MATHEMATICS 155 COLLEGE ALGEBRA WORKBOOK
|
|
- Laura O’Neal’
- 7 years ago
- Views:
Transcription
1 MATHEMATICS 155 COLLEGE ALGEBRA WORKBOOK Southeastern Louisiana University Department of Mathematics Revised Summer 2009
2 MATHEMATICS 155 WORKBOOK TABLE OF CONTENTS Section Page 1.1 Linear Equations Solving Inequalities Quadratic Equations Radical Equations; Equations Quadratic in Form; Factorable Equations Distance and Midpoint Formulas Graphs of Equations in Two Variables; Intercepts; Symmetry Lines Functions The Graph of a Function Properties of Functions Library of Functions; Piecewise-defined Functions Graphing Techniques; Transformations Linear Functions and Their Properties Quadratic Functions and Their Properties Polynomial Functions and Models Properties of Rational Functions The Graph of a Rational Function Polynomial and Rational Inequalities Composite Functions One-to-One Functions; Inverse Functions Exponential Functions Logarithmic Functions Properties of Logarithms Logarithmic and Exponential Equations Compound Interest Exponential Growth and Decay Models Systems of Linear Equations Systems of Nonlinear Equations 28
3 1 Mathematics 155, Section 1.1 Linear Equations Solve each of the following equations for the given variable. 1. 2(1 v) = d = 7d x + 1 = x (y 3 2 ) + 7y = 1 2 y 5. p = 2p (x 3(x 4)) = 12x 7. Solve for x : ax b c + d = 2x 8. x 1 x x 2 20x + 36 = x + 1 x 2
4 2 Mathematics 155, Section 1.5 Linear Inequalities (1) Solve each inequality, and then graph the solution. (a) 2a 3 < 15 (b) 4 z 2 (2) Find the solution to each inequality. Write your answer using interval notation. (a) 2(x 1) > 0 (b) 1 2 m 3 < 7 (c) 2 5 z 4 (d) 1 r > 9 (e) (2 3x) 1 < 0 (f) 3 < 5 (2k + 1) < 10 (3) What is the domain of the variable in the expression 4x + 3?
5 3 Mathematics 155, Section 1.2 Quadratic Equations Find the real solutions, if any, to each equation. 1. (c + 6)(2c 1) = 0 2. n 2 4 = 0 3. (3n 4) 2 = 9 4. t 2 5t = q(q 5) = 8 6. x 2 + 4x + 7 = x + 4 = x d d 2 = 0
6 4 Mathematics 155, Section 1.4 Miscellaneous Equations Find the real solutions of each equation. (1) 12 x = x (2) (a 2 6a) 2 2(a 2 6a) 35 = 0 (3) s 2 s 3 = 0 (4) 6x 3/2 5x 1/2 = 0 (5) 3x 3 + 4x 2 = 27x + 36
7 5 Mathematics 155, Section 2.1 The Distance and Midpoint Formulas (1) Draw an xy-plane and plot the points A( 3, 2) and B(4, 1). Draw the line segment AB. Find the length of the line segment by constructing a right triangle with vertical and horizontal line segments, finding the lengths of those line segments, and using the Pythagorean Theorem. (2) Find all points having a y-coordinate of 3 whose distance from the point (1, 2) is 13. (3) Find the midpoint of line segment AB from number (1). (4) The midpoint of the line segment from P 1 to P 2 is (5, 4). If P 2 = (7, 2), what is P 1?
8 6 Mathematics 155, Section 2.2 Graphs of Equations in Two Variables Find the intercepts and graph each equation in (1) and (2) by plotting points. Be sure to label the intercepts. (1) 5x + 2y = 10 (2) 4x 2 + y = 4 (3) List the intercepts for the equation y = x2 4 2x and test for symmetry.
9 7 Mathematics 155, Section 2.3 Lines Find an equation of the line for each of the following criteria. (1) Containing the points ( 3, 10) and (2, 12) (2) Horizontal and containing the point ( 50, 62) (3) Vertical and containing the point ( 5, 6) (4) Passing through the point (4, 1) and perpendicular to the line 2x 3y = 4
10 8 Mathematics 155, Section 3.1 Functions (1) Which of the following relations define y as a function of x? EXPLAIN why or why not for each. (a) y = x (b) x + y 2 = 1 (2) Find the domain of the function f(x) = x x 4. For the functions f(x) = 2x and g(x) = 3x 4, find: (3) (f g)(x) (4) ( ) f (1) g
11 9 Mathematics 155, Section 3.2 The Graph of a Function (1) Use the given graph of the function f to answer parts (a) - (f). (a) Find f(0) and f( 2). f(0) = f( 2) = (b) Is f(3) positive or negative? (c) What is the domain of f? (d) What is the range of f? (e) How often does the line y = 1 intersect the graph? (f) For what value of x does f(x) = 0? (2) For the function g(x) = 2x x 2, (a) Is the point ( 1, 2 ) on the graph of g? 2 3 (b) If x = 4, what is g(x)? What point(s) does this yield? (c) If g(x) = 1, what is x? What point(s) does this yield? (d) What is the domain of g? (e) List the intercepts for the graph of g.
12 10 Mathematics 155, Section 3.3 Properties of Functions (1) Use the given graph of the function f to answer parts (a) - (e). (a) Identify the domain and range of f. (b) Identify the intervals on which f is increasing, decreasing or constant. (c) Identify the local minima and local maxima. (d) Is f even, odd, or neither? (e) Identify the intercepts, if any. (2) g(x) = 2x 2 2x (a) Find the average rate of change from 0 to 3. (b) Find the equation of the secant line containing (0, g(0)) and (3, g(3)).
