the first term. y 7 = y 3 y = y 3 y This now satisfies the rules for simplification and so we are done. Before moving on let s briefly discuss how we figured out how to break up the exponent as we did. To do this we noted that the index was. We then determined the largest multiple of that is less than 7, the exponent on the radicand. This is 6. Next, we noticed that 7=6+. Finally, remembering several rules of exponents we can rewrite the radicand as, 7 6 ( 3) 3 y = yy= y y= ( y) y In the remaining examples we will typically jump straight to the final form of this and leave the details to you to check. (b) 9 6 x This radical violates the second simplification rule since both the index and the exponent have a common factor of 3. To fix this all we need to do is convert the radical to exponent form do some simplification and then convert back to radical form. 007 Paul Dawkins 9
27 x = x = x = x = x = x 6 (c) 8x y Now that we ve got a couple of basic problems out of the way let s work some harder ones. Although, with that said, this one is really nothing more than an extension of the first example. There is more than one term here but everything works in exactly the same fashion. We will break the radicand up into perfect squares times terms whose exponents are less than (i.e. ) xy = 9xy ( y) = 9( x) ( y) ( y) Don t forget to look for perfect squares in the number as well. Now, go back to the radical and then use the second and first property of radicals as we did in the first example = 9 = 9 = 3 xy x y y x y y xy y Note that we used the fact that the second property can be expanded out to as many terms as we have in the product under the radical. Also, don t get excited that there are no x s under the radical in the final answer. This will happen on occasion. 9 5 (d) 4 3x yz This one is similar to the previous part except the index is now a 4. So, instead of get perfect squares we want powers of 4. This time we will combine the work in the previous part into one step x y z = 6x y z xy = 6 x y z xy = x y z xy 4 4 (e) 5 x yz Again this one is similar to the previous two parts x yz = x z xyz = x z xyz = xz xyz In this case don t get excited about the fact that all the y s stayed under the radical. That will happen on occasion. (f) 3 9x 3 6x This last part seems a little tricky. Individually both of the radicals are in simplified form. However, there is often an unspoken rule for simplification. The unspoken rule is that we should have as few radicals in the problem as possible. In this case that means that we can use the second property of radicals to combine the two radicals into one radical and then we ll see if there is any simplification that needs to be done. 007 Paul Dawkins 0
28 9x 6x = 9x 6x = 54x Now that it s in this form we can do some simplification. 9x 6x = 7x x = 7x x = 3x x Before moving into a set of examples illustrating the last two simplification rules we need to talk briefly about adding/subtracting/multiplying radicals. Performing these operations with radicals is much the same as performing these operations with polynomials. If you don t remember how to add/subtract/multiply polynomials we will give a quick reminder here and then give a more in depth set of examples the next section. Recall that to add/subtract terms with x in them all we need to do is add/subtract the coefficients of the x. For example, 4x+ 9x= x= 3x 3x x= 3 x= 8x Adding/subtracting radicals works in exactly the same manner. For instance, x + 9 x = x = 3 x = 3 5 = 8 5 We ve already seen some multiplication of radicals in the last part of the previous example. If we are looking at the product of two radicals with the same index then all we need to do is use the second property of radicals to combine them then simplify. What we need to look at now are problems like the following set of examples. Example 4 Multiply each of the following. Assume that x is positive. x + x 5 [Solution] (a) (b) ( 3 x y)( x 5 y) (c) ( 5 x )( 5 x ) [Solution] + [Solution] Solution In all of these problems all we need to do is recall how to FOIL binomials. Recall, 3x 5 x+ = 3x x + 3x 5 x 5 = 3x + 6x 5x 0 = 3x + x 0 With radicals we multiply in exactly the same manner. The main difference is that on occasion we ll need to do some simplification after doing the multiplication (a) ( x + )( x 5) x + x 5 = x x 5 x + x 0 = x 3 x 0 = x 3 x Paul Dawkins
29 As noted above we did need to do a little simplification on the first term after doing the multiplication. (b) ( 3 x y)( x 5 y) Don t get excited about the fact that there are two variables here. It works the same way! 3 x y x 5 y = 6 x 5 x y x y + 5 y = 6x 5 xy xy + 5y = 6x 7 xy + 5y Again, notice that we combined up the terms with two radicals in them. (c) ( 5 x + )( 5 x ) Not much to do with this one. ( 5 x + )( 5 x ) = 5 x 0 x + 0 x 4 = 5x 4 Notice that, in this case, the answer has no radicals. That will happen on occasion so don t get excited about it when it happens. The last part of the previous example really used the fact that ( a+ b)( a b) = a b If you don t recall this formula we will look at it in a little more detail in the next section. Okay, we are now ready to take a look at some simplification examples illustrating the final two rules. Note as well that the fourth rule says that we shouldn t have any radicals in the denominator. To get rid of them we will use some of the multiplication ideas that we looked at above and the process of getting rid of the radicals in the denominator is called rationalizing the denominator. In fact, that is really what this next set of examples is about. They are really more examples of rationalizing the denominator rather than simplification examples. Example 5 Rationalize the denominator for each of the following. Assume that x is positive. (a) 4 x [Solution] (b) 5 3 x [Solution] (c) 3 x [Solution] 5 (d) 4 x + 3 [Solution] Solution There are really two different types of problems that we ll be seeing here. The first two parts illustrate the first type of problem and the final two parts illustrate the second type of problem. 007 Paul Dawkins
30 Both types are worked differently. 4 (a) x In this case we are going to make use of the fact that n a n = a. We need to determine what to multiply the denominator by so that this will show up in the denominator. Once we figure this out we will multiply the numerator and denominator by this term. Here is the work for this part. 4 4 x 4 x 4 x = = = x x x x x Remember that if we multiply the denominator by a term we must also multiply the numerator by a the same term. In this way we are really multiplying the term by (since = ) and so aren t a changing its value in any way. (b) 5 3 x We ll need to start this one off with first using the third property of radicals to eliminate the fraction from underneath the radical as is required for simplification. 5 5 = 3 x 5 3 x Now, in order to get rid of the radical in the denominator we need the exponent on the x to be a 5. This means that we need to multiply by 5 x so let s do that x x x 5 = = = 3 x x x x x (c) 3 x In this case we can t do the same thing that we did in the previous two parts. To do this one we will need to instead to make use of the fact that a+ b a b = a b When the denominator consists of two terms with at least one of the terms involving a radical we will do the following to get rid of the radical. 3+ x 3+ x 3+ x = = = 3 x 3 x 3+ x 3 x 3+ x 9 x 007 Paul Dawkins 3
31 So, we took the original denominator and changed the sign on the second term and multiplied the numerator and denominator by this new term. By doing this we were able to eliminate the radical in the denominator when we then multiplied out. 5 (d) 4 x + 3 This one works exactly the same as the previous example. The only difference is that both terms in the denominator now have radicals. The process is the same however. 5 5 ( 4 x 3 ) 5 ( 4 x 3 ) 5 ( 4 x 3 ) = = = 4 x x x 3 4 x x 3 6x 3 Rationalizing the denominator may seem to have no real uses and to be honest we won t see many uses in an Algebra class. However, if you are on a track that will take you into a Calculus class you will find that rationalizing is useful on occasion at that level. We will close out this section with a more general version of the first property of radicals. Recall that when we first wrote down the properties of radicals we required that a be a positive number. This was done to make the work in this section a little easier. However, with the first property that doesn t necessarily need to be the case. Here is the property for a general a (i.e. positive or negative) n n a if n is even a = a if n is odd where a is the absolute value of a. If you don t recall absolute value we will cover that in detail in a section in the next chapter. All that you need to do is know at this point is that absolute value always makes a a positive number. So, as a quick example this means that, 8 8 x = x AND x = x For square roots this is, x = x This will not be something we need to worry all that much about here, but again there are topics in courses after an Algebra course for which this is an important idea so we needed to at least acknowledge it. 007 Paul Dawkins 4
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30413963
ISBN: 0130413968
Edition: 3
Publication Date: 2003
Publisher: Prentice Hall
AUTHOR
Wallace, Edward, West, Stephen
SUMMARY
Clarifying, extending and unifying concepts discussed in basic high school geometry courses, this text gives readers a comprehensive introduction to plane geometry.Wallace, Edward is the author of 'Roads to Geometry', published 2003 under ISBN 9780130413963 and ISBN 01304139 | 677.169 | 1 |
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Grades Teachers, and Number Theory for Middle Grades TeachersThis course
examines in depth geometry content appropriate for middle grades
mathematics teachers, including the use of technology to study
geometry and historical connections to geometry. Topics studied
include fundamentals of geometry, two- and three-dimensional
figures, transformations and isometries, basic measurement properties
of perimeter, area, and volume. Teachers experience instructional
approaches appropriate for use in middle grades classrooms.
This course is required in the MAT in Middle Grades Mathematics.
Prerequisite: Admission to the MAT program in middle grades
mathematics or CIED EDO This course
permits a student to explore a topic of
interest in depth under the direction and supervision of a faculty
member
MAE 6945 – (3) Practicum in Mathematics Education
MAE 6947
Internship (6) ED EDI PR: CI.
Provides students with an extended school-based experience,
under the guidance of a cooperating teacher and university supervisor,
for a full semester at or near the end of their graduate program.
Open to graduate degree candidates only. S/U (PR: CI)
This course
discusses a broad range of issues related to assessment in mathematics
education at all levels, including state, national, and international
assessments in mathematics. In addition, issues related to rubrics
and alternative assessments as they particularly relate to mathematics
are discussed from curricular and research perspectives. Prerequisite:
Admission to the Ph.D. Program with emphasis in Mathematics
Education or CI.
This course surveys curriculum
history in mathematics education, discusses current research
on mathematics education curricula, and explores issues related
to conducting research on curriculum in this field. Prerequisite:
Admission to the Ph.D. Program with emphasis in Mathematics
Education or CI.
This course focuses on
issues surrounding the use of technology in mathematics education.
