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Create professional-quality mathematics worksheets to provide students in grades K to ... part of a complete numeracy program. Over 70 mathematics worksheet activities can be produced to advance and ... and font. The worksheets that you create with Mathematics Worksheet Factory are not pre-designed but are randomly ... complex set of algorithms corresponding to the specific mathematical structure of each type of worksheet. This allows .... Free download of Math Resource Studio 4.4.2
Mathematics program intended for High School pupils (age 14-16) This Title comprises 24 chapters of complete courses completed with exercises covering every subject undertaken. The exercises are corrected step by step using the Evalutel Teaching Method which reconciles the struggle against failure in school and the valorisation of the most .... Free download of ALGEBRA 2 : Developments & applications 4.00.005 | 677.169 | 1 |
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Number and Operations, Measurement, Geometry, Data Analysis and Probability, Algebra
COMPETENCY GOAL 5: The learner will demonstrate an understanding of patterns, relationships, and elementary algebraic representation.
Technical Mathematics I
Number and Operations
Competency Goal 1: The learner will apply various strategies to solve problems.
3rd Grade
Algebra
The student will demonstrate through the mathematical processes an understanding of numeric patterns, symbols as representations of unknown quantity, and situations showing increase over time.
7th Grade
Algebra
The student will demonstrate through the mathematical processes an understanding of proportional relationships.
Intermediate Algebra
Algebra
The student will demonstrate through the mathematical processes an understanding of sequences and series.
3rd Grade
Algebra
Content Standard 2.0 The student will understand and generalize patterns as they represent and analyze quantitative relationships and change in a variety of contexts and problems using graphs, tables, and equations.
4th Grade
Algebra
The student will understand and generalize patterns as they represent and analyze quantitative relationships and change in a variety of contexts and problems using graphs, tables, and equations.
5th Grade
Algebra
The student will understand and generalize patterns as they represent and analyze quantitative relationships and change in a variety of contexts and problems using graphs, tables, and equations.
6th Grade
Algebra
Content Standard 2.0 The student will understand and generalize patterns as they represent and analyze quantitative relationships and change in a variety of contexts and problems using graphs, tables, and equations.
7th Grade
Algebra
The student will understand and generalize patterns as they represent and analyze quantitative relationships and change in a variety of contexts and problems using graphs, tables, and equations.
8th Grade
Algebra
The student will understand and generalize patterns as they represent and analyze quantitative relationships and change in a variety of contexts and problems using graphs, tables, and equations.
Algebra I
Algebra
Students will describe, extend, analyze, and create a wide variety of patterns and functions using appropriate materials and representations in real world problem solving.
Algebra II
Algebra
Students will describe, extend, analyze, and create a wide variety of patterns and functions using appropriate materials and representations in real-world problem solving, and will demonstrate an understanding of the behavior of a variety of functions and their graphs.
Geometry
Algebra
Students will recognize, extend, create, and analyze a variety of geometric, spatial, and numerical patterns; solve real-world problems related to algebra and geometry; and use properties of various geometric figures to analyze and solve problems.
Grade 4
Patterns, Relationships, and Algebraic Thinking
7. The student uses organizational structures to
analyze and describe patterns and relationships. The student is expected to describe the
relationship between two sets of related data such as ordered pairs in a table.
3rd Grade
Patterns, Functions, and Algebra
3.24 The student will recognize and describe a variety of patterns formed using concrete objects, numbers, tables, and pictures, and extend the pattern, using the same or different forms (concrete objects, numbers, tables, and pictures).
4th Grade
Patterns, Functions, and Algebra
4.21 The student will recognize, create, and extend numerical and geometric patterns, using
concrete materials, number lines, symbols, tables, and words.
4.21
5th Grade
Patterns, Functions, and Algebra
5.20 The student will analyze the structure of numerical and geometric patterns (how they change or grow) and express the relationship, using words, tables, graphs, or a mathematical sentence. Concrete materials and calculators will be used.
7th Grade
Patterns, Functions, and Algebra
7.19 The student will represent, analyze, and generalize a variety of patterns, including arithmetic sequences and geometric sequences, with tables, graphs, rules, and words in order to investigate and describe functional relationships.
Teacher Preparation
Key Terms
combinatorics
The science that studies the numbers of different combinations, which are groupings of numbers. Combinatorics is often part of the study of probability and statistics
fractal
Term coined by Benoit Mandelbrot in 1975, referring to objects built using recursion, where some aspect of the limiting object is infinite and another is finite, and where at any iteration, some piece of the object is a scaled down version of the previous iteration
multiples
The product of multiplying a number by a whole number. For example, multiples of 5 are 10, 15, 20, or any number that can be evenly divided by 5
Lesson Outline
Focus and Review
Remind students what has been learned in previous lessons that will be pertinent to this lesson
and/or have them begin to think about the words and ideas of this lesson.
Ask the students to recall what a
multiple is and to think of an example. Have a student share his example with the class
Have the students also consider
Pascal's Triangle. If your class has not studied it previously, ask students, "Did you know that multiples make
a pattern in Pascal's Triangle?"
Objectives
Let the students know what it is they will be doing and learning today. Say something like this:
Today, class, we will be talking about the patterns that multiples create in Pascal's Triangle
We are going to use the computers to learn about these patterns, but please do not turn your
computers on or go to this page until I ask you to. I want to show you a little about Pascal's
Triangle and its patterns first.
Teacher Input
In this part of the lesson you will explain to the students how to do the assignment. You should
model or demonstrate it for the students, especially if they are not familiar with how to use our
computer applets.
Check to be sure that the students understand how to make Pascal's Triangle by having them
create a portion on paper, or by drawing one on the board or overhead projector as they tell
you what to write.
Open your browser (but don't let the students open theirs yet) to
Coloring Multiples in Pascal's Triangle in order to demonstrate this activity to the students. Ask students if the triangle that they
created looks like the one displayed on the screen.
You must now explain the applet to the students. This can best be done by setting your own
number: 4 is a good number to choose when explaining this to students
Ask students to name multiples of 4 that they see in the triangle. They will probably name
numbers such as 4, 8, 12, 20, 28, and 36. Click on these numbers to highlight them as the
students call them out
You may have to give hints to help students determine the larger multiples of: 56, 84, 120,
220, 252, 364, 792, 924, 1716, and 3432. Encourage the students to look for the pattern and
make an educated guess about the larger multiples of 4.
Ask a student to describe the pattern that she sees after all the multiples have been found.
Ask the students what types of shapes are made by the multiples within the Pascal's Triangle.
Try another example, letting the students direct your moves. Or, you may simply ask, "Can anyone
describe the steps you will take for this assignment?
If your class seems to understand the process for doing this assignment, simply ask, "Can
anyone tell me what I need to do to complete this worksheet?" or ask, "How do I run this
applet?"
If your class seems to be having a little trouble with this process, do another example
together, but let the students direct your actions:
This time, choose a number such as 8 to try the example with. Let the students call out
multiples of 8 that they see in the triangle."
The multiples of 8 include: 8, 56, 120, 792, and 3432. You might want to ask students to
compare this pattern to the one that was formed by the multiples of 4. Be sure to point
out that all of the multiples of 8 are also multiples of 4 and yet the patterns are very
different (since the multiples of 4 are not necessarily multiples of 8)
Independent Practice
Allow the students to work on their own to complete the rest of the worksheet. Monitor the
room for questions and to be sure that the students are on the correct web site.
Students may need help with finding the multiple of the harder numbers, such as 7. Encourage
the students to devise their own methods for determining the multiples. Suggest that the
students attempt to use their knowledge of the patterns they already discovered to aid in
finding the harder patterns!
Closure
It is important to verify that all of the students made progress toward understanding the concepts
presented in this lesson. You may do this in one of several ways:
Take up the individual or group worksheets to evaluate for completion
Bring the class together and have different groups or individuals share their result for a
particular number with the rest of the class. Allow students who did not get to finish that
number to sketch the result so that they will not lack some of the information needed for full
understanding
Have the students write a short paragraph explaining the type of patterns that they saw
including the similarities between the different pictures, and the type of shapes that
recurred in the pictures
Alternate Outline
This lesson can be rearranged in several ways:
The students may wish to tackle the worksheet in groups.
You may wish to assign different groups with particular numbers to ensure that every option is
attempted for the class discussion later.
Suggested Follow-Up
As an extension, you may have students predict the entended pattern for a particular number when
the Pascal's Triangle is made larger. The class could work together to extend the triangle by hand
(on a bulletin board, perhaps) and see if the predictions were correct. Again, 4 may be a good
number to use for this extension.
You may wish to do a similar lesson to discuss patterns formed by
Coloring Remainders in Pascal's Triangle This activity may prove to be a little more challening for students, may require more
supervision, and may best be done as a class discussion and demonstration. | 677.169 | 1 |
Numbers
Getting numbers, i.e., real numbers of the form 6.26E+3, into a program
can be difficult because standard Delphi objects only understand characters.
SNumbers were created to solve this problem. Just draw
an SNumber on a Delphi form. The
SNumber takes care of converting the keystrokes into
the double precision representation necessary to do calculations. The SNumber
will turn red to warn the user if s/he makes a typing error. It will turn yellow
when a number has been changed but that the computer has not yet read the number.
SSliders are another object in Science Tools. Their maximum and minimum
values can be floating point numbers, unlike Windows sliders which can only take on
integer values. Notice that
the slider can be tied to a SNumber component so that these components mirror each other's
values. See the OnFormCreate method in this application.
Matrix Plot
Plot a function of two variables, F(x,y), as a contour plot, a 2D surface plot,
or as a checker plot. Switch between these representations at run time and
compare rendering speed. Be sure and right mouse click on the plot to see
how the inspector works.
Pendulum
Pendulum demonstrates how to solve an ODE and animate the solution.
Animation is an advanced technique and is not required for
homework. Write your own ODE code for the homework exercise.
It is better to use the Euler or Verlet method than to
use a method, such as Runge-Kutta, that you don't understand yet.
Finding Roots
Galton
Many of you will recognize the relationship between this simulation and the "penny toss"
experiment that we do in Physics 120/130 lab. A ball is dropped onto a board with rows of pegs., i.e., a Galton board.
It has a 50/50 probability of bouncing to the right or left at a peg before it moves on to
the next row. After 10 rows we see how many more times the ball bounced to the right than to the
left. Remember that the bounce is random so it is possible-- but not likely-- that the ball bounces
to the left (or right) 10 times. | 677.169 | 1 |
included in this chapter are: Definition of circle, Concepts related to a circle and its important properties.
Here you will get the CBSE Class 9 Science Solved Practice Paper for the Summative Assessment-II, 2017. This paper designed as per the latest CBSE pattern, is completely solved giving the students an idea about how to write an appropriate answer to every question.
Here you will get the CBSE Class 9 Science Practice Paper for the Summative Assessment-II, 2017. This paper will also make you familiar with the latest CBSE Exam Pattern and also help you get an idea of the important topics to be picked to prepare for SA-II, 2017.
Jagranjosh presents NCERT solution of CBSE Class 9 Mathematics in the form of eBook. These eBooks are completely free and can be downloaded in PDF format. One can access these eBooks anytime and anywhere with their mobile devices. | 677.169 | 1 |
H2 Maths: Verifying if vector line equations are equivalent
Is there life after O/A-Levels? Definitely! How well a person does in tertiary education is correlated with job opportunities open to the person. Discuss issues pertaining to nstitutes of higher learning here. | 677.169 | 1 |
Math is one of those subjects that, if not explained correctly from an early age, can cause anxiety and even boredom for many of its learners. Without the right mindset about its usefulness, a positive attitude and a willingness to try, students quickly feel disconnected from this important field of study. This guide intends to provide any math learner the mental tools they need to successfully tackle any mathematical challenge
The Modern Scholar: Mathematics Is Power
William Goldbloom Bloch is a respected professor of mathematics at Wheaton College. This intriguing lecture series, Mathematics Is Power, delves into both the history of mathematics and its impact on people's everyday lives from a non-mathematician's perspective. Bloch first examines the history of mathematics and age-old questions pertaining to logic, truth, and paradoxes. Moving on to a discussion of how mathematics impacts the modern world, Bloch also explores abstract permutations such as game theory, cryptography, and voting theory learning and living itMotivational Hypnotherapy's Joel Thielke is a world-renowned hypnotherapist and author who has helped millions of people learn faster and focus easier. And now you have the power of his hypnosis programs in the palm of your hand with this hypnosis program for speed reading. If you've ever wanted to learn to read faster, you won't be disappointed.
Clever people put their talents to work on their behalf. They don't get distracted or let difficult concepts overwhelm them. They focus on what needs to be done, soak up the data, study the important points, and reproduce it when necessary. And you can learn how to do all of this in just a few hours - with help from hypnosis essays and magazine articles.
If you could sum up Improve Your Math in three words, what would they be?
Had to make a choice before a maxed out my credits, so I gave this a shot. Although it could be confirmation bias, I found working through the tedious job of adding and subtracting algebraic expressions not so tedious.
Any additional comments?
The talk over in the beginning is a little too loud; However, it quickly fades after a few minutes. | 677.169 | 1 |
Grade Levels
math
Suppose A is the set of students registered at the University of Calgary, and C is the set of courses currently being offered at the University of Calgary. Under what conditions is each of the following a function?
a)
{(a, c) | a's first class each week is in c}
b)
{(a, c) | a has a class in c Saturday evening} | 677.169 | 1 |
Welcome to Ms. Amey's class page. I am teaching Algebra 2, Occupationally Applied Math and Foundation Math courses. Under each course tab you will find information pertaining to that course such as class schedule, homework, and any posted assignments.
Late Work:
Any work not turned in when it is due will be considered. You may turn in LATE work until the day before the test on that material. For each day an assignment is late, it will be deducted by 10%. I will not go lower than 50%. As long as you turn in the assignment, you will get credit for it. When you miss an assignment, you will be issued a ticket for tutoring after school. If you go and complete the assignment there and it gets signed by the supervising teacher, I will give you full credit.
The instructor also reserves the right to assign an alternative assignment if the answers to the original assignment have already been reviewed in class.
No additional assignments will be given to boost a grade.
Absent Policy
Students have one day for each absence to turn work in. For example, if a student is absent on Tuesday and returns on Wednesday, Tuesday's work is due on Thursday. If a student misses Tuesday and Wednesday, then work for both of those days is due the following Monday. There will be an absent file that you can go to and get any missed work. You must get notes from a classmate.
If a student is absent on the day the assignment or project is due, the assignment is due the first day the student returns. If the student is absent on test day, he/she/they is responsible for taking the test the day that he/she/they returns. It is the student's responsibility to see me about taking the test.
Not all work can be made up. Sometimes we watch videos in class, conduct lab investigations, hold class discussions, and students are given credit for these activities. If a student misses class, they may not be able to make up the assignment. It is imperative for students to be in class every day. It is the responsibility of the student to collect all missed work.
Tardy Policy:
Students are expected to be in class when the bell rings, otherwise they are considered tardy. When the bell rings, students should be in their seats, with all their materials out and ready to work. Therefore, if a student hangs out in the hallway after the bell, they will be marked tardy. even though they may have been to class on time.
For every 5 unexcused tardies (came to class after the bell rings without a pass from a staff member), a write up will be made in Powerschool. Being tardy that many times is considered skipping because the student is not in class. | 677.169 | 1 |
Be sure that you have an application to open
this file type before downloading and/or purchasing.
334 KB|28 pages
Product Description
In this 8 lesson unit, the square root function is explored along with the algebra of solving square root equations, including those with extraneous roots. Rational exponents are covered and the properties of exponents are used to help rewrite expressions involving roots and rational powers. Finally the quadratic formula is reviewed and used to solve quadratic equations with rational and irrational roots.
To access the lesson videos on YouTube use your smartphone or tablet to scan the QR code at the top of each lesson. | 677.169 | 1 |
Students
Instructors
Available formats and resources for instructors
Making It Count: Math for the Beauty and Wellness Industry (Print)
Making It Count: Math for the Beauty and Wellness Industry lays out the basics of math and uses pertinent, real-life industry scenarios allowing the student to view math as it relates to their future career. Topics include scheduling, planning appointments, performing inventory, ordering products, determining volume-based discounts and reading financial documents. All of these topics are covered in an appealing style with activities and examples that will keep the student engaged and help them to understand the role math plays in the industry. This resource helps make the challenge of math in the salon or spa into a manageable and rewarding skill set.
eBook: Making it Count: Math for the Beauty and Wellness Industry | 677.169 | 1 |
The Saga of Mathematics:
A Brief History
Overview
For undergraduate-level courses in the History of Mathematics,
or Liberal Arts Mathematics.
Perfect for the non-math major, this inexpensive paperback text
uses lively language to put mathematics in an interesting,
historical context and points out the many links to art,
philosophy, music, computers, navigation, science, and
technology. The arithmetic, algebra, and geometry are presented
in a way that makes them relevant to daily life as well as
larger issues.
Features
Many worked out examples in the text.
Allows students to follow along step-by-step without
getting lost.
Plentiful collection of homework exercises—Ranging
from easy to hard.
Gives instructors a wide range of choices when
assigning homework and allows students to check
their comprehension of topics.
Suggested Readings—Listed at the end of each chapter.
Encourages students to learn more about those topics
that interest them.
Lively writing style.
Makes the text engaging and fun to read.
The math is presented in a historical context—Illustrates
its relation to art, philosophy, music, computers, navigation,
science, and technology.
Shows non-math majors how mathematics applies to their
majors and their lives. | 677.169 | 1 |
Introduction to Sequences and SeriesGeometry
Sequences
Math
Series
Convergence
Programma
In my course, you can broadly learn some basic sequences and series, from arithmetic and geometric progression to Fibonacci sequence and some methods to test the convergence or divergence of series.
You can apply this knowledge not only in tests, but also in math modeling projects, design algorithm in computer programming and even appreciate the beauty of nature (like Fibonacci sequence and golden ratio in life).
When I did a project in Math modeling on decide the appropriate locations to put traffic signs under road construction time, I used the knowledge of sequence to give out a solution. Moreover, in the time of big data, it's important to find order in disorder and optimize the problems. | 677.169 | 1 |
This course will follow the Topic Outline for AP Calculus AB. Class will meet for 90 minutes, every other day. Students are expected to actively participate in class discussion and collaborate as they discover new topics in Calculus. Students will complete guided explorations to investigate course material. Guided practice will give students opportunities to solve problems using graphing calculators and a variety of other methods. This course emphasizes problem solving and multiple representations (graphical, numerical, analytic/algebraic and verbal/written). Assessments will include individual quizzes and tests as well as partner and small group assessments. Assessments will also include both calculator active and non-calculator portions. Students will be asked to explain and justify results in words during class discussions and in complete sentences on assessments | 677.169 | 1 |
The main purpose of this course is to serve as a preparation for MATH 105, MATH 109C, MATH 111, and MATH 112. Work in the course is primarily self-directed, with mandatory weekly interaction with the instructional team. Content includes the following topics: linear, quadratic, polynomial, rational, and absolute value equations and inequalities, algebraic expressions, graphing techniques,
factoring techniques, exponents and logarithms. Students who wish to continue to higher level math courses will have the option to work with additional course material in algebra and trigonometry to facilitate this preparation. This course by itself cannot be used to satisfy the foundations math requirement for
any degree program. Examinations are proctored.
The main purpose of this course is to serve as a preparation for Math 100. Work in the course is primarily self-directed, with mandatory weekly interaction with the instructional team. Content may include the following topics: selected topics in beginning algebra, linear, quadratic, polynomial, rational, and absolute value equations and inequalities, algebraic expressions, graphing techniques, factoring techniques, exponents and logarithms. By the end of the sequence of courses MATH 100A-100B, students will have mastered the same course content as in MATH 100; therefore, students may earn credit for either MATH 100 or the MATH 100A-100B sequence, but not both. This course cannot be used to satisfy the foundations math requirement for any degree program. Examinations are proctored.
Please note: Units from this course will count toward full time eligibility for scholarships, financial aid and other campus related activities; however, units from this course will not count toward graduation requirements.
This course will examine how the mathematics learned in high school is applied to real life situations. Topics may include personal finance, statistics, elections, symmetry, and scheduling. Some of the applications may be how the site of the Olympic Games is chosen, why spirals occur in nature, and how statistical data is collected and how it can be used to mislead the public. The course is designed for elementary education majors, fine arts majors, humanities majors, and those social and behavioral science majors whose further courses do not require College Algebra as a prerequisiteCollege algebra course that emphasizes data analysis. Topics include functions, rates of change, linear functions, systems of equations, exponential & logarithmic functions, and quadratic functions. Graphing calculators and spreadsheets will be used. It is not intended for students planning to take MATH 124, and it will not serve as a prerequisite for that course. Except as per University policy on repeating a course, credit will not be given for this course if the student has credit in a higher level math course. Such students may be dropped from the course. Examinations are proctored. Credit will be allowed for only one of the following courses: MATH 109, MATH 109C, MATH 110, or MATH 112.
Topics include right triangle trigonometry, trigonometric functions and graphs, trig identities, inverse trig functions, law of sines, and law of cosines Not applicable to the mathematics major or minorTopics include properties of functions and graphs, linear and quadratic equations, polynomial functions, exponential and logarithmic functions with applicationsIntroductory topics in differential and integral calculus. Students are expected to have a graphing calculatorIntroductory topics in differential and integral calculus, with particular emphasis on understanding the principal concepts and their applications to business. Microsoft Excel and graphing calculators will be used as tools for further understanding these concepts. Except as per University policy on repeating a course, credit will not be given for this course if the student has credit in a higher level math course. Such students may be dropped from the course.
Review of algebra and trigonometry; study of functions including polynomial, rational, exponential, logarithmic and trigonometric For students who have high school credit in college algebra and trigonometry but have not attained a sufficient score on the UA Math Placement Test to enter calculusElementary functions, their properties, and uses in modeling. A graphing calculator is required for this course. We recommend the
TI-83 or TI-84 models. Calculators that perform symbolic manipulations, such as the TI-89, NSpire CAS, or HP50g, cannot be used.
An introduction to first-semester calculus for engineering, science and math students, from rates of change to integration, with an emphasis on understanding, problem solving, and modeling. Topics covered include key concepts of derivative and definite integral, techniques of differentiation, and applications, using algebraic and transcendental functions Except as per University policy on repeating a course, credit will not be given for this course if the student has credit in a higher level math course. Such students may be dropped from the course.
An accelerated version of MATH 122B. Introduction to calculus with an emphasis on understanding and problem solving. Concepts are presented graphically and numerically as well as algebraically. Elementary functions, their properties and uses in modeling; the key concepts of derivative and definite integral; techniques of differentiation, using the derivative to understand the behavior of functions; applications to optimization problems in physics, biology and economicsContinuation of MATH 122B or MATH 125. Techniques of symbolic and numerical integration, applications of the definite integral to geometry, physics, economics, and probability; differential equations from a numerical, graphical, and algebraic point of view; modeling using differential equations, approximations by Taylor series
Organizing data: displaying distributions, measures of center, measures of spread, scatterplots, correlation, regression, and their interpretation. Design of experiments: simple random samples and their sampling distribution, models from probability, normal distributions, and normal approximations. Statistical inference: confidence intervals and hypothesis testing, t procedures and chi-square tests. Not intended for those who plan further studies in statisticsThis course is designed to introduce the mathematics teaching profession to mathematically talented college students. Students are given opportunities to observe and tutor in middle and high school mathematics classrooms. Additionally, class time will be dedicated to developing tutor techniques, examining learning styles, and exploring various methods of instruction. Readings, reflections, discussions, and group work will facilitate student understanding of the teaching and learning of mathematics. Students with a math placement level of calculus or higher will be given preference in the application process
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This course is designed as a complement to MATH 116. Students enrolled in the course will participate in a weekly problem session pertaining to material covered in MATH 116. Concurrent registration in MATH 116 is required.
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This course is designed as a complement to MATH 120R. Students enrolled in the course will participate in a weekly problem session pertaining to material covered in MATH 120R. Concurrent registration in MATH 120R is required.