13 11 Mathematics 155, Section 3.4 Library of Functions + Piecewise-Defined (1) f(x) = { x + 3, for x 1, x 2, for x > 1. Find: f( 4) = f(0) = f(1) = f(5) = Graph f(x). (2) 1, for x < 0, x h(x) = 2, for x = 0, x, for x > 0. Find: h( 2) = h(0) = h(1) = h(4) = Graph h(x).
14 12 Mathematics 155, Section 3.5 Graphing Techniques; Transformations (1) EXPLAIN how the four given transformations in the second equation affect the graph of f(x) = x. f(x) = 2 x (2) The graph of f(x) is given below on the viewing window indicated. Sketch a graph of each of the following: (a) y = f(x 2) (b) y = f(x + 1) 3 (c) y = 2f(x) (d) y = f(2x) (3) Find the function that is finally graphed after the following transformations are applied in order to the graph of y = x. (1) Reflect about the x-axis (2) Shift right 3 units (3) Shift down 2 units
15 13 Mathematics 155, Section 4.1 Linear Functions and Their Properties (1) Determine the slope and y-intercept for each linear function and graph. (a) f(x) = 1 x 3 (b) g(x) = 3x (2) The monthly cost C, in dollars, for international calls on a certain cellular phone plan is a flat rate of 12 dollars plus 38 cents per minute used. (a) Write a linear function that expresses the monthly cost C in terms of the number of minutes used, x. (b) What is the cost if you talk on the phone for 1 hour and 15 minutes? (c) Suppose that you budget yourself $60 per month for the phone. What is the maximum number of complete minutes that you can talk?
16 14 Mathematics 155, Section 4.3 Quadratic Functions and Their Properties (1) Find the vertex of each quadratic graph. (a) y = x 2 6x (b) y = x x 1 (c) y = 2x 2 6x 13 (d) y = 3x 2 24x + 18 (2) For f(x) = (x + 3) 2 + 4, give: Domain: Axis of Symmetry: x-intercepts: Vertex: Range: y-intercept: (3) Give an equation for a parabola which is concave up, has a vertex of ( 3, 2), and has an x-intercept of ( 5, 0).
17 15 Mathematics 155, Section 5.1 Polynomial Functions and Models (1) Write equations of polynomial functions which satisfy each set of criteria specified below. (a) zeros of 2 and 3 (b) zeros of 1 2, 0 and 5 (c) zeros of 4 and 2 and a y-intercept of 2 (2) Write equations of polynomial functions which could fit each of the graphs shown. Each graph is shown on a standard viewing window. Show your equation in factored form, and give the power function that the graph resembles for large values of x. Factored: f(x) = Factored: g(x) = Power Function: y = Power Function: y =
18 16 Mathematics 155, Section 5.2 Properties of Rational Functions For each of the following rational functions, find and identify the domain, find and identify the intercepts, find and identify the vertical and horizontal asymptotes. (1) f(x) = x2 + 1 x 2 5x + 6 Domain: x-intercepts: y-intercept: Equation(s) of asymptote(s): (2) y = 1 (x + 2) Domain: x-intercepts: y-intercept: Equation(s) of asymptote(s): (3) Graph y = using transformations and the info found in (2). (x + 2) 2
19 17 Mathematics 155, Section 5.3 The Graph of a Rational Function For each of the following rational functions, find and identify the domain, find and identify the intercepts, find and identify the vertical and horizontal asymptotes, construct a sign chart to determine where f(x) is positive and negative, draw a complete graph of f. (1) f(x) = Domain: x (x 5)(x + 6) x-intercepts: y-intercept: Eq of asymptote(s): (2) y = Domain: 2(x + 4)(x 6) x 2 9 y-intercept: x-intercepts: Eq of asymptote(s):
20 18 Mathematics 155, Section 5.4 Polynomial and Rational Inequalities (1) Find the solution to each inequality. Write your answer using interval notation. (a) x (b) 2x 3 x 2 > 3x (c) (x + 5) 2 x (2) What is the domain of the function f(x) = x x x 2?
21 19 Mathematics 155, Section 6.1 Composite Functions (1) Let f(x) = x 2 9, and g(x) = x + 5. Find the following compositions. (a) (f g)( 10) (b) (f f)(0) (c) (f g)(x) (d) (g f)(x) (2) A dress store advertised a series of discounts. A discount of 25% was followed by an additional discount of 50%. (a) Express each discount separately in functional format, labeling the first discount as f(x) and the second discount as s(x). (b) Express the series of discounts as a composition of the two functions designated in part (a). (c) Evaluate the composition of the functions for a value of x = $85. (d) Is the discount described equivalent to a 75% reduction? Explain why or why not.
22 20 Mathematics 155, Section 6.2 One-to-One and Inverse Functions (1) The drawing which follows gives the graph of f(x). Draw the graph of f 1 (x) on the same set of axes. (2) Find f 1 (x) given f(x) = 5x 3 4. (3) Find g 1 (x) given g(x) = x 4 2x + 1.
23 21 Mathematics 155, Section 6.3 Exponential Functions (1) Let f(x) = 3 x + 2. (a) What is f( 2)? What point is on the graph of f? (b) If f(x) = 83, what is x? What point is on the graph of f? (2) Graph each of the following. Give coordinates of at least 3 points on each graph. (a) y = 3 x 2 (b) y = e x 2 (3) The population of a large U.S. city is growing according to the the function P = 1, 400, 000(1.023) t, where t is the number of years since (a) What was the population in 2000? (b) What will the population be in 2015 according to this formula?