It includes an examination of perspectives and
research about technology in mathematics education and the implications
for technology instruction in school mathematics programs. More
specifically, this course examines the characteristics of technology
in mathematics education and its impact on mathematics curricula,
learning, instruction, and teacher preparation. Â
Prerequisite: Admission to the Ph.D. Program with emphasis in
Mathematics Education or CI.
This course
focuses on analyzing and examining the research in mathematics
teaching and teacher education. Course participants will consider
the various ways of studying the teaching of mathematics and
analyze what has been learned from the study of teaching. Participants
will analyze research and identify issues related to the initial
preparation of teachers of mathematics and to the professional
development of practicing teachers of mathematics. Prerequisite:
Admission to the Ph.D. Program with emphasis in Mathematics
Education or CI.
MAE 7796
RESEARCH ISSUES IN MATHEMATICS EDUCATION (3) This course focuses on the analysis of current research
in mathematics education and its implications for instruction
in school mathematics programs. More specifically, the course
examines the characteristics of research in mathematics education
and its impact on mathematics curricula, learning, and instruction.
Prerequisite: Admission to the Ph.D. program with emphasis in
Mathematics Education or CI.
ED EDO PR: CI. This
course permits a doctoral student to conduct
advanced research and to pursue specific areas of interest with
a faculty member as supervisor. A contract is required with
the faculty member. S/U.
MAE 7945 PRACTICUM
IN MATHEMATICS EDUCATION (taken twice) This practicum
provides doctoral students in mathematics education an opportunity
to engage in professional experiences in teaching or research
that are individualized to meet future academic needs and goals.
Prerequisite: Admission | 677.169 | 1 |
Functions and Graphs resources
Latex source, image files and metadata for the Fact & Formulae leaflet "Exponential and Logarithm for Economics and Business Studies" contributed to the mathcentre Community Project by Morgiane Richard (University of Aberdeen) and reviewed by Shazia Ahmed (University of Glasgow) and Anthony Cronin (University College Dublin).
Overview of the properties of the functions e and ln and their applications in Economics. This leaflet has been contributed to the mathcentre Community Project by Morgiane Richard (University of Aberdeen) and reviewed by Shazia Ahmed (University of Glasgow) and Anthony Cronin (University College Dublin).
In many business applications, two quantities are related linearly. This means a graph of their relationship forms a straight line. This leaflet discusses one form of the mathematical equation which describes linear relationships.
The letter e is used in many mathematical calculations to stand for a particular number known as the exponential constant. This leaflet provides information about this important constant, and the related exponential function.
A quantity whose value can change is known as a variable. Functions are used to describe the rules which define the ways in which such a change can occur. The purpose of this leaflet is to explain functions and their notation. | 677.169 | 1 |
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Math programs follow a normal progression – each one builds upon the awareness you've attained and mastered from your previous class. In case you are discovering it challenging to stick to new concepts in class, pull out your outdated math notes and critique previous substance to refresh oneself. Be sure that you satisfy the prerequisites prior to signing up for a class.
Assessment Notes The Night Right before Class
Hate when a trainer phone calls on you and you have neglected the way to solve a specific trouble? Keep away from this moment by reviewing your math notes. This may enable you to identify which concepts or queries you'd love to go over in class the subsequent working day.
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Examine Ahead To stay Ahead
If you need to minimize your in-class workload or the time you devote on homework, make use of your free time following faculty or about the weekends to go through ahead to your chapters and concepts that will be covered the following time you are at school.
Evaluation Outdated Tests and Classroom Examples
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If you are having a hard time being familiar with principles at school, then make sure to get help beyond course. Inquire your folks to create a research group and stop by your instructor's business hrs to go more than hard challenges one-on-one. Show up at examine and review periods once your instructor announces them, or seek the services of a non-public tutor if you need 1.
Discuss To Your self
If you are examining problems for an exam, test to elucidate out loud what technique and approaches you accustomed to get the methods. These verbal declarations will arrive in useful during a check any time you must recall the methods you ought to consider to find a remedy. Get more practice by attempting this tactic which has a good friend.
Use Examine Guides For Extra Observe
Are your textbook or course notes not assisting you realize that which you ought to be discovering in school? Use analyze guides for standardized examinations, including the ACT, SAT, or DSST, to brush up on aged product, or . Study guides ordinarily appear geared up with extensive explanations of the best way to address a sample difficulty, , so you can typically find where by could be the superior purchase mathcomplications | 677.169 | 1 |
Welcome to Pre Calculus!
Pre Calculus is a course designed for college-bound students who plan to
major in the sciences, engineering, computers, architecture, mathematics,
business, psychology or any other math related field. Precalculus combines the trigonometric,
geometric and algebraic concepts needed to prepare students for the study of
Calculus, and strengthens students' conceptual understanding of problems and
mathematical reasoning and solving problems:
·
Each
homework assignment will be worth 5 points.
Points are awarded based on the above criteria.
·
If you
are absent, it is your responsibility to obtain the missing assignments and
make sure they are completed and turned in for credit. Any work due the day you were absent, is due
the day you return. Make-up work must be turned in no later than one class
meeting after the day you return.
Test Make-up:
·
If you are absent on a test date, a
make-up test will be given on the day of return.
·
If the absence is an extended one, it
is your responsibility to make arrangements with me to set a test make-up
date and schedule for missed assignments.
Tests must be made up within one week.
Re-tests:
No re-test will be offered if you keep up with your homework and study your notes, re-tests should
not be necessary; however, at the end of the SEMESTER the lowest test grade will be dropped (unless the score is
a 0 for cheating).
Extra Assistance:
If you are having difficulty with the curriculum and need
additional help, I will usually be available for tutoring Monday, Tuesday,
Thursday, and Friday in room C105 from 7:05 a.m. to 7:40 a.m. Tutoring days are subject to change.
The weekly tutoring schedule will be posted on my front white board each week. Students
will be notified if tutoring becomes available after school.
Grading Policy:
The following types of assessment will be utilized and
weighted in the following manner.
·
Tests/Quizzes 80%
·
Homework/Classwork 15%
·
Personal Points (being on-time, bring book, work in class) 5%
(Each student starts with 100 points, 5 point
deductions will be taken for infractions such as cell phones, tardies,
excessive restroom passes, not working on Pre-Calculus until end of period,
etc)
Grading Scale:
Grades will be assigned based on the following scale:
A 90-100%
B 80-89%
C 70-79%
D 60-69%
F less than 60%
Grades on Q:
You will
be able to check your grade on the Internet throughout the year on the Q
website. I will update these grades about every week or so. Call the school for
information on signing into Q.
Classroom Guidelines:
·
Be in assigned seat ready to work
when tardy bell rings. Tardies will
lower citizenship marks. No "socializing" during lectures.
·
No profanity, put-downs, or other
disrespectful behavior to teacher or classmates.
·
No food or beverages other than water
is allowed in class. Cell phones and other electronic devices should be put
away and tuned off.
Note to Parents/Guardians:
If you have any questions, please feel free to contact me.
You may reach me by e-mail: skatykhin@cnusd.k12.ca.us. Please be aware that your student may not switch classes after 20 days due to undesired grades.
Pre-Calculus
Please
Initial, Sign and Return as your 1st assignment of the Year.
Please read and initial the following:
Student
Parent
1)
If
you struggle with tests, please come in for extra assistance BEFORE the day
of the exam to become more comfortable with the material and practice.
2)
If
you have a history of not doing the vast majority of your assignments, you
will struggle in Pre-Calculus.
3)
If
you had to re-take tests last year to improve your grade, you should come in
for assistance prior to the exam date for prior practice.
4)
You
need to come in for extra help as soon as possible - do not wait until the
morning of the exam.
5)
Do
not wait for progress reports to come home, please check Q at least once a
week for grades and attendance tardiness/absences.
6)
Contact
the registrar's office if you do not already have access to Q
7)
Be
sure the registrar's office has your current email address in order to
receive grade update notifications.
8)
Homework
assignment sheets are given to students and posted in the classroom.
9)
Please
email me at skatykhin@cnusd.k12.ca.us
for questions.
10) Most colleges will revoke your
acceptance letter if you don't pass both semesters with a "C" or higher. | 677.169 | 1 |
Synopsis
This book presents a variety of techniques for solving ordinary differential equations analytically and features a wealth of examples. Focusing on the modeling of real-world phenomena, it begins with a basic introduction to differential equations, followed by linear and nonlinear first order equations and a detailed treatment of the second order linear equations. After presenting solution methods for the Laplace transform and power series, it lastly presents systems of equations and offers an introduction to the stability theory.
To help readers practice the theory covered, two types of exercises are provided: those that illustrate the general theory, and others designed to expand on the text material. Detailed solutions to all the exercises are included.
The book is excellently suited for use as a textbook for an undergraduate class (of all disciplines) in ordinary differential equations. | 677.169 | 1 |
Synopses & Reviews
Publisher Comments
This is a very successful textbook for undergraduate students of pure mathematics. Students often find the subject of complex analysis very difficult. Here the authors, who are experienced and well-known expositors, avoid many of such difficulties by using two principles: (1) generalising concepts familiar from real analysis; (2) adopting an approach which exhibits and makes use of the rich geometrical structure of the subject. An opening chapter provides a brief history of complex analysis which sets it in context and provides motivation.
Synopsis
A new approach to complex analysis that attempts to make it less complicated than traditional texts suggest. | 677.169 | 1 |
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Are you just starting out teaching Algebra? Variable and expressions are the base of learning how to solve equations and the base for all of Algebra! Here are three nice practice worksheet and answer key for you and your students. | 677.169 | 1 |
This book is fully cross-referenced to the Year 3 Targeting Maths App. Children will benefit from the combination of book-based and digital learning that this powerful learning program provides. This edition fully aligns each student page to the NSW syllabus and the Australian Curriculum.
AU $18.15
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"ACCESS TO MATHS - HSC" provides all round support for NSW General Mathematics students. "ACCESS to GENERAL MATHS - HSC". By: SUE THOMSON & IAN FORSTER. It has been written by experienced authors and teachers with excellent knowledge of HSC maths.