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This course is designed as a complement to MATH 129. Students enrolled in the course will participate in a weekly problem session pertaining to material covered in MATH129. Concurrent registration in MATH 129 is required.
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This course is designed as a complement to Math 223. Students enrolled in the course will participate in a weekly problem session pertaining to material covered in Math 223. Concurrent registration in Math 223 is required.
Development of a basis for understanding the common processes in elementary mathematics related to whole numbers, fractions, integers, and probability. This course is for elementary education majors only. Examinations are proctored.
Development of a basis for understanding the common processes in elementary mathematics related to estimation, graphing of functions, measurement, geometry, and data analysis. This course is for elementary education majors only. Examinations are proctored.
Applications and methods of linear algebra emphasizing matrices and systems of equations, determinants, eigenvectors and eigenvalues. This course is an excellent introduction to linear algebra for students who are interested in a math minor. It does not satisfy requirements for the math major. Students who might be interested in the math major should consider taking Math 313.
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An algorithmic approach to solving systems of linear equations transitions into the study of vectors, vector spaces and dimension. Matrices are used to represent linear transformations and this leads to eigenvectors and eigenvalues. The precise use of definitions plays an important role. Examinations are proctored. This course is required in the math major and prepares students to take Math 323. It is a prerequisite to the majority of the higher level courses in mathematics.
Elementary real analysis as an introduction to abstract mathematics and the use of mathematical language. Elementary logic and quantifiers; manipulations with sets, relations and functions, including images and pre-images; properties of the real numbers; supreme and infimum; other topics selected from cardinality, the topology of the real line, sequence and limits of sequences and functions; the emphasis throughout is on proving theorems.
Focusing on statistical inference, the course has two goals in addition to teaching the statistical techniques. One is theoretical: To explore the links between probability, statistics and calculus, showing students the mathematical underpinnings. The second is applied: Provides experience with real data sets, many bearing on education. Students who complete this course will be prepared to teach high school level statistics courses.
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In Introduction to Statistical Methods, we shall be using your background in biology and your previous knowledge of calculus and differential equations to consider the issues of collection, model derivation and analysis, interpretation, explanation, and presentation of data. Even though our examples derive mainly from the life sciences, statistics is applicable to a wide variety of academic disciplines, from the natural and social sciences to the humanities.
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Several different faculty members will present 2-4 lectures each on research topics/projects in which undergraduates can become involved. This course may not be used to fulfill degree requirements for the math major or minor.
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This course is designed as a complement to Math 323. Students enrolled in the course will participate in a weekly problem session pertaining to material covered in Math 323. The primary purpose of this course is to give students many opportunities to share their mathematical conjectures and their justifications to classmates. During class meetings students will debate the validity of mathematical statements and formal proofs. Concurrent registration in Math 323 is required.
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Selected topics from modern mathematics. Content varies. The primary purpose of the course is to provide students the opportunity to gain knowledge, experience, and exposure to topics in modern mathematics beyond what is presented in the core subjects required for the math major.
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Section
Days
Time
Location
Instructor
MATH 401B-001
Mo, We, Fr
11:00am-11:50am
MATH 406A: Curriculum & Assessment in Secondary School Mathematics
Examination of secondary school mathematics curricula with emphasis on the development of math topics; study of assessment with emphasis on its alignment with instruction; and practicum experiences with emphasis on curriculum analysis and implementation of assessment measures.
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Advanced topics from modern mathematics. Content varies. The primary purpose of the course is to provide students the opportunity to gain knowledge, experience, and exposure to advanced topics in modern mathematics beyond what is presented in the core subjects for the math major.
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Advanced propositional logic and quantification theory; metatheorems on consistency, independence, and completeness; set theory, number theory, and modal theory; recursive function theory and Goedel's incompleteness theorem. Graduate-level requirements include an in-depth research project on a central theme or topic of the course. Courses for which students receive the grade of P (Pass) do not satisfy requirements for the M.A. or Ph.D. or minor in philosophy.
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Section
Days
Time
Location
Instructor
MATH 501B-001
Mo, We, Fr
11:00am-11:50am
MATH 506C: Research on the Teaching of Mathematics
Examination of approaches to the study of mathematics teaching including evaluation of the theories and perspectives of mathematics instruction, the factors influencing instructional practice, studies of teachers' mathematical knowledge and beliefs, and research on teacher development and change.
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Development, analysis, and evaluation of mathematical models for physical, biological, social, and technical problems; both analytical and numerical solution techniques are required. Graduate-level requirements include more advanced projects.
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The exchange of scholarly information and/or secondary research, usually in a small group setting. Instruction often includes lectures by several different persons. Research projects may or may not be required of course registrants.
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Section
Days
Time
Location
Instructor
MATH 595A-001
Tu
4:00pm-5:15pm
MATH 596A: Topics in Mathematics
The development and exchange of scholarly information, usually in a small group setting. The scope of work shall consist of research by course registrants, with the exchange of the results of such research through discussion, reports, and/or papers.
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Section
Days
Time
Location
Instructor
MATH 596A-001
Tu
4:00pm-5:00pm
MATH 596G: Research Tutorial Group
Introduction to research interests of the faculty. Required in Spring of first year in Ph.D. program in Mathematics and in the following Fall. Content varies. | 677.169 | 1 |
Acceleration Worksheet.
Name: _
Date: _
14.2 Acceleration
Acceleration is the rate of change in the speed of an object. To determine the rate of acceleration, you use the
formula below. The units for acceleration are meters per second per second or m/s2.
Calculus BC Advice
Showing 1 to 3 of 8
This class is a great introductory course for students who enjoy math and want to further their math skills. The majority of BC was to review for the AP test and most of it was self-taught. However, the teacher is there to answer any questions!
Course highlights:
Always do your homework on the assigned nights. (don't wait til the day before the unit test when it is due). Be very thorough on your tests, all of the little mistakes add up, however, the grading is lenient enough for you to have a bad test here and there.
Hours per week:
9-11 hours
Advice for students:
Even if AB Calc was difficult, you should still take the class even if you didn't do well. Many students who take BC Calc ended up just taking the AB Calc test, which if you do your homework and pay attention in class, Mr. Branson prepares you very well for.
Course Term:Summer 2016
Professor:Branson
Course Tags:Math-heavyMany Small Assignments
Oct 21, 2016
| Would not recommend.
This class was tough.
Course Overview:
It deeply took away some of my love for math.
Course highlights:
I don't remember there being many positives of taking this class.
Hours per week:
3-5 hours
Advice for students:
Make sure you fully understand every concept of Calculus AB because you need to be able to recall every section of information. | 677.169 | 1 |
Linear Algebra examples
Break-even analysis
A nice way you understand the value of matrix algebra use it in simple practical examples. One such example is a break even analysis: For instance with certain fixed costs, as well as a pay rate for labour, how many hours do need to charge out in order to break-even?
This can be calculated in an OpenMx model, optimising on profit, and solving with the constraint the we break-even. This model has one free parameter-namely the hours of work.
You have ingredients:
Inputs: 142 gallons of Apple, 108 gallons of Pear
You make products from these:
Outputs: light juice (7l of appl and 3l of pear per case) and golden juice (4l of apple and 6l of pear per case)
The products require different amounts of ingredients. How can you use all your available ingredients by balancing production between the two products? | 677.169 | 1 |
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PCI Ed's Algebra City Covers 28 Common Gaps in Student Understanding
By Dian Schaffhauser
06/26/12
PCI Education, a company that develops curriculum products, has published a set of learning materials specifically for kids in grades eight through 10 having trouble with Algebra 1 concepts. "Algebra City" is a set of four workbooks that address 28 common algebraic misconceptions using a graphic novel approach and web-based practice problems. According to the company, the program is intended to be used not for standard curriculum but for intervention, pinpointing areas where students are struggling.
The materials consist of four student editions, each one covering seven of the 28 topics, as well as a teacher set with an assessment CD, a teacher resource CD, and access to the interactive activities.
An ExamView Assessment Suite includes pre- and post-tests for the program, the book, and individual unit levels, as well as an item bank and test generator, and reporting features.
"Too often, students struggle to learn critical algebra skills they need both inside and outside the classroom," said Lee Wilson, president and CEO of PCI Education. "Algebra City is targeted intervention that encourages students to reconnect to algebra in one or more areas of misunderstanding, while allowing teachers to leverage the investment in their core algebra curriculum."
A classroom starter pack is priced at $599.95 and includes the teacher's kit and a five-pack of student editions, which has five copies of each of the four books in the series | 677.169 | 1 |
Showing 1 to 9 of 9
Applications of College Algebra
Author:
Joselyn Cendejas
*MAT250 Project 1
Grand Canyon University, Phoenix, AZ, USA
Introduction. By doing this project student will be able to calculate and learn how to use
excel. The two parts of this project was learne
MATH 250 Advice
Showing 1 to 3 of 4
it is something that is needed because you need to be able to do calculations especially if your going to be a manager because you have to be able to know budgets and how to stay within the allotted budget.
Course highlights:
The highlight was that I finished the class with a decent grade. It also challenges you.
Hours per week:
9-11 hours
Advice for students:
This course will build patience. You must be diligent in completing assignments because it is easy fall behind.
Course Term:Spring 2013
Professor:John Nicholson
Course Required?Yes
Course Tags:Math-heavyMany Small Assignments
Jan 23, 2017
| No strong feelings either way.
Not too easy. Not too difficult.
Course Overview:
This was a required course that I had to take, and it is a bit hard, and there is a lot of studying.
Course highlights:
from this course I learned many new mathematical formulas. I also learned how to use Microsoft excel as a calculator, and it is very helpful, and it is used for completing homework.
Hours per week:
6-8 hours
Advice for students:
Make sure that you understand the different formulas, when to use which formula. Also learn how to use excel, it will be your best friend. Make sure that you also understand the different symbols and when to use them. Do not be scared to ask questions, or bother the instructor, that is what they are there for. | 677.169 | 1 |
Concepts inThe package CRACK for solving large overdetermined systems
Overdetermined system
In mathematics, a system of linear equations is considered overdetermined if there are more equations than unknowns. The terminology can be described in terms of the concept of counting constraints. Each unknown can be seen as an available degree of freedom. Each equation introduced into the system can be viewed as a constraint that restricts one degree of freedom. Therefore the critical case occurs when the number of equations and the number of independent variables are equal.
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Project Prevention
Project Prevention (formerly Children Requiring a Caring Kommunity or CRACK) is an American non-profit organization that pays drug addicts cash for volunteering for long-term birth control, including sterilization. Originally based in California and now based in North Carolina, the organization began operating in the United Kingdom in 2010. The organization offers US$300 (£200 in the UK) to each participant.
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Algebraic function
In mathematics, an algebraic function is informally a function that satisfies a polynomial equation whose coefficients are themselves polynomials with rational coefficients. For example, an algebraic function in one variable x is a solution y for an equation where the coefficients ai(x) are polynomial functions of x with rational coefficients. A function which is not algebraic is called a transcendental function
Dependent and independent variables
The terms "dependent variable" and "independent variable" are used in similar but subtly different ways in mathematics and statistics as part of the standard terminology in those subjects. They are used to distinguish between two types of quantities being considered, separating them into those available at the start of a process and those being created by it, where the latter (dependent variables) are dependent on the former (independent variables).
more from Wikipedia
Algebraic structure
In mathematics, and more specifically abstract algebra, the term algebraic structure generally refers to an arbitrary set with one or more finitary operations defined on it. Common examples of structures include groups, rings, fields and lattices. More complex algebraic structures can be defined by introducing multiple operations, different underlying sets, or by altering the defining axioms. Examples of more complex structures include vector spaces, modules and algebras.
more from Wikipedia
Factorization
In mathematics, factorization (also factorisation in British English) or factoring is the decomposition of an object into a product of other objects, or factors, which when multiplied together give the original. For example, the number 15 factors into primes as 3 × 5, and the polynomial x ¿ 4 factors as (x ¿ 2)(x + 2). In all cases, a product of simpler objects is obtained.
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Vector field
In vector calculus, a vector field is an assignment of a vector to each point in a subset of Euclidean space. A vector field in the plane for instance can be visualized as an arrow, with a given magnitude and direction, attached to each point in the plane. Vector fields are often used to model, for example, the speed and direction of a moving fluid throughout space, or the strength and direction of some force, such as the magnetic or gravitational force, as it changes from point to point.
more from Wikipedia | 677.169 | 1 |
Before enrolling in Business Math Part 2, students should have
successfully completed Business Math Part 1 or equivalent coursework. This
course will cover a variety of real-world concepts, including examples related
to retail and finance. The course will also introduce students to mathematical
applications in typical business situations and examine how a business
functions. Students will develop an understanding of buying, markups,
selling prices, markdowns, and inventory. In addition, students will learn
about simple interest, compound interest, annuities, and loans, while also
gaining knowledge of depreciation, stocks, and bonds. Video tutorials and
online math activities will ensure students receive the in-depth instruction
necessary to conceptualize these real-world concepts.
Available Sept. 1, 2013
It is recommended that students successfully complete Business Math Part 1 or equivalent course work before enrolling in this course.
Course Objectives
Unit 1: Essential Content and Skills
Calculate simple interest.
Compute
the maturity value of a note.
Calculate compound interest.
Compute interest compounded daily.
Analyze time deposit accounts and inflation.
Unit 2: Essential Content and Skills
Analyze retirement accounts.
Assess sinking funds and stocks.
Compute mutual funds and bonds.
Calculate revolving charge accounts and unpaid balances.
Analyze loan consolidation.
Unit 3: Essential Content and Skills
Utilize the United States Rule and Rule of 78 to calculate the interest on a loan. | 677.169 | 1 |
Word problems are the most difficult part of any math course –- and the most important to both the SATs and other standardized tests. This book teaches proven methods for analyzing and solving any type of math word problem | 677.169 | 1 |
This manual opens with a diagnostic test that includes explained answers to help students pinpoint their math strengths and weaknesses. In chapters that follow, detailed topic reviews cover polynomial, trigonometric, exponential, logarithmic, and rational functions; coordinate and three-dimensional geometry; numbers and operations; data analysis, statistics, and probability. Six full-length model tests with answers, explanations, and self-evaluation charts conclude this manual. The manual can be purchased alone or with an optional CD-ROM that presents two additional full-length practice tests with answers, explanations, and automatic scoring.
Both Calculus AB and Calculus BC are covered in this comprehensive AP test preparation manual, which has been updated to align with the new curriculum framework taking effect for the 2017 AP Calculus AB and BC exams. The book's main features include:
Four practice exams in Calculus AB and four more in Calculus BC, modified to reflect the new exam format
All test questions answered with solutions explained
A detailed subject review covering topics for both exams
Advice to students on efficient use of their graphing calculators
BONUS ONLINE PRACTICE TEST: Students who purchase this book will also get FREE access to one additional full-length online AP Calculus test with all questions answered and explained.
The AP Calculus AB course and exam have changed! Created to align with the new exam content, and written by the experts at The Princeton Review, Cracking the AP Calculus AB Exam arms you to take on the test with:
Everything You Need to Know to Help Achieve a High Score. • Up-to-date information on the new 2017 AP Calculus AB Exam • Comprehensive content review for all test topics • Engaging activities to help you critically assess your progress • Access to AP Connect, our online portal for late-breaking news, exam updates, and more
Techniques That Actually Work. • Tried-and-true strategies to help you avoid traps and beat the test • Tips for pacing yourself and guessing logically • Essential tactics to help you work smarter, not harder
The AP Calculus BC course and exam have changed! Created to align with the new exam content, and written by the experts at The Princeton Review, Cracking the AP Calculus BC Exam arms you to take on the test with:
Techniques That Actually Work. • Tried-and-true strategies to avoid traps and beat the test • Tips for pacing yourself and guessing logically • Essential tactics to help you work smarter, not harder
Everything You Need to Know for a High Score. • Up-to-date information on the revised 2017 AP Calculus BC Exam • Comprehensive content review for all test topics • Engaging activities to help you critically assess your progress • Access to AP Connect, our online portal for late-breaking news, exam updates, and more doing data science as quickly as possible.
Banish math anxiety and give students of all ages a clear roadmap to success
Mathematical Mindsets provides practical strategies and activities to help teachers and parents show all children, even those who are convinced that they are bad at math, that they can enjoy and succeed in math. Jo Boaler—Stanford researcher, professor of math education, and expert on math learning—has studied why students don't like math and often fail in math classes. She's followed thousands of students through middle and high schools to study how they learn and to find the most effective ways to unleash the math potential in all students.
There is a clear gap between what research has shown to work in teaching math and what happens in schools and at home. This book bridges that gap by turning research findings into practical activities and advice. Boaler translates Carol Dweck's concept of 'mindset' into math teaching and parenting strategies, showing how students can go from self-doubt to strong self-confidence, which is so important to math learning. Boaler reveals the steps that must be taken by schools and parents to improve math education for all. Mathematical Mindsets:
Explains how the brain processes mathematics learning
Reveals how to turn mistakes and struggles into valuable learning experiences
Gives examples of how assessment and grading policies need to change to support real understanding
Scores of students hate and fear math, so they end up leaving school without an understanding of basic mathematical concepts. Their evasion and departure hinders math-related pathways and STEM career opportunities. Research has shown very clear methods to change this phenomena, but the information has been confined to research journals—until now. Mathematical Mindsets provides a proven, practical roadmap to mathematics success for any student at any age.
This access kit will provide you with a code to get into MyMathLab, a personalized interactive learning environment, where you can learn mathematics and statistics at your own pace and measure your progress.In order to use MyMathLab, you will need a CourseID provided by your instructor; MyMathLab is not a self-study product and does require you to be in an instructor-led course. This product is for the national MyMathLab access kit. If your school has a custom MyMathLab course the printed access card will not work. MyMathLab includes:
Interactive tutorial exercises: MyMathLab's homework and practice exercises are correlated to the exercises in the relevant textbook, and they regenerate algorithmically to give you unlimited opportunity for practice and mastery. Most exercises are free-response and provide an intuitive math symbol palette for entering math notation. Exercises include guided solutions, sample problems, and learning aids for extra help at point-of-use, and they offer helpful feedback when students enter incorrect answers.
eBook with multimedia learning aids: MyMathLab courses include a full eBook with a variety of multimedia resources available directly from selected examples and exercises on the page. You can link out to learning aids such as video clips and animations to improve their understanding of key concepts.
Study plan for self-paced learning: MyMathLab's study plan helps you monitor your own progress, letting you see at a glance exactly which topics you need to practice. MyMathLab generates a personalized study plan for you based on your test results, and the study plan links directly to interactive, tutorial exercises for topics you haven't yet mastered. You can regenerate these exercises with new values for unlimited practice, and the exercises include guided solutions and multimedia learning aids to give students the extra help they need.
NOTE: Access codes can only be used one time. If you purchased a used book that claimed that it included an access code, your code may already have been used and it will not work again. In this case, you must purchase a new access code.
For Customer Technical Support go to
Phone Support 800-677-6337
Please note the packaging on this product has changed, whether you receive the current cover or earlier cover the product is still the same. | 677.169 | 1 |
Math
Algebra I - 9th Grade 1 Credit ~ 2 Semesters Algebra I reinforces concepts learned in PreAlgebra (such as solving multi-step equations and linear graphing) and expands into solving systems of equations and inequalities, factoring and simplifying polynomials, solving quadratic equations and working with exponents and radicals. Students are given a foundation for concepts that will be learned in Geometry, Algebra II and PreCalculus. A TI-84 graphing calculator is required.
Geometry - Academic 9th or 10th Grade 1 Credit ~ 2 Semesters Informal proofs and discovery activities are used to help students develop a foundation in Euclidean geometry, including the study of parallel lines and planes, triangles, quadrilaterals, other polygons, and circles. A TI-84 graphing calculator is required.
Algebra II - Academic 10th or 11th Grade 1 Credit ~ 2 Semesters Algebra II includes the concepts of solving open sentences with one or more variables, algebraic operations with polynomials and rational expressions, properties of functions, matrices and determinants, graphing, quadratic and higher degree functions, complex numbers, conic sections, exponential and logarithmic functions, sequences and series, and probability. Technological applications of these topics will be integrated into the course. A TI-84 graphing calculator is required.
Algebra II - Honors 10th or 11th Grade 1 Credit ~ 2 Semesters Prerequisite and Limitations: Selection criteria. Algebra II Honors focuses on the algebraic concepts of solving open sentences of different degrees, polynomials and rational expressions, function analysis, matrices and determinants, graphing, complex numbers, conic sections, exponential and logarithmic functions, sequences and series, and probability. This course emphasizes higher-level thinking and problem solving. Applications and technology are integrated into this course. This course is designed as preparation for PreCalculus or PreCalculus Honors. A TI-84 graphing calculator is required.
PreCalculus - Honors 11th or 12th Grade 1 Credit ~ 2 Semesters Prerequisite and Limitations: Algebra II and selection criteria. Precalculus Honors includes the study of trigonometry, analytic geometry, and function analysis. In-depth study of functions, graphs, advanced algebraic topics, proofs, and applications is emphasized in their relation to the calculus. This course is designed as preparation for AP Calculus AB or BC or AP Statistics. A TI-84 graphing calculator is required.
Calculus - Honors 12th Grade 1 Credit ~ 2 Semesters Prerequisite and Limitations: PreCalculus or PreCalculus Honors and Selection criteria. This course is primarily intended for students intending to major in business or the social sciences in college. Calculus is the study of rates of change of various functions and their applications. In our development of the Calculus we will study applications to business, including the cost, revenue and profit functions as well as various social science applications such as rates of learning, population growth and equity of income distribution. A TI-84 graphing calculator is required.
AP® Calculus - AB 12th Grade 1 Credit ~ 2 Semesters Prerequisite and Limitations: PreCalculus Honors and Selection criteria. Calculus applies the study of limits, derivatives, integrals, and functions to various applications. Using the calculus as a problem-solving tool and preparation for taking the Calculus AB exam is emphasized in this course
AP® Calculus - BC 12th Grade 1 Credit ~ 2 Semesters Prerequisite and Limitations: PreCalculus and Selection criteria. The primary goal and intended audience for this course is the same as for Calculus AP® – AB; however this is a more intense course as it covers the additional topics of convergence and divergence of infinite series, applications of Calculus to both polar and parametric functions, logistic growth and additional methods of finding antiderivatives. It is the only math course offered that covers college-level material at a college pace This course is subject to both teacher and scheduling availability and having sufficient students to make a viable class.
Introduction to Dual Credit College Algebra - 11th or 12th Grade .5 Credit ~ 1 Semester Prerequisite and Limitations: Algebra I, Geometry, Algebra II and Selection criteria, page 9. The goal of this class is to prepare students to take College Algebra Dual Credit (online). In-depth study of prerequisite knowledge needed for College Algebra as well as an overview of topies covered in College Algebra.
College Algebra - Dual Credit (online) MATH 1314 - 11th or 12th Grade .5 Credit ~ 1 Semester Prerequisite and Limitations: Introduction to Dual Credit College Algebra and Selection criteria, page 9. Students who qualify for dual credit on the TSI math placement test will be taking this class (MATH 1314) online from Lone Star College. These students will be placed in the classroom with an instructor who will act as a facilitator. In-depth study and applications of polynomial, rational, radical, absolute-value, piecewise defined, exponential and logarithmic functions, equations, inequalities, graphing skills and systems of equations using matrices. Additional topics such as sequences, series, probability, conics and inverses may be included. Dual Credit courses require an additional fee which is determined by Lone Star College.
AP® Statistics 11th or 12th Grade 1 Credit ~ 2 Semesters Prerequisite and Limitations: Honors Algebra II with Teacher Recommendation or PreCalculus. The AP® Statistics course is equivalent to a one-semester, introductory, non-calculus-based college course in statistics. The course introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. There are four themes in the AP® Statistics course: exploring data, sampling and experimentation, anticipating patterns, and statistical inference. Students use technology, investigations, problem solving, and writing as they build conceptual understanding | 677.169 | 1 |
The course introduces basic mathematical techniques to understand qualitatively the
long-term behaviour of systems evolving in time. Most of the phenomena occurring
in nature, and around us, are nonlinear in nature and often these exhibit interesting
behaviour which could be unpredictable and counterintuitive. Tools and techniques
of dynamical systems theory help in understanding the behaviour of systems and in
gaining control over their behaviour, to a certain extent. Dynamical systems theory
has wide applications in the study of complex systems, including physical &
biological systems, engineering, aerodynamics, economics, etc. | 677.169 | 1 |
Calculus
One thousand millimeters is equal to 1 meter. The meter is the standard unit of length in the International System of Units, also known as the metric system. "Metre" is the standard spelling for all English-speaking countries except the United States. "Meter" is the accepted U.S. spelling.