24 22 Mathematics 155, Section 6.4 Logarithmic Functions (1) (a) Change e x = 4 to an equivalent expression involving a logarithm. (b) Change log 3 x = 2 to an equivalent expression involving an exponent. (2) Graph each of the following. Give coordinates of at least 3 points on each graph. (a) y = log 2 (x + 1) (b) y = ln(x) (3) Determine the domain, range, and intercept(s) for each of the graphs given above. Identify any asymptotes by giving the equations. (a) For y = log 2 (x + 1)... Domain: Range: Asymptote: Intercept(s): (b) For y = ln(x)... Domain: Range: Asymptote: Intercept(s):
25 23 Mathematics 155, Section 6.5 Properties of Logarithms (1) Write each expression as a single logarithm. Simplify result as much as possible. (a) log 5 (250) log 5 (10) (b) 2 log 5 (a) + log 5 (2a) (c) 3 log 2 (p) 1 2 log 2(p) (d) ln(m 2 4) ln(m + 2) (2) Write each expression as a sum and/or difference of logarithms. Express powers as factors. Simplify as much as possible. (a) log 2 ( 4 x ) (b) log 3 (27m 2 ) ( ) (x 1) 2 (c) log x 3 (d) ln (xe x )
26 24 Mathematics 155, Section 6.6 Logarithmic and Exponential Equations Solve each equation. Express solutions in exact form. (1) 3 x 2 = 64 (2) log(2x) log(x 3) = 1 (3) 2 49 x 9 7 x 5 = 0 (4) log 6 (x + 4) + log 6 (x + 3) = 1 (5) 2 x+1 = 5 1 2x
27 25 Mathematics 155, Section 6.7 Compound Interest (1) A student wishes to invest $1500 in a savings account yielding 3.5% annual interest compounded monthly. How much will his investment be worth at the end of 2 years? (2) You have a credit card which currently holds a balance of $2500. You are not required to pay anything for two years (something for a special customer ). If the credit card company figures your interest by compounding daily at a rate of 21.9% and if you choose not to make any payments for that time period, what will be your new balance be at the end of the second year? (3) How many years will it take for an initial investment of $2500 to grow to $5500? Assume a rate of interest of 5.2% compounded continuously?
28 26 Mathematics 155, Section 6.8 Exponential Growth and Decay Models (1) A radioactive substance decays exponentially at an annual rate given by r = How many grams are left after 200 years from a 10-gram specimen? Round to the nearest tenth of a gram. (2) A different radioactive element decays continuously at a rate of 5% per year. If we begin with 20 grams of this element, how long (to the nearest tenth of a year) will it take for only 10 grams to remain? (3) At 45 C, dinitrogen pentoxide (N 2 O 5 ) decomposes into nitrous dioxide (NO 2 ) and oxygen (O 2 ) according to the law of uninhibited decay. An initial amount of 0.25 M of dinitrogen pentoxide decomposes to 0.15 M in 17 minutes. How much dinitrogen pentoxide will remain after 30 minutes?
29 27 Mathematics 155, Section 8.1 Systems of Linear Equations (1) Solve the system. x 2y = 6 x + 2y = 30 (2) Solve the system. y = 5 3x 4x y = 9 (3) My friend and I went out to lunch last week, but we did not pay attention to the the cost of each item we ordered until we compared receipts. I had one soft drink and one taco. My bill showed a tax of 15 cents and a total of $2.25. My friend had two soft drinks and three tacos. His bill showed a tax of 36 cents and a total of $5.51. How much was each item (before tax)?
30 28 Mathematics 155, Section 8.6 Systems of Nonlinear Equations Solve each of the following systems. (1) x + y = 5 x 2 + y = 5 (2) x y = 2 x 2 + y 2 = 4 (3) x 2 + y 2 = 12 x 2 + y = 10 (4) log x (2y) = 3 log x (4y) = 2
Simplify the rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression.