The book is in very good used condition with no marks or writing on the pages. There are some slight creases on the front cover, particularly in the corners, some writing impression marks on the front cover and correction tape covering a name on page 1 (see photos).
Title:Calculus From Graphical Numerical & Symbolic Points Of View. Author:Ostebee & Zorn. Do not assume anything. Number of pages:810. See Pictures for Details. We warrant that the item is in the condition described above.
Strategies to Achieve Mathematics Success provides students with explicit instruction of 16 maths topics, which cover both concepts and skills, that have been identified as the most important instructional goals for each year level.
G.I. Taylor, one of the most distinguished physical scientists of this century, used his deep insight and originality to increase our understanding of phenomena such as the turbulent flow of fluids. His interest in the science of fluid flow was not confined to theory; he was one of the early pioneers of aeronautics, and designed a new type of anchor that was inspired by his passion for sailing.
Maths Textbooks
One of the most important parts of education, from preschool to graduate school, is mathematics. Because of this, maths textbooks are a necessity throughout all your years of school. There are different levels of mathematics, as well as different types of textbooks, to help you get through this phase of your learning. From hardcover to paperback books, there are many types for various maths classes.
Hardcover
Perhaps the most common types of maths textbooks are hardcover textbooks. Durable and built to last for many years of use, the hard cover protects against wear and tear so the book can last for many a season. From simple addition to geometry, you can also cover a hardcover maths textbook with paper or a book cover to help promote its longevity.
Paperback
Maths paperback textbooks may be a regular textbook, or they may be a companion to your harcover textbook as a workbook. Simple to write in and easy to stow in a bag, paperback textbooks are convenient. These paperback books are great for grade school through college. Paperback topics can range from several different studies of mathematics, from counting and recognising numbers through precalculus and calculus.
Multi-Language
Perhaps you're studying abroad and need a maths textbook in a different language; or English is your second language, and you're more comfortable learning mathematics in your native language. Either way, there are plenty of maths textbooks in print that are in different languages for your convenience. Look for choices in Spanish, German, French, Russian and more.
Age Ranges
If you're purchasing a book for homeschooling, preschool or for post-grad, be sure to check the age range and type of mathematics. For example, preschool age children will be learning number sense and counting, while high school classes will focus on algebra, geometry and precalculus. College level and beyond is suited for calculus, statistics and other higher level mathematics. | 677.169 | 1 |
Maple Player
By Maplesoft
Description
Mathematics comes to life with the Maple™ Player!
Explore mathematical concepts and solve advanced problems with these interactive calculators based on Maple technology.
The Maple Player is an application for the iPad® that lets you view and interact with documents created in desktop Maple. The Maple Player takes advantage of the powerful Maple computation engine, so you can enter values, move sliders, and click buttons to perform new calculations and visualize the results. You can even rotate 3-D plots with a brush of your fingertips!
This first release of the Maple Player for the iPad comes with a collection of interactive calculators and conceptual explorations that allow you to:
-Find solutions to integrals, derivatives, limits -Visualize the methods for finding the area of a circle and the volume of a cylinder -Understand the definition of limit -Plot arbitrary functions -Calculate solutions to linear systems -And more!
These documents can be used to liven up a classroom and to provide additional insight to students outside of class.
The Maple Player for the iPad will evolve quickly. Today, it can be used with the sample documents that are bundled with the application. In the next phase, you will be able to access a much wider collection of documents dynamically from an online repository. Ultimately, you will be able to use any Maple document on the iPad, whether distributed by us, contributed by the Maple community, or authored by you.
We are very interested in hearing your feedback on the Maple Player for the iPad, as well as your ideas on how you would like to use Maplesoft technology on the iPad. Please share your thoughts with Maplesoft and the Maplesoft community at
About Maple
Mathematics plays a critical role in our modern world, which is why mathematicians, engineers, and scientists everywhere rely on Maple software. Maple helps you analyze, explore, visualize, and solve mathematical problems quickly, easily, and accurately. With close to 5000 functions covering virtually every area of mathematics, Maple has the depth, breadth, and performance to meet all your mathematical challenges. To learn more about Maple and other Maplesoft products, visit
iPad Screenshots
Customer Reviews
Maple
by
copisetic
I use maple 13 now, with what they have planned for the future I am excited I bought an iPad and maple software. Who would have guessed they would leverage the two together to achieve more than the sum of its parts. Smart thinking!
Great Idea...
by
Industrial Emgineer
Maple for pc is an outstanding program. But those programmers didn't have the (time/resource$) to do this app justice. No attempt at an upgrade for years now, dead, forgotten. This app was a great idea, just never got the development it deserved.
Nice first attempt but very little usefulness
by
Oscar F.
The app is great in what it currently does (display pre-made worksheets) but can currently do nothing else. I'd love to be able to transfer a worksheet over from my MacBook Air and display/manipulate it on the iPad. | 677.169 | 1 |
About this course: The goal of this course is to develop your
understanding of the concepts of integral calculus, infinite series,
and differential equations and your ability to apply
them to problems both within and outside of mathematics.
Calculators: A calculator is not required for this course, but
you may find using a graphing calculator helpful. (I prefer a laptop).
However, be careful how you use it. Many students become dependant on
their calculators, and wind up being unable to do anything without
them. In this course, no calculators will be allowed on exams.
Homework: You can not learn calculus without working
problems. Expect to spend at least 8 hours a week solving problems;
do all of the assigned problems, as well as additional ones to study.
If you do not understand how to do something, get help from your TA,
your lecturer, your classmates, or in the Math Learning Center.
You are encouraged to study with and discuss problems with
others from the class, but write up your own homework by yourself, and make
sure you understand how to do the problems.
Specific problem assignments can always be found on the web at
A significant fraction of the homework problems will be done on WebAssign;
see the class web page
for details.
WebAssign homeworks are due every wednesday in the morning (think ``Tuesday
before I go to sleep''); problems solved at least 2 days before the due date
get extra credit. Paper homeworks will be due at the second recitation of
each week.
Examinations and grading:
There will be two evening exams, and the ever-popular final
exam. The dates and times are listed below; the locations will be
announced later. Success on the exams will require correct and
efficient solutions to the more difficult of the homework problems.
Part of your grade will be based on class participation in both
recitation and lecture.
What
When
% of Final Grade
Exam 1
Monday, March 4
8:45-10:15 pm
25%
Exam 2
Wednesday, April 10
8:45-10:15 pm
25%
Final Exam
Monday, May 20
8:00-10:45 am
35%
homeworks (WebAssign and paper)
10%
participation in lecture and recitation
5%
Make sure that you can attend the exams at the scheduled times;
make-ups will not be given. If you have evening classes,
resolve any conflicts now. If one midterm exam is missed because
of a serious (documented) illness or emergency, the semester grade
will be determined based on the balance of the work in the course.
Reading: The textbook is intended to be read. Read the assigned
sections before the lecture! This will greatly increase your
comprehension, and enable you to ask intelligent questions in class.
Furthermore, the lectures will not always be able to cover all of the
material for which you will be responsible.
Office Hours:
All lectures and TAs must hold at least three scheduled office hours per
week. They are there to help you, so make use of these hours. You
may go to any hours for any of the people associated with the course; the
various office hours are listed on the
Teaching Staff
section of the
class web page. You can also make appointments at other times.
Math Learning Center: The
Math Learning Center,
in Math S-240A, is there for you to get help with Calculus. It is staffed most
days and some evenings-- your lecturer or TA may hold some of his or
her office hours there. A schedule should be posted outside the room
and at the Math Undergraduate Office.
Disabilities:
If you have a physical, psychological, medical, or learning
disability that may impact your course work, please contact
Disability Support Services at
or (631) 632-6748.
They will determine with
you what accommodations are necessary and appropriate. All
information and documentation is confidential.
Students who require assistance during emergency evacuation are
encouraged to discuss their needs with their professors and
Disability Support Services. For procedures and information go to the
following website:
Academic Integrity:
Each student must pursue his or her academic goals honestly and be
personally accountable for all submitted work. Representing another person's
work as your own is always wrong. Faculty are required to report any
suspected instances of academic dishonesty to the Academic Judiciary.
For more comprehensive information on academic integrity, including
categories of academic dishonesty, please refer to the academic judiciary
website at
Critical Incident Management:
Stony Brook University expects students to respect the rights,
privileges, and property of other people. Faculty are required
to report to the Office of Judicial Affairs any disruptive
behavior that interrupts their ability to teach, compromises
the safety of the learning environment, or inhibits students'
ability to learn. | 677.169 | 1 |
More Information
Give students a head start on college math! Made for those who've completed Algebra II, SOS Trigonometry for grades 9-12 prepares high schoolers for future advanced math courses. Offering a five-unit study with a review, this high school elective helps teach students how to develop trigonometric formulas and use them in real world applications. Topics include:
right angle trigonometry
graphing
trigonometric identities
the laws of sines and cosines
polar coordinates
Helping students see the big picture of mathematics, SOS Trigonometry shows the use of trigonometry as a tool for indirect measurement, explains the natural phenomenon of trigonometric functions, and gives an understanding of how algebraic and geometric concepts work together. SOS Trigonometry is a great alternative to students not pursuing calculus! | 677.169 | 1 |
Accessibility links
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Core Maths at The Corsham School
Course description
Core Maths is a new qualification designed for students who want to keep up their mathematical skills but are not planning to take A-level mathematics.
Course content
Core Maths has been designed to maintain and develop real-life maths skills. What you study is not purely theoretical or abstract; it can be applied on a day-to-day basis in work, study or life and will include units on finance, analysing data and problem
solving. It will also help with other A-level subjects – in particular with science, geography, business studies, psychology and economics.
Core Maths is about developing mathematical thinking and reasoning skills through meaningful mathematical problems and to increase confidence in using maths. This will lead to students being better equipped for the mathematical demands of other courses,
higher education, employment and life.
The skills developed in the study of mathematics are increasingly important in the workplace and in higher education; studying Core Maths will help you keep up these essential skills. Most students who study maths after GCSE improve their career choices
and increase their earning potential.