A:The abbreviations "sin," "cos," "tan," "csc," "sec" and "cot" stand for the six trigonometric functions: sine, cosine, tangent, cosecant, secant and cotangent. Each function represents a particular relationship between the measure of one of the angles and the ratio between two sides of a right triangle.
A:A nonlinear function in math creates a graph that is not a straight line, according to Columbia University. Three nonlinear functions commonly used in business applications include exponential functions, parabolic functions and demand functions. Quadratic functions are common nonlinear equations that form parabolas on a two-dimensional graph.
A:A few examples of how logarithms are used in the real world include measuring the magnitude of earthquakes or the intensity of sound and determining acidity. A logarithm explains how many times a number is multiplied to a power to reach another number. It is expressed as loge(x) and is commonly written as ln(x).
A:To calculate bulk density, simply weigh the sample and divide its mass by its volume. Bulk density is commonly used when referring to solid mixtures like soil. Just like particle density, bulk density is also measured in mass per volume.
A:According to class notes from Bunker Hill Community College, calculus is often used in medicine in the field of pharmacology to determine the best dosage of a drug that is administered and its rate of dissolving. Usually, the drug is slowly dissolved in the stomach.
A:The definition of a limit in calculus is the value that a function gets close to but never surpasses as the input changes. Limits are one of the most important aspects of calculus, and they are used to determine continuity and the values of functions in a graphical sense.
A:A Riemann sum is a method of approximating the area under the curve of a function. It adds together a series of values taken at different points of that function and multiplies them by the intervals between points. The midpoint Riemann sum uses the x-value in the middle of each of the intervals.
A:A:The antiderivative of cos(x) is sin(x) + c, where c is an arbitrary constant. The antiderivative is more commonly called the indefinite integral. One must add an arbitrary constant into the antiderivative because sin(x) + c differentiates to cos(x) for all values of c.
A:"Cot" is the abbreviation for "cotangent," a trigonometric function used to find the value of an angle in a right triangle by dividing the length of an adjacent side by the length of the opposite side. The numerical value of cot x varies depending on the value of x.
A:The items contained in a matrix are its entries; an entry is a single piece of data from within a matrix. Matrix notation refers to the use of a subscript to identify the row and column location of a single entry within a matrix.
A:The factors of 75 are 1, 3, 5, 15, 25 and 75. The factors may be determined by dividing 75 by whole numbers starting from 1. If the resulting quotient is also a whole number, then both the divisor and quotient are factors of the number.
A:The antiderivative of sec(x) is equal to ln |sec(x) + tan(x)| + C, where C represents a constant. This antiderivative, also known as an integral, can be solved by using the integration technique known as substitution.
A:Learners can take calculus courses online through Massachusetts Institute of Technology, San Francisco State University, University of California in Berkeley or Brigham Young University. These courses range from introductory offerings to specific, advanced focuses. | 677.169 | 1 |
Scientific Computing
Content
Many interesting projects in natural sciences and engineering require the
computation of numerical solutions to certain mathematical problems, such as
solving systems of equations or minimizing some cost function. This course
introduces the most frequently used numerical methods in a compact manner,
based on intuitive and interesting examples from computer graphics and
physics-based dynamic simulations.
We will not focus on the theoretical derivation of the presented
techniques. Instead, our goal is to effciently and robustly solve numerical
problems in practical applications, which requires these three steps:
Given an engineering problem, formulate it as a mathematical problem, for
instance as a system of equations or an optimization problem.
Given a mathematical problem, analyze its properties to understand which
numerical methods can be employed for its solution.
Given a numerical method, know which open-source implementation can be
used and/or how to implement it yourself as an efficient and robust
algorithm.
The numerical methods to be discussed include solving dense and sparse linear
systems, least squares approximations, and partial differential equations. We
will also discuss efficient C++ programming and shared memory parallelization.
To facilitate a better understanding we will implement most of the techniques
that we discuss in the lecture in the programming assignments. Our exercises
therefore consist of several mini-projects, which you can work on alone or in
groups. Our tutors have weekly consulting hours, where students can get help
if they have trouble with the implementation. At the end of each mini-project,
students will present their results in the exercise course.
Prerequisites
Basic knowledge of linear algebra and analysis is required. You should
have passed your Mathe 1+2 courses.
The programming exercises will be done in C++. We'll have a C++ crash
course at the beginning. | 677.169 | 1 |
Earth History at Adams State College
Instructor: Rob Adams Enrollment: 10 to 15
Challenges to using math in introductory geoscience
The biggest perceived challenge is poor math preparation, which makes application of quantitative concepts a distracting challenge. The class population often has a range of math skills and the skills do not necessarily match math confidence. In other words, some students think they know math when they really do not know it well enough. A poorly-defined institutional challenge or obstacle may be a general faculty frustration with the low level of student math preparation, and a reluctance to be proactive on resolving the problem. The modules in TMYN provide opportunities to assess student math preparation in quantitative applications.
More about your geoscience course
GEOL 112 is an introduction to the geological evolution of the earth through time using basic principles of stratigraphy and paleontology. The course is the second core class in the BS and BA Earth Science, Geology degree tracks. Students are usually geology majors or minors, although many students with a completed GEOL 111, Physical Geology, prerequisite take the class as an elective. Laboratory work includes identification and classification of fossils and correlation of sedimentary environments. The lecture part of the course will address evolution of the continents, ocean basins, mountain systems and major life forms throughout the earth's history. Special emphasis is given to the North American continent and the description of the geology preserved in the rock record. The associated laboratory course will consist of practical exercises illustrating the various techniques and concepts that allow geologists to decipher the earth's history. TMYN modules taken as an assessment test indirectly assist in the quantitative materials encountered in lab. The course is delivered with a TA, when funding is available.
Which Math You Need Modules will/do you use in your course?
Plotting Points
Topographic Profile when available
Rearranging Equations
Trigonometry
Unit Conversions:
Strategies for successfully implementing The Math You Need
Conduct an assessment of student math proficiencies for course quantitative concepts. A pre-test and a post-test will bookend the modules listed above. The test will not be graded and will be delivered as an opportunity for students to examine their own math skill sets. The test will be given early in the semester, with an open completion date.
Reflections and Results (after implementing)
The implementation intent was to give students an opportunity to brush up on their math skills, see why those math skills are important in geosciences, and to provide me with some assessment data on student success.
The result were not as good as I hoped, for several reasons:
There were no grade stakes involved, participation was not graded
Plenty to time was given to complete the modules, and the entire package | 677.169 | 1 |
AM 108 S17 Nonlinear Dynamical Systems
This course provides an introduction to nonlinear dynamical phenomena, with a focus on the behavior of systems described by ordinary differential equations.
Dynamical systems theory provides a framework for thinking about the time evolution of models of real-world systems. Our focus in this course is on building intuition for this geometric way of thinking. To that end, we will study stability and bifurcations in depth. In addition, the course will touch on the following topics: chaos; routes to chaos and universality; approximations by maps; strange attractors; fractals. Techniques for analyzing nonlinear systems are introduced with applications to physical, chemical, and biological systems such as forced oscillators, chaotic reactions, and population dynamics.
Dynamical systems theory is an area of mathematics that has found a number of applications. Searching Google Books for "dynamical systems"yields results such as "Dynamical Systems and Their Applications in Biology", "Dynamical Systems in Cosmology", and "Dynamical Systems in Neuroscience" as well as a number of books that add noise to dynamical systems or are oriented towards control of a system. Talks at SIAM's 2015 Applied Dynamical Systems conference included ones on extreme events, on cancer, on energy transfer, on climate, on fluids, on the brain, and on dynamical systems on networks. | 677.169 | 1 |
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8.17 MB
PRODUCT DESCRIPTION
The Algebraic Concepts Warm Ups & Answers are designed to be used as a problem of the day, daily question, bell ringer, or morning work to get your students thinking about math in an Algebraic way. The 50 problems can also be used as math enrichment, homework, or anchor activities when your students finish assignments early. The Algebraic Concepts Warm Ups can be projected on the board or passed out as a hard copy. The following formats are included: one problem per page, one problem per page with answers, hand- outs with 2 problems per page, hand-outs with 4 problems per page, and hand-outs with 6 problems per page. Skills addressed throughout the warm ups are | 677.169 | 1 |
Becoming a Mental Math Wizard
Covers the basics of squaring, multiplication, division, logarithms, powers and roots, and shows how to apply the math to real-life situations.
"synopsis" may belong to another edition of this title.
From School Library Journal:
Grade 11 Up-- The goal of this recreational mathematics book is to give readers a feeling of accomplishment by finding that they can master what seems at the onset to be an impossible task. Explanations are well structured, but readers should have a solid grounding in beginning and, possibly, intermediate algebra. Techniques for doing squares, multiplication, and division are presented. YAs learn to use logarithms and Taylor series to simplify difficult calculations. Trigonometric functions and triangulation enable them to measure distances (across a lake, to the horizon, to landmarks from a plane in flight). Probability theory helps in predictions as well as game playing. Charts and graphs are used when needed to enhance explanations. This is a rewarding read for those interested in mathematics. The human brain is still faster than the pocket calculator, and the techniques in this book enable readers to do more mathematics in their heads. A good purchase for collections serving young adults. --Margaret M. Hagel, Norfolk Public Library System, VA Copyright 1992 Reed Business Information, Inc. | 677.169 | 1 |
Teaching algebra can be a difficult proposition, and at times, those who have just entered the field of mathematics education can feel a bit overwhelmed. Stepping in to provide a bit of assistance is this series of...
Brought to you by Elizabeth Stapel and purplemath.com, this collection of learning modules contains over 100 mathematics modules designed to teach beginning, intermediate, and advanced algebra concepts. Some algebra...
Provided by the University of Vienna's futureMedia initiative, the Maths Online Gallery consists of a large collection of extremely useful interactive learning units that demonstrate mathematical concepts. A large...
Practice solving algebraic equations with this interactive quiz brought to you by Interactivate and the Computational Science Education Reference Desk. The quiz allows you to select the difficulty level, time limit and... | 677.169 | 1 |
English
Writing & Grammar 9 reviews the eight parts of speech, five basic sentence patterns, usage, and mechanics. The 9th-grade English curriculum introduces relative pronouns, pronoun reference problems, and indicative/imperative mood. Dictionary skills, library skills, study skills, and the writing process are exercised and implemented throughout the course. Writing projects include a comparison/contrast paragraph, a personal narrative, a research essay, a personal response to literature.
Social Studies
World History guides students through the story of history from the dawn of civilization to the present world. Students are encouraged to explore the past and delve in to the twists and turns of world history through relevant activities and class discussions. The text emphasizes how a Christian worldview affects the study of history, illustrating the crucial nature of viewing history through the lens of the Bible. World History provides a survey of history essential to future study.
Science
Physical Science is an exciting and engaging introduction to the world of physics and chemistry. Designed and written for the 9th-grade level, it provides an essential foundation for subsequent science courses, including Biology, Chemistry, and Physics. It builds a foundation of basic knowledge regarding matter and measurements early in the text, then furnishes the student with the key principles and scientific laws of classical physics, thermodynamics, electricity, magnetism, sound, light, and optics.
MAth
Algebra 1 focuses on the integration of algebraic concepts in technology and real-life applications, presenting topics in logical order with detailed examples that promote student comprehension and retention. Students explore the simplification, solving, graphing and interpretation of linear, exponential, radical, quadratic, and rational functions both manually and with technology. Internet search keywords help students locate online tools and enrichment. Additional review exercises are carefully designed for student review, retention, and preparation for the next lesson. Each chapter features graphing calculator tutorials, lessons in sequences and series, and a mathematical biography or career segment. Biblical truths and principles are taught through Dominion Modeling exercises that illustrate how mathematics is used to serve others and glorify God.
Bible
Bible class in high school is broken up into a three-year cycle. Throughout the 9th, 10th, and 11th grade the students will be presented with a full overview of the Old Testament, beginning with Genesis and finishing up in Malichi. They will learn God's promise to His people and the victories and struggles the Jewish people faced in their culture and walk with God.
The students will also be presented the Gospels, the Good News, through the writings of Matthew. They class will take an in-depth look at the life of Jesus of Nazareth through the account of Matthew, one of Jesus' disciples. The class will take the full year to fully comprehend the magnitude of Jesus' influence on our daily lives and the lives of those he interacted with.
The students will spend one more year going through the letters of Peter, James, Paul, and John. They will spend time understanding that the life application these men were delivering to the early church movement are still relevant to them today. They year will end with a study of the book of Revelation written by John while he was exiled in Patmos. | 677.169 | 1 |
only objection I have is to anytime I've used PhotoMath on my algebra homework, it did something completely different that what we learned that day. maybe it was just bugging for me, so you should still try it? . ♕ pinterest// bracecake ♕ | 677.169 | 1 |
EquationsPro 10.0
EquationsPro is a chemical engineering,mathematical and chemistry program. Software suitable for chemistry,chemical engineering students and professionals. Solves 500+ chemical/electrical/civil/mechcanical engineering,design,distillation, physics, and mathematical equations. Contains 200+ unit conversions. Solve for matrices, triangles, finance, geometry,area/surface/volume,statistics and many other mathematical problems and equations. Solve and plot graphs using the Zgraphs program. In addition interfaces with media player to allow playing of music,videos, ripping,burning cd's and includes a web browser to further solve problems, obtain information using the web. Plot and display data in numerous ways, 2D/3D,using the graphing interface included. | 677.169 | 1 |
My Profile
why create a profile on shaalaa.com? 1. Inform you about time table of exam. 2. Inform you about new question papers. 3. New video tutorials information.
By Prem Kumar (Author) M.R.P 425/-
215 (49%)
440 -
Product Description
Written by an examiner with years of experience in the subject, fully revised & updated edition of All in One Mathematics has been designed for the students studying in Class XII following the CBSE Mathematics curriculum for Class XII. The book has been designed so as to contain the explanation of various concepts covered under the CBSE Class XII Mathematics curriculum. The book provides guidance to the students starting from the stage of learning, to practicing what has been learnt and at last assessing the concepts learnt and practiced. The whole syllabus has been divided into 13 chapters covering Relations & Functions, Inverse Trigonometric Functions, Matrices, Determinants, Continuity & Differentiability, Application of Derivatives, Integrals, Application of Integrals, Differential Equations, Vector Algebra, Three Dimensional Geometry, Linear Programming and Probability. The book has been designed strictly in sync with the latest CBSE Mathematics syllabus & NCERT Textbook for Class 12th, with each chapter divided into individual topics for better understanding. Each individual topic contains detailed topical theory supported by illustrations, tables, flow charts, etc which will help in effective understanding of the concepts. Questions given in each chapter have been grouped as Very Short Answer Type, Short Answer Type, Long Answer Type and Value Based Questions. These questions cover NCERT Questions, Previous Years' Examination Questions, NCERT Exemplar questions as well as other important questions from the examination point of view. Solutions and explanations to all the questions have been given to facilitate easy learning and understanding. Practice Exercises have been given at the end of each chapter, which will help the students in assessing their level of understanding. The Revision Map and Self Assessment Sheet at the end of each chapter will help in quick revision and self analysis of the concepts covered under the syllabi of Mathematics for Class XII. For thorough practice and to give students a real feel of the examination ten Sample Question Papers have been provided after the chapterwise study. CBSE Examination Papers 2015 (All India & Delhi) have been given at the end of the book with complete solutions to give the students an insight into the current exam pattern and types of questions asked therein. Also the book covers latest CBSE Sample Question papers which will give the students idea about the types of questions which can be expected in the forthcoming examination and excerpts from topper's answer sheet have also been provided in the book. A complete book in itself, this book will serve as a true companion and a guide on your way of achieving highest grades in upcoming Class 12 CBSE Mathematics examination 2016. | 677.169 | 1 |
ISBN: 9780190306472 Format: Paperback Published: 29 August 2016 Country of Publication: AU Description: Maths Plus:follows a graded and spiralling approach, allowing teachers to revisit concepts throughout the year provides students with opportunities to sequentially develop their skills and knowledge in the three strands of the Australian Curriculum: Mathematicsis comprised of student, assessment and mentals and homework books.Mentals and Homework Books: Essential revision and consolidation activities that directly correspond to the concepts and units of work presented in the Student Books. All unit activities arranged under the three Australian Curriculum: Mathematics strands | 677.169 | 1 |
Calculator
The calculator is available by selecting "Calculator" in the List. On the iPhone there is also a landscape version of the calculator. Rotate to landscape orientation from the List, Calculator or any template to access it.
This information, number entry information and function examples are all available by selecting ? button in the calculator.
Keypads
On the iPhone and iPod touch there are four keypads: primary, math, trig and history. (Primary is always visible in landscape calculator.) Select each icon below the calculator frame to move between keypads. The math keypad includes measurement, power and log functions. The trig keypad includes trigonometric and hyperbolic functions. The history keypad includes both a calculation log and memory locations. History and memory are described below.
On the iPad there are four tabs and the primary keypad is always visible. The four tabs, from left to right, are history, memory, math and trig. Math tab displays power and log functions while the trig tab displays trigonometric and hyperbolic functions. History and memory are described below.
View Window, Moving the Cursor & Copy/Paste
The view window is where numbers, math functions and symbols appear as you select buttons. To perform mathematics, enter the entire expression and select '=' button to return a result.
To adjust a number either use the backspace key or select down on the cursor and drag to the desired location.
Selecting down on the cursor and releasing will display a menu for copy and paste. Copy copies the entire view window's contents and paste inserts the clipboard's contents at the cursor position. Copy and paste are available in the calculator and the template's number editor. The clipboard functions across the iOS device so copy and paste work within and outside of the app.
History & Memory
The calculator includes two types of storage. History (calculation log) includes a log of previous entries and calculations while memory includes 10 locations to store any numbers or equations. See the Keypad section above for details on accessing them.
Select a row to recall it to the cursor position in view window. To store the view window's contents, select the STO button on the desired memory location.
LAST is a special variable. The calculator evaluates based on what is actually displayed on the screen, rounded results create inaccurate follow-on results. For instance, 1/3 = is .333 but the rounded result means multiplying by 3 will leave a result of .999 instead of 1. LAST retains the full precision of the previous result, which is more complete than the history result or the result displayed in the view window. LAST can be returned by selecting its button in the history keypad.
To clear the history and/or memory locations, select the grey 'x' button in the history keypad on the iPhone or iPod touch or select either the history or memory tab twice on the iPad.
Settings
Select the gear icon (button) in the top, right corner to change the calculator settings. Settings are broken into three groups:
Display
Keyboard: different calculation types offer different keyboard configurations. Default is feet-inch (ft-in). The current keyboard has no impact on the kinds of math that can be performed. For instance, ft-in keyboard can still perform real and fractional math.
Real: whether real number results should be displayed in decimal or fractional format.
Other
Key Clicks: hear or mute the sound made when clicking keyboard keys. This affects the calculator and templates.
Calculator-Template Integration
The number editor in the templates and landscape calculator are integrated together. When the number editor is displayed, rotate your iPhone or iPod to landscape mode to access the calculator. The template row's result is available via the "T" memory location and any calculations are automatically inserted back in the number editor when rotating back to portrait mode. This feature is not available on the iPad. Instead either use copy/paste or the math capabilities built into the number editor. | 677.169 | 1 |
Essential math skills for engineers features concise, easy-to-follow explanations that quickly bring readers up to speed on all the essential core math skills used in the daily study and practice of engineering. These fundamental and essential skills are logically grouped into categories that make them easy to learn while also promoting their long-term retention. | 677.169 | 1 |
CK-12's Life Science delivers a full course of study in the life sciences for the middle school student, relating an understanding of the history, disciplines, tools, and modern techniques of science to the exploration of cell biology, genetics, evolution, prokaryotes, protists, fungi, plants, the animal kingdom, the human body, and ecology. This digital textbook was reviewed for its alignment with California content standards.
CK-12 Physical Science Concepts covers the study of physical science for middle school students. The 5 chapters provide an introduction to physical science, matter, states of matter, chemical interactions and bonds, chemical reactions, motion and forces, and the types and characteristics of energy.
This text respects the traditional approaches to algebra pedagogy while enhancing it ...
This text respects the traditional approaches to algebra pedagogy while enhancing it with the technology available today. In addition, textual notation is introduced as a means to communicate solutions electronically throughout the text. While it is important to obtain the skills to solve problems correctly, it is just as important to communicate those solutions with others effectively in the modern era of instant communications.While algebra is one of the most diversely applied subjects, students often find it to be one of the more difficult hurdles in their education. With this in mind, John wrote Elementary Algebra from the ground up in an open and modular format, allowing the instructor to modify it and leverage their individual expertise as a means to maximize the student experience and success. Elementary Algebra takes the best of the traditional, practice-driven algebra texts and combines it with modern amenities to influence learning, like online/inline video solutions, as well as, other media driven features that only a free online text can deliver.
This course is also intended to provide the student with a strong foundation for intermediate algebra and beyond. Upon successful completion of this course, you will be able to: simplify and solve linear equations and expressions including problems with absolute values and applications; solve linear inequalities; find equations of lines; and solve application problems; add, subtract, multiply, and divide various types of polynomials; factor polynomials, and simplify square roots; evaluate, simplify, multiply, divide, add, and subtract rational expressions, and solve basic applications of rational expressions. This free course may be completed online at any time. It has been developed through a partnership with the Washington State Board for Community and Technical Colleges; the Saylor Foundation has modified some WSBCTC materials. (Mathematics 001)
This is an Internet-based probability and statistics E-Book. The materials, tools and ...
This is an Internet-based probability and statistics E-Book. The materials, tools and demonstrations presented in this E-Book would be very useful for advanced-placement (AP) statistics educational curriculum. The E-Book is initially developed by the UCLA Statistics Online Computational Resource (SOCR). However, all statistics instructors, researchers and educators are encouraged to contribute to this project and improve the content of these learning materials. There are 4 novel features of this specific Statistics EBook. It is community-built, completely open-access (in terms of use and contributions), blends information technology, scientific techniques and modern pedagogical concepts, and is multilingualAdvanced Algebra II provides three complementary resources for teachers and students that ...
Advanced Algebra II provides three complementary resources for teachers and students that combine to provide a friendly, easy-to-understand explanation of Algebra II concepts. The main text, "Activities and Homework", consists of a series of worksheets for both in-class group work as well as homework assignments. The concepts behind those activities are described in detail in the "Conceptual Explanations" text. The third book, the "Teacher's Guide", provides instructors with guides and suggestions for presenting these materials.
Over a period of time, I have developed a set of in-class assignments, homeworks, and lesson plans, that work for me and for other people who have tried them. If I give you the in-class assignments and the homeworks, but not the lesson plans, you only have ⅔ of the story; and it may not make sense without the other third. So instead, I am giving you everything: the in-class assignments and the homeworks (the Homework and Activities book), the detailed explanations of all the concepts (the Conceptual Explanations book), and the lesson plans (the Teacher's Guide). Once you read them over, you will know exactly what I have done.
This digital textbook was reviewed for its alignment with California content standards.
CK-12's Life Science delivers a full course of study in the life sciences for the middle school student, relating an understanding of the history, disciplines, tools, and modern techniques of science to the exploration of cell biology, molecular biology, genetics, evolution, prokaryotes, protists,fungi, plants, animals, invertebrates, vertebrates, human biology, and ecology. This digital textbook was reviewed for its alignment with California content standards.
The main goal of Algebra is to develop fluency in working with linear equations. In this course, students will work with tables, graphs, and equations and solve linear equations and inequalities and systems of linear equations and inequalities. Students will learn how to simplify polynomials and begin to study quadratic relationships, along with analyzing mathematical situations verbally, numerically, graphically, and symbolically. Throughout the course, students will have opportunities to apply mathematical skills and make meaningful connections to lifeŐs experiences.