MAC 1105 Final Review Simplify the rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. 1) 8x 2-49x + 6 x - 6 A) 1, x 6 B) 8x - 1, x 6 x -
More informationFINAL EXAM SECTIONS AND OBJECTIVES FOR COLLEGE ALGEBRA
FINAL EXAM SECTIONS AND OBJECTIVES FOR COLLEGE ALGEBRA 1.1 Solve linear equations and equations that lead to linear equations. a) Solve the equation: 1 (x + 5) 4 = 1 (2x 1) 2 3 b) Solve the equation: 3x
More informationa. all of the above b. none of the above c. B, C, D, and F d. C, D, F e. C only f. C and F
FINAL REVIEW WORKSHEET COLLEGE ALGEBRA Chapter 1. 1. Given the following equations, which are functions? (A) y 2 = 1 x 2 (B) y = 9 (C) y = x 3 5x (D) 5x + 2y = 10 (E) y = ± 1 2x (F) y = 3 x + 5 a. all
More informationHigher Education Math Placement
Higher Education Math Placement Placement Assessment Problem Types 1. Whole Numbers, Fractions, and Decimals 1.1 Operations with Whole Numbers Addition with carry Subtraction with borrowing Multiplication
More informationMath 120 Final Exam Practice Problems, Form: A
Math 120 Final Exam Practice Problems, Form: A Name: While every attempt was made to be complete in the types of problems given below, we make no guarantees about the completeness of the problems. Specifically,
More informationAlgebra and Geometry Review (61 topics, no due date)
Course Name: Math 112 Credit Exam LA Tech University Course Code: ALEKS Course: Trigonometry Instructor: Course Dates: Course Content: 159 topics Algebra and Geometry Review (61 topics, no due date) Properties
More informationThnkwell s Homeschool Precalculus Course Lesson Plan: 36 weeks
Thnkwell s Homeschool Precalculus Course Lesson Plan: 36 weeks Welcome to Thinkwell s Homeschool Precalculus! We re thrilled that you ve decided to make us part of your homeschool curriculum. This lesson
More informationMATH 095, College Prep Mathematics: Unit Coverage Pre-algebra topics (arithmetic skills) offered through BSE (Basic Skills Education)
MATH 095, College Prep Mathematics: Unit Coverage Pre-algebra topics (arithmetic skills) offered through BSE (Basic Skills Education) Accurately add, subtract, multiply, and divide whole numbers, integers,
More informationhttp://www.aleks.com Access Code: RVAE4-EGKVN Financial Aid Code: 6A9DB-DEE3B-74F51-57304
MATH 1340.04 College Algebra Location: MAGC 2.202 Meeting day(s): TR 7:45a 9:00a, Instructor Information Name: Virgil Pierce Email: piercevu@utpa.edu Phone: 665.3535 Teaching Assistant Name: Indalecio
More informationCORRELATED TO THE SOUTH CAROLINA COLLEGE AND CAREER-READY FOUNDATIONS IN ALGEBRA
We Can Early Learning Curriculum PreK Grades 8 12 INSIDE ALGEBRA, GRADES 8 12 CORRELATED TO THE SOUTH CAROLINA COLLEGE AND CAREER-READY FOUNDATIONS IN ALGEBRA April 2016 www.voyagersopris.com Mathematical
More informationAlgebra 1 Course Title
Algebra 1 Course Title Course- wide 1. What patterns and methods are being used? Course- wide 1. Students will be adept at solving and graphing linear and quadratic equations 2. Students will be adept
More informationPrentice Hall Mathematics: Algebra 2 2007 Correlated to: Utah Core Curriculum for Math, Intermediate Algebra (Secondary)
Core Standards of the Course Standard 1 Students will acquire number sense and perform operations with real and complex numbers. Objective 1.1 Compute fluently and make reasonable estimates. 1. Simplify
More informationHow To Understand And Solve Algebraic Equations
College Algebra Course Text Barnett, Raymond A., Michael R. Ziegler, and Karl E. Byleen. College Algebra, 8th edition, McGraw-Hill, 2008, ISBN: 978-0-07-286738-1 Course Description This course provides
More informationEquations. #1-10 Solve for the variable. Inequalities. 1. Solve the inequality: 2 5 7. 2. Solve the inequality: 4 0
College Algebra Review Problems for Final Exam Equations #1-10 Solve for the variable 1. 2 1 4 = 0 6. 2 8 7 2. 2 5 3 7. = 3. 3 9 4 21 8. 3 6 9 18 4. 6 27 0 9. 1 + log 3 4 5. 10. 19 0 Inequalities 1. Solve
More informationAlgebra II End of Course Exam Answer Key Segment I. Scientific Calculator Only
Algebra II End of Course Exam Answer Key Segment I Scientific Calculator Only Question 1 Reporting Category: Algebraic Concepts & Procedures Common Core Standard: A-APR.3: Identify zeros of polynomials
More informationBookTOC.txt. 1. Functions, Graphs, and Models. Algebra Toolbox. Sets. The Real Numbers. Inequalities and Intervals on the Real Number Line
College Algebra in Context with Applications for the Managerial, Life, and Social Sciences, 3rd Edition Ronald J. Harshbarger, University of South Carolina - Beaufort Lisa S. Yocco, Georgia Southern University
More informationSouth Carolina College- and Career-Ready (SCCCR) Pre-Calculus
South Carolina College- and Career-Ready (SCCCR) Pre-Calculus Key Concepts Arithmetic with Polynomials and Rational Expressions PC.AAPR.2 PC.AAPR.3 PC.AAPR.4 PC.AAPR.5 PC.AAPR.6 PC.AAPR.7 Standards Know
More informationMath 131 College Algebra Fall 2015
Math 131 College Algebra Fall 2015 Instructor's Name: Office Location: Office Hours: Office Phone: E-mail: Course Description This course has a minimal review of algebraic skills followed by a study of
More informationAdministrative - Master Syllabus COVER SHEET
Administrative - Master Syllabus COVER SHEET Purpose: It is the intention of this to provide a general description of the course, outline the required elements of the course and to lay the foundation for
More informationPRE-CALCULUS GRADE 12
PRE-CALCULUS GRADE 12 [C] Communication Trigonometry General Outcome: Develop trigonometric reasoning. A1. Demonstrate an understanding of angles in standard position, expressed in degrees and radians.
More informationDear Accelerated Pre-Calculus Student:
Dear Accelerated Pre-Calculus Student: I am very excited that you have decided to take this course in the upcoming school year! This is a fastpaced, college-preparatory mathematics course that will also
More informationMATH BOOK OF PROBLEMS SERIES. New from Pearson Custom Publishing!
MATH BOOK OF PROBLEMS SERIES New from Pearson Custom Publishing! The Math Book of Problems Series is a database of math problems for the following courses: Pre-algebra Algebra Pre-calculus Calculus Statistics
More informationAlgebra I Credit Recovery
Algebra I Credit Recovery COURSE DESCRIPTION: The purpose of this course is to allow the student to gain mastery in working with and evaluating mathematical expressions, equations, graphs, and other topics,
More informationAlgebra 2 Chapter 1 Vocabulary. identity - A statement that equates two equivalent expressions.