Entry requirements
Grade 4 or better at GCSE.
Assessment
Core maths is a two year course and exams will be sat at the end of the second year.
At the end of the course, you will gain a level 3 qualification, similar to an AS and worth the same number of UCAS points as an AS level qualification.
How to apply
If you want to apply for this course, you will need to contact The Corsham School directly. | 677.169 | 1 |
In Algebra 1,
students will learn more about manipulating equations, exponents and
roots, scientific notation, converting decimals into fractions and
vice versa, polynomials, rational expressions, and basic graphing.
We will introduce Algebra students to the Pythagorean theorem,
algebraic proofs, quadratic equations, and beginning geometry
problems. | 677.169 | 1 |
An Introduction to Calculus
by John Beachy
All of nature is in a state of constant motion and change.
The branch of mathematics that provides methods
for the quantitative investigation of various process
of change, motion, and dependence of one quantity on another
is called mathematical analysis, or simply analysis.
A first course in calculus
establishes some of the basic methods of analysis,
done in relatively simple cases.
The development of the methods of analysis
was stimulated by problems in physics.
During the 16th century the central problem of physics
was the investigation of motion.
The expansion of trade, and the accompanying explorations,
made it necessary to improve the techniques of navigation,
and these in turn depended to a large extent on developments in astronomy.
In 1543 Copernicus published the ground-breaking work
"On the revolution of the heavenly bodies".
The "New astronomy" of Kepler,
containing his first and second laws for the motion of planets around the sun,
appeared in 1609.
The third law was published by Kepler in 1618
in his book "Harmony of the world".
Galileo, on the basis of his study of Archimedes and his own experiments,
laid the foundations for the new mechanics,
an indispensable science for the newly arising technology.
During the Renaissance, Europeans became acquainted with Greek mathematics,
by way of the Arabic translations.
This finally occurred after a period of almost one thousand years
of scientific stagnation.
The books of Euclid, Ptolemy, and al-Khwarizmi were translated
in the 12th century from Arabic into Latin,
the common scientific language of Western Europe.
At the same time the earlier Greek and Roman system of calculation
was gradually replaced by the vastly superior Indian method,
which also reached Europe via the Arabs.
It was not until the 16th century
that European mathematicians finally surpassed the achievements
of their predecessors,
with the solution by the Italians Tartaglia and Ferrari
of the general cubic equation and
(later) of the general equation of the fourth degree.
The concepts of variable magnitude and function arose gradually,
as a result of the interest in laws of motion,
as, for example, in the work of Kepler and Galileo.
Galileo discovered the law of falling objects by establishing
that the distance fallen increases proportionally to the square of the time.
The appearance in 1637 of the new "geometry" of Descartes
marked the first definite step toward a mathematics of variable magnitudes.
This combined algebraic and geometric techniques,
and is now known as "analytic geometry".
The main content of the new geometry was the theory of conic sections:
the ellipse, hyperbola, and parabola.
This theory had been developed extensively by the ancient Greeks,
in geometric form,
and the combination of their knowledge,
together with algebraic techniques
and the general idea of a variable magnitude, produced analytic geometry.
For the Greeks, the conic sections were a subject
of purely mathematical interest,
but by the time of Descartes they were of practical importance
for astronomy, mechanics, and technology.
Kepler discovered that the planets move around the sun in elliptical orbits,
and Galileo established that an object thrown into the air travels
along a parabolic path.
(Of course, both of these models are only first approximations
of the actual paths.)
These discoveries made it necessary to calculate various magnitudes
associated with the conic sections,
and it was the method of Descartes that solved this problem.
The next decisive steps were taken by Newton and Leibnitz
during the second half of the 17th century,
and resulted in the founding of differential and integral calculus.
The Greeks and later mathematicians had studied the geometric problems
of drawing tangents to curves
and finding areas and volumes of irregular figures.
The remarkable discovery of the relation of the problems
to the problem of the new mechanics
and the formulation of general methods for solving them
was brought to completion in the work of Newton and Leibnitz.
This relationship was discovered because of the possibility,
through the use of analytic geometry,
of making a graphical representation of the dependence
of one variable on another.
In short,
what is involved is the construction of a geometric model
to describe relationships involving variable magnitudes.
We next discuss the construction of a mathematical model
for a particularly simple kind of motion.
We will consider the motion of a car along a straight road.
The first problem is to give an analytic description
of the relationship between position and time.
The language of sets and functions provides a general way
of describing relationships between quantities,
and in this case we can use this language in talking about a function
from one set of real numbers to another.
We will now discuss the construction of a mathematical model for a
particularly simple kind of motion. Consider the motion of a car along
a straight road. The first problem is to give an analytic description
of the relationship of position and time. The language of set theory
provides a general way of describing relationships between quantities,
and in this case we can use it in talking about a function from one set
of real numbers to another. In order to define a numerical
relationship, we can select a reference point on the road and a
reference point in time. Then we can express the position of the car in
terms of a real number, the distance of the car from the reference
point, letting one direction be positive and the other negative. This
position only requires one number since the car is moving along a
straight road, and similarly the time can be given by a single number,
the elapsed time.
We can abstract the situation a little further, by representing the car
as a point moving along a straight line, whose position is given by a
number expressing the distance and direction from the point to a fixed
reference point, usually called the origin. Specifying the position of
the point at each instant in time is thus equivalent to defining a
function from the set of all real numbers (representing time) to the set
of all real numbers (representing position).
The following questions are some of those which arise in this situation.
If you know the function giving the position of car at each instant, can
you give the function which describes its velocity at each instant? If
you know only the velocity at each instant, can you tell the distance
traveled during a particular interval of time? If you know only the
function giving the velocity at each instant, can you reconstruct the
function giving the position at each instant?
Answering the first question would be equivalent to giving a function
listing the speedometer readings at each instant. Here we assume that
we have a speedometer which gives both positive and negative readings,
depending on the direction of travel. The function describing the rate
of change or velocity at each instant is called the derived function or
simply the derivative of the original function. Sometimes information
about the motion of the car can be obtained more easily from the derived
function than it can from the original function. For example, you could
find out when the car is stationary by simply finding out when the
derived function is zero. A positive value for the derivative
indicates forward motion and a negative value indicates the reverse, so
if you know that in a particular time interval the derivative is
positive, then zero, and then negative, this tells you that the car was
moving forward, then stopped and started moving backwards. The point of
farthest advance during this interval can then be found by solving the
equation obtained by setting the derived function equal to zero.
The second problem was the following: Knowing only the velocity at each
instant, find the distance traveled during a given time interval.
If the velocity is constant, the problem can be solved rather easily, by
multiplying the velocity by the amount of time. But in general
situations, the velocity will be changing all the time, so this method
will not work. If we could find an average value for the velocity, then
we could just multiply this average value by the amount of time. The
problem lies in the fact that there are infinitely many readings of the
speedometer involved, as given by the function describing the velocity,
and familiar methods deal only with finding the average of a finite
number of values.
In physical processes depending on time, there are normally only
relatively small changes in the process during short intervals of times.
Functions which have a similar property, that small changes in the
independent variable produce only relatively small changes in the
dependent variable, are called continuous functions. (We must make
precise what we mean by ``relatively".) It can be shown that an average
can be found for any continuous function, so that the methods we will
develop will work win almost all physical situations. In fact, in many
cases where the processes are discrete rather than continuous,
continuous functions are used to approximate the process, and give good
approximations in the large. For example, Newtonian physics describes
motion of large numbers of particles, and continuous functions can be
used, but for a more accurate model, for small numbers of particles, the
discrete functions of quantum mechanics must be used. Unfortunately we
will meet continuous processes for which it is impossible to talk about
an instantaneous rate of change at certain points.
Integral calculus deals with this second problem. If the rate at which
a process is being carried out is known, and described analytically by a
function, then the number which gives the total outcome of the process
during a particular time interval is called the definite integral of
this function, over the given interval of time.
The third problem, where we are given a function describing the velocity
of the car and are then asked to find a function giving its position at
each instant, is investigated in the branch of analysis know as
differential equations. Of course, if we know the answer to this
question, we can answer the second one quite easily. This is a
difficult area of study, but it is very important, since many physical
situations can be described by giving simply equations involving rates
of change. An equation involving derivatives of a function is called a
differential equation, and such equations often give the simplest
statements of physical laws. For example, by solving a differential
equation expressing the assumption that the only force acting on a
planet is the gravitational attraction of the sun, and that this is
inversely proportional to the square of the distance between them, it is
possible to show that the planet must follow an elliptical path. This
was one of the early triumphs of the techniques of calculus and
differential equations.
The Fundamental Theorem of Calculus connects the two areas of
differential and integral calculus. It says that finding the
instantaneous rates of change of a function and then averaging them
gives the average rate of change of the function. It shows that the
infinite processes used to define the instantaneous rate of change and
average of a function lead to good definitions, at least in the sense
that you would certainly expect the above kind of connection. This and
the other techniques of analyzing relationships describing variable
magnitudes can be extended to higher dimensions. Functions of more than
one variable arise naturally in industrial applications, where
describing rates of change and finding maximum and minimum values are
extremely important.
A general statement on mathematics
Mathematics involves the construction and study of abstract models of
physical situations. The construction of a model involves the selection
of a finite number of explicitly stated and precisely formulated
premises. These assumptions are called axioms, and the study of the
model then involves drawing conclusions from these fundamental
assumptions, using as high a degree of logical rigor as possible. The
rigor of mathematics is not absolute, but is rather in the process of
continual development. Euclid's axiomatization of geometry and his
study of this model of our spatial surroundings was accepted as
completely rigorous for over two thousand years, even though a modern
geometer could point out serious flaws in the logical development of the
theory.
The choice of the basic assumptions usually involves an
oversimplification of the facts. Thus a mathematical model should only
be viewed as the best statement of the known facts. In many
cases a model should be viewed as merely the most efficient,
incorporating only enough assumptions to give a desired degree of
accuracy in prediction. In an area small in comparison to the total
surface of the earth, plane geometry gives a good approximation for
questions involving relationships of figures. As soon as the problems
involve large distances, spherical geometry must be used as the model.