Students will take active roles in learning the game of chess and improving their skills, ability, and knowledge of the game. Students will read the course material, complete practice drills for each module, complete and submit all assessments and submit properly recorded (notated) games that they played. Course content includes: rules, strategy, tactics and algebraic notation (the 'language' of chess).
All materials on the site were revised for the 2014/2015 academic year. ...
All materials on the site were revised for the 2014/2015 academic year.
On the 8th Student Materials page you will find: the Mathematical Foundation (an explanation of the mathematical content in each chapter), the Student Workbook (an overview of the chapter, daily class activities and matching homework sets, Practice Standards connections for the chapter, and student self-assessments), a link to purchasing a soft-cover version of the workbook (these are available at cost, however you are free to print all materials yourself), and a parent manual (this is the student workbook with selected answers and explanations.)
On the 8th Teacher Support Materials page you will find a Teachers' Edition to the Student Workbook. It contains answers to all problems, pedagogical suggestions, and explanations of the mathematical flow of the workbook. Additionally, you will find the word version of the Student Workbook.
This is an activity about observing and mapping sunspots by direct solar ... of paper. Additionally, learners will mark the direction of the Sun image's motion. This is Activity 2 of the Space Weather Forecast curriculum. | 677.169 | 1 |
Intermediate Algebra
Beschreibung
Beschreibung
This presentation of intermediate algebra emphasizes skills, concepts, and their applications. The authors pay attention to reducing math anxiety, promoting good study habits, and showing the connection between mathematics and everyday life. | 677.169 | 1 |
Mathematics is the study of function and pattern in number, logic, space and structure, and of randomness, chance, variability and uncertainty in data and events. It provides both a framework for thinking and a means of symbolic communication that is powerful, logical, concise and precise. Mathematics also provides a means by which people can understand and manage human and natural aspects of the world and inter-relationships between these. Essential mathematical activities include calculating and computing, abstracting, proving, refuting and inferring; applying, investigating, modelling and problem solving.
This study is designed to provide access to worthwhile and challenging mathematical learning in a way which takes into account the interests, needs and aspirations of a wide range of students, and introduces them to key aspects of the discipline. It is also designed to promote students' awareness of the importance of mathematics in everyday life in a technological society, and to develop confidence in making effective use of mathematical concepts, processes and skills in practical and theoretical contexts.
In VCE Mathematics it is expected that students will have an approved CAS calculator. The College recommends the Casio Classpad 400.
Students intending to undertake Mathematical Methods and Specialist Mathematics at Year 12 (Units 3 and 4) level must take Mathematical Methods (Units 1 and 2) and Specialist Mathematics (Units 1 and 2) at Year 11 level.
The Mathematics courses at Year 12 may form pre-requisites for entry into a range of tertiary courses. It is HIGHLY RECOMMENDED THAT ADVICE IS OBTAINED FROM THE CAREERS COUNSELLOR BEFORE SELECTION. | 677.169 | 1 |
An introduction to differential equations. Diff equations are some of the most useful types of equations in all of mathematics. They tend to show up in all types of fields such as physics, chemistry, economics and even in biology and medicine. It is therefor important that one understands the theory behind differential equations prior to using them.
This video presents 10 different graphs every student should have mastered. They tend to come up time and time again, might as well learn these by heart. This is not to say that only these 10 graphs or important but hey, you've gotta start somewhere! | 677.169 | 1 |
This straightforward guide describes the main methods used to prove mathematical theorems. Shows how and when to use each technique such as the contrapositive, induction and proof by contradiction. Each method is illustrated by step-by-step examples.
Mathematics is not a spectator sport: successful students of mathematics grapple with ideas for themselves. Distilling Ideas presents a carefully designed sequence of exercises and theorem statements that challenge students to create proofs and concepts. | 677.169 | 1 |
I would most definitely recommend this course. The class is challenging and offers excitement through different ways to solve mathematical problems. Many of the problems are based off of real life situations which also helps keep all the information fresh in your mind.
Course highlights:
I gained more knowledge about how math can be used for everyday situations and even find myself a year later using that information to solve problems at work and at home!
Hours per week:
3-5 hours
Advice for students:
Make sure you have your own calculator. Having to share a calculator is very frustrating when time is limited.
Course Term:Spring 2016
Professor:Mr. Viso
Course Required?Yes
Course Tags:Math-heavyParticipation CountsCompetitive Classmates
Aug 23, 2016
| Would recommend.
This class was tough.
Course Overview:
If you plan to further your knowledge in math, take this class and really work at it. If not, it's still a great class to take to further knowledge in general and get some cheap college credit in early.
Course highlights:
Although the I didn't learn to use math in everyday scenarios, I did learn how to use critical thinking skills outside the classroom. This also prepared me for college math.
Hours per week:
3-5 hours
Advice for students:
In this course you will need time for homework and maybe a study buddy or just be able to go to a tutor session she does Wednesday's. | 677.169 | 1 |
Fair.Customer Reviews
Good Book
This is the book I learned Calculus from in college. I recently lost my copy from school, so decided to replace it. I've never used a different book, so I can't say it's the best, but it gets the job done. Never heard any complaints about it from fellow students either | 677.169 | 1 |
Color Coded Algebra
Presentation (Powerpoint) File
Be sure that you have an application to open this file type before downloading and/or purchasing.
0.16 MB | 12 pages
PRODUCT DESCRIPTION
On my way home from a day of introducing algebraic equations, I asked myself which step my students struggled with the most. My answer was "THE FIRST STEP - COMBINING LIKE TERMS!" Once I realized the problem, I decided to devise a way to help my students understand the hows and the WHY in solving algebraic equations. This Power Point is used in conjunction with a free worksheet from . The questions I ask my students are every bit as important as the coloring process. I did an action research project when I created this file. I gave my students a pretest and a post test. These tests were identical, but the students never saw the pretest after they took it. The students studied improved their scores by an average of over 240%! I hope this product will help your students solve | 677.169 | 1 |
Problems and Algorithms
It is useful to have in mind some 'classic' graphic theory problems. Those algorithms are often part of the base graph courses and it is likely that what you are trying to solve is in fact one of those problems. For each definition, we show how to solve this
problem with QuickGraph.
The interested reader is encouraged to get back to his favorite graph theory book to get a more formal definition of each of those problems. | 677.169 | 1 |
2005
Bunker Hill CC
Charlestown, MA
NEMATYC 2005 was held at Bunker Hill Community College
on Friday and Saturday, April 8, 9, 2004. The theme was "Mathematics
for the Real World". The conference co-chairs were Shirley
MacKenzie and Geri Curley, both of Bunker
Hill CC.
Besides a great program other events enjoyed by the
participants included the following.
Friday Reception: Held at the Boston Science Museum,
a walkable distance from BHCC, this was followed by visiting the museum
itself.
Saturday's lunch was at the Royal Sonesta Hotel, next
to the Science Museum.
Bank Account Balance, March 15, 2005
$10691.58
Respectfully submitted,
Lois A. Martin
Treasurer
Program
FRIDAY
Wall Street Statistics: Diversify Your Investment Portfolio
This paper session presents a thorough study of basic
statistical
methods in investment analysis. The theory of asset allocation along
with intuitive probabilistic thinking will be emphasized. We will
also discuss the mathematical rationale behind diversification.
Tried Methods to Meet Student Needs
Presenter: Dr. Prem Singh
Johnson and Wales University
Teaching has become a very challenging profession. Our
classrooms
are becoming increasingly diverse in age and background, personal
interests, physical and mental abilities. This presentation will
discuss tried methods, ranging from the use of technology to
cooperative learning to classroom assessment techniques.
Problem Mathematics Students: A New Instructional Paradigm
Presenter: Rev. Dr. Christian Agunwamba
Bunker Hill Community College
In this presentation, we go beyond the usual lists (skills,
methods, attitudes, technologies, etc.) that teachers are rightly
required to acquire. We present a number of other issues that are
relevant to teaching difficult mathematics students. One can often
hear instructors discussing these problems in the hallway or in their
offices. The purpose of this presentation is to widen this discussion
and suggest possible solutions.
The Power of 1 in the Developmental Mathematics Classroom
Presenter: Adele Miller
Central Connecticut State University
The unit is the simplest and most universal idea humans have
about
number, and understanding variety in the unit creates a foundation
for understanding whole numbers and builds a bridge for understanding
rational numbers. Students' resistance to fraction ideas may arise
from being unclear about what the unit is. This workshop will present
games and activities which may help students gain a better
understanding of the unit and unit fractions so that they can grasp
rational number concepts.
All the Baseball Statistics About the Boston Red Sox that You
Ever Wanted to Know
Presenter: Steve Krevisky
Middlesex (CT) Community College
The 2004 World Series win by the Sox completes a cycle of 100
years of Red Sox baseball. In this presentation, we examine the
history and statistics of this storied franchise which has included
such greats as Ted Williams, Tris Speaker, Cy Young, Roger Clemens,
Jimmie Foxx and many others. Various formulas and statistical
calculations will be used to examine the legacy of this franchise.
This will be of interest to teachers of various levels of
mathematics, and baseball can be a tool to motivate our students,
thus making math more relevant to them. Come join the discussion and
be ready to talk about your favorite Red Sox player! At the end, we
can pick an all-time Red Sox team!
Teaching and Learning with Tablet PCs
Presenters: Lois Martin, Kerryn Snyder
Massasoit Community College
The presenters received an EAST grant to use Tablet PCs for
instruction in mathematics and science classes. Although the grant
was written to address teaching and learning of students with
disabilities, the benefits to other students and faculty were
evident. Learn about partnering the use of a tablet PC with WebCT to
create and deliver both traditional and online lessons with Microsoft
Word, Microsoft Journal, a whiteboard, and virtual office hours.
Math Models, Multiple Representations and Conceptual
Understanding
A contributing factor to students' difficulties in mathematics
is
their belief that math is memorization of formulas and replication of
procedures. A modeling approach utilizes methods and materials which
contribute to student awareness that mathematical ideas should have
meaning and that mathematical procedures are based on underlying
relationships. Session participants will work with materials which
facilitate conceptual understanding of topics in arithmetic,
geometry, algebra, and precalculus. Concepts, relationships and
procedures will be introduced using concrete or visual models
physical objects or movements, sketches, graphs, calculator screens
and computer illustrations. The models will provide a foundation for
understanding the same mathematical ideas expressed in words, numbers
and symbols.
SATURDAY
Pythagoras: The First Mathematician
The significant contributions of Pythagoras and the members of
his
school will be discussed in a historical, philosophical, and
mathematical context. His intellectual legacy and overall impact upon
subsequent thinkers such as Plato, Kepler, and Descartes will also be
discussed.
Seven Principles to Build Success in Developmental
Mathematics
Students
Presenter: Dr. John Tobey
North Shore Community College
In most cases, students taking developmental mathematics
courses
in college were taught algebra for two or three years in high school
but they failed to learn it successfully. After years of frustration
and failure in mathematics how do we give hope to the college student
who enrolls in developmental math but feels hopeless about learning
the material? Dr. Tobey presents seven time-tested principles that
help the college student to succeed in a developmental mathematics
course. Come and find out some ways that will help motivate students
to master a subject that they have often hated and avoided all their
lives.
EXCELlent Statistics - Using Excel and Fisheries Biology in
the
Teaching of Statistics
Presenter: Barry Woods
Unity College
At Unity College, statistics courses are taught using
Microsoft
Excel and the fish data collected from nearby Lake Winnecook. In
collaboration with the Fisheries Science and Techniques class, both
descriptive and inferential statistics are taught using realworld
fish data. Excel will be used to demonstrate the teaching of
statistics in this ongoing environmental study.
The Eureka! Experience - Instructional Techniques that
Encourage
It!
Presenter: Alan Tussy
Citrus College
Watch as several of your colleagues participate in an
intriguing
experiment that explores the relationship between thought and
language. Learn about the successive changes that your students go
through to assimilate mathematical terms and concepts. Witness the
Eureka! Experience - that point in the learning process when students
confidently claim, "Now I get it!" You'll leave with some specific
instructional techniques that help students better speak, write, and
think mathematically using the language of algebra.
Peer Led Team Learning in Calculus I at the University of
Maine
Presenters: Jen Tyne, Paula Drewniany
University of Maine
We are in the third semester of using the national Peer Led
Team
Learning (PLTL) model in our Calculus I course. The PLTL Workshop
model engages teams of eight to ten students in learning sciences,
mathematics and other undergraduate disciplines guided by a peer
leader. Our four credit course meets three days per week in lecture,
and one day for 75 minutes in small groups. The small groups, led by
a peer leader, work through in-depth calculus problems, called
"workshops". In our session, we will briefly describe our experience
creating workshop materials, hiring and training leaders, and
implementing PLTL in the classroom. We will include evaluation
results to date and plans for the future. Attendees will then
participate in a workshop session.
A Historical Tour of Numeration Systems
Please join us as we tour the development of numeration
systems
and numerals, over the course of many eras and through many cultures
an interesting, interdisciplinary topic that demonstrates arithmetic
concepts and number sense.
Addison-Wesley and Prentice Hall will present two web-based
resources available with both company's math and statistics texts.
These resources, MathXL and MyMathLab, would be of interest to
instructors looking to offer easily accessible practice problems and
tutorials to enhance both traditional lecture and online courses.
Online homework and testing with a robust grade book are also
available. Both MathXL and MyMathLab correlate directly with the
scope, sequence, and problems in the AW and PH texts.
Using Multiple Choice Exams in an Introductory Biostatistics
Course
The speaker will discuss the challenges of using a multiple
choice
format versus the traditional examination method for assessing
student learning in biostatistics. Advantages and disadvantages of
both types of testing will be presented.
How are "Differential Equations" and "Standard Deviations"
Relevant to my Training as a Pharmacist or Health Care Worker?
In this presentation, I will discuss how I incorporate
applications from personal real-world collaborations into teaching
Calculus and Statistics to pharmacy and health sciences students. My
intention is to address how the challenge of teaching mathematics to
future health care workers turns into an extremely rewarding activity
when students understand and enjoy mathematics through the use of
real biomedical applications in lectures.
An Online Precalculus Course and an Online Statistics Course
-
Two Different Approaches to Online Learning
Presenters: Judy Carter, Lora Connelly
North Shore Community College
Pedagogy is an important consideration in any course. Get some
good ideas for online mathematics courses that meld effective
pedagogy and user friendliness. A precalculus course that uses a
standard text with web support and a statistics course that adopts
materials developed specifically for the web will be presented.
Ayuh! There is Meaningful Life After Retirement
Presenter: Gary Getchell
Cape Cod Community College (retired)
Gary Getchell is sixty-nine, has been retired from Cape Cod
Community College since 2001, and lives full-time in Dresden, Maine.
He is Vice-Chairperson of the local school committee, the
"Mathematician-in-Residence" at a local middle school, a stand-up
comic performing throughout Maine and Massachusetts, has built a
barn, and still teaches algebra to Four C's Students through
television and the Internet. In this informative and sometimes zany
presentation, Gary shares with you his "life-inretirement".
Puzzles, Games and Fun Projects
Presenter: Charles Mazmanian
Johnson and Wales University
Mathematics can be interesting and entertaining to both
teachers
and students. The puzzles and games are not only fun but educational
as well other than mere drill in fundamentals.
Engaging, Assessing, and Helping Your Student with New Tools
from
Houghton Mifflin
Presenter: Leonid Tunik
Houghton Mifflin Company
Houghton Mifflin will be demonstrating new teaching tools that
help you engage and empower your students - while saving you time.
The presenter will walk participants through an integrated suite of
online and CD-based products containing current, media-rich
self-paced tutorials and guided practice, one-on-one tutoring
support, assessment content, enhanced electronic book content,
instructional video options, and other elements that tie directly to
the material presented in the text. The presentation will highlight
examples in Developmental Math, Calculus, and Statistics.
Are We Teaching All the Essentials?
Presenter: Rev. Dr. Christian Agunwamba
Bunker Hill Community College
The NCTM Standards state that curriculum at all levels, up to
and
including grade 12, should include proofs. All students should know
that logical reasoning is fundamental in mathematics. In agreement
with these standards, we maintain that mathematical proofs, which
provide training in logical reasoning, should be included in the
community college mathematics curriculum.
Unusual and Creative Teaching Techniques
Presenter: Dr. Andrew B. Perry
Springfield College
As a math teacher, I experiment frequently with different
teaching
techniques, some of them unusual, and some of them arguably
eccentric. For example, I've developed a complex math game called
"Wheel of Functions", and utilize daily feedback from each student in
many of my classes. I will share some of my ideas and hope audience
members will share some of theirs as well. | 677.169 | 1 |
2
Intro Some of the most important applications of differential calculus are optimization problems, in which we are required to find the optimal (best) way of doing something. Here are examples of such problems that we will solve in this chapter: What is the shape of a can that minimizes manufacturing costs? What is the maximum acceleration of a space shuttle? (This is an important question to the astronauts who have to withstand the effects of acceleration.) | 677.169 | 1 |
College Algebra
Description
This text covers all of the standard topics for college algebra. The first four chapters give an introduction to algebra for those students who need it. There is also a cumulative review exercise at the end of Chapter 4.The exercises are a normal lesson apart, and the problems in each exercise are in groups of four similar ones. This makes it a simple matter for even the inexperienced instructor to make a good assignment regularly. Most classes only need to be assigned every fourth problem, but other problems are available for practice. There are about 5000 problems in some 75 regular and 12 review exercises. About half of the problems are new, and there are many drill problems which are closely keyed to the examples.Answers are given in the text for three-fourths of the regular and all of the review problems.show more | 677.169 | 1 |
ninth edition of Mathematics for Elementary Teachers: A Conceptual Approachcontinues the innovative time-tested approach of the previous editions: an emphasis on learning via specific, realistic examples and the extensive use of visual aids,More...
The ninth edition of Mathematics for Elementary Teachers: A Conceptual Approachcontinues the innovative time-tested approach of the previous editions: an emphasis on learning via specific, realistic examples and the extensive use of visual aids, hands-on activities, problem-solving strategies and active classroom participation. Features of the text focus on ensuring ninth edition represents a significant step forward in terms of online course management as roughly half of all problems in the text will be assignable through our new online homework platform, Connect Mathematics. In addition, Connect Mathematics will be fully integrated with Blackboard, providing the deepest integration of an online homework and course management system in the market today. Additionally, this text contains an activity set that corresponds to each section of the companion text, Mathematics for Elementary Teachers: An Activity Approach,also by the Bennett, Burton, and Nelson team. Mathematics for Elementary Teachers: An Activity Approachcan be used independently or along with its companion, Mathematics for Elementary Teachers: A Conceptual Approach | 677.169 | 1 |
Accessibility links
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Mathematics at Tring School
Course description
Maths is a popular choice at Tring School, with 3 or 4 classes in each year.
Every student studies 2 modules of Core Mathematics and 1 module of Mechanics or Statistics each year
Core Mathematics: This compulsory component includes the subject core for Mathematics at A level and as such makes up the majority of an A level in Mathematics. It continues the study of algebra, number work and trigonometry and makes up two-thirds of the
work each year.
Mechanics: In this course Mathematics is used to describe and explain real-world situations. It includes the action of forces on physical structures and moving bodies. Chosen by future Physicists, Engineers, Architects and others, it complements some of
the topics covered in A level Physics.
Statistics: This is concerned with data handling and is applicable to a wider range of subjects. The presentation, collection and interpretation of data are studied, together with further applications of the ideas of probability to predict and explain results.
Course content
AS Level Mathematics: Units Core 1, Core 2 and either Statistics 1 or Mechanics 1 Students may then choose to study three further A2 units towards an A level qualification in Mathematics.
A2 Level Mathematics: Units Core 3, Core 4 and either Statistics 2 or Mechanics 2 (building on what was studied in Year 12)
Entry requirements
A minimum of 310 UMS at GCSE Maths (EdExcel) For external students who are sitting the AQA paper a minimum of 230 UMS
For Year 13 students should achieve a minimum of a grade D at AS
Assessment
There is no coursework - all assessment is by examination. There are 3 x 90 minute exams each year in June.
Financial information
All students following AS Mathematics courses will be required to have a graphical calculator (cost approximately 45.50 - can be ordered through school).
Future opportunities
A level Mathematics is of benefit to those intending to embark on a scientific or engineering career and provides support to those students wishing to study business, accounting, architecture or humanities. Maths has wide applications in industry, business,
finance, science and technology. Maths qualifications can help you towards a future career in these areas. It is also a useful support for many University courses, which increasingly can involve statistics modules.
Further information
The results for both AS and A2 Maths at Tring School have exceeded targets for many years. Last summer, 70% of our students achieved A*-B grades at A2 Maths.
How to apply
If you want to apply for this course, you will need to contact Tring School directly. | 677.169 | 1 |
Believe it or not, algebra is a simple subject which anyone can master. Much of the difficulty that we face when it comes to learning algebra, comes from the fact that we have already decided that it is boring, difficult, and unnecessary. While it may appear complicated to first time learners, the rules and principles of this subject are remarkably straight-forward and logical. In time, students will learn the pattern of thought required to solve algebra problems successfully.
Algebra is a problem subject for many students who go through high school with a vague idea about the subject and a hundred and one doubts which are never cleared. The reasons why students find algebra so difficult is that the transition from simple arithmetic to this more complex branch of math does not occur smoothly for most students.
One of the best ways to learn algebra is to take it seriously right from the start. The basics of algebra like integers, and the rules of division, multiplication, addition, and subtraction are important as they continue to be used in the advanced topics as well. If you are not a math person or you find that algebra eludes your understanding, consider using the services of an algebra problem solver to learn effectively.
Algebra 2 can be difficult for many students as it covers slightly more advanced topics and if students are not well versed in algebra 1, the next step up can prove to be quite steep. Algebra is a great subject to know as it may come in handy later on and many college courses, particularly science and technology, and math related courses will require students to take mandatory algebra classes.
Learning to solve equations can be a fun and interesting process, which will teach students skills like using a step by step approach to solving math, looking at the problem as a whole and, most importantly, to keep trying different methods till you hit on the right one. | 677.169 | 1 |
081764150ynamical Systems with Applications using Maple
This work covers material for an introductory course in the theory of dynamical systems. There is a short tutorial in MAPLE to facilitate the understanding of the theory. The text is divided into two parts: continuous systems using differential equations and discrete dynamical systems. Differential equations are used to model examples taken from various topics such as mechanical systems, interacting species, electronic circuits, chemical reactions, and meterology. The second part of the text deals with real and complex dynamical systems. Examples are taken from population modelling, nonlinear optics, and materials science. Linear algebra and real and complex analysis are prerequisites | 677.169 | 1 |
HyperMath is "a growing collection of examples of applied mathematics with links to their applications to problems in physics and astronomy." The author, Carl R. (Rod) Nave of the Department of Physics and Astronomy at...
High school and college students are the target audience of this outstanding math site. The main topics addressed in the nine essays are trigonometry, algebra, and basic calculus. The author does a good job of...
The Annenberg Foundation has been an active part of creating educational and professional development tools and instructional aids for teachers for many years. To reach the broadest audience possible, their Annenberg...
Presented by Professor Jody Harris at Broward Community College, these handouts are an excellent resource to print and give to community and technical college students in the algebra classroom. The subjects of the...
The introduction to this site remarks, "If you need help in college algebra, you have come to the right place." Their statement is accurate, as the staff members at the West Texas A&M University's Virtual Math Lab have... | 677.169 | 1 |
Two Dimensional Vectors (Level 5)
Video Description
This video is a review of Two Dimensional Vectors. This video goes over 12 examples covering vector addition, vector subtraction and scalar multiplication. These problems are solved by using the geometric interpretation of these particular vector operations. | 677.169 | 1 |
Written Topics for 2016-2017
All symbolic manipulators, including HP's and the TI-Nspire CAS, are
prohibited for the freshmen and sophomore levels at all meets.
Laptops, PDAs, phones, and other non-calculating devices are not allowed.