Chapter 1 Vocabulary identity - A statement that equates two equivalent expressions. verbal model- A word equation that represents a real-life problem. algebraic expression - An expression with variables.
More informationCHAPTER FIVE. Solutions for Section 5.1. Skill Refresher. Exercises
CHAPTER FIVE 5.1 SOLUTIONS 265 Solutions for Section 5.1 Skill Refresher S1. Since 1,000,000 = 10 6, we have x = 6. S2. Since 0.01 = 10 2, we have t = 2. S3. Since e 3 = ( e 3) 1/2 = e 3/2, we have z =
More informationThis unit will lay the groundwork for later units where the students will extend this knowledge to quadratic and exponential functions.
Algebra I Overview View unit yearlong overview here Many of the concepts presented in Algebra I are progressions of concepts that were introduced in grades 6 through 8. The content presented in this course
More informationWeek 1: Functions and Equations
Week 1: Functions and Equations Goals: Review functions Introduce modeling using linear and quadratic functions Solving equations and systems Suggested Textbook Readings: Chapter 2: 2.1-2.2, and Chapter
More informationUnderstanding Basic Calculus
Understanding Basic Calculus S.K. Chung Dedicated to all the people who have helped me in my life. i Preface This book is a revised and expanded version of the lecture notes for Basic Calculus and other
More information2312 test 2 Fall 2010 Form B
2312 test 2 Fall 2010 Form B 1. Write the slope-intercept form of the equation of the line through the given point perpendicular to the given lin point: ( 7, 8) line: 9x 45y = 9 2. Evaluate the function
More informationALGEBRA REVIEW LEARNING SKILLS CENTER. Exponents & Radicals
ALGEBRA REVIEW LEARNING SKILLS CENTER The "Review Series in Algebra" is taught at the beginning of each quarter by the staff of the Learning Skills Center at UC Davis. This workshop is intended to be an
More informationAlgebra I Vocabulary Cards
Algebra I Vocabulary Cards Table of Contents Expressions and Operations Natural Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers Absolute Value Order of Operations Expression
More informationAlgebra 2 Year-at-a-Glance Leander ISD 2007-08. 1st Six Weeks 2nd Six Weeks 3rd Six Weeks 4th Six Weeks 5th Six Weeks 6th Six Weeks
Algebra 2 Year-at-a-Glance Leander ISD 2007-08 1st Six Weeks 2nd Six Weeks 3rd Six Weeks 4th Six Weeks 5th Six Weeks 6th Six Weeks Essential Unit of Study 6 weeks 3 weeks 3 weeks 6 weeks 3 weeks 3 weeks
More informationSolving Quadratic Equations
9.3 Solving Quadratic Equations by Using the Quadratic Formula 9.3 OBJECTIVES 1. Solve a quadratic equation by using the quadratic formula 2. Determine the nature of the solutions of a quadratic equation
More information12.6 Logarithmic and Exponential Equations PREPARING FOR THIS SECTION Before getting started, review the following:
Section 1.6 Logarithmic and Exponential Equations 811 1.6 Logarithmic and Exponential Equations PREPARING FOR THIS SECTION Before getting started, review the following: Solve Quadratic Equations (Section
More informationCRLS Mathematics Department Algebra I Curriculum Map/Pacing Guide
Curriculum Map/Pacing Guide page 1 of 14 Quarter I start (CP & HN) 170 96 Unit 1: Number Sense and Operations 24 11 Totals Always Include 2 blocks for Review & Test Operating with Real Numbers: How are
More informationAlgebra 2: Themes for the Big Final Exam
Algebra : Themes for the Big Final Exam Final will cover the whole year, focusing on the big main ideas. Graphing: Overall: x and y intercepts, fct vs relation, fct vs inverse, x, y and origin symmetries,
More informationMA107 Precalculus Algebra Exam 2 Review Solutions
MA107 Precalculus Algebra Exam 2 Review Solutions February 24, 2008 1. The following demand equation models the number of units sold, x, of a product as a function of price, p. x = 4p + 200 a. Please write
More informationWhat are the place values to the left of the decimal point and their associated powers of ten?
The verbal answers to all of the following questions should be memorized before completion of algebra. Answers that are not memorized will hinder your ability to succeed in geometry and algebra. (Everything
More informationVocabulary Words and Definitions for Algebra
Name: Period: Vocabulary Words and s for Algebra Absolute Value Additive Inverse Algebraic Expression Ascending Order Associative Property Axis of Symmetry Base Binomial Coefficient Combine Like Terms
More informationCourse Outlines. 1. Name of the Course: Algebra I (Standard, College Prep, Honors) Course Description: ALGEBRA I STANDARD (1 Credit)
Course Outlines 1. Name of the Course: Algebra I (Standard, College Prep, Honors) Course Description: ALGEBRA I STANDARD (1 Credit) This course will cover Algebra I concepts such as algebra as a language,
More informationStudents Currently in Algebra 2 Maine East Math Placement Exam Review Problems
Students Currently in Algebra Maine East Math Placement Eam Review Problems The actual placement eam has 100 questions 3 hours. The placement eam is free response students must solve questions and write
More informationALGEBRA 2: 4.1 Graph Quadratic Functions in Standard Form
ALGEBRA 2: 4.1 Graph Quadratic Functions in Standard Form Goal Graph quadratic functions. VOCABULARY Quadratic function A function that can be written in the standard form y = ax 2 + bx+ c where a 0 Parabola
More informationMSLC Workshop Series Math 1148 1150 Workshop: Polynomial & Rational Functions
MSLC Workshop Series Math 1148 1150 Workshop: Polynomial & Rational Functions The goal of this workshop is to familiarize you with similarities and differences in both the graphing and expression of polynomial
More informationPolynomial and Rational Functions
Polynomial and Rational Functions Quadratic Functions Overview of Objectives, students should be able to: 1. Recognize the characteristics of parabolas. 2. Find the intercepts a. x intercepts by solving
More information100. In general, we can define this as if b x = a then x = log b
Exponents and Logarithms Review 1. Solving exponential equations: Solve : a)8 x = 4! x! 3 b)3 x+1 + 9 x = 18 c)3x 3 = 1 3. Recall: Terminology of Logarithms If 10 x = 100 then of course, x =. However,
More informationExtra Credit Assignment Lesson plan. The following assignment is optional and can be completed to receive up to 5 points on a previously taken exam.