Newtonian physics is good enough for many problems in mechanics, and it
is necessary to introduce the additional assumptions of quantum
mechanics only if much greater accuracy is needed.
If any distinction at all is to be made between applied mathematics and
theoretical mathematics, it is perhaps at this point. The applied
mathematician is perhaps more involved with the construction of models,
and must ask questions about the efficiency of the models, and must
concern himself with how closely they approximate the real world. The
theoretical mathematician is concerned with developing the model, by
investigating the implications of the basic assumptions or axioms. This
is done by proving theorems. Of course, if a theorem is proved which is
obviously contrary to nature, it is clear to everyone concerned that the
basic assumptions do not coincide with reality. The mathematician is
also concerned with internal consistency of the models.
In order to make logical deductions from the basic axioms, the language
used must be extremely precise. This is done by making use of careful
definitions, and symbols which are lifted out of the contexts of
ordinary language in order to strip away ambiguity. Much of the
particular precision and clarity of mathematics is made possible by its
use of formulas. The modern reader is usually unaware that this is an
achievement only of the past few centuries. For example, the signs +
and - appeared in manuscripts for the first time in 1481: parentheses
first appeared in 1544; brackets and braces appeared essentially for the
first time in 1593 in the works of Vieta; the sign = appeared in
1557; the modern way of writing powers was first used in 1637 by
Decartes, but Gauss still wrote xx instead of x2 in 1801.
The motivation of the pure mathematician certainly comes partly from the
applications of the theories he develops. But perhaps more than this,
it comes from the joy of creating a theory of particular simplicity,
elegance and broad scope. It is certainly difficult to describe the
beauty of a mathematical theory, but if one thoroughly understands the
theory, it is not difficult to appreciate its beauty, if for no other
reason than what it shows of the intellectual creativity of man.
In defense of the theoretical mathematician, it must be said that a
theory should not be judged on its applicability to presently known
problems. The history of mathematics is filled with examples of
particular theories which seemed at the time to be mere intellectual
exercises devoid of any relationship to physical problems, and which
later were discovered to have important applications. One particularly
impressive example is provided by non-Euclidean geometry, which arose
from the efforts, extending for two thousand years from the time of
Euclid, to prove the parallel axiom from Euclid's other, more obvious
axioms. This seemed to be a matter of interest only to mathematicians.
Even Lobacevskii, the founder of the new geometry, was careful to label
it ``imaginary", since he could not see any meaning for it in the actual
world. In spite of this, his ideas laid the foundation for a new
development of geometry, namely the creation of theories of various
non-Euclidean spaces. These ideas later became, in the hands of
Einstein, the basis of the general theory of relativity, in which the
mathematical model consists of a form of non-Euclidean geometry of
four-dimensional space.
The generalizations and abstractions of mathematics often seem at first
to be strange and difficult. But with the very general expansion of
knowledge and technology we are currently experiencing, it becomes
necessary to identify and elucidate general underlying principles, in
order to tie this information together. The language and concepts of
mathematics help to fill this need. | 677.169 | 1 |
Tag Archives: civil service exam review guide
After learning work problems, we learn about rate, base, and percentage. If you want to further your knowledge about them, you may also want to study about their applications which are discount and interest. PART I: MATH A. RATE BASE AND PERCENTAGE Part 1 Introducing Rate, Base, and Percentage Part 2 Calculating for Percentage Part… Read More »
This is the tenth review guide for the Philippine Civil Service Review. In this guide, we will learn about solving equations. We will also learn new sets of words in our Vocabulary review as well as a spelling quiz. Week 10: June 4 – June 10 PART I: MATH A. Videos Lesson on Equations Lesson 1:… Read More »
PCSR 2017 CIVIL SERVICE EXAM REVIEW GUIDE 9 Week 9: May 28 – June 3 This is the ninth review guide for the Philippine Civil Service Review. In this guide, we will learn about PEMDAS and order of operations. We will also learn new sets of words in our Vocabulary review as well as a… Read More » | 677.169 | 1 |
Teaching Complex Systems with Mathematica
Streamlines of wind direction over North America 2 February 2009, created by "Cloudruns" using Mathematica modeling program. Image from Wikipedia.
Mathematica is a tool for engineering analysis and modeling, and can be used for applications as varied as simple calculator operations to large-scale programming. Mathematica integrates a numeric and symbolic computational engine, graphics system, programming language, documentation system, and advanced connectivity to other applications. The Mathematica product site (more info) includes a description of Mathematica, key elements of the tool, a tour of its features, technical requirements, revision history and a free trial version of the calculation tool | 677.169 | 1 |
Yarnell's World of Math
C2
C2 builds on some of the ideas you learned in C1. For this reason, lots of people find C1 quite easy after
C2.
You will learn more about algebra, including how to do long division. In C1 you learnt equations of
straight lines; in C2 we move onto circles. In C1 you learned about arithmetic series; C2 develops geometric series.
In addition to this we have two new topics: logarithms and trigonometry. | 677.169 | 1 |
Section 3.01 in the book. This is the first of the lessons for the reasoning and properties we are going to use to achieve complete simplification. These are basic definitions of operations we already use and take for granted.5:04
Basic Definitions of Linear Algebra #1
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Kinematics: Basic Definitions
Kinematics: Basic Definitions
Kinematics: Basic Definitions
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Programming Language: Basics Definitions & Terms
Programming Language: Basics Definitions & Terms
Programming Language: Basics Definitions & Terms
This lecture tell you about the basic terms and definitions needed as background of any programming language. To ask your doubts on this topic and much more, click here:
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Basic English Grammar Definitions For All Students
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Unit 1 Basic Definitions and Notation Part 1
Unit 1 Basic Definitions and Notation Part 1published: 23 Jun 2015published: 02 Feb 2009
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Definitions about distance, displacement, speed, velocity, and acceleration. Please comment to give us some feedback.
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This lecture tell you about the basic terms and definitions needed as background of any programming language. To ask your doubts on this topic and much more, click here:
published: 14 Jul 2014published: 22 Dec 2014 ...
Section 3.01 in the book. This is the first of the lessons for the reasoning and properties we are going to use to achieve complete simplification. These are basic definitions of operations we already use and take for granted. c...The Professor gives the definitions of a vector space, a linearly independent set, and a linearly dependent set. In the definition of linearly independent the condition should read \alpha_1=\alpha_2 = ... = \alpha_k =0$. He says this but does not write it on the board.
Programming Language: Basics Definitions & Terms
This lecture tell you about the basic terms and definitions needed as background of any programming language. To ask your doubts on this topic and much more, cl...
This lecture tell you about the basic terms and definitions needed as background of any programming language. To ask your doubts on this topic and much more, click here:
This lecture tell you about the basic terms and definitions needed as background of any programming language. To ask your doubts on this topic and much more, click here:
Basic English Grammar Definitions For All Students
This is video of English grammar, covering all the basic definitions of English grammar that your kids should know to secure pretty marks in school exams. This... ...published: 17 Dec 2014
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Differential Equations -- Lesson1 -- Basic definIn a joint report with the World Bank, the United Nations health agency said it was completely unacceptable that more than half the world's people still don't get the most basic healthcare ... The report did have some good newsThe company's revenue rose 25 percent in the first of financial year 2017-18 led by robust sales in the agrochemicals and basic chemicals segments, outpacing the single digit-growth for the industry overall....
We will continue to work closely with the Early ChildhoodCommission to ensure that more of our basic schools and infant departments meet the required standards," Senator Reid said ... This number includes three infant schools, 31 infant departments, 76 basic schools, and 29 prep and kinder institutions, the ministry said ... ....
BENGALURU. The Karnataka government's ambitious affordable housing scheme through the BDA has come as a disappointment to the allottees, as the area lacks basic amenities ... "It's been a year since we were allotted sites but building a house still remains a pipe dream for many of us, as the BDA has failed to develop basic amenities at the layout ... Around 60,000 sites were to be developed in the layout ... ....
members aim to achieve by 2030. Abe made the announcement alongside U.N ... Abe also proposed a new interim universal health coverage target. that 1 billion more people are able to receive basic health services by 2023. At present, the WHO aims to ensure by 2030 that 80 percent of the population of developing countries have access to basic health services and that no one falls into poverty due to out-of-pocket expenses on health care ... .... | 677.169 | 1 |
Friday, May 20, 2011
Module 2: Deductive Method
DEDUCTIVE METHOD
Deductive method is based on deduction. In this approach we proceed from general to particular and from abstract and concrete. At first the rules are given and then students are asked to apply these rules to solve more problems. This approach is mainly used in Algebra, Geometry and Trigonometry because different relations, laws and formulae are used in these sub branches of mathematics. In this approach, help is taken from assumptions, postulates and axioms of mathematics. It is used for teaching mathematics in higher classes.
Deductive approach proceeds form
ØGeneral rule to specific instances
ØUnknown to know
ØAbstract rule to concrete instance
ØComplex to simple
Steps in deductive approach
Deductive approach of teaching follows the steps given below for effective teaching
üClear recognition of the problem
üSearch for a tentative hypothesis
üFormulating of a tentative hypothesis
üVerification
Example 1:
Find a2 X a10 = ?
Solution:
General : am X an = am+n
Particular: a2 X a10 = a2+10= a12
Example 2:
Find (102)2= ?
Solution:
General: (a+b)2 =a2+b2+2ab
Particular: (100+2) 2 = 1002 + 22 + (2 x 100 x 2)
= 10000+4+400= 10404
MERITS
ØIt is short and time saving method.
ØIt is suitable for all topics.
ØThis method is useful for revision and drill work
ØThere is use of learner's memory
ØIt is very simple method
ØIt helps all types of learners
ØIt provides sufficient practice in the application of various mathematical formulae and rules.
ØThe speed and efficiency increase by the use of this method.
ØProbability in induction gets converted into certainty by this method.
DEMERITS
ØIt is not a psychological method.
ØIt is not easy to understand
ØIt taxes the pupil's mind.