Freshmen
Ratios, Proportion and Percent:
May include money, interest, discounts, unit conversions, percents of increase decrease and error, and direct variations. It should not require knowledge of advanced algebra. While questions should not be trivial, they should be approachable to most contestants. (2015-16)
Counting Basics and Simple Probability:
Includes tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas. (2015-16)
Sophomores
Geometric Probability:
Emphasis on the concept of geometric probability rather than on difficult geometry problems. Students are not required to have a comprehensive knowledge of geometry. UMAP module 660 is a good source, as is HIMAP module 11. (2015-16)
NO CALCULATOR.
Similarity:
The standard geometric treatment including perimeter, area, and volume relationships, conditions determining similarity, similarity in right triangles and polygons. It may include a few proportion theorems that are not specifically similarity, such as the angle bisector theorem. (2014-15)
NO CALCULATOR.
Advanced Geometry Topics:
Restricted to: Brahmagupta's formula, point to line distance formula, area of a triangle given vertices, Stewart's Theorem, Ptolemy's Theorem, Mass points, inradius and circumradius, Ceva's Theorem, and Theorem of Menelaus. A good reference would be Geometry by Rhoad, Milauskas, and Whipple, Chapter 16. (2015-16)
Probability:
The standard treatment of probability. It may include combinations, permutations, mutually exclusive events, dependent and independent events, and conditional probability. It should not include binomial distribution nor expected value. (2015-16)
NO CALCULATOR.
Modular Arithmetic:
May include arithmetic operations in different moduli, divisibility, solving simple linear congruences in one or two variables, Fermat's Little Theorem, Wilson's Theorem, and Chinese Remainder Theorem. (2014-15)
NO CALCULATOR.
Sequences and Series:
Including, but not restricted to, sequences and series defined by recursion, iteration, or pattern; may include arithmetic, geometric, telescoping, and harmonic sequences and series. No calculus. (2015-16)
Seniors
Triangle Trigonometry with Applications:
Including right triangle trigonometry, laws of sines and cosines, and of course, word problems. (2015-16)
NO CALCULATOR.
Vector Analytic Graphing:
Includes two dimensional vector applications, two and three dimensional vectors, equations of lines and planes in space, scalar, inner and cross products, perpendicularly and parallels. distance between lines, points and planes. (No calculus) (2014-15) | 677.169 | 1 |
The U symbol means "union". A union of two sets means that the distinct elements of each set are combined together. For example, the union of {1,2,3} and {4,5,6} is {1,2,3} U …{4,5,6} = {1,2,3,4,5,6}. If a number is an element of both sets, the union of the sets will only contain one instance of that number. For example: {1,2,3} U {2,3,4} = {1,2,3,4}, and does NOT equal {1,2,2,3,3,4}.
Algebra comes from the Arabic "al-jabr" meaning "restoration". Algebra differs from arithmetic through the use of non-number symbols, such as x, y, and z. The "restoration" re…ferred is the combination of Indian, Babylonian, and Greek classical methodology that were lost to civilization during the European Dark Ages.
In basic algebra a discrete variable is one that can only take on specific set of values. For example, if we were to say that X can only take on a whole value between 1 and …10, then X would be a discrete variable. On the other hand, a continuous variable is one that can take on an unlimited number of values. For example, if we were to say X can take on ANY value between 1 and 10, then X is called a continious variable. The important thing to note is that the range of a variable (the min and max values it can take) is different than whether it is discrete or continuous. Discrete only implies a fixed (and known) set of values is possible for a variable
An equation cannot exist (has no meaning) without an '=' sign. Therefore, and somewhat simplistically, an equation MEANS that, for specific instances, the entities on bo…th sides of the '=' sign are in balance (equal in worth). Example 1: x + 2 = 5; means there is a value of 'x' which when substituted into the entity 'x + 2' will make it equal in value to what's on the other side of '=', ie: 5. In this example the balance is achieved when and only when x has the value 3. Example 2: x2 + 5x - 8 = 66 (where x2 represents x-squared) means there are > 1 value of 'x' which when substituted into the entity 'x2 + 5x - 8' wll make it equal in value to 66. In this example the values of x ('+' and '-'values) can be determined iteratively or by using the quadratic formula. Hope this helps.
Algebra is a branch of mathematics concerning the study of structures, relation and quantity. Together with geometry, analysis, combinatorics and number theory, Algebra is one… of the main branches of mathematics. | 677.169 | 1 |
Simple Scientific Calculator - This is simple Scientific Calculator that can perform basic arithmetic operation like +,-,*,/ and some trigonometric function like sin, cos, tan, and solve linear and quadratic equation with 2 or 3 variables.mPustakMultiply Mathematics Practice app that lets you learn with a lot of fun! | 677.169 | 1 |
Probability and Permutations
High School Math based on the topics required for the Regents Exam conducted by NYSED.
Lesson on Probability and Permutations.
Probability Permutations part 1 lesson
Probability Permutations part 2 lesson | 677.169 | 1 |
ADVANCE CALCULUS FOR APPLICATIONS II Documents
Showing 1 to 12 of 12
SECTION 2.2 MATRIX INVERSES If the matrix A is square and there is a matrix C such that CA = AC = I, then A is called invertible and C is called the inverse of A, which we write as A-1 . A matrix that is not invertible is called singular. FACT. Products a
SECTION 3.2 PROPERTIES OF DETERMINANTS Adding a multiple of one row to another row does not change the determinant. Multiplying a row by a constant also multiplies the determinant by that constant. Switching two rows multiplies the determinant by -1. A sq
SECTION 6.1 INNER PRODUCT, LENGTH, ORTHOGONALITY SOME MOTIVATION. (1) Suppose we want to solve Ax = b, but the system is inconsistent. Then we'd like to do the best we can, that is, we'd like to find an x so that Ax is as close as possible to b. We need t
SECTION 1.2 ROW REDUCTION AND ECHELON FORMS Our aim is to transform a system of linear equations into an equivalent system from which the solutions can easily be read. It's easiest to do this by performing row operations on the augmented matrix of the sys
SECTION 1.3 VECTOR EQUATIONS Until further notice, a vector will be a matrix with exactly one column. Vectors with two rows can be identified with points in the plane; vectors with three rows can be identified with points in three-dimensional space. The c
SECTION 1.5 SOLUTION SETS OF LINEAR SYSTEMS Systems of linear equations can always be written as a matrix equation Ax = b. When b = 0 we say the system is homogeneous. Homogeneous systems always have at least one solution. The question is usually whether
SECTION 1.8 ANOTHER WAY TO THINK ABOUT Ax = b
Ax = b is a way to write a system of equations. Here's the new way to think about Ax . Given a vector x, then Ax is another vector y. When the matrix A is m n, then we get a function or transformation T from
SECTION 2.1 MATRIX ALGEBRA You can multiply matrices by scalars (numbers); when two matrices are the same size you can add and subtract them; when two matrices are appropriate sizes you can multiply them. We know about the matrix-vector product Ax, so to
SECTION 3.1 DETERMINANTS A square matrix A has a determinant, denoted by det A. To calculate det A, we start with the 2 2 case: a b det = ad - bc c d For any matrix A, when we cross out row i and column j, we get a new matrix denoted by Aij . Then for any | 677.169 | 1 |
Algebra I EOC STAAR Review: Functions TEKS A.2(A)
Presentation (Powerpoint) File
Be sure that you have an application to open this file type before downloading and/or purchasing.
2.1 MB | 20 pages
PRODUCT DESCRIPTION
This interactive lesson is designed to prepare students for the Algebra I EOC STAAR test. The examples focus on finding the domain and range (TEKS A.2(A)) and are aligned to the released test items on the 2014, 2015, and 2016 tests. Practice includes functions shown as mapping, graphs, and word problems. A pdf practice page and key is attached | 677.169 | 1 |
Key Stage 5
Key Stage 5
AS and A2 Mathematics Course
Students study the Edexcel Mathematics Syllabus – 8371. The AS/A2 mathematics course is open to students who achieve an B-A* and show a flair and sound working knowledge of the subject.
What is this subject about?
Mathematics at this level consists of the study of Pure Mathematics and the study of application of Mathematics to the physical world:
Statistics (for understanding and interpreting information) – in year 12
Mechanics (talking about movement of objects and forces acting on them) – in year 13
The course develops understanding and resourcefulness in the use of mathematics.
Course Content
To gain the AS award, students will study two pure mathematics core units (C1 and C2) covering topics in algebra, trigonometry, calculus and coordinate geometry, amongst others, and the S1 application unit in Statistics 1.
To convert AS level Mathematics into A level Mathematics students study two further pure mathematics core units (C3 and C4) covering more algebra, trigonometry, calculus and other topics, and an application unit in Mechanics 1.
Teaching and Learning Styles
Students will experience formal lectures, self-study units, use of ICT, tutorial support and regular structured homework assignments.
Entry requirements
Students wishing to study AS/A2 Mathematics must have at least a high grade B or above in GCSE Mathematics.
For progressions to A2 students must have an AS qualification at grade D or above.
Progress & Assessment
Each module is examined by means of 1 hour and 30 minutes long paper. These can be taken only in June 2015.
However, there will be an official Mock test in January for C1 in first year and C3 in second year, with other shorter assessments each module of the year to follow the progress of the students.
It is very important to take these Mock tests seriously as the real exams as it will be important indicator for decision will some students continue with the course or not.
Where can this subject lead me?
Students intending to follow degree path in Computing, Engineering or Physics will probably find AS and A level GCEMathematics a condition of entry to university courses. Mathematical skills are highly prized and an AS or A level qualification in some form of mathematics will be valuable when applying for university entry and will give you a very significant advantage in the job market | 677.169 | 1 |
A Decade of the Berkeley Math Circle - The American Experience (Paperback)
Zvezdelina Stankova, Tom Rike
Series: MSRI Mathematical Circles Library, v. 1
(sign in to rate) Loot Price R702Discovery Miles 7 020Many mathematicians have been drawn to mathematics through their
experience with math circles: extracurricular programs exposing
teenage students to advanced mathematical topics and a myriad of
problem-solving techniques and inspiring in them a lifelong love
for mathematics. Founded in 1998, the Berkeley Math Circle (BMC) is
a pioneering model of a U.S. math circle, aspiring to prepare our
best young minds for their future roles as mathematics leaders.
Over the last decade, 50 instructors - from university professors
to high school teachers to business tycoons - have shared their
passion for mathematics by delivering more than 320 BMC sessions
full of mathematical challenges and wonders.Based on a dozen of
these sessions, this book encompasses a wide variety of enticing
mathematical topics: from inversion in the plane to circle
geometry; from combinatorics to Rubik's cube and abstract algebra;
from number theory to mass point theory; from complex numbers to
game theory via invariants and monovariants. The treatments of
these subjects encompass every significant method of proof and
emphasize ways of thinking and reasoning via 100 problem-solving
techniques.Also featured are 300 problems, ranging from beginner to
intermediate level, with occasional peaks of advanced problems and
even some open questions. The book presents possible paths to
studying mathematics and inevitably falling in love with it, via
teaching two important skills: thinking creatively while still
"obeying the rules," and making connections between problems,
ideas, and theories. The book encourages you to apply the newly
acquired knowledge to problems and guides you along the way, but
rarely gives you ready answers. "Learning from our own mistakes"
often occurs through discussions of non-proofs and common
problem-solving pitfalls.The reader has to commit to mastering the
new theories and techniques by "getting your hands dirty" with the
problems, going back and reviewing necessary problem-solving
techniques and theory, and persistently moving forward in the book.
The mathematical world is huge: you'll never know everything, but
you'll learn where to find things, how to connect and use them. The
rewards will be substantial. | 677.169 | 1 |
Polynomials Bundle - 7 worksheets
PDF (Acrobat) Document File
Be sure that you have an application to open this file type before downloading and/or purchasing.
0.61 MB | 23 pages
PRODUCT DESCRIPTION
Polynomials Bundle – 7 Worksheets
This bundle has 7 self-checking puzzle worksheets. Once the worksheets are completed, the answer to a riddle or a saying is revealed. The following are the descriptions of the worksheets included in this bundle.
1. End Behavior and Zeros of Polynomial Functions
This worksheet gives the students an equation. The students are to choose the end behavior picture, tell whether the function is even or odd and find the maximum number of zeros. The solutions are given solutions in a 3x3 grid. The puzzle is solved by matching the pattern in the grid to the patterns on the next page.
2. Performing Operations on Polynomial Functions - Addition, Subtraction, Multiplication and Division
This worksheet gives the students functions f and g as well as a set of directions which tells the students to add, subtract, multiply or divide. The students will find the solution on the next page. (No domain is declared in the division problems.)
3. Descartes Rule of Signs for Polynomials
This worksheet gives the students an equation. The students are then asked to find either the number of possible positive or negative zeros by using Descartes' Rule of Signs. A line is drawn to the solution. That line passes through a letter which is matched at the bottom of the worksheet to reveal the answer to a famous quote of Descartes'.
4. Dividing Polynomials Including Negative Exponents
The problem and solutions are given on this worksheet, except part of the solution is covered up. The students are to find the missing part of the solution and match the letter at the bottom to reveal the solution to a Mad Gab type quote. If the solution contains a negative exponent, the solution will be printed as 2/x, not
2x^(-1)
5. Factor and Remainder Theorems for Polynomials
The students are given a polynomial function. Possible, complete solutions are given based on matching the degree and zeros from the graph of the polynomial. (Therefore, each student will need to use a graphing calculator with this worksheet … which is not included.) The students are to pick the possible solutions written in factored form. The students are NOT looking for the exact solution, just possible solutions.
6. Factoring Cubic Polynomials Using Zeros
A cubic polynomial is given along with 6 factors. From the graph, the students are to select the three correct factors. (Therefore, each student will need to use a graphing calculator with this worksheet … which is still not included.) The student will match the pattern of the solution to a pattern on the decoder key to solve the riddle.
7. Writing Polynomial Equations in Vertex Form
The students are to calculate and write a quadratic equation given the vertex and a point on the graph in the form y=a(x-h)^2+k. However, there are twice as many solutions as there are problems, so the student will need to select the correct answer based on the 'a' term as well and the (h,k) value | 677.169 | 1 |
CALCULATOR OPERATIONS Review of Introductory MathematicsCALCULATOR OPERATIONSThis chapter gives the student a chance to reacquaint himself withbasic calculator operations.The teaching of the "mechanics of mathematics" (division, multiplication, logarithms, etc.) inrecent years has focused more on the skills of using a calculator than on the pure principles ofthe basic subject material. With the decreased cost of hand calculators, virtually every personowns, or has access to, a calculator. A nuclear plant operator would be wise to learn how to usemost of the calculators available today. Such knowledge will help the operator make quickdecisions when circumstances arise for the need of a "quick calculation" of flow rate or someother parameter.Many calculators are available on the market today, and each one is a little different. For thepurpose of this module, a scientific calculator will be needed. The Texas Instruments scientificcalculator TI-30 will be used for the examples in this module. Most calculators work on thesame principles, but some do not. Some calculators operate on a programming principle likeHewlett-Packard (HP). An HP calculator does not use an equal key. To perform a mathematicaloperation, the first number is inserted, the ENTER key is pressed, the second number is inserted,and then the mathematical function key is pressed. The result will be displayed. If a differentcalculator is used, the student will need to refer to the reference manual for his or her calculator.The following section will review the general use function keys on a TI-30 calculator. In eachfollowing chapter of this module, the applicable calculator operations will be addressed.Appendix A of this module gives a representation of a TI-30 keyboard to assist the student.KeysClear entry/Clear keyPressing this key once will clear the last operation and the display. Pressing thiskey twice will clear all operations except the memory.Note: To clear the memory, press clear then STO.Note: Many brands break this function into two separate keys, usually labeled"clear" and "all clear," where the "clear" key clears the last entry and the"all clear" key clears the display and all pending operations.MA-01 Page 4 Rev. 0 | 677.169 | 1 |
Curriculum - Year 11 - General Mathematics.
11 General Mathematics
Entry Recommendations:
Satisfactory completion of Year 10 Mathematics
Overview
General Mathematics extends students' mathematical skills in ways that apply to practical problem solving. A problem-based approach is integral to the development of mathematical models and the associated key ideas in the topics.
These topics cover a diverse range of applications of mathematics, including personal financial management, measurement and trigonometry, the statistical investigation process, modelling using linear and nonlinear functions, and discrete modelling using networks and matrices.
Course topics
Investing and Borrowing
Measurement
Statistical Investigation
Applications of Trigonometry
Linear and Exponential Functions and their Graphs
Matrices and Networks | 677.169 | 1 |
Find a PottstownMy approach to algebra 2 is designed to make the study as useful as possible to students in the long term, while encouraging the best current results in their classroom and testing experience. Calculus studies the quantities that are related to change. If algebra and trigonometry are tools, then calculus can be thought of as a maker of tools. | 677.169 | 1 |
Tired of Discrete Math
I am a computer science major and math is a major part of our curriculum. A year ago I took my first ever discrete math course, and it honestly fried my brain. Now I'm in a computer science course that uses discrete math to analyze algorithms, and my brain has simply shutdown. But what irritates me the most is I cannot figure out how the hell to do 50% of my assigned problems! I went from taking 1 step forward and 2 steps back, to taking 2 steps backwards every time I do something. I've taken so many steps back that my brain is in the negatives already! I can follow proofs alright, but to duplicate that kind of logic goes beyond me. This is a difficult subject for many of my classmates and I just don't understand why nobody has figured out a better way of teaching it... The book is hard to follow, and the professor is no better, I'm loosing my mind you guys! I don't enjoy it one bit - it's pure torture... Every single class that I have EVER had has NEVER given me these kind of problems; I would never stress about exams, I would never procrastinate on homework, but this is different. I cannot do the homework assignments right now; I read through the first problem, sat there for 10 minutes to think about it, started working it out, and then bam I got stuck... I'll get stuck at least 15 times on any given problem, get pissed off and go do something else.
Math, indiscrete or otherwise, is your friend, but it is hard to give specific advice on surviving this course without knowing more about the course. Those titled "discrete math" may cover a mix of combinatorics, linear difference equations, Markov chains, graph theory, among other topics, but given the wealth of subjects to choose from, different authors make different choices, and from the topics on offer in the assigned textbook, different instructors make different selections (and possibly an addition or two).Another thing to consider, and this is something you should discuss with your academic advisor very soon, is whether you need to withdraw from that course for now, get tutoring on what you missed learning in your first discrete math course, and then come back and retake the comp sci course that requires that background. You don't want to keep plodding on barely passing, and not even understanding the comp sci part of the course just because you're being held back by the math you didn't grasp the first time. This problem will just keep compounding. It's better to withdraw early in the semester and retake the class knowing what you need to fix before retaking it than it is to keep struggling and risk failing the class. You'll want to discuss these options with an academic advisor soon, because you may be close to the cut-off dates for withdrawing from a class without penalties.Obviously if the student doesn't care about the material, no instructor / textbook will help them. I simply don't understand the instructor / textbook; that's where my frustration is. It's almost as if I entered a class that's too advance, causing my brain to go :zzz: .Tutor = Money = Something I don't have. I do have the internet though; it got me through my first discrete math course so hopefully it will do the same this time around. I need to find some other books for this subject though; I have a copy of Schaum's Outlines, Discrete Math which does a fairly good job with the basics. But this algorithm course will need something else *sigh* .
It's almost as if I entered a class that's too advance, causing my brain to go :zzz: .
That may be exactly what has happened. Perhaps the math majors around here would know of some course that would be helpful to remediate if the problem is as you described, that the approach to math is too different from what you've ever done before and you didn't enter the course properly prepared. You're actually a step ahead of most struggling students in that you can at least identify what course was the one you got lost in. That makes solving this problem a lot more straightforward, because you know what course you need to remediate. While you may have to withdraw from the current one you're in, that's not the one you need to remediate, it's the discrete math course you need to go back and figure out. Sure, it'll slow you down working toward your degree, but better to graduate a semester or year late knowing what you're doing than in the expected amount of time while scraping by by the skin of your teeth and not being particularly employable because you only were a mediocre student. You know what you need to fix to be a better student, so start finding ways to get it fixed.
Discrete math is awesome, one of my favorite areas. What part are you having trouble with specifically? Post some questions that you are having trouble with and what part is bothering you. Also, as Chris said, discrete structures is a mixture of a bunch of different subjects. So if the book is what is bothering you, look for a book on a specific area. For example, if you are doing combinatorics in your discrete class look for a combinatorics book (which will go more in depth and maybe provide more insight). Also if you are having trouble writing proofs look for a book (or online notes) on writing proofs (I would recommend An Introduction to Mathematical Reasoning: it is a fairly easy book and just reading the first 50-100 pages will probably help you quite a bit; there is also a thread around here somewhere that has a bunch of online resources for proof writing.) Also use the homework help section!Most schools offer free tutoring programs. Also, you could just tell the professor you feel lost and see what he suggests. I struggled in a physics class and talked to the prof, and he sent his TA to help me through the hw. It helped a lot. You can also try looking online for notes and such. It helps me a lot to read from 3 or 4 different sources on a subject i struggle with. Try to do more problems than the homework requires too. Extra practice on stuff you know will help you face the stuff you don't know so well.If anybody can offer some advice for good books on the subject that would be great. I'm going to take a gander at An Introduction to Mathematical Reasoning by Peter J Eccles. I'll try to pick up tomorrow. | 677.169 | 1 |
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For courses in Elementary Number Theory for non-math majors, for mathematics education students, and for Computer Science students. This is an introductory undergraduate text designed to entice non-math majors into learning some mathematics, while teaching them to think mathematically at the same time. Starting with nothing more than basic high school algebra, the reader is gradually led from basic algebra to the point of actively performing mathematical research while getting a glimpse of current mathematical frontiers. The writing style is informal and includes many numerical examples, which are analyzed for patterns and used to make conjectures. The emphasis is on the methods used for proving theorems rather than on specific results. | 677.169 | 1 |
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Guided Notes and Worksheet (with answer keys) which cover finding an equation from sequences, tricky function rules from a table (example: y = 5(x-1) + 2), predicting y values given x, finding the difference in observed and predicted values, and finding the percent of values that are different from the observed values and the predicted values from the line of best fit.
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Algebra and Trigonometry (Print)
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ALGEBRA
Students will investigate relationships between two quantities. They will write and solve proportions and simple one-step equations that result from problem situations.
M6A1. Students will understand the concept of ratio and use it to represent quantitative relationships.
M6A2. Students will consider relations between varying quantities.
a. Analyze and describe patterns arising from function rules, tables, and graphs.
b. Use manipulatives or draw pictures to solve problems involving proportional relationships.
c. Use proportions (a/b=c/d) to describe relationships and solve problems, including percent problems.
d. Describe proportional relationships mathematically using y = kx, where k is the constant of proportionality.
e. Graph proportional relationships in the form y = kx and describe characteristics of the graphs.
f. In a proportional relationship expressed as y = kx, solve for one quantity given values of the other two. Given quantities may be whole numbers,
decimals, or fractions. Solve problems using the relationship y = kx.
g. Use proportional reasoning (a/b=c/d and y = kx) to solve problems.
M6A3. Students will evaluate algebraic expressions, including those with
exponents, and solve simple one-step equations using each of the four basic operations.
Process Standards
Each topic studied in this course should be developed with careful thought toward helping every student achieve the following process standards.
See below for specific standards.
SEVENTH GRADE
ALGEBRA
Students will demonstrate an understanding of linear relations and fundamental algebraic concepts.
M7A1. Students will represent and evaluate quantities using algebraic expressions.
M7A2. Students will understand and apply linear equations in one variable.
a. Given a problem, define a variable, write an equation, solve the equation, and interpret the solution.
b. Use the addition and multiplication properties of equality to solve one- and two step linear equations.
M7A3. Students will understand relationships between two variables.
a. Plot points on a coordinate plane.
b. Represent, describe, and analyze relations from tables, graphs, and formulas.
c. Describe how change in one variable affects the other variable.
d. Describe patterns in the graphs of proportional relationships, both direct (y = kx) and inverse (y = k/x).
Process Standards
The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.
See below for specific standards.