Extra Credit Assignment Lesson plan The following assignment is optional and can be completed to receive up to 5 points on a previously taken exam. The extra credit assignment is to create a typed up lesson
More informationLyman Memorial High School. Pre-Calculus Prerequisite Packet. Name:
Lyman Memorial High School Pre-Calculus Prerequisite Packet Name: Dear Pre-Calculus Students, Within this packet you will find mathematical concepts and skills covered in Algebra I, II and Geometry. These
More informationEstimated Pre Calculus Pacing Timeline
Estimated Pre Calculus Pacing Timeline 2010-2011 School Year The timeframes listed on this calendar are estimates based on a fifty-minute class period. You may need to adjust some of them from time to
More informationAlgebra II. Weeks 1-3 TEKS
Algebra II Pacing Guide Weeks 1-3: Equations and Inequalities: Solve Linear Equations, Solve Linear Inequalities, Solve Absolute Value Equations and Inequalities. Weeks 4-6: Linear Equations and Functions:
More information2.1 Increasing, Decreasing, and Piecewise Functions; Applications
2.1 Increasing, Decreasing, and Piecewise Functions; Applications Graph functions, looking for intervals on which the function is increasing, decreasing, or constant, and estimate relative maxima and minima.
More informationMATH 21. College Algebra 1 Lecture Notes
MATH 21 College Algebra 1 Lecture Notes MATH 21 3.6 Factoring Review College Algebra 1 Factoring and Foiling 1. (a + b) 2 = a 2 + 2ab + b 2. 2. (a b) 2 = a 2 2ab + b 2. 3. (a + b)(a b) = a 2 b 2. 4. (a
More informationAlgebra 1 Course Information
Course Information Course Description: Students will study patterns, relations, and functions, and focus on the use of mathematical models to understand and analyze quantitative relationships. Through
More informationIndiana State Core Curriculum Standards updated 2009 Algebra I
Indiana State Core Curriculum Standards updated 2009 Algebra I Strand Description Boardworks High School Algebra presentations Operations With Real Numbers Linear Equations and A1.1 Students simplify and
More informationAlgebra II A Final Exam
Algebra II A Final Exam Multiple Choice Identify the choice that best completes the statement or answers the question. Evaluate the expression for the given value of the variable(s). 1. ; x = 4 a. 34 b.
More informationAlgebra Unpacked Content For the new Common Core standards that will be effective in all North Carolina schools in the 2012-13 school year.
This document is designed to help North Carolina educators teach the Common Core (Standard Course of Study). NCDPI staff are continually updating and improving these tools to better serve teachers. Algebra
More informationCreating, Solving, and Graphing Systems of Linear Equations and Linear Inequalities
Algebra 1, Quarter 2, Unit 2.1 Creating, Solving, and Graphing Systems of Linear Equations and Linear Inequalities Overview Number of instructional days: 15 (1 day = 45 60 minutes) Content to be learned
More informationLinear Equations. Find the domain and the range of the following set. {(4,5), (7,8), (-1,3), (3,3), (2,-3)}
Linear Equations Domain and Range Domain refers to the set of possible values of the x-component of a point in the form (x,y). Range refers to the set of possible values of the y-component of a point in
More informationMATH 2 Course Syllabus Spring Semester 2007 Instructor: Brian Rodas
MATH 2 Course Syllabus Spring Semester 2007 Instructor: Brian Rodas Class Room and Time: MC83 MTWTh 2:15pm-3:20pm Office Room: MC38 Office Phone: (310)434-8673 E-mail: rodas brian@smc.edu Office Hours:
More informationMBA Jump Start Program
MBA Jump Start Program Module 2: Mathematics Thomas Gilbert Mathematics Module Online Appendix: Basic Mathematical Concepts 2 1 The Number Spectrum Generally we depict numbers increasing from left to right
More informationPrerequisites: TSI Math Complete and high school Algebra II and geometry or MATH 0303.
Course Syllabus Math 1314 College Algebra Revision Date: 8-21-15 Catalog Description: In-depth study and applications of polynomial, rational, radical, exponential and logarithmic functions, and systems
More informationSouth Carolina College- and Career-Ready (SCCCR) Algebra 1
South Carolina College- and Career-Ready (SCCCR) Algebra 1 South Carolina College- and Career-Ready Mathematical Process Standards The South Carolina College- and Career-Ready (SCCCR) Mathematical Process
More information6.4 Logarithmic Equations and Inequalities
6.4 Logarithmic Equations and Inequalities 459 6.4 Logarithmic Equations and Inequalities In Section 6.3 we solved equations and inequalities involving exponential functions using one of two basic strategies.