ØIt does not impart any training is scientific method
ØIt is not suitable for beginners.
ØIt encourages cramming.
ØIt puts more emphasis on memory.
ØStudents are only passive listeners.
ØIt is not found quite suitable for the development of thinking, reasoning, and discovery.
Applicability of Deductive Approach
Deductive approach is suitable for giving practice to the student in applying the formula or principles or generalization which has been already arrived at.This method is very useful for fixation and retention of facts and rules as at provides adequate drill and practice. | 677.169 | 1 |
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Device Combines Features Of Computer & Calculator
11/01/95
Expressly designed for high-school and college mathematics instruction, the TI-92 combines the power of computer software and the independence of a calculator. The portable, hand-held unit sports a full QWERTY keyboard, numeric keypad, eight-direction cursor and function keys that operate pull-down menus. It supports NCTM standards and accommodates a broad range of math subjects from algebra through calculus. For example, the TI-92's interactive geometry applications allow students to build objects using points, lines, triangles, polygons, circles, arcs and other basic shapes. Objects can be translated, rotated and dilated. Its symbolic manipulation features, meanwhile, were developed in conjunction with Soft Warehouse, authors of DERIVE. Students may explore polynomial factors, roots of equation, indefinite integrals, derivatives, limits and Taylor polynomials. Expressions appear on the screen just as they would in a printed textbook. The device graphs functions, parametric equations, polar equations, recursively defined sequences and 3D surfaces. With optional TI-GRAPH LINK software, one may transfer data and programs between the TI-92 and a computer. The TI-92 is also compatible with the firm's Calculator-Based Laboratory (CBL) System, for analyzing real-world data. Texas Instruments, Dallas, TX, (800) TI-CARES | 677.169 | 1 |
Secondary Mathematics I
Part 1
MATH 051
$ 152.00
Prerequisite:
Pre-Algebra, Part 2 (ALG 043) or equivalent.
Description:
This integrated math course is a study of the properties of sets of real numbers, linear equations and graphs, linear functions, systems of equations and inequalities, segments and angles, mathematical reasoning, parallel lines, and sequences and series. This is the first course in a six-part High School Integrated Math series (MATH 051, MATH 052, MATH 053, MATH 054, MATH 055, and MATH 056). This course also encompasses Common Core content.
Course Content:
Working with a Set of Real Numbers
Solving Linear Equations and Graphing
Linear Functions
Systems of Equations and Inequalities
Segments and Angles
Mathematical Reasoning
Parallel Lines
Sequences and Series
Online Courses:
Course materials are accessed online, and all assignments must be submitted online. Optional course readings may be available but do not include the self-check assignments or graded assignments.
Notes:
Note for Mac users: It is strongly recommended that Chrome or Safari be used as the browser; Adobe Reader must be used to view this course. | 677.169 | 1 |
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Home
CAPSTONE COURSE OVERVIEW
The units shown below have all undergone several reviews by the teachers in the first and/or second cohort. Please feel free to use them as is, or to alter them to meet the needs of your students. If you use a unit and have some suggestions for improving that unit, please do not hesitate to share those improvements with us at this website, or at mthmtcs@verizon.net
The units were developed with support through the VADOE Mathematics and Science Partnership Grant Program NCLB Title II Part B program by participants in the University of Virginia's School of Continuing and Professional Studies Office of Mathematics Outreach 21st Century Grant Project.
The matrix below presents the title of each unit, a predication for the minimum number of class hours required, and the mathematics strands emphasized in the unit.
A Task-Based Unit is designed for 3 to 8 hours of class time and generally includes more teacher direction along with students working collaboratively in pairs or groups of three.
A Project-Based Unit is designed for more than 8 hours of class time with limited teacher direction during the project.There is an expectation that student groups will work independently and will engage in research and data collection during the unit.
A Problem-Based Unit is one that entails giving students a real world problem, and asking them to do their best to develop a solution on their own or in groups, using research and problem solving skills, over a period of 3-4 weeks or over the length of a semester as an ongoing project. The teacher is a coach/advisor throughout the project, but this is totally student-centered. It may be considered a culminating activity for the course. | 677.169 | 1 |
Copyright Statement
Abstract
Purpose:
The uptake of mathematics in schools is falling, partially due to the learning
techniques employed by teachers. This project investigated the possibility of
introducing the concept of calculus and its capabilities to students aged 10 to 12
years using computer based algebra system software.
Methodology:
Teachers from five schools were brought to the university for a day of training in
the use of computer algebra software MAPLE. They returned to their classes in
four Australian states to deliver a sequence of 11 lessons where students had
individual computer access. At the end of the program, the students attempted a
test based on first year engineering degree calculus examinations.
Important findings:
The findings of this study showed that properly structured learning programmes
utilising appropriate technology can impart high level knowledge and skills to
students and provide them with a good understanding of the applications, thus
motivating them to engage in such studies. Females also demonstrated better skills
at solving real world problems contrary to published data.
Conclusions:
Curriculum designers and school communities should consider providing access
to more advanced mathematics instruction than previously available, using the
affordances of new technology. | 677.169 | 1 |
System requirements:
Our users:
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Find the LCD for the given rational expressions and convert the rational expressions into equivalent rational expressions with the LCD as the denominator | 677.169 | 1 |
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Basic Algebra Practice
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Do you grasp the basics of algebra? Find out with this instantly scored practice set. Complete answer explanations for each question help you work through each problem, and a detailed score report will help you identify areas that need work. | 677.169 | 1 |
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Product Description
Solving equations is a foundational skill needed in pre-algebra and algebra. Being able to solve a variety of equations enables students to analyze functional relationships.
Students need practice in solving equations in order to develop fluency in uncovering unknown values. These equations include multiple steps, including the use of integers, distributive property and variables on both sides. | 677.169 | 1 |
Geometry is a course that explores properties, measurements, and relationships of points, lines, surfaces, and solids in space. Students integrate their extensive knowledge of Algebra 1 with Euclidian geometry concepts to solve real world problems. It is a year-long course and meets for 45 minutes each day.
Students are required to have a full credit in Algebra I with a preference for college prep Algebra I prior to taking this course. Students must have passed Algebra I or have obtained permission of the building principal in order to take geometry.
Algebra II
Course Description
Algebra II include all the essential topics needed to be successful in College Algebra, Pre-Calculus or Trigonometry. Topics covered are listed specifically under the scope and sequence
and include: operations on vectors and matrices; factorial notation; analyzing families functions; quadratic formula; logarithms; trigonometric functions; families of functions with graphs that have rotation symmetry or reflection symmetry; graphs of conic sections; complex numbers; recursive functions; least squares regression lines; regression coefficient; correlation coefficient; random sampling; analyze and summarize data; use technology to compute standard deviation; and use of spreadsheets and graphing calculators. Algebra II meets 45 minutes each day and covers the entire school year. One math credit is earned. Prerequisite for Algebra II: Students must earn a C or better in both Geometry and Algebra I or permission of the instructor.
Consumer Math
Course Description
Math skills needed to survive as an intelligent consumer in today's society will be developed in Consumer Math. Topics will include the mathematics of personal income, buying a car and related expenses, purchasing various types of insurance, housing, unit pricing, discounts and mark-ups, banking, budgeting, investments, taxes, travel and fitness. All juniors and seniors would benefit by taking this course.
A study of limits, derivatives, and integration, considered analytically, numerically and graphically.
Algebra III
This course covers quadratics, conics, polynomials, functions, logarithms, clever factorizations and substitutions, systems of equations, sequences and series, symmetric sums, advanced factoring methods, classical inequalities, and functional equations. This class covers much of the curriculum of a standard Algebra 2 class and most of the non-trigonometric topics of a typical Pre-Calculus course. It also includes many challenging aspects of algebraic problem solving that are beyond that presented in a typical Algebra 2 or Pre-Calculus course.
Algebra II – College Prep – can earn college credit
This is an accelerated course. Most of the topics are the same as those found in Algebra II but are covered more rapidly and in greater depth. This course begins with connections back to earlier work, efficiently reviewing Algebraic and statistical concepts that students have already studied while at the same time moving students forward into new concepts. Students expand their library of functions to include polynomial functions, logarithmic functions, rational functions, and trigonometric functions. With a larger library of functions, students increase their ability to model situations, make predictions and answer questions about the situation. | 677.169 | 1 |
This is the first lesson in an elective credit class for Medical Careers. It includes a SmartBoard presentation, student guided notes sheet, and student worksheet. This lesson presents a brief overall history of health care throughout time.
This is the second lesson in an elective credit class for Medical Careers. It includes a SmartBoard presentation, student guided notes sheet, and student worksheet. This lesson presents a brief look at some of the important figures in the history
This bundle includes guided notes, SmartBoard lesson and worksheet.
Objectives: You will be able to:
1) explain how medical terms are developed
2) describe the process of pluralizing terms
3) describe how to interpret pronunciation marks
4) list
This is a basic lesson concerned with introducing students to the most frequently used special keys on the TI graphing calculators. This file is the worksheet for students to use to explore the graphing calculator.
This packet includes a fill in the blank type proof that may either have the statements, reasons, or a combination of the two missing. Answer key is included. This packet covers the various algebraic properties.
This is a project that was designed for my Functions class after learning about how to solve systems of equations. The project contains a silly scenarios where the students will need to find information and use systems of equations to arrive at
This project was created for my Functions A class. The project contains real life types of problems where students need to write a linear equation based on the information in the problem. Additionally, they need to identify the independent and
This packet was designed for my functions B class. It includes graphing single and systems of inequalities, determining if a coordinate is a solution to an inequality or system of inequalities, and writing systems of inequalities from word problems.
This bundle includes guided notes, SmartBoard presentation, and worksheet. Objectives: You will be able to
1) define the elements of the human body structure
2) describe the planes of the body
3) locate the body cavities and list organs that are | 677.169 | 1 |
Algebraic Proof Poster
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Product Description
This is an activity to get students ready for two-column proofs in Geometry. They use Properties of Equalities to describe each step in solving the algebraic equation. The "T" table method is to show the algebraic steps on the left side of the T table, and state the property on the right side.