EIGHTH GRADE
ALGEBRA
Students will use linear algebra to represent, analyze and solve problems. They will use equations, tables, and graphs to investigate linear relations and functions, paying particular attention to slope as a rate of change.
M8A1. Students will use algebra to represent, analyze, and solve problems.
M8A2. Students will understand and graph inequalities in one variable.
a. Represent a given situation using an inequality in one variable.
b. Use the properties of inequality to solve inequalities.
c. Graph the solution of an inequality on a number line.
d. Interpret solutions in problem contexts.
M8A3. Students will understand relations and linear functions.
a. Recognize a relation as a correspondence between varying quantities.
b. Recognize a function as a correspondence between inputs and outputs where the output for each input must be unique.
c. Distinguish between relations that are functions and those that are not functions.
d. Recognize functions in a variety of representations and a variety of contexts.
e. Use tables to describe sequences recursively and with a formula in closed form.
f. Understand and recognize arithmetic sequences as linear functions with whole number input values.
g. Interpret the constant difference in an arithmetic sequence as the slope of the associated linear function.
h. Identify relations and functions as linear or nonlinear.
i. Translate among verbal, tabular, graphic, and algebraic representations of functions.
M8A4. Students will graph and analyze graphs of linear equations.
a. Interpret slope as a rate of change.
b. Determine the meaning of the slope and y-intercept in a given situation.
c. Graph equations of the form y = mx + b.
d. Graph equations of the form ax + by = c.
e. Determine the equation of a line given a graph, numerical information that defines the line, or a context involving a linear relationship.
f. Solve problems involving linear relationships.
M8A5. Students will understand systems of linear equations and use them to solve problems.
a. Given a problem context, write an appropriate system of linear equations.
b. Solve systems of equations graphically and algebraically, using technology as appropriate.
c. Interpret solutions in problem contexts.
Process Standards
The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.
See below for specific standards.
ALL GRADES
Process Standards
P1. Students will solve problems (using appropriate technology).
a. Build new mathematical knowledge through problem solving.
b. Solve problems that arise in mathematics and in other contexts.
c. Apply and adapt a variety of appropriate strategies to solve problems.
d. Monitor and reflect on the process of mathematical problem solving.
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a. Recognize reasoning and proof as fundamental aspects of mathematics.
b. Make and investigate mathematical conjectures.
c. Develop and evaluate mathematical arguments and proofs.
d. Select and use various types of reasoning and methods of proof.
P3. Students will communicate mathematically.
a. Organize and consolidate their mathematical thinking through
communication.
b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
c. Analyze and evaluate the mathematical thinking and strategies of others.
d. Use the language of mathematics to express mathematical ideas precisely.
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b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
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b. Select, apply, and translate among mathematical representations to solve problems.
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...The department offers a number of mathematics courses designed to suit your interests and career aims, with this stream offering a substantial number of third year modules in Pure Mathematics. Our three-year BSc Mathematics (Pure Mathematics) course aims to provide a specialised and in-depth... Learn about: GCSE Mathematics...
...Programme overview This programme is designed to be as flexible as possible; you will have a choice of modules taken from our BSc Mathematics. You will meet with the programme director before the start of the academic year and decide on a suitable programme of study, based on your interests... Learn about: GCSE Mathematics...
...Mathematics concerned with finding patterns and solving problems. Every day we encounter patterns, which can be described using mathematics, for example, in numbers, shapes or data. We can use mathematics to identify these patterns, solve problems, inspire new technologies and make informed... Learn about: GCSE Mathematics...
... The course will be based at the University for four days each week with the exception of a two week placement in schools. There will be mathematical modules on: Algebra... Learn about: GCSE Mathematics...
.... There is work on further trigonometry logs and exponentials ,etc. You will develop your mathematical skills to identify and analyse problems, understand and apply knowledge. At AS you will also study either a statistics option or a mechanics option (S1/M1), depending on timetable organisation and whether... Learn about: IT for adults, GCSE Mathematics...
...Children's learning is at the heart of the programme; we'll ask you to consider what 'understanding' means and how it can be developed and assessed... Learn about: Secondary Mathematics, Educational Setting, GCSE Mathematics...
... Further Mathematics to A level will normally be required to achieve grade A in Further Mathematics AS level in addition to A* (Mathematics) A A at A level International Baccalaureate: Diploma with 38 points including 7 6 6 at Higher level (with 7 in Mathematics) Other qualifications are considered... Learn about: GCSE Mathematics... | 677.169 | 1 |
2.1 Reflecting on your mathematical history Reading articles for mathematical information2.6 Mathematical communication There is increasing recognition that the reductionist mindset that is currently dominating society, rooted in unlimited economic growth unperceptive to its social and environmental impact, cannot resolve the converging environmental, social and economic crises we now face. The primary aim of this unit is to encourage the shift away from reductionist and human centred thinking towards a holistic and ecological worldview. Author(s): The Open University
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Except for third party materials and otherwise stated (see terms and conditions), this content is made available under a Mathematical analysis of peer to peer communication networks Distributed protocols for peer to peer file sharing, streaming video, and video on demand have revolutionised the way the majority of information is conveyed over the Internet. The peers are millions of computers, acting as both clients and servers, downloading and uploading information. Information to be shared is broken into chunks, and the chunks are traded among peers in the network. There can be turnover in the set of chunks of information being collected and/or in the set of peers collecti Author(s): No creator set
Quilts as Mathematical Objects The connection between textiles and mathematics is intimate but not often explored, possibly because textiles and fiber arts have traditionally been the domain of women while mathematics was viewed as a male endeavour. How times have changed! Author(s): No creator set No creator set
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How and why we do mathematical proofs This is a module framework. It can be viewed online or downloaded as a zip file. As taught in Autumn Semester 2009/10 The aim of this short unit is to motivate students to understand why we might want to do proofs (why proofs are important and how they can help us) and to help students with some of the relatively routine aspects of doing proofs. In particular, the student will learn the following: * proofs can help you to really see why a result is true; * problems that are easy to state can be Author(s): No creator set
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Mathematical language In our everyday lives we use we use language to develop ideas and to communicate them to other people. In this unit we examine ways in which language is adapted to express mathematical ideas. Author(s): Creator not set
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Mathematical Visualization Toolkit This site consists of a collection of plotting and solving applets featuring a uniform user interface. This site was selected as the 2005 MERLOT Classics Award winner for the Mathematics discipline due to its value and effectiveness as a set of teaching/learning tools. Visualizing mathematical concepts, especially in three-dimensional space, can be quite difficult for students. These tools and applications enable students to see the concepts in action and to come a deeper understanding of the un Author(s): No creator set
Estimate is a great interactive site that allows students to estimate a number that an arrow is pointing to on a number line. This is great for students who are first learning about estimation. It is an easy to use site that is fairly robust and would
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No related items provided in this feed Feinstein Joel F. Dr.
Mathematical analysis This is a module framework. It can be viewed online or downloaded as a zip file. As taught in 2007-2008 and a Author(s): Feinstein Joel F. Dr | 677.169 | 1 |
Mathematics
9th Grade
Students work toward becoming more independent, learning to make notes and complete exercises to master math skills. Students also work on online adaptive learning programs that differentiate, reinforce, and enrich their current math course. Most ninth grade students are enrolled in Geometry, where students deepen their understanding of two and three-dimensional objects and their properties. They use both deductive and inductive reasoning to draw conclusions about the properties and relationships of geometric objects. Students further develop an understanding of proof and logic.
10th Grade
Most students are enrolled in Algebra II, where they conceptualize, analyze, and identify relationships among many classes of functions, learn to solve associated equations and inequalities, and create and analyze mathematical models that are applicable to real life situations. Students continue developing their independence, practicing skills on their own and seeking help in tutorials when needed. They continue to use the online adaptive learning programs for additional support within their current math course.
11th Grade
Students enter International Baccalaureate Year 1 math courses. In these courses, students learn a variety of topics, including Algebra, Functions, Trigonometry, and Vectors. Communication of mathematics in a logical and organized manner is emphasized. Students are challenged by longer, multi-step questions that can encompass multiple topics, and learn to use the graphing calculator to solve complex equations and to graph unknown functions.
12th Grade
Students continue their study of their chosen International Baccalaureate math course. Topics include Differential Calculus, Integral Calculus, Probability, and Statistics. Students engage in a mathematical exploration on a topic of their own choosing. | 677.169 | 1 |
Quadratic Transformations & More
Presentation (Powerpoint) File
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0.13 MB | 19 pages
PRODUCT DESCRIPTION
This powerpoint contains 18 multiple choice questions that can be used to assess student knowledge or review for the test. The questions center around the following: transformations, domain, range, and roots.
I use this teaching tool with "ABCD" laminated flashcards. Students hold up the letter corresponding to their answer. It allows me to see who knows the information. I typically ask students to explain why or why not it is the correct answer, which allows for peer-to-peer tutoring in the classroom | 677.169 | 1 |
Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains describes a comprehensive framework for the identification and analysis of nonlinear dynamic systems in the time, frequency, and spatio-temporal domains. This book is written with an emphasis on making the algorithms accessible so that they can be... more...
Introduction to Computational Modeling Using C and Open-Source Tools presents the fundamental principles of computational models from a computer science perspective. It explains how to implement these models using the C programming language. The software tools used in the book include the Gnu Scientific Library (GSL), which is a free software library... more...
A ground-up approach to explaining dynamic spatial modelling for an interdisciplinary audience. Across broad areas of the environmental and social sciences, simulation models are an important way to study systems inaccessible to scientific experimental and observational methods, and also an essential complement to those more conventional... more...
This lecture presents a modern approach for the computation of Mathieu functions. These functions find application in boundary value analysis such as electromagnetic scattering from elliptic cylinders and flat strips, as well as the analogous acoustic and optical problems, and many other applications in science and engineering. The authors review the... more...
Almost every year, a new book on mathematical modeling is published, so, why another? The answer springs directly from the fact that it is very rare to find a book that covers modeling with all types of differential equations in one volume. Until now. Mathematical Modeling: Models, Analysis and Applications covers modeling with all kinds of differential... more...
Make a geodesic dome big enough to sit in. Solve one of the world?s hardest two-piece puzzles. Pass a straight line through a curved slot. From prime numbers to paraboloids, Amazing Math Projects You Can Build Yourself introduces readers ages 9 and up to the beauty and wonder of math through hands-on activities. Kids will cut apart shapes to discover... more...
With an emphasis on mathematical thinking and problem solving, Mathematics in Games, Sports, and Gambling ? The Games People Play shows how discrete probability, statistics, and elementary discrete mathematics are used in games, sports, and gambling situations. It draws on numerous examples, questions, and problems to explain the application of... more... | 677.169 | 1 |
AP Calculus BC Help
Study concepts, example questions, & explanations for AP Calculus BC
Students in need of AP Calculus BC help will benefit greatly from our interactive syllabus.
We break down all of the key elements so you can get adequate AP Calculus BC help.
With the imperative study concepts and relevant practice questions right at your fingertips, you'll have plenty of AP Calculus BC help in no time.
Get help today with our extensive collection of essential AP Calculus BC information.
For many, AP Calculus BC will be one of the toughest AP-level classes they take. Taking that into consideration, when it comes time to take the AP Calculus BC exam, stresses often run at an all-time high. Still, AP-level classes are worth the time you invest into them, as they allow you to differentiate yourself from your peers on college applications. AP-level classes may also earn you college credit, which could save you time and money in college. This is why it's so important to have the proper resources when embarking upon your AP Calculus BC exam review.
In order to receive potential college credit, you will have to score well on the AP Calculus BC exam. Luckily, there are many resources out there to assist in your studying process. You may enjoy using Varsity Tutors' Learning Tools resources, which include an AP Calculus BC Learn by Concept interactive syllabus. Learn by Concept is designed with you in mind and offers unique studying benefits. There are several AP Calculus BC example questions that cover all of the relevant concepts and include thorough explanations of the answers. These sample questions are one of the most popular aspects of Learn by Concept, and with good reason. The questions allow you to get a glimpse at the format the real AP Calculus BC exam will be presented in. All of this free AP Calculus BC study material is available online, providing you with an easy way to review AP Calculus BC concepts.
Some of the many topics you can expect to be covered on the interactive Learn by Concept AP Calculus BC syllabus include:
- Derivatives - Functions, Graphs, and Limits - Integrals - Polynomial Approximations and Series - Fundamental Theorem of Calculus and Techniques of Antidifferentiation - And many other important topics covered on the AP Calculus BC exam.
When you're finished going over the AP Calculus BC Learn by Concept study guide, Varsity Tutors' Learning Tools offer many other free and online AP Calculus BC review resources. In addition, Full-Length AP Calculus BC Practice Tests, Concept-Specific Practice Tests, Flashcards, and a Question of the Day are available for you to take advantage of. The Full-Length AP Calculus BC Practice Tests will allow you to get a more complete idea of where you should begin studying, and you can gauge your performance against your peers to see where you current level of understanding stacks up. You can then use the Learn by Concept, Flashcards, and Question of the Day Learning Tools to refine specific skills. You can also periodically test yourself with Concept-Specific Practice Tests to track your progress. All of the Learning Tools are designed to work together.
The easy-to-use AP Calculus BC Learn by Concept syllabus, and the other review resources available from Varsity Tutors' Learning Tools, may help ease some of the stress of exam preparation as you move forward toward test day. You can use Varsity Tutors' AP Calculus BC Learning Tools to stay focused and organized throughout your review.
If you need help studying for the AP Calculus BC exam, check out the free resources provided by Varsity Tutors in order to get a good sense of the numerous ways in which you can study. You can start by taking a free AP Calculus BC Diagnostic Test to get a sense of which concepts you know well and which you still need to learn. After that, you can take free AP Calculus BC Practice Tests to focus on learning the topics that you understand least well. If you don't have time to take an entire AP Calculus BC Practice Test, you can use Varsity Tutors' free AP Calculus BC Flashcards to study for shorter periods of time. Also, be sure to check out the AP Calculus BC Question of the Day for daily practice. | 677.169 | 1 |
Every
student is expected to have a 3" x 5" or 4" x 6" SPIRAL bound
notebook. A spiral bound notebook of index cards instead of paper will last the longest. This notebook will be used as a formula, concept and unit summary collection. (I will model what goes in your notebook during the, "Kinematics by Graphical Means," unit.) It will be
turned in the day of a test as you walk in the room. The notebook will
count as a separate grade. Late notebooks are not allowed without an acceptable
note from an parent or guardian explaining why it is late. (Forgetting
it in your friend's car is not an acceptable excuse.) You are not allowed to take notes in it during class.
This notebook will be a study aide. Because of its small size you can carry it around in your pocket. Then in between classes or when you have a few minutes. Pull it out and review parts of the unit. It will also help you to collect all the information before the final exam each semester.
The
layout for a notebook page is simple.
At
the top of each page is the title of the unit.
This
is followed by the formula itself.
Under
the formula will be a list of the variables and their definitions.
Each
definition will have its S.I. units.
Underneath
this will be a statement describing how the formula is used and/or
any hints or pitfalls to its use.
You
are to put only ONE formula on each page. You may write
on the back of the pages. You may write in pen or pencil. Neatness
is part of your grade. If a formula has been introduced in a previous
unit and is used in the same manner in the current unit, then the
formula does not need to be rewritten.
After the formulae pages, you are to write any concepts we discussed.
After this explain what detwermines when to use the stuff in this unit. (You might include any diagrams that would help understand the unit or some of its parts.)
by T. Wayne
August 22, 2010 9:02 PM
by Tony Wayne ...(If you are a teacher, please feel free to use these resources in your teaching.) | 677.169 | 1 |
Graphing Linear Equations Lesson Notes and Practice
PDF (Acrobat) Document File
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1.47 MB | 4 pages
PRODUCT DESCRIPTION
The goal with this product is that these notes not only help your students understand a new algebra concept but also helps you teach your students about graphing in an organized way. This two page notes and practice is organized in the following way:
•Intro Question : Helps your students to make a connection to new information
•Words to Know: Highlights essential terms in the lesson
•Examples: Guided examples with step by step instruction
•Practice: Ideally this would be non graded work that gives students the confidence in understanding the concept
•Reflection Questions:Helps your students to write about the concept of the lesson | 677.169 | 1 |
Algebra I and 8th Grade Math Bundle
Compressed Zip File
Be sure that you have an application to open this file type before downloading and/or purchasing. How to unzip files.
53.01 MB
PRODUCT DESCRIPTION
This mega bundle includes all of my Algebra I and 8th grade math resources, organized into topics.
The resources are a variety of activities, assessments, games, projects, guided notes, and more that I have created over the past three years while teaching Algebra I to 8th graders. Therefore, the resources begin with 8th grade topics and extend into Algebra I standards. They are not meant to be a complete curriculum, but the bundle will definitely give you plenty of material to use throughout your year of Algebra. I hope you find it helpful in teaching your class.
(I do have a separate bundle available that includes only the 8th grade resources. Click here if you are interested in this resource.)
Most resources are in PDF format and some are powerpoints. The majority have answer keys. Please browse the Rise over Run store to see more details about individual resources included in this bundle.
The Mega Bundle for Algebra I + 8th Grade Math includes...
RATIONAL AND IRRATIONAL NUMBERS
Number Vocabulary
Rational and Irrational Numbers on a Number Line
Rational and Irrational Numbers Puzzle | 677.169 | 1 |
PDF (Acrobat) Document File
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0.08 MB
PRODUCT DESCRIPTION
I made this as a review and warm-up for Middle School students in PreAlgebra and Algebra that struggle with inequalities, as it reviews the basics of what the signs mean and vocabulary.
Many developing students that I work with struggle with inequalities! Some of those students struggle because they were never taught how to read inequalities. They read 'x < y' as 'x eats the bigger one y?!?!?' (If you work with younger students as well, you might be interested in my worksheet "Less Than, Greater Than, and Equals Signs.")
In order to complete this sheet, students already need to be familiar with the concept of variables. This sheet covers the foundations of inequalities, which students then learn how to solve, graph and more around Algebra I | 677.169 | 1 |
Synopses & Reviews
Publisher Comments
Intended for a one year course, this volume serves as a single source, introducing students to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry. This is one of the few works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory, while also presenting the most up-to-date research. This book will appeal to readers with a knowledge of standard manifold theory, including such topics as tensors and Stokes theorem. Various exercises are scattered throughout the text, helping motivate readers to deepen their understanding of the subject. Important additions to this new edition include: * A completely new coordinate free formula that is easily remembered, and is, in fact, the Koszul formula in disguise; * An increased number of coordinate calculations of connection and curvature; * General fomulas for curvature on Lie Groups and submersions; * Variational calculus has been integrated into the text, which allows for an early treatment of the Sphere theorem using a forgottten proof by Berger; * Several recent results about manifolds with positive curvature. From reviews of the first edition: "The book can be highly recommended to all mathematicians who want to get a more profound idea about the most interesting achievements in Riemannian geometry. It is one of the few comprehensive sources of this type." - Bernd Wegner, Zentralblatt
Review
Review
From the reviews of the second edition:P. Petersen Riemannian Geometry "A nice introduction to Riemannian geometry, containing basic theory as well as several advanced topics." --EUROPEAN MATHEMATICAL SOCIETY "This is an introduction to modern methods in Riemannian geometry containing interesting and original approaches to many areas in this field. ... After a general introduction (metrics, curvature, geodesics) and concrete calculations for many examples, the second half of the book considers Bochner-Cartan techniques and comparison geometry. Particularly for these aspects it continues to play an outstanding role among textbooks in Riemannian geometry." (M. Kunzinger, Monatshefte für Mathematik, Vol. 154 (1), May, 2008)
Synopsis
This volume introduces techniques and theorems of Riemannian geometry, and opens the way to advanced topics. The text combines the geometric parts of Riemannian geometry with analytic aspects of the theory, and reviews recent research. The updated second edition includes a new coordinate-free formula that is easily remembered (the Koszul formula in disguise); an expanded number of coordinate calculations of connection and curvature; general fomulas for curvature on Lie Groups and submersions; variational calculus integrated into the text, allowing for an early treatment of the Sphere theorem using a forgotten proof by Berger; recent results regarding manifolds with positive curvature.
Synopsis
This comprehensive introduction to Riemannian Geometry offers a detailed and engaging account of the topic, plus numerous exercises and examples. It combines both the geometric parts of Riemannian geometry and the analytic aspects of the theory, and reviews the latest research.
Designed for a one year introductory course, this volume introduces students to the important techniques and theorems of Riemannian geometry, while presenting sufficient background on advanced topics to appeal to students who wish | 677.169 | 1 |
Getting Creative With Options Advice
There are a wide array of calculators. Some are specialized, some quite simple. Some calculators can only do simple arithmetic, and others that can establish a single point on a parabola. Price points for these devices are normally determined by the complexity of the calculator, thus deciding the right calculator can conserve money and annoyance.
Firstly, there are basic calculators. These are used for simple functions. Typically they cost less than ten dollars, and simple functions such as add, multiply, deduct and divide. Some include a memory function, large display, big keys or a transparent design with overhead projectors. Basic calculators are for basic mathematics. Batteries or a solar cell may be used to power them up.
Next, we have the printing calculators. These are made for use in bookkeeping and accounting. They include all of the keypads in a simple calculator but have additional keys for other functions such as finding per centum, subtotal, total, duty rate, as well as several other functions utilized when summing up huge amounts. The print capability enables the consumer to check out for typical entry blunders or skipped numbers, make use of the printout like a receipt or avoid printing it. Most also include an ability to select decimal places' variety and a rounding purpose.
There are also scientific calculators. Scientific calculators are utilized by pupils. They are used for chemistry, physics or math. They are likewise frequently permitted for use in standard assessments. These calculators also come with multifunction keys for a smaller full-featured tool. They are capable of determining root values, with separate keys for square root, cube root and so forth. They also possess logarithmic, trigonometric and exponential function keys.
We also have financial and business calculators. Business and finance calculators are made to be properly used primarily in determining enterprise-related equations, for pupils studying calculus, as well as for planning or monitoring economic info. Financial calculators may build tables for loan obligations, compute APR, evaluate compound interest; total paid, interest and other characteristics of cash overtime.
Business calculators have more outstanding positioning of the most typical functions utilized in business calculus or mathematics. They frequently contain evaluation capabilities and sophisticated mathematical designs. More costly models contain more cash runs greater storage, and much more functions.
Last on the list, we have graphic calculators. These calculators are some of the most expensive ones. They have large memory capability, programmability, the graphing capability and a sizable display itself make graphing calculators different from other types of calculators. They are essential in physics and several college-level mathematics, in addition to in certain finance classes. They have the ability to execute most of the functions though very few have print capabilities within additional specialized calculators. These calculators are designed to chart and plan capabilities, and simplify solving equations. | 677.169 | 1 |
Chapter 22 Objectives
Understanding the meaning of local and global truncation
errors and their relationship to step size for one-step
methods for solving ODEs.
Knowing how to implement the following Runge-Kutta (RK)
methods for a single ODE:
Euler
Heun
Chapter 23 Objectives
Understanding how the Runge-Kutta Fehlberg
methods use RK methods of different orders to
provide error estimates that are used to adjust step
size.
Familiarizing yourself with the built-in MATLAB
function for solving ODEs.
Learnin
Chapter 19Chapter 14 Objectives
Familiarizing yourself with some basic descriptive
statistics and the normal distribution.
Knowing how to compute the slope and intercept of
a best fit straight line with linear regression.
Knowing how to compute and understand th
Chapter 16 Objectives
Understanding sinusoids and how they can be used for
curve fitting.
Knowing how to use least-squares regression to fit a
sinusoid to data.
Knowing how to fit a Fourier series to a periodic
function.
Understanding the relationship
Chapter 15 Objectives
Knowing how to implement polynomial regression.
Knowing how to implement multiple linear
regression.
Understanding the formulation of the general linear
least-squares model.
Understanding how the general linear least-squares
mode
NAME_
CS412 Introduction to Numerical Methods
Quiz # 5 (Submit to [email protected] dropbox by 8/7, 11AM)
1)
What order of approximation with respect to h does the Composite
(i.e. multiple application) Trapezoidal Rule for integration provide?