More informationThe Point-Slope Form
7. The Point-Slope Form 7. OBJECTIVES 1. Given a point and a slope, find the graph of a line. Given a point and the slope, find the equation of a line. Given two points, find the equation of a line y Slope
More informationNEW YORK STATE TEACHER CERTIFICATION EXAMINATIONS
NEW YORK STATE TEACHER CERTIFICATION EXAMINATIONS TEST DESIGN AND FRAMEWORK September 2014 Authorized for Distribution by the New York State Education Department This test design and framework document
More information7.1 Graphs of Quadratic Functions in Vertex Form
7.1 Graphs of Quadratic Functions in Vertex Form Quadratic Function in Vertex Form A quadratic function in vertex form is a function that can be written in the form f (x) = a(x! h) 2 + k where a is called
More informationAlgebra I. In this technological age, mathematics is more important than ever. When students
In this technological age, mathematics is more important than ever. When students leave school, they are more and more likely to use mathematics in their work and everyday lives operating computer equipment,
More informationMath Placement Test Study Guide. 2. The test consists entirely of multiple choice questions, each with five choices.
Math Placement Test Study Guide General Characteristics of the Test 1. All items are to be completed by all students. The items are roughly ordered from elementary to advanced. The expectation is that
More information6.1 Add & Subtract Polynomial Expression & Functions
6.1 Add & Subtract Polynomial Expression & Functions Objectives 1. Know the meaning of the words term, monomial, binomial, trinomial, polynomial, degree, coefficient, like terms, polynomial funciton, quardrtic
More informationHIBBING COMMUNITY COLLEGE COURSE OUTLINE
HIBBING COMMUNITY COLLEGE COURSE OUTLINE COURSE NUMBER & TITLE: - Beginning Algebra CREDITS: 4 (Lec 4 / Lab 0) PREREQUISITES: MATH 0920: Fundamental Mathematics with a grade of C or better, Placement Exam,
More informationMathematics Georgia Performance Standards
Mathematics Georgia Performance Standards K-12 Mathematics Introduction The Georgia Mathematics Curriculum focuses on actively engaging the students in the development of mathematical understanding by
More informationUnit 1 Equations, Inequalities, Functions
Unit 1 Equations, Inequalities, Functions Algebra 2, Pages 1-100 Overview: This unit models real-world situations by using one- and two-variable linear equations. This unit will further expand upon pervious
More informationClovis Community College Core Competencies Assessment 2014 2015 Area II: Mathematics Algebra
Core Assessment 2014 2015 Area II: Mathematics Algebra Class: Math 110 College Algebra Faculty: Erin Akhtar (Learning Outcomes Being Measured) 1. Students will construct and analyze graphs and/or data
More informationSome Lecture Notes and In-Class Examples for Pre-Calculus:
Some Lecture Notes and In-Class Examples for Pre-Calculus: Section.7 Definition of a Quadratic Inequality A quadratic inequality is any inequality that can be put in one of the forms ax + bx + c < 0 ax
More informationPolynomial Operations and Factoring
Algebra 1, Quarter 4, Unit 4.1 Polynomial Operations and Factoring Overview Number of instructional days: 15 (1 day = 45 60 minutes) Content to be learned Identify terms, coefficients, and degree of polynomials.
More informationMATH 60 NOTEBOOK CERTIFICATIONS
MATH 60 NOTEBOOK CERTIFICATIONS Chapter #1: Integers and Real Numbers 1.1a 1.1b 1.2 1.3 1.4 1.8 Chapter #2: Algebraic Expressions, Linear Equations, and Applications 2.1a 2.1b 2.1c 2.2 2.3a 2.3b 2.4 2.5
More informationDRAFT. Algebra 1 EOC Item Specifications
DRAFT Algebra 1 EOC Item Specifications The draft Florida Standards Assessment (FSA) Test Item Specifications (Specifications) are based upon the Florida Standards and the Florida Course Descriptions as
More information1.1 Practice Worksheet
Math 1 MPS Instructor: Cheryl Jaeger Balm 1 1.1 Practice Worksheet 1. Write each English phrase as a mathematical expression. (a) Three less than twice a number (b) Four more than half of a number (c)
More informationCENTRAL COLLEGE Department of Mathematics COURSE SYLLABUS
CENTRAL COLLEGE Department of Mathematics COURSE SYLLABUS MATH 1314: College Algebra Fall 2010 / Tues-Thurs 7:30-9:00 pm / Gay Hall Rm 151 / CRN: 47664 INSTRUCTOR: CONFERENCE TIMES: CONTACT INFORMATION:
More informationNorth Carolina Math 2
Standards for Mathematical Practice 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4.
More informationLAKE ELSINORE UNIFIED SCHOOL DISTRICT
LAKE ELSINORE UNIFIED SCHOOL DISTRICT Title: PLATO Algebra 1-Semester 2 Grade Level: 10-12 Department: Mathematics Credit: 5 Prerequisite: Letter grade of F and/or N/C in Algebra 1, Semester 2 Course Description:
More informationList the elements of the given set that are natural numbers, integers, rational numbers, and irrational numbers. (Enter your answers as commaseparated
MATH 142 Review #1 (4717995) Question 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Description This is the review for Exam #1. Please work as many problems as possible
More informationDefinition 8.1 Two inequalities are equivalent if they have the same solution set. Add or Subtract the same value on both sides of the inequality.