They must produce a poster.
Four different equation sets are given so that you can differentiate the difficulty of the problem that you give the student. | 677.169 | 1 |
Don't let quadratic equations make you irrational If you are absolutely confused by absolute value equations, or you think parabolas are short moral stories, College Algebra DeMYSTiFied, Second Edition is your solution to mastering the topic's concepts and theories at your own pace. This thoroughly revised and updated guide eases you into the subject, beginning with the math fundamentals then introducing you to this advanced form of algebra. As you progress, you will learn how to simplify rational expressions, divide complex numbers, and solve quadratic equations. You will understand the difference between odd and even functions and no longer be confused by the multiplicity of zeros. Detailed examples make it easy to understand the material, and end-of-chapter quizzes and a final exam help reinforce key ideas. It's a no-brainer! You'll learn about: The x-y coordinate plane Lines and intercepts The FOIL method Functions Nonlinear equations Graphs of functions Exponents and logarithms Simple enough for a beginner, but challenging enough for an advanced student, College Algebra DeMYSTiFieD, Second Edition is your shortcut to a working knowledge of this engaging subject.
Preempt your anxiety about PRE-ALGEBRA! Ready to learn math fundamentals but can't seem to get your brain to function? No problem! Add Pre-Algebra Demystified, Second Edition, to the equation and you'll solve your dilemma in no time. Written in a step-by-step format, this practical guide begins by covering whole numbers, integers, fractions, decimals, and percents. You'll move on to expressions, equations, measurement, and graphing. Operations with monomials and polynomials are also discussed. Detailed examples, concise explanations, and worked problems make it easy to understand the material, and end-of-chapter quizzes and a final exam help reinforce learning. It's a no-brainer! You'll learn: Addition, subtraction, multiplication, and division of whole numbers, integers, fractions, decimals, and algebraic expressions Techniques for solving equations and problems Measures of length, weight, capacity, and time Methods for plotting points and graphing lines Simple enough for a beginner, but challenging enough for an advanced student, Pre-Algebra Demystified, Second Edition, helps you master this essential mathematics subject. It's also the perfect way to review the topic if all you need is a quick refresh.
Your step-by-step solution to mastering precalculus Understanding precalculus often opens the door to learning more advanced and practical math subjects, and can also help satisfy college requisites. Precalculus Demystified, Second Edition, is your key to mastering this sometimes tricky subject. This self-teaching guide presents general precalculus concepts first, so you'll ease into the basics. You'll gradually master functions, graphs of functions, logarithms, exponents, and more. As you progress, you'll also conquer topics such as absolute value, nonlinear inequalities, inverses, trigonometric functions, and conic sections. Clear, detailed examples make it easy to understand the material, and end-of-chapter quizzes and a final exam help reinforce key ideas. It's a no-brainer! You'll learn about: Linear questions Functions Polynomial division The rational zero theorem Logarithms Matrix arithmetic Basic trigonometry Simple enough for a beginner but challenging enough for an advanced student, Precalculus Demystified, Second Edition, Second Edition, helps you master this essential subjectElementary Statistics: A Step by Step Approachis for beginning statistics courses with a basic algebra prerequisite. The book is non-theoretical, explaining concepts intuitively and teaching problem solving through worked examples and step-by-step instructions. This edition places more emphasis on conceptual understanding and understanding results. It also features increased emphasis on Excel, Minitab, and the TI-83 Plus and TI-84 Plus graphing calculators, computing technologies commonly used in such coursesStudent Study Guide for use with Elementary Statistics A Step By Step Approach has been writing in one form or another for most of life. You can find so many inspiration from Student Study Guide for use with Elementary Statistics A Step By Step Approach also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Student Study Guide for use with Elementary Statistics A Step By Step Approach book for free.
ELEMENTARY STATISTICS: A STEP BY STEP APPROACH is for general beginning statistics courses with a basic algebra prerequisite. The book is non-theoretical, explaining concepts intuitively and teaching problem solving through worked examples and step-by-step instructions. This edition places more emphasis on conceptual understanding and understanding results. This edition also features increased emphasis on Excel, MINITAB, and the TI-83 Plus and TI 84-Plus graphing calculators, computing technologies commonly used in such courses.
Elementary Statistics: A Brief Version is for Introductory Statistics courses with a Basic Algebra prerequisite. The book is non-theoretical, explaining concepts intuitively and teaching problem solving through worked examples and step-by-step instructions. In recent editions, Al Bluman has placed more emphasis on conceptual understanding and understanding results, along with increased focus on Excel, MINITAB, and the TI-83 Plus and TI-84 Plus graphing calculators; computing technologies commonly used in such courses.
Elementary Statistics A Step By Step Approach has been writing in one form or another for most of life. You can find so many inspiration from Elementary Statistics A Step By Step Approach also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Elementary Statistics A Step By Step Approach book for free.
Paris ve Londra da Be Paras z has been writing in one form or another for most of life. You can find so many inspiration from Paris ve Londra da Be Paras z also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Paris ve Londra da Be Paras z | 677.169 | 1 |
David E. Coates, AZ
Your program saved my grade this semester. It didn't just help me with my homework, it taught me how to solve the problems. Sean O'Connor
I consider this software as replacement of human algebra tutor. That too, at a very affordable price. Tabitha Wright, MN28:
dividing a decimal fraction by a percentage
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Math Quadratic Formula Worksheets and instructions on how to solve the quadratic formula
objective question in math mathematics+ 10th standard
variable exponent problems
For a single substance at atmospheric pressure, classify the following as describing a spontaneous process, a nonspontaneous process, or an equilibrium system. | 677.169 | 1 |
Note: Citations are based on reference standards. However, formatting rules can vary widely between applications and fields of interest or study. The specific requirements or preferences of your reviewing publisher, classroom teacher, institution or organization should be applied.
Complex analysis
The guiding principle of this presentation of ``Classical Complex Analysis'' is to proceed as quickly as possible to the central results while using a small number of notions and concepts from other fields. Thus the prerequisites for understanding this book are minimal; only elementary facts of calculus and algebra are required. The first four chapters cover the essential core of complex analysis: - differentiation in C (including elementary facts about conformal mappings) - integration in C (including complex line integrals, Cauchy's Integral Theorem, and the Integral Formulas) - sequences and series of analytic functions, (isolated) singularities, Laurent series, calculus of residues - construction of analytic functions: the gamma function, Weierstrass' Factorization Theorem, Mittag-Leffler Partial Fraction Decomposition, and -as a particular highlight- the Riemann Mapping Theorem, which characterizes the simply connected domains in C. Further topics included are: - the theory of elliptic functions based on the model of K. Weierstrass (with an excursions to older approaches due to N.H. Abel and C.G.J. Jacobi using theta series) - an introduction to the theory of elliptic modular functions and elliptic modular forms - the use of complex analysis to obtain number theoretical results - a proof of the Prime Number Theorem with a weak form of the error term. The book is especially suited for graduated students in mathematics and advanced undergraduated students in mathematics and other sciences. Motivating introductions, more than four hundred exercises of all levels of difficulty with hints or solutions, historical annotations, and over 120 figures make the overall presentation very attractive. The structure of the text, including abstracts beginning each chapter and highlighting of the main results, makes this book very appropriate for self-guided study and an indispensable aid in preparing for tests. This English edition is based on the fourth forthcoming German editionProviding a description of classical complex analysis, this book presents the fundamental results, followed by elliptic functions and elliptic modular functions. Rounded by excursions to analytic number theory, it includes more than 400 exercises with hints for solutions.Read more...
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Publisher Synopsis
From the reviews: "The guiding principle of the presentation of classical complex analysis is to proceed as quickly as possible to the central results while using a small number of notions and concepts from other fields. Thus the prerequisites for understanding this book are minimal; only elementary facts of calculus and algebra are required. a ] Motivating introductions, more than four hundred exercises of all levels of difficulty with hints or solutions, historical annotations, and over 120 figures make the overall presentation very attractive." (La (TM)Enseignement Mathematique, Vol. 52 (2), 2006) "The first four chapters cover the essential core of complex analysis a ] . The second part of the book is devoted to an extensive representation of the theory of elliptic functions a ] . Interesting introductions, over four hundred exercises with hints or solutions, historical remarks, and over 120 figures make this book very appropriate and attractive for students at all levels." (F. Haslinger, Monatshefte fA1/4r Mathematik, Vol. 149 (3), 2006) "It is, in fact, a massive introduction to complex analysis, covering a very wide range of topics. a ] This is the material that I like to cover in an undergraduate course. a ] Theorems and proofs are clearly delimited, which many students find helpful. a ] There are problems at the end of each section, and sketches of solutions are given a ] . Overall, this is quite an attractive book." (Fernando Q. GouvAaa, MathDL, February, 2006)Read more... | 677.169 | 1 |
Math In Automotive Technology
Math in Automotive Technology is an eleven-minute video which is part of the series, Math in Technology. "But why do I need math?" Now, using this series, give students a clear, definitive, and logical answer. Math is necessary to get the job done in most technical fields, including auto mechanics, electricity/electronics, and the building trades. Each video shows real-life problem situations solved by using practical math and actual computations on the screen. Use Introduction to Math in Technology as an overview and then progress to specific topics. At last..a program to help your students succeed in the world of technical math. | 677.169 | 1 |
GED Mathematics (Steck-Vaughn Ged Series)
Provides instructions for studying for and taking the mathematics section of the high school equivalency test.
"synopsis" may belong to another edition of this title.
From the Back Cover:
The GED Mathematics Test focuses on the practical use of basic arithmetic, algebra, and geometry. You will be tested on your understanding of how to solve a problem and your ability to do the math to find a solution.