2)
If two results us
QUIZ # 4
NAME_
SUBMIT TO [email protected] DROPBOX BY MONDAY, 7/22, 11:00AM
1) A linear least-squares curve fit problem can be solved by the exact
and unique solution of an overdetermined system of equations?
(True/False?, Why?)
2) What is the purpose of the coeff
QUIZ # 3
NAME_
SUBMIT ON MONDAY, 7/8/13, by email before 11:59PM
Given the canonical form Ax=b of a system of linear equations where A is
(n x n), x is (n x 1) and b is (n x 1), please answer the following:
1) What are the requirements for a (n x n) syste
CS412
INTRODUCTION TO NUMERICAL METHODS
HOMEWORK # 6
DUE ON FRIDAY 8/2/13, 11:59 PM
19.3 Do by hand.
19.6 Do by hand. See Example 19.8
19.14 Plan a suitable solution approach based on textbook discussions in
Chapters 19. You are free to use Matlab built-i
CS412
INTRODUCTION TO NUMERICAL METHODS
HOMEWORK # 4
DUE ON MONDAY 7/22/13, 11:00AM
Problems:
14.5
Do problem by hand by establishing the Normal Equations.
You could use, however, Matlab to do all the computations (i.e.
summations and the solution of the | 677.169 | 1 |
About the Course
Comprehensive coverage of quantitative concepts in the form of an e-book
Recommended to the aspirants of various competitive exams
Topics Covered
Number System
Interesting Facts
Properties of Prime Number
Squaring Techniques
Cubing Techniques
Finding Square Root & Cube Root of Number
Divisibility Rules
Factors / Divisors of Given Composite Number
HCF / LCM of Numbers
Applications of HCF / LCM of Numbers
Digital Sum of a Number
Concept of Cyclicity / Power Cycle
Remainder Theorem
Finding the Last / Unit Digit
Finding the Last Two Digits of a Number
Number of Exponents / Highest Power / Number of Zeroes
Fundamental Principle of Counting
Introduction to Permutations & Combinations
Different Corollaries of Permutations
Circular Permutations
Different Corollaries of Combinations
Selection out of Identical / Non-Identical things
Distribution of Things
Groupings & Dividing of Things
Derangement Principle
Geometrical Applications of P & C
Use of P & C in Solution of Equations
Trick for Finding the Rank of a Given Word
Roots of Quadratic Equation
Nature of Roots
To find Equation with given roots
Graphical Representation of Quadratic Equations
Higher Order Equations
Relation between Roots & Coefficients
Descarte's Rule of Signs
Finding the Common Root
Sets, Venn Diagram & Averages
Properties of Sets
Properties of Venn Diagrams
De-Morgan's Laws
Problems Based on Venn-Diagrams
Problems Based on Averages | 677.169 | 1 |
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Unformatted text preview: P RE C ALCULUS
A guide
This guide was compiled for one purpose, to help people who are having
difficulty understanding the way Pre Calculus is taught. I think visually , so
I wrote this guide visually. I wish you good luck, and please enjoy this
resource. Austin Schafer
2011 PR EFAC E
Why m ak e di g i tal no te s
Many people have asked me why I would go through the effort of making a digital
guide to a mathematics course. I have many reasons, at first I really just wanted to
use my computer for something new; I thought I could make better notes using a
computer. I later learned that my digital notes, which would become this guide, were
not better because they were more extensive or better illustrated, they were better
because they are distributable. A guide of a class is not helpful when there is only
one copy of it. The power of these notes lies in their ability to be reproduced. I would
be proud to have my work spread to new people, please though, don't take credit for
what you didn't write. A g ui de b as e d o n w hat?
I have used many sources in creating this guide. The person who influenced it most
was my course teacher, Mr. Torre. I also used the course textbook for reference; the
textbook is titled, Precalculus: Graphical, Numerical, Algebraic: Seventh Edition
published by Pearson. My final resource was the internet, I would like to give some
extra credit to Wikipedia, which is an excellent free resource for even the most
complicated mathematics. Unit 1 •
•
•
•
• Lines
Systems of Equations
Matrixes
Determinants
Cramer's Rule of Expansion by Minors Pre Calculus Page 1 Lines and Stuff
Monday, August 30, 2010 Point: An infinitely small spot. That can be defined as a location
at the intercept of two or more axis values. An example is the
point x-value 4, y value 3. This would be written (4,3), and is
located at 4 "over(right)" and 3 "up", from the origin, which is
an arbitrary point labeled (0,0). Linear Equation
Typically a linear has a first degree x-term and y-term.
A solution is (5,2), but there is infinitely more. I can represent all the points as a picture on a
graph. This linear equation forms a line that is infinitely long, and made of infinite solution points.
A line is a representation of all of a linear equations solutions.
If What is a Slope? then the line is horizontal It is a rational number that describes the 'tilt' of a line.
Commonly we think
Specifically, slope is a rate of change of y as x changes, and can be determined by any two points on a
line. (Slopes do exist in Quadratic Functions too, see "A New Way To Slope") then the line is vertical. Parallel Lines : Lines are parallel if their slopes are
equivalent .
Perpendicular Lines: Lines that intersect at a 90⁰ angle.
This means that the line's slopes have inverse reciprocals
of each other.
Intersecting Lines: This type of lines comprises all other
lines. Since all lines not that are not parallel must
intersect, all lines that are not parallel or perpendicular
must intersect at some other angles. These types of lines
are called intersecting. Writing the equation of the line..
Slope Intercept Form Standard Form Point Slope Form A and B must be
whole integers
slope y-intercept Vocab Note: Singular Functions have no Inverse When a function is in standard form, the following equations can be used
to determine the characteristics of the line and quickly graph it.
Slope Y-intercept X-intercept Practice Problem:
Suppose & line passes through (-7,1), what is the equation of the line ? What is the standard form of the line? Practice Problem Answers:
The Equation is Pre Calculus Page 3 Systems of Equations
Wednesday, September 01, 2010 A system of Equations is a set of equations (duh). A system usually has a solution, if it does not then it is inconsistent.
When working with an system, there is some basic manipulation rules you can use.
1. Multiply an entire equation by a non-zero constant
2. Interchange any two equations
3. Replace an equation with a linear combination of addition An Example of Replacing an Equation with a Linear Combination of Addiction Pre Calculus Page 4 Graphing Vocabulary
Friday, September 03, 2010 Consistent & Independent Inconsistent Constant & Dependent One Solution Zero Solutions Infinite Solutions ----------------------- If you don't want to substitute the 'y' you just
found (i.e. It would be messy), you can use the
same elimination process that you just used to
find the 'y', to find 'x'. Pre Calculus Page 5 Matrix Stuff
The Matrix Saturday, October 23, 2010 The Matrix is a simulated reality perceived by most humans created by sentient
machines. This is chronicled in The Matrix, a 1999 scientific documentary. The coding of
the matrix is show right. Alternatively in math, a Matrix is simply a rectangular arrangement of elements, which are numbers. This is a 2x2 matrix For Example, [1,0] is row 1 of Matrix A. Rows are the horizontal Columns are vertical These are elements Matrix A can be written as [A] The dimension are called order, as in the order of these matrixes are the same
and have the same order. Matrix Arithmetic
(A)
(B) (C) E.M.O. - Study Chapter 7.2 pg 579 Addition - Must be of Equal Order
Subtraction - Must be of Equal Order
Scalar Multiplication - In matrix land, there are nebular numbers called scalars or Rock Climbers
Matrix Addition, it works for Subtraction using the same principle. Augmented Matrixes
An augmented matrix is a square matrix which has an extra column.
This last column is not manipulated with the matrix. Augmented
Matrixes are used in matrixes for solving systems of equations. Pre Calculus Page 1 Identity and Augmented Matrixes
Tuesday, January 25, 2011 The Identity Matrix - the scalar matrix with the main diagonal all 1's Matrix Algebra Equation
Classic Linear System
This system of equations is equal to:
This Matrix can be "Augmented" to look like this:
this augmented matrix represents the standard form of the system of equations Pre Calculus Page 7 Solving with Matrixes
Sunday, February 06, 2011 Solving Systems of Equations with Matrixes
Since Matrixes are just representations of system of equations, they can be
manipulated just like systems of equations to solve the system.
We can convert a system of equations to a matrix in the following way:
Augment Line This Becomes We solve it like this:
Multiple Row 1 by
, add
result to Row 2, and replace
Row 2 with this result
Multiple Row 1 by
, add
result to Row 3, and replace
Row 3 with this result
Multiple Row 2 by
, add
result to Row 3, and replace
Row 3 with this result
Multiple Row 2 by , add result
to Row 1, and replace Row 1
with this result
Multiple Row 3 by , add result
to Row 2, and replace Row 2
with this result
Pre Calculus Page 1 Multiple Row 3 by , add result
to Row 2, and replace Row 2
with this result
Multiple Row 3 by , add result
to Row 1, and replace Row 1
with this result Next we convert
the matrix back
into a system of
equations This matrix form is called reduced row echelon form and is the easiest way to solve
systems of equations using Matrixes. A reduced row echelon matrix will be an
identify matrix with an augmented section. This allows for the simple conversion
to find the values of the variables. Pre Calculus Page 2 Matrix Multiplication
Saturday, November 06, 2010 Consider the matrix products [A] x [B]. This product only exists if the
number of rows in [B] is equal to the number of columns in [A]
Matrix multiplication works like this: You can determine the size of the resultant matrix of [A] x [B]
[A] x [B]
[B] x [A] Consider the Matrixes Obviously it makes a big difference what order the Matrixes are in. Pre Calculus Page 9 Matrix Determinants and Inverses
Monday, October 18, 2010 The Determinant represents the
numerical (ordinal) value of a matrix. Note: Determinants are defined only for square
matrixes. Determinants
There is a simple test that determines if a 2x2 matrix has an inverse: If ad - bc ≠ 0, then The Value of a Determinant
The value of can be written and solved like this: Matrix Inverses Pre Calculus Page 10 Unit 2 •
•
•
•
•
•
•
•
•
•
•
•
• Interval Notation
F(x) Notation
Extrema and Inflection Points
Piece-wise functions
Pasta Sauce
Vertical, Horizontal and Slant Asymptotes
Types of Symmetry
Concavity and Tone
Implicit and Explicit Concavity
Function Characteristics
Continuity
Types of SPOD
Partial Fraction Decomposition Pre Calculus Page 11 Determining Domain and Range Graphically
Thursday, January 20, 2011 Domain: Not a function, does ; Pre Calculus Page 13 F(x) Notation
Wednesday, January 19, 2011 F(x) Notation Take, for example,
becomes using F(x) notation, use F(x) in lieu of y.
"F" is the Function Name, it could be any letter, but X is the
most common. "X" Indicates the domain variable Examples: Variable
Unspecified Constants Arithmetic Combinations of Functions:
Domain: All real
Domain: All Real
Domain: All Real
Domain: All Real
Domain: All Real
Domain: Denominator cannot equal 0, because you cannot divide by zero. Function Compositions: Compounding 2 Functions "F of G of x" Take these two functions as a given. Input g(x) into the f(x) equation
for f(g(x)) Pre Calculus Page 14 Input g(x) into the f(x) equation
for f(g(x)) Input f(x) into the g(x) equation
for g(f(x)) Pre Calculus Page 15 Extrema, Inflection, Decreasing, and Concave relations
Tuesday, October 05, 2010 Pre Calculus Page 16 Mr. Torres Pasta Sauce
Monday, October 11, 2010 Tomatoes 1 can + 3/4 can of water Onions 2 Garlic 4 cloves Salt, Pepper, Sugar 1, 1/2, 2 tsp
Olive Oil 3 TBSP Basil 1 bunch Fresh Oregano 1 Sprig Tomato Paste 1 can + 2 cans of water Simmer 90 minutes →Purée →cook 1/2 hour more Pre Calculus Page 17 Asymptotes
Wednesday, December 01, 2010 An asymptote is most commonly encountered are of curves of
the form y = ƒ(x). They are simply a line where as x approaches
a value, f(x) gets increasingly "wild".
A textbook example is when
, as x approaches zero,
like when it is
gets increasingly large. This is
demonstrated by the graph at right.
In this case, asymptotes, it is a vertical asymptote. As you may notice, at
, there is no value for
, all
vertical asymptotes have an undefined
or y value. This is
because they are caused by dividing , or more nearly dividing
by, zero. As the function approaches anything/0, the output
gets really strange.
Take for example , the function works well until the x value approaches x=3, because at x=3, the value of
is undefined. The graph looks like this. Horizontal Asymptotes
Friday, December 03, 2010
4:25 PM A horizontal asymptotes exists whenever a
value approaches a constant as x approaches
. Simply put, it is
when a function approaches a constant value of y as its x value gets REALLY big. A graph of a function with two
horizontal asymptotes is show at right. The dotted lines are the horizontal asymptotes, while the solid line is the
function. For example, the function ƒ(x) = 1/(x 2+1) has a horizontal asymptote at y = 0 when x tends both to
and
because, respectively, This function's asymptote would be described like this: Pre Calculus Page 18 Slant Asymptotes
Wednesday, December 01, 2010 When a linear asymptote is not parallel to the x - or y-axis, it is called an oblique asymptote or slant asymptote. This equation has the following slant asymptote;
BLUE is the asymptote
BLACK is the function This function also has a vertical asymptote at Pre Calculus Page 20 Sketching an Asymptotic Functions and Some Practice Problems
Friday, October 15, 2010 1)
2)
3)
4) Check for Spods
Vertical Asymptotes
Slant Asymptotes
Interesting features (aka single point discontinuity) Practice Problems F(x) = x2 + 8x - 11
y= x2 + 8x -11
X=y2 + 8y - 11
X+27= y2 + 8y + 16
X + 27 = (y + 4)2
Y = -4 Pre Calculus Page 21 N=Numerator
D=Denominator Partial Fractions Decomposition
Friday, October 15, 2010 Proper or Improper
Proper Numerator≥Denominator
Think 'Degree' now!!!
Step 1: Factor the denominator. If the denominator is not factorable, Stop!!! And put a sad face, it does
not exist.
Step 2:
Find A and B Expansion Expression
Step 3:
Step 4: Throw algebra at it until it dies Step 5: Extract the System
A+B=5
A - 4B = -10
Step 6: Solve it A=2
B=3 Step 7: is the decomposition of Pre Calculus Page 22 Algebra Slugfest Problem
Tuesday, October 19, 2010 A+D=3
2D+E=4
6A+B+3D+2E=16
2B+C+6D+3E=20
9A+2C+6E=9 1 0 0 1 0 3 0 0 0 2 1 4 6 1 0 3 2 16 0 2 1 6 3 20 9 0 2 0 6 9 Pre Calculus Page 23 RREF A=1
B=4
C=0
D=2
E=0 Improper RPF
Tuesday, October 19, 2010 Use Polynomial Long Division
Top is larger degree, so it is improper How to use, See "Algebra Slugfest Problem" Pre Calculus Page 24 Unit 3 •
•
•
•
•
• New Sloping Method
Brutal Algebra
Slope of a Point
Tangent Line Equation
Exponent Rule Shortcut for Finding Derivatives
Horizontal Tangent Lines Pre Calculus Page 25 A New Way to Slope
Tuesday, October 19, 2010 Speed Formula Slope indicates the
inclination of a line Miles for every Hour
Speed is a rate of change over distance as time changes Distance
225 Miles Average Rate of Change of Distance with Respect to Time 4.5 hours Linear Functions Are Lines, and thus have a
Defined slope for the entire length of the line. Slope
Is
(+) Non-Linear Slope
is BAD UNLESS
you look at
"Local Slope" Quadratic Functions have
no defined slope over their
entire length. This Function looks line -ish if you zoom in
enough, that's called "local Linearity" Local linear at X=A
Defined at X=A This has a limit,
but will never
have a constant
slope until we
have only two
points Locally
Linear Continuous at X=A Continuous Defined This determines the
neighborhood, the
local slope, & we're
trying to find the exact
slope of f(x) at x=2
I'm gonna re-establish the neighborhood! What is the local
linearity slope of
f(x)=
at (2.9) M=11.41 (1.99,8.880599 M=11.9401 (2,9) (1.999,8.988005999) M=11.994001 (2,9) (2,9) (1.9,7.859) (2,9) (1.9999,8.9888000599) M=11.99990001 Connecting two points
locally is called the
secant line.
M=11.stuff
The closet the points are
together, the closer the
slope of the secant line is
to the actual local slope. Pre Calculus Page 27 (2,9)
Tangent
The tangent line is the
slope of the line at x=2,
or at x= anything on the
function.
In this case the tangent
line is the instantanious
slope Answer to Practice Problem Left Practice Problems
2nd Point x G(x) 257.542 208.47132 247.132402 3.001 206.24611 246.113024 3.0001 At 231.7542 3.01 At x=3
Find the slope of G(x) at x=3 Secant Line Slope 3.1 206.02460 246.0113002 So the slope of G(x) AT x=3 is 246
:) Mtan = 246 at x=3 Now, what is the equation of the tangent line to G(x) at x=3 point of tangency
246
G(3) so 206 Pre Calculus Page 28 Finding a Slope at ANY Point
Friday, October 22, 2010 Find the slope Point of Tangency H is not equal to
zero yet, this
slope is still a
secant line This is the
tangent Line
Equation
Specific to Lim h→0 Lim h→0 Lim h→0 Lim h→0 Lim h→0
2x is the TAN slope function!!! Pre Calculus Page 29 Lim h→0 Brutal Algebra to Find Tangent Line Slope Formula
Monday, October 25, 2010 Find Find the Tangent Line Slope Formula
For
In general your goal is to start with 'h' being the
difference
between the
two points Now find , Use and let h=0 The Secant Line
formula for G(x)
at any two points
(x,F(x)) and
another point H
away. Is For any point on G(x) is
ith h=0, so with h=0 Tangent Line Equation
Monday, October 25, 2010
12:10 PM Stay Variables X-Coordinate of your Point of Tangnecy usually given
I.e. "At x=-1" Pre Calculus Page 30 Exponent Rule Shortcut for
Wednesday, November 03, 2010 "F prime of X"
"The derivative of X"
"The tangent line slope function at any X"
Multiply coefficient
by exponent Find If
Subtract one from each Exponent 5-1 Pre Calculus Page 32 4-1 3-1 2-1 1-1 0-1 Horizontal Tangent Line
Friday, November 05, 2010 The local slope around an extrema is 0 The slope of the actual function at ay X
Where does F(x) have a horizontal Tangent Line The slope of the tangent Line at any X
Slope while f(x)=0 Set Setting F(x) = 0 solving finds the x -coordinates for
"points of horizontal tangency" Wait, this doesn't work!!
What else has to be true about in order to prove Extremaness? There must be a sign change in the neighborhood!! + - - + Maxima
Minima The organized way to explore the sign of
with a sign chart
----------0++++++++0------------ -4 -3 -2 Pre Calculus Page 33 0 2 3 4 is More Horizontal Tangent Lines
Monday, November 08, 2010 Set equal to zero Find Points of Horizontal Tangency must change signs of locally for there to be an extremun.
+0-------0+++0------0+++++++0 -4 -3 -2 +++++++++0-----0+++++++++++ -4 -3 -2 Pre Calculus Page 34 0 2 3 4 0 2 3 4 Unit 4 •
•
•
• Sign Charts
Prime Functions
Tone and Concavity
Rectilinear Motion Pre Calculus Page 35 Superimpose Sign Charts
Monday, November 08, 2010 Describes the y coordinate
describes the tone of F(x)
Describes the concavity of F(x)
Describes the tone of Study Sheet on Primes
Tuesday, November 09, 2010
11:23 AM
2) ƒ(x) = x3 + 3x2 – 45x – 50
3) ƒ(x) = 2x3 + 27x2 + 84x
4) ƒ(x) = -x3 – 12x2 – 66x – 92
5) ƒ(x) =
6) ƒ(x) = x3 + 9x2 + 15x + 2 Pre Calculus Page 37 Study Sheet on Primes Answers
Tuesday, November 09, 2010 2) ƒ(x) = x3 + 3x2 – 45x – 50 3) ƒ(x) = 2x3 + 27x2 + 84x 4) ƒ(x) = -x3 – 12x2 – 66x – 92 5) ƒ(x) = 6) ƒ(x) = x3 + 9x2 + 15x + 2 Pre Calculus Page 39 Study Sheet Number 4
Wednesday, November 10, 2010 No Zeros, means that there is no horizontal tangent lines in the original equation
----------------------------------- 4) ƒ(x) = -x3 – 12x2 – 66x – 92 -4
++++++++++0------------------- Before x=-4, from the negative side, F(x) has negative tone, and positive concavity
After x=-4, from the negative side, F(x) has negative tone, and negative concavity Pre Calculus Page 40 Tone and Concavity of the Derivative
Wednesday, November 10, 2010 Consider the above graph. Y5 is the prime of Y4 Correspond in the following ways:
a)
b) c) x-intercepts* of
correspond to extrema in
x-intercepts* of
correspond to extrema on
as
well as points of inflection on
Tone of
is the concavity of
and the y-output of *as long as there's a sign change at X-intercept Pre Calculus Page 41 Rectilinear Motions
Monday, November 15, 2010 Rules and Conventions
Motion back and forth along a number line(axis) 1. The Placement/Orientation of the number axis is arbitrary
2. Unless otherwise stated, number axis is horizontal; right being (+) and left
being (-).
3. The velocity and acceleration are and not necessarily constant!
4. We will have 3 functions to work with:
a. S(T) "Position"
b. V(T) "Velocity" T is the universal independent variable
c. a(T) "Acceleration"
5. "T" is in seconds unless otherwise stated In motion Example:
A particle in rectilinear motion (call him Fred), has a
position function of At T=2 Fred is at 55 on number line, you don't know
anything else except that at 2 seconds he is at 55
When T=3, then
number line. , Fred is now at 48 on the "Velocity is Speed and Direction" This is the Velocity Equation!! Velocity MPH , so 3 is the initial point, or = Example: Does Fred Turn Around at Where is Fred Stopped? Justify
0 2 5 Plug the times into the position formula
T=2,5
++++++0-----------0+++++++++++++++++++ 5.5
This is what it would look like it time was made a vertical dimension, stretching out
the overlapping movements. 5
4
2
3 28 40 55 0.5 Pre Calculus Page 42 Exam 4 Study Sheet With Answers
Tuesday, November 16, 2010 Do a sign chart to determine if
there is a sign change. Pre Calculus Page 43 A-III
B-I
C-II Pre Calculus Page 44 Cannot use exponent Rule Find the zeros in the prime
x=0 When Sally has stopped T=12, y Pre Calculus Page 45 Unit 5 •
•
•
•
•
• Velocity Function
Acceleration
Free Fall
Rounding Conventions
Rectilinear Motion
Rectilinear Displacement Bonus: My Responses to Exam 5 Pre Calculus Page 46 Velocity Function
Monday, November 29, 2010 I can stop without changing directions.
TRUE In 1 dimensional world I can change directions without stopping.
FALSE Why do I care about stopping points?
Because they represent possible direction change-points I determine change-points for certain by seeing a sign change in
0------------------ 0++++++++++++++++ Speed& direction "right" moving
"Left" moving Extrapolation Fred starts out left moving, and changes direction at 4 sec Extrapolation is inaccurate Data This is silly, or so I hope Copyright XKCD Acceleration How do we interpret a(T)? By itself, a(T) being positive, negative, or zero doesn't mean much. However
combined with velocity…. Monday, November 29, 2010
11:47 AM Speeding up: positive velocity and positive velocity
negative velocity and negative acceleration m
m/s Slowing Down: positive velocity and negative acceleration
negative velocity and positive velocity m/s2 Acceleration is the tending force on velocity
If Fred is said to be uniformly accelerated 0------------------------------- 0+++++++++++++ V(T) 0-----------0++++++++++++++++++++++++++ a(T)
During what intervals of time is Fred Slowing
Down? Speeding Up?