8 Inequalities Concepts: Equivalent Inequalities Linear and Nonlinear Inequalities Absolute Value Inequalities (Sections 4.6 and 1.1) 8.1 Equivalent Inequalities Definition 8.1 Two inequalities are equivalent
More informationCOWLEY COUNTY COMMUNITY COLLEGE REVIEW GUIDE Compass Algebra Level 2
COWLEY COUNTY COMMUNITY COLLEGE REVIEW GUIDE Compass Algebra Level This study guide is for students trying to test into College Algebra. There are three levels of math study guides. 1. If x and y 1, what
More informationCOMPETENCY TEST SAMPLE TEST. A scientific, non-graphing calculator is required for this test. C = pd or. A = pr 2. A = 1 2 bh
BASIC MATHEMATICS COMPETENCY TEST SAMPLE TEST 2004 A scientific, non-graphing calculator is required for this test. The following formulas may be used on this test: Circumference of a circle: C = pd or
More informationReview of Fundamental Mathematics
Review of Fundamental Mathematics As explained in the Preface and in Chapter 1 of your textbook, managerial economics applies microeconomic theory to business decision making. The decision-making tools
More informationPrentice Hall Algebra 2 2011 Correlated to: Colorado P-12 Academic Standards for High School Mathematics, Adopted 12/2009
Content Area: Mathematics Grade Level Expectations: High School Standard: Number Sense, Properties, and Operations Understand the structure and properties of our number system. At their most basic level
More informationPOLYNOMIAL FUNCTIONS
POLYNOMIAL FUNCTIONS Polynomial Division.. 314 The Rational Zero Test.....317 Descarte s Rule of Signs... 319 The Remainder Theorem.....31 Finding all Zeros of a Polynomial Function.......33 Writing a
More informationPearson Algebra 1 Common Core 2015
A Correlation of Pearson Algebra 1 Common Core 2015 To the Common Core State Standards for Mathematics Traditional Pathways, Algebra 1 High School Copyright 2015 Pearson Education, Inc. or its affiliate(s).
More informationFlorida Math for College Readiness
Core Florida Math for College Readiness Florida Math for College Readiness provides a fourth-year math curriculum focused on developing the mastery of skills identified as critical to postsecondary readiness
More informationGraphic Designing with Transformed Functions
Math Objectives Students will be able to identify a restricted domain interval and use function translations and dilations to choose and position a portion of the graph accurately in the plane to match
More informationWORKBOOK. MATH 30. PRE-CALCULUS MATHEMATICS.
WORKBOOK. MATH 30. PRE-CALCULUS MATHEMATICS. DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE Contributor: U.N.Iyer Department of Mathematics and Computer Science, CP 315, Bronx Community College, University
More informationManhattan Center for Science and Math High School Mathematics Department Curriculum
Content/Discipline Algebra 1 Semester 2: Marking Period 1 - Unit 8 Polynomials and Factoring Topic and Essential Question How do perform operations on polynomial functions How to factor different types
More informationMATH. ALGEBRA I HONORS 9 th Grade 12003200 ALGEBRA I HONORS
* Students who scored a Level 3 or above on the Florida Assessment Test Math Florida Standards (FSA-MAFS) are strongly encouraged to make Advanced Placement and/or dual enrollment courses their first choices
More informationFlorida Math 0028. Correlation of the ALEKS course Florida Math 0028 to the Florida Mathematics Competencies - Upper
Florida Math 0028 Correlation of the ALEKS course Florida Math 0028 to the Florida Mathematics Competencies - Upper Exponents & Polynomials MDECU1: Applies the order of operations to evaluate algebraic
More informationFunctions Modeling Change: A Precalculus Course. Marcel B. Finan Arkansas Tech University c All Rights Reserved
Functions Modeling Change: A Precalculus Course Marcel B. Finan Arkansas Tech University c All Rights Reserved 1 PREFACE This supplement consists of my lectures of a freshmen-level mathematics class offered
More informationPrecalculus REVERSE CORRELATION. Content Expectations for. Precalculus. Michigan CONTENT EXPECTATIONS FOR PRECALCULUS CHAPTER/LESSON TITLES
Content Expectations for Precalculus Michigan Precalculus 2011 REVERSE CORRELATION CHAPTER/LESSON TITLES Chapter 0 Preparing for Precalculus 0-1 Sets There are no state-mandated Precalculus 0-2 Operations
More informationLecture 3 : The Natural Exponential Function: f(x) = exp(x) = e x. y = exp(x) if and only if x = ln(y)
Lecture 3 : The Natural Exponential Function: f(x) = exp(x) = Last day, we saw that the function f(x) = ln x is one-to-one, with domain (, ) and range (, ). We can conclude that f(x) has an inverse function
More informationMath 0980 Chapter Objectives. Chapter 1: Introduction to Algebra: The Integers.
Math 0980 Chapter Objectives Chapter 1: Introduction to Algebra: The Integers. 1. Identify the place value of a digit. 2. Write a number in words or digits. 3. Write positive and negative numbers used
More informationALGEBRA 2 Functions/Relations/Polynomial Operations 1A, 1B, 1C, 1D, 1E, 1F, 1G,2D, 7I, 7B, 7C
Unit 1 Unit 2 1) Domain/Range - Multiple Representations Interval Notation/Set Notation/Inequalities 2) Function notation, composite functions 3) Operations with Functions - Incude add/sub/multiply polynomials,
More informationAnswer Key for California State Standards: Algebra I
Algebra I: Symbolic reasoning and calculations with symbols are central in algebra. Through the study of algebra, a student develops an understanding of the symbolic language of mathematics and the sciences.
More information