Book Description Paperback. Book Condition: New. 2001st. Paperback. The GED Mathematics Test focuses on the practical use of basic arithmetic, algebra, and geometry. You will be tested on your understanding of how to solve a problem and your ability to do.Shipping may be from multiple locations in the US or from the UK, depending on stock availability. 480 pages. 0.953. Bookseller Inventory # 97 | 677.169 | 1 |
MATH mat131 Advice
Showing 1 to 1 of 1
The class is very informative, fast paced, and interactive. Ms Legault is knowledgeable, available, and approachable. She has set forth clear instructions and a detailed outline of course work. The class, though not easy, is very organised and focused. The material is practical and basic, and can be applied daily in our lives.
Course highlights:
I am currently learning percents and fractions, and how it is used in our daily lives with word problems and very real live situations. We are also learning how to convert English system to the Metric system and vise versa and the importance of knowing the two. We also have in depth discussions on the importance of math, metrics, and usage in real world situations.
Hours per week:
6-8 hours
Advice for students:
Study hard and do not procrastinate. There are several problems in my math lap that took me 30 minutes to complete with multi answers per question. You need to set several hours a week aside to focus quietly and learn. Doing math needs to be distraction free. | 677.169 | 1 |
MATLAB Lecture 2 Handout - Aerospace Practicum Introduction...
Aerospace Practicum Introduction to MATLAB Lecture #2 In-Class Practice Exercises Complete these problems if you finish all of the in-class demonstrations before the laboratory is over. If you do not get to these in class, take a look at them during your own time, but you need not hand in these exercises with laboratory homework assignment #2. Notes: • First, remember that you are learning MATLAB for the first time. Like any new piece of software, it will take you a while to figure out how to use the program and it will certainly take a while before you have mastered the full capabilities of what the program can do. Please be patient with it; once you get the hang of how to use MATLAB, you will have a very powerful tool at your disposal that you can use throughout your career. • Remember that any time you forget what a MATLAB command does you can simply type help and the name of the command. For example, if you need a refresher on how the plot command works, you can type: help plot
This
preview
has intentionally blurred sections.
Sign up to view the full version. | 677.169 | 1 |
Objective Approach to Mathematics –Vol 1 For JEE Main & Advanced
horough and comprehensive knowledge of the concepts is required by the aspirants appearing for popular engineering entrances like JEE Main & Advanced, MHT CET, BITSAT, GUJ-CET, VIT, Manipal, OJEE, Karnataka CET, WBJEE, etc. And to help aspirants master the concepts of Mathematics, Arihant has come up with the revised edition of Objective Mathematics Volume 1. The present book has been designed in sync with Class XI Mathematics NCERT textbook to help aspirants prepare for the competitions along with their school studies. The book contains more than 5000 objective questions of all types like single option correct, matching, assertion-reason and statement based questions. The book has been divided into 21 chapters namely Sets, Fundamentals of Relation & Function, Sequence & Series, Complex Numbers, Inequalities & Quadratic Equation, Permutation & Combination, Mathematical Induction, Binomial Theorem, Trigonometric Functions & Equations, Properties of Triangles, Heights & Distances, Cartesian System of Rectangular Coordinates, Straight Line & Pair of Straight Lines, Circle, Parabola, Ellipse, Hyperbola, Introduction to Three Dimensional Geometry, Introduction to Limits & Derivatives, Mathematical Reasoning, Statistics and Fundamentals of Probability, each sub-divided into number of topics. The ample number of solved and unsolved questions provided in the book | 677.169 | 1 |
Editor's review
Mathematics is a subject that encompasses study of space and quantity that mathematicians ascertain with the use of numbers and equations that also include calculations and measurement. Teachers and educational professionals strive to prepare interactive quizzes and tests to facilitate greater learning through effectual practice that strengthens an individual's grasp over the subject. Since the arrival of computer systems and other digital media, the educational sector has benefited a lot in the form of processing varied learning procedures that can be imparted through the web crossing barriers of borders and even nations. Several applications are available nowadays that aid in preparation of concepts and tests for training purposes; however in case of Mathematics, Mathpad 1.0 is a unique device that one can use for preparing quizzes and analysis.
Mathpad opens with a neatly arranged interface with the main options placed at the top panel and main screen displaying the prepared equations intuitively. This easy to operate text editor for Mathematics that facilitates effective mixing of ordinary text and any other mathematical expression which is useful for Math teachers to create handouts, tests and interactive quizzes or even save the formatted text as an image for future reference. The program works easily with the user just requiring to type in the characters at the keyboard and various other features to help in creating equations easily. Moreover, the program also includes implementation of standard italics for inserting mathematical symbols easily and even allows simple making of exponents, fractions and roots. It also features mathematical drawings and graphs and is a delight for any Mathematics teacher and even students who love math as a subject.
To conclude, Mathpad 1.0 comes across as a useful utility for preparing Mathematics quiz modules and tests that will intuitively help the learners to practice and hence gets a rating score of 3.5 points for its utility value.
Publisher's description With most equation editors you choose a template with the mouse, type a few keystrokes and repeat the process. Mathpad doesn't work this way. Mainly, you just type characers at the keyboard. Most people find this to be easier and faster.
Mathpad has some unusual features. For example, the implementation of standard italics for math symbols is simplified by the "automatic math" specification. In this mode, the ordinary text and math expressions get italicized correctly. Another example - the macros feature allows macros with arguments and is easier to use than more sophisticated macros as in Tex/
User comments
+simple, logical interface
-poor file compatibility
-full range of greek letters and logical indicators not included
The product is an easy to use mathematical keyboard interface and suitable for many basic applications, but since it does not include the full range of commonly used mathematical indicators and other greek lettering it is difficult to generate concise and logical mathematical, logical and scientific notes beyond a certain level. Furthermore the files and symbols are stored as images rather than font/text based data, hampering compatibility with other notes and programs used. The `dual screen` interface does facilitate easy use and comprehension, but I would personally rather use software which automatically generated the stated characters in one text window.
The developers need to add those numbers, with the infinity line above each, so infinity numbers can be written, considering infinity numbers are a significant part of math but cannot be expressed in MathPad. :( | 677.169 | 1 |
¥These courses are based on the premise that teachers not only need to
understand concepts of higher level
mathematics, but also need to know how these
concepts are manifested in high school
and middle school mathematics
curricula. The courses connect problems suitable for exploration by middle or high school
students to problems from the college
courses. | 677.169 | 1 |
Mathematics and music! Sounds odd! But no we believe that they go hand in hand, they synergize! And that is why we had a unique competition called "Mathathon" which stands for a marathon of Mathematics. We conducted a logical mathematics competition with a soothing music back ground! And trust us it rocked!
Students from grades 7 – 9 competed against each other(in their own grades) and themselves in a contest that tested their logical reasoning and that too at a high speed. Students set a very high benchmark and met it with their zeal, enthusiasm and sincerity. As it was an inter-house event, students participated with high spirits to earn maximum scores for their house. Mathematics was what got them going and music was what supported. Thanks to all SS teachers and the Math team for making it a success!!
Dear Parents and Students,
Please find below the details of the syllabus of Mathematical Studies SL for the 1st Term examination of 2017-2018.
Syllabus for first term examination :
(1) Number & Algebra
(2) Descriptive Statistics
(3) Geometry & Trigonometry
There will be two papers for Mathematical Studies SL for the first term examination:
Paper 1:
Total Marks- 50
Duration- 1 hour
8 compulsory short-response questions based on the topics mentioned above.
Weightage- 50%
Syllabus coverage
• Knowledge of all topics is required for this paper. However, not all topics are necessarily assessed in
every examination session.
• The intention of this paper is to test students' knowledge and understanding across the breadth of the
syllabus. However, it should not be assumed that the separate topics are given equal emphasis.
Question type
• Questions may be presented in the form of words, symbols, diagrams or tables, or combinations of these.
• Questions of varying levels of difficulty are set.
• One or more steps may be needed to answer each question.
Paper 2:
Total Marks- 50
Duration- 1 hour
3 compulsory extended-response questions based on the topics mentioned above.
Weight-age- 50%
Questions in this section will vary in terms of length and level of difficulty.
Individual questions will not be worth the same number of marks. The marks allocated are indicated at
the start of each question.
Syllabus coverage
• Knowledge of all topics is required for this paper. However, not all topics are necessarily assessed in
every examination session.
• The intention of this paper is to test students' knowledge and understanding of the syllabus in depth. The
range of syllabus topics tested in this paper may be narrower than that tested in paper 1.
Question type
• Questions require extended responses involving sustained reasoning.
• Individual questions may require knowledge of more than one topic.
• Questions may be presented in the form of words, symbols, diagrams or tables, or combinations of these.
• Normally, each question reflects an incline of difficulty, from relatively easy tasks at the start of aquestion to relatively difficult tasks at the end of a question. The emphasis is on problem-solving.
Important Note:
Calculators:
1) For both examination papers, students will have an access to a GDC at all times.
Mathematical studies SL formula booklet
1) Each student will have access to a clean copy of the formula booklet during the examination.
Awarding of marks
1) In addition to correct answers, marks are awarded for method, accuracy and reasoning.
2) In paper 1, full marks are awarded for each correct answer irrespective of the presence or absence of working.
Where an answer is incorrect, marks are given for correct method. All students should therefore be advised to
show their working.
3) In paper 2, full marks are not necessarily awarded for a correct answer without working. Answers must be
supported by working and/or explanations. Where an answer is incorrect, marks are given for correct method. All students should therefore be advised to show their working.
Feel free to communicate your queries. | 677.169 | 1 |
Linear Algebra
For half a century, more than 40 million students have trusted Schaum's to help them study faster, learn better, and get top grades. Now Schaum's celebrates its 50th birthday with a brand-new look, a new format with hundreds of practice problems, and completely updated information to conform to the latest developments in every field of study.
Schaum's Outlines-Problem Solved
More than 500,000 sold
Linear algebra is a foundation course for students entering mathematics, engineering, and computer science, and the fourth edition includes more problems connected directly with applications to these majors. It is also updated throughout to include new essential appendices in algebraic systems, polynomials, and matrix applications.
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Comment
This book helped me sooo much! With it, I was able to pull my marks in university up a lot!! Some high schools don't teach enough linear algebra for university, so I highly suggest reading it before university, especially if you're just going into first year!! | 677.169 | 1 |
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