(0,2) SU
(2,4) SD
(4, + ) SU It always switches at 0 velocity, so there is
no sign to compare, so there is always
parenthesis SU SD SU T=4
S(T) T=2
-32
Pre Calculus Page 48 0 In Class Problem
Tuesday, November 30, 2010 Plug in to S(T) to
find position when
not moving. S(T) Solve for 0 16 20 0+++++++0--------------------------------0++++++++++++++++++++++ For SU &SD, I need to
compare T 0---------------------------0+++++++++++++++++++++++++++++++ 0 2 3 4 (0,2) SD
(2,3) SU
(3,4) SD
(4, + SU
Values of T Pre Calculus Page 50 Practice Problem (LONG)
Tuesday, November 30, 2010 Suppose that an object is moving up and down on an axis that
Let Feet, assume the object start out falling. a) What is V(6)?
b) What is S(6)?
c) What is the average velocity for the time interval [0,6]? a) Using by reverse engineering get b)
c)
V(T) Output is V(T)
TONE is a(T) SU Output +
Tone - SD Pre Calculus Page 51 T The Mathematical Model for Free Fall
Tuesday, November 30, 2010 Your number axis is vertical. The ground is zero as a position. Moving upward is positive velocity, therefore falling is
negative velocity. Acceleration is a constant, -32 ft/sec or -9.81 m/s2 No air resistance Height (h) a(T)=-32 ft/sec You can choose any starting point, because all the values are
relative to each other. If the starting point of a 200 ft
building is the top, the street below is just -200 ft. Earth Not drawn to Scale Pre Calculus Page 52 Rounding
Monday, December 06, 2010 At
1.
2.
3.
4. For word questions S(T) , Fred is….
Since
so Fred is left moving.
Since S(T) is concave up at
,
SD BecauseC
&
have opposite signs.
Fred is in "Positivenessland" , so Fred has a positive acceleration. T V(T)
At T2 , Bob is….
1. Stopped because
2.
because at
,
decreasing
3. Neither! Since SU & SD result from the comparison of signs of
Output, since
it doesn't have a sign. T T2 "Displacement" is the NET difference between Si and Sf Displacement is not total distance traveled necessarily.
Example, start at 5, go to -1, then back to 4, displacement is 1. Pre Calculus Page 53 , V(T) +
+ + + Area =9
+ T, which is This tells you the Meters traveled, using this
You can determine the displacement and the
distance traveled using the velocity data and
initial position, or any position for that matter. Area = -2
- - For V(T), your "Tools" output & the tone 2 units of distance in the negative direction Displacement is the sum of the signed area regions. Total distance
traveled is the sum of the absolute value of the signed area of all the
regions. An object is thrown downward from a height of 112
ft and reaches the ground in 2 sec. What is Vi
0= Try It
A car is traveling on a straight road & goes from 55 mi/hr
to 25 mi/hr in 30 sec. If the acceleration is constant, what
is it? Pre Calculus Page 54 Pre Calculus Page 56 Calculus Rectilinear Motion Problem
Monday, December 13, 2010 20
10
0
-10 (2,20) (7,20)
(16,10)(18,10) A=140 A=25 2 4 6 8 10 12 14 16 18 20 22 24
A= -50
(10,-10) (14,-10) A squirrel starts at building A at time t=0 and travels along a straight horizontal wire connected to
building B. For
The squirrels velocity is model by the piecewise function shown above.
(a) At what times in
At t=9 and t=15
(b) At what time interval in does the squirrel change direction. Give a reason.
is the squirrel farthest from the building. Pre Calculus Page 57 12-14-10 In Class Problem
Wednesday, December 15, 2010 Pre Calculus Page 58 Unit 6 •
•
•
•
• Polynomials
Graphing Polynomials
Descartes' Rule of Signs
Really Big Polynomials
Estimating Irrational Roots Pre Calculus Page 59 Polynomials
Monday, January 03, 2011 Variable This will be on Exam 6 Base Exponent The sum/difference of monomials
"ONE" "THING"
Coeff.
Constant Descending Order N=1 N=3 This is a Fourth Degree Polynomial N=1 N=3 Pre Calculus Page 61 N=2 N=4 N=2 N=4 N=5 N=5 N=6 These are all only possibilities, and do in no way represent all possible functions of the described type. In Summary…
1) If
then the right end goes up
then the right end goes down
2) If
3) If N is ODD, the ends are "Opposite"
4) If N is EVEN, the ends are the "Same" Pre Calculus Page 62 N=6 Graphing a Polynomial
Monday, January 03, 2011 Explanation of Derivation of the Formula Every derivative of a polynomial is itself a polynomial.
Let
Assume Let
Let
I want
( ) (
( have roots of -2,1,4 Throw Algebra at it, UNTIL IT DIES ) ) Finding the Roots: Assuming you don't randomly pick a root out of thin air….. Roots of F(x) There is an organized way to find roots…
If real roots exist, then they are either irrational or rational
If there are rational, they must be in the form where P is a factor of
& Q is a factor of Rational Root Theorem Pre Calculus Page 63 RRT Process
Factor This, to Get These Check These Roots: -3,
These are the roots of Using Pre Calculus Page 64 Descartes' Rule of Signs
Thursday, January 06, 2011 Descartes' Rule of Signs - Quantity of changes in sign in indicates the number of (+) real roots….potentially Descartes' Rule of Signs - Quantity of changes in sign in indicates the number of (-) real roots….potentially It has to have some combination of roots, either (-), (+), or imaginary. Because roots must have pairs,
the number of each type must be even. We can chart all the possibilities, and will (below). Descartes' Table
(+)
(-)
Im 2
2
0
0 2
0
2
0 It will be one of these root combinations 0
2
2
4 Hint: it's this one. :) Find the Roots Pre Calculus Page 65 Practice Problem
Thursday, January 06, 2011 Step 1 Step 2 Since it's positive, rule out... Step 3 Step 4 Pre Calculus Page 67 More Complicated Practice Problems
Thursday, January 06, 2011 Pre Calculus Page 68 Really Big Polynomial Factoring
Monday, January 10, 2011 an TV sun Note: All roots are rational and have an absolute value less than 10.
27 in Plugin, Find Roots Make a Decartes' Table 1, -3, 6 all work Now divide the roots out Synthetic Division Rinse, Wash, Repeat. Pre Calculus Page 69 (+)
5
3
1
1
5
3 (-)
2
2
2
0
0
0 Im
0
2
4
6
2
4 ext ext poi Pre Calculus Page 70 Estimating Irrational Roots
Tuesday, January 11, 2011 Intermediate value theorem
If is continuous on and if K is in , then there exists a "c" in Here's an example
I'm picking I know that Input Interval and the "c" will be 1) Between what 2 consecutive integers is a root? Why? I'm to lazy to write this in the computer, so here's a picture. Pre Calculus Page 71 such that Exam 6 Study Guide Answers
Thursday, January 13, 2011 Pre Calculus Page 73 Pre Calculus Page 74 Pre Calculus Page 75 Pre Calculus Page 76 Unit 7 • Logarithms
○
○
(ln)
• Exponential Growth and Decay
• Natural Log
• Log Rules Pre Calculus Page 77 Introduction to Logs, Exponents, & Stuff Note: Those Algebra Rules include: Monday, January 24, 2011 Exponent Rules
Please recall all exponent rules from Algebra 2 In short, Logarithms are exponents!!!
Vocabulary: Pronounced "The Log Base 10 of 10,000" If , then Decreasing LOG Graphing
Rule: LOGS are not defined for negative bases or negative
powers. Graph Pre Calculus Page 79 Never equals -12 Logarithm Manipulation
Monday, January 24, 2011 Formulae for Manipulating LOG Expressions
1) M & N are any factors of MN. 2)
3)
4) 5) "Logarithmic Property of Inequality"
If
Change of Base Formula a. For C, pick any non-stupid choice of a new base. Good choices are 10 and e. 6) Pre Calculus Page 80 Euler and His Girlfriend, Ellen Pronounced "Oiler" Ellen=ln haha….ha Friday, January 28, 2011 'e' Constant Value (Like ) that is Grossly equal to 3
Common log Natural Log Exponent Equations
This Problem Doesn't Require LOGs The only way to solve this problem is with LOGs Practice Problems
Solve these in terms of Ellen
1.
2.
3.
4. 5. Pre Calculus Page 81 One Problem for Calculator Exponential Growth and Decay Model
Monday, January 31, 2011 Exponential Growth and Decay Model Note: K is the Growth/Decay Constant. is the function whose input is "T" and whose
output is the quantity at that "T" value.
Notice something about C? <- Example Problem
1990, world population was 6 billion and growing at an
exponential rate of 2% annually.
, T is years since 1990.
According to that model, when will the Earth's population reach
7,000,000,000? According to that model, what is the doubling time? Pre Calculus Page 82 More Practice
A city's population doubles every 23 years. Find K, OK? Pre Calculus Page 83 Miscellaneous Other Log Notes
Wednesday, February 02, 2011 If
If
If
If , then
, then
, then
, then Pre Calculus Page 84 Unit 8 •
•
•
•
•
•
• Radians
Arc Length
Negative Angles
Trigonometric Functions and Ratios
Unit Circle
Quadrantal Angles
Breaking the Triangle Model Pre Calculus Page 85 Angles and Stuff
Thursday, February 03, 2011 Vertex Angle of opening is measured in degrees. Internal and External Area Types of Angles "internal" inside the angle Acute Angles (0⁰ through 90⁰) Obtuse Angles (90⁰ through 180⁰) "external" outside the angle "Right Angle" 90⁰ Central Angles and Arcs
An angle vertexed at the center of a circle.
Arc subtended by A. It's length is notated Pre Calculus Page 87 Arc subtended by A. It's length is notated A
62⁰ L R=3
B Radian Angle Measure
Is the Real Number equivalent to any number of degrees. How many radians is 360⁰ equivalent to?
radians L=K This is 1 Radian A⁰
R=K One Radian is a unit. Definitions: The length of the arc on the unit circle
formed by the corresponding degree Angle Measure
Pre Calculus Page 88 OK
Not OK,
Don't get lazy Pre Calculus Page 89 2 , RAD, and Conversions
Wednesday, February 09, 2011 Conversion: Unit Circle Circumference simplified Conversion Shortcut: This is the number of radians Pre Calculus Page 90 Common Conversions: Negative Angles / Standard Position and Arc Length
Wednesday, February 09, 2011 120 I Between 0 and 1/2 III Between 1 and 3/2 II Between 1/2 and 1 IV Between 3/2 and 3 Positive Angle Measure Negative Angle Measure! Determining the Arc Length with the Radian Number and the Radius , assuming A is the central angle in radians Pre Calculus Page 91 Vocab: Coterminal angles are angles
that have the same terminal and initial
angles, but different measured, this is
most commonly caused by one angle
containing an extra
, or by one
angle being negative and the other not.
See below. Pre Calculus Page 92 Quadrantal Angles
Monday, February 14, 2011 Quadrantal Angles are: Angles in standard position whose
terminal sides coincide with one of the axes.
Let's Introduce Theta, the angle variable! For example: initial Every in standard position has its own Reference Angle is the acute* angled formed between the terminal
side of and the nearest x-axis! Sector: A part of a circle, like a pizza slice. Pre Calculus Page 93 Chapter 4-2 in text book Trigonometric Ratios
Monday, February 14, 2011 Trig + = Trigonometric Ratios Sine
Cosine
Tangent These ratios are angle dependent The Sine Ratios of Angle Sin
Cos
Tan
Cos
12 13 Sin
5 Tan
x Tan
Note: Do not (Yet!) consider 90 Pre Calculus Page 94 5 5 The 3 Secondary Trigonometric Ratios
Tuesday, February 22, 2011 Calculator Play
CoTangent Secant CoSecant Evaluate COT
:
Never, never, never do this Geometry Flashback:
Triangles Reciprocals
2S N
M S Reciprocals S Reciprocals N/2 Reciprocals Geometry Flashback:
Triangles S
S S Pre Calculus Page 95 This also means that, for example, Pre Calculus Page 96 Breaking the Triangle
Tuesday, February 22, 2011 What are
is a point on 's terminal side. for in S.P. such that (-3,7) This allows you to determine the distance to any point from the origin Let Given the reference triangle, you can let
all ratios of with 7 -3 !! Every can be drawn in S.P. (Standard Position)
In SP, every has a
(Reference angle, such as )
combined with terminal side creates a reference
triangle for every imaginable! Pre Calculus Page 97 Circular Function Re Definition and Ghost Triangles
Wednesday, February 23, 2011 There is new definitions for the Trig Ratios Where is any point on 's terminal side and Ghost Triangles Important: Remember, the y-axis is effectively the "opposite"
leg, and the x-axis is effectively the "adjacent" leg. Pre Calculus Page 98 Some Practice Problems
Wednesday, March 02, 2011 14 Pre Calculus Page 99 Trigonometric Functions Review
Wednesday, March 02, 2011 Important: Remember, the y-axis is effectively the "opposite"
leg, and the x-axis is effectively the "adjacent" leg. Pre Calculus Page 100 Unit 9 •
•
•
•
•
• Trigonometry for Non-Right Triangles
Law of Sines
Area of Any Triangle Trig Formula
Graphing Trig Functions
Trig Functions Domain, Period, and Range Cycle
Trig Function and Angle Variable Coefficients Pre Calculus Page 101 Trig for Non-Right Triangles Chapter 5.5 Friday, March 04, 2011 Determining the Area of Non-Right Triangles
You may have noticed that normal trigonometric means of determining the
area, angle and leg length measures of a triangle only work with right triangles.
Since all triangles are not right (most aren't), we need a method to determine
these things using trigonometry for other non-right triangles. To do this, we will
divide the triangle into two right triangles and then and then calculate the
measures of those triangles. Vocab: Axillary Lines are lines that
are not part of an original
geometric construction, but
which can be proven to exist. Split the triangle in half with an axillary line. (Shown as
red.) Determine the length of Use standard methods to determine the areas of both triangles, and
take the sum for the area of the whole triangle.
The example triangle has an area of Triangle Labeling Convention c Partially Constructed Triangles
This triangle started with only the following information:
Pre Calculus Page 103 This triangle started with only the following information: a=8
See if you can construct it, here's a hint, it looks like this: Example Problem
Solve the triangle h Step 1: Dar what you know. 6 c Step 2: Draw the height.
Step 3: Dar the 'a' leg
Step 4: Calculate the height But wait, there is two possible triangles here 6 h c This triangle works anywhere that the constructed triangle with radius
Pre Calculus Page 104 This triangle works anywhere that the constructed triangle with radius
6 center point d (at the end of leg b) intersects leg c. basically, if we
draw a circle around the defined point at angle AB with the length of
leg a, a triangle can exist anywhere that circle intersects the third leg. Point d 6 h 6 c Triangle can exist Here and Here Math Behind It Note: Your calculator will show you the
acute one, but the obtuse one may still
exist. Find angle Answers Pre Calculus Page 105 Definition of a Sinusoid, Law of Sine, Law of Cosine
Thursday, March 10, 2011 Sinusoid
A sinusoid is a function that can be written in the form: Where a, b, c, and d are constants and neither a nor b are 0.
Law of Sines
The Law of Sines states that the ratio of the sine of an angle to the
length of its opposite side is the same for all three angles of any
triangle.
This can also be said as follows: In any
with angles A, B, and C
opposite sides a, b, c, respectively, the following is true. Law of Cosine
This can be used when:
1. Two sides of a triangle and their enclosed angle are known
2. All three sides are known. Pre Calculus Page 106 Area of Any Triangle
Friday, March 11, 2011 Area of Any Triangle Vocab: Semi Perimeter is half of the perimeter. Area =
to b and pass through Formula Semi Perimeter All Sides In this triangle,
Now look at the triangle on the right.
We can see here that therefore If we substitute this new expression for height, we have a formula
You can choose which equation to use based on what variables you have. This equation
could also be written:
or even Pre Calculus Page 107 Graphing Trig Functions
Monday, March 14, 2011 Quick notes:
, where is an angle measure. We will use 'Zoom - 7"
Because that will give us the following integers when we use RAD mode, which we
will. Which makes it easier to look at sine waves, because degrees are pi
approximations for the integers we will get. Zoom 7 graphed in radians
Domain: All Real
Range: [-1, 1] Pre Calculus Page 108 graphed in radians Domain: All Real
Range: [-1, 1] graphed in radians Domain: All Real except multiples of
Range: All Real Pre Calculus Page 109 and together graphed in radians Quick tip. For approximations,
and
Are identical at very small values. They are
identical at the origin and multiples of 2π, and
become increasingly differentiated with
absolute value distance from the origin or
multiples of 2π. The Period of Sine
The period of Sine is the minimum repeatable domain interval. The Period of Sine
Interval of domain necessary to contain all possible domain values.
(Extrema to Extrema) Pre Calculus Page 110 Pre Calculus Page 111 Domain, Period, and Range Cycle
Tuesday, March 15, 2011 The Period: The minimum width of domain
needed to capture a repeatable pattern. The
period is simply the width value. Period Range Cycle Range Cycle: A domain interval that
creates a 'mini-function' that has the
same range as the entire function.
The enclosed domain has the same range
as the whole function and passes the
horizontal line test. Range Cycle for Tan COT COT has asymptotes where TAN has intercepts Pre Calculus Page 112 COT
COT has asymptotes where TAN has intercepts Range Cycle is SEC
Blue is the cosine, green is the
secant, red is the asymptotes.
Notice how the secant and the
cosine share extrema.
: All Real except multiples of Or
and Range Cycle Relation to ARCfunction
A range cycle is really a domain interval, that will eventually serve as
the range for ARCfunction
Range Cycle of SEC :
and Pre Calculus Page 113 : and Pre Calculus Page 114 Function and Angle Variable Coefficient
Sunday, March 20, 2011 Coefficients Graphing Coefficients and Amplitudes Function Mid-Line
3
1 2 Amplitude and Coefficients
For Sine and CoSine, the amplitude is 1 when the coefficient is 1.
This is useful, because it means that: Remember that Tangent and CoTangent do NOT have defined amplitudes
Pre Calculus Page 115 Remember that Tangent and CoTangent do NOT have defined amplitudes
because they have asymptotes. Angle Variable Coefficient Angle Variable Coefficient We know that
We also know that
Now, with
When
When Pre Calculus Page 116 Heron's Principle
Wednesday, March 30, 2011 Where S = of the perimeter
a,b, and c are the triangle sides
A is area
Pre Calculus Page 117 Amplitude and Period
Sunday, April 03, 2011 Amplitude
The Amplitude of the Sinusoid
is
Graphically the amplitude is half the height of the wave. (from y = 0 to
the extrema.)
Period
The Period of the Sinusoid
Similarly, is
is Graphically the period is the length of one full cycle of the wave The Graph above shows CoSine with increasing period (in integers starting at 1)
This next graph shows CoSine with increasing amplitude (integers starting at 1) Pre Calculus Page 118 Here are some other graphs… Increasing amplitude and Decreasing Period Pre Calculus Page 119 Increasing Amplitude and Increasing Period Pre Calculus Page 120 Analytical and Perspective Sketch
Sunday, April 03, 2011 Take
We graph this, because the amplitude is , and the Period is This graph is drawn to look like a standard CoSine graph, but this is not
the way the graph looks like on a 1x to 1y scale, this is just convenient.
This is called analytical graphing. This is what the graph looks like when compared to a standard CoSine
(y =cos x). Pre Calculus Page 121 The second graphing method is called perspective graphing. Pre Calculus Page 122 Unit 10 • More Trig Function Work Pre Calculus Page 123 Trigonometric Identities
Monday, April 18, 2011 An example ID such that , so Trig IDs are equations that are true for all values such that they are
defined.
Here are some basic IDs
Pythagorean IDs CoFunction IDs Odd-Even Ideas Pre Calculus Page 125 Pre Calculus Page 126 Sum and Diff IDs
Friday, April 15, 2011 Sum and Difference for Sine Why?
Find the exact value of Sum and Difference for Cosine Why?
Find the exact value of Pre Calculus Page 127 Trigonometric Functions Visualized
Monday, April 18, 2011 View all trig functions relative to a circle This isn't really necessary for most people, but can be really helpful
Need to Know Angles
Remember these you will need them and it can save time: Pre Calculus Page 128 Pre Calculus Page 129 Trigonometric Functions Graphed
Tuesday, April 19, 2011 Pre Calculus Page 130 Pre Calculus Page 131 Unit 11 - Bits and Pieces •
•
•
•
•
• Binomial Expansion
Factorials
Pascal's Triangle...Again
Sigma Notation
Binomial Theorem
Converging Series Pre Calculus Page 132 Factorials
Friday, April 29, 2011 Note:
Definition
"!" is defined only for whole numbers!
Most Calculators overflow at
Mine overflows at
Which is equivalent to
,
which is over
times the number of atoms in the universe!! Lotteries
Choose 6 numbers from 1 to 52 inclusive,
and get them in the correct order.
How many combinations of 52 items chosen
6 at a time exist? Your odds of winning are or 0.000004911949% Pre Calculus Page 134 Pascal's Triangle
Friday, April 29, 2011 Derived like this:
So it ends up looking like this: Pre Calculus Page 135 Book Assignment Page 715 #1-25 Binomial Expansion
Friday, April 29, 2011 Using Pascal's Triangle
Expand: Expansion Power Pascal Coefficients
1, 5, 10, 10, 5,1 Interior Coefficients Pre Calculus Page 136 Binomial Theorem
Friday, April 29, 2011 The Binomial Theorem
Gives the Kth term of Example of Usage K What is the 47th term of 96 46
C= 96 46 46
Example Problem Find the 23rd term.
- Solve in terms of X and Y Pre Calculus Page 137 Sigma
Monday, May 02, 2011 Upper Index Red is optional Expression Lower Index of Summation Evaluation
Formula How it works: The Last Term Included This is the Formula that the terms are based off of. K is the integer
value of the term; for example, term 2 has
. is just a variable,
and is treated like any constant. The First Term Included Pre Calculus Page 138 When
Tuesday, May 03, 2011 Dealing with this You change the lower limit.
Use j, Pre Calculus Page 139 Converging (or not) Series
Tuesday, May 03, 2011 Pre Calculus Page 140 ...
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This note was uploaded on 12/09/2011 for the course MATH 1113 taught by Professor Sills during the Summer '11 term at Montgomery College. | 677.169 | 1 |
For undergraduate Introduction to Numerical Analysis course in mathematics, science, and engineering departments. This book provides a fundamental introduction to numerical analysis for undergraduate students in the areas of mathematics, computer science, physical sciences, and engineering. Knowledge of calculus is assumed. - NEW - Expanded emphasis on analysis of competing methods and issues of error - Helps students understand that one can't rely blindly on a given numerical package. - NEW - Rewritten chapter on numerical optimization - Provides a presentation that flows more smoothly. - NEW - New topics for minimization of y=f(x) are included - Gives students a more thorough treatment that is useful here. - NEW - New topics for minimization of z=f(x,y) are included. - NEW - Projects for undergraduate library research experience have been added - Provides students with opportunities for further study. - Explicit use of the software MATLAB is offered - Builds on students' knowledge of structured programming and provides the opportunity to practice scientific programming. - Each numerical method is presented in a self-contained format - Clearly explains numerical methods to students. - Balance of theory and application - Builds on students' knowledge of calculus and basic linear algebra in a clear and readable presentation. - A variety of problems - Sharpens students skills with extensive problem sets with a wide variety of activities. - A wealth of tables and graphs - Illustrates computer calculations in examples making the resulting numerical approximations easier to interpret.
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Descrizione libro Pearson. Condizione libro: New. 013065248230652485127777293 | 677.169 | 1 |
Translations of Encyclopedia about Mathematics
Exponential equations and inequalities are equations or
inequalities in which a variable appears at least once as an exponent.
Examples:
a)
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In this appealing and well-written text, Richard Bronson starts with the concrete and computational, and leads the reader to a choice of major applications. The first three chapters address the basics: matrices, vector spaces, and linear transformations. The next three cover eigenvalues, Euclidean inner products, and Jordan canonical forms, offering possibilities that can be tailored to the instructor's taste and to the length of the course. Bronson's approach to computation is modern and algorithmic, and his theory is clean and straightforward. Throughout, the views of the theory presented are broad and balanced and key material is highlighted in the text and summarized at the end of each chapter. The book also includes ample exercises with answers and hints.
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