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   "Now, what DID Mr. Runyan say . . ?"

Select Chapter 1 - 9

Ch 1
Ch 2
Ch 3
Ch 4
Ch 5
Ch 6
Ch 7
Ch 8
Ch 9


Chapter 1 Functions

Section 1.1 Functions and Their Properties

Section 1.2 Functional Notation and Mathematical Language

Section 1.3 Translations and Reflections of Graphs of Functions

Section 1.4 Changes of Scale of Graphs of Functions

Section 1.5 Operations, Compositions, and Inverse Functions

Chapter 2 Linear and Quadratic Functions

Section 2.1 Linear Functions

Section 2.2 Linear Regression

Section 2.3 Graphs of Quadratic Functions and Optimization

Section 2.4 Finding Equations of Quadratic Functions

Chapter 3 Polynomial and Rational Functions

Section 3.1 Graphs of Polynomial Functions

Section 3.2 Finite Differences

Section 3.3 Interpolating and Best-Fitting Polynomial Functions

Section 3.4 Graphs of Rational Functions

Section 3.5 More Rational Functions: Limit Notation, Holes, and Oblique Asymptotes

Chapter 4 Exponential and Logarithmic Functions

Section 4.1 Exponential Functions

Section 4.2 Logarithmic Functions

Section 4.3 Theorems on Logarithms

Section 4.4 More on Exponential and Logarithmic Functions

Section 4.5 More Applications Including Logistic Equations

Section 4.6 Logarithmic Scales and Curve Fitting

Chapter 5 Trigonometry and The Circular Functions


Section 5.1 Right Triangle Trigonometry

Section 5.2 The Circular Functions

Section 5.3 Graphs of the Circular Functions

Section 5.4 Reciprocals, Sums, and Products of the Circular Functions

Section 5.5 Inverses of the Circular Functions

Chapter 6 Trigonometric Equations and Applications


Section 6.1 Trigonometric Identities

Section 6.2 More Trigonometric Identities

Section 6.3 Equations Involving the Circular Functions

Section 6.4 Applications of the Circular Functions to Triangles

Section 6.5 More Applications: Simple Harmonic Motion and Vectors

Chapter 7 Polar Coordinates and Parametric Equations


Section 7.1 Introduction to Polar Coordinates

Section 7.2 Polar Form of Complex Numbers and DeMoivre's Theorem

Section 7.3 Parametrc Equations

Chapter 8 Conic Sections and Quadric Surfaces


Section 8.1 The Distance Formula and the Circle

Section 8.2 The Ellipse and the Hyperbola

Section 8.3 The Parabola and a Review of Conic Sections

Section 8.4 Rotations and Conic Sections

Section 8.5 Graphs in a Three-Dimensional Coordinate System

Section 8.6 Quadric Surfaces

Chapter 9 Matrices, Determinants, and Vectors

Section 9.1 Introduction to Matrices

Section 9.2 Introduction to Determinants

Section 9.3 Vectors in Two and Three Dimensions

Section 9.4 Equations of Lines and Planes in Three Dimensions


 



Select Chapter 1 - 5

Ch 1
Ch 2
Ch 3
Ch 4
Ch 5


Chapter 1 Functions

Section 1.1 Functions and Their Properties

Section 1.4 Changes of Scale of Graphs of Functions

Section 1.5 Operations, Compositions, and Inverse Functions

Chapter 2 Linear and Quadratic Functions

Section 2.1 Linear Functions

Section 2.2 Linear Regression

Section 2.3 Graphs of Quadratic Functions and Optimization

Section 2.4 Finding Equations of Quadratic Functions

    Chapter 3 Polynomial and Rational Functions

    Section 3.1 Graphs of Polynomial Functions

    Form A

    Form A contains problems that are analogous to selected examples from Precalculus: Making Connections. The answer to each problem and the reference to the appropriate example are given. This form is designed as a personal diagnostic tool. Studying the corresponding example for any problems you miss will help you master the material for that chapter.

    Form B

    Form B contains problems that cover the material in each chapter, but the directions, context and applications may differ from those found elswhere on the web site or in the text.

    Form C

    Form C contains forms that can be completed on-line and submitted to your instructor if your course is designed to use them. Answers are not provided.

    Select Chapter 1 - 9

    Ch 1
    Ch 2
    Ch 3
    Ch 4
    Ch 5
    Ch 6
    Ch 7
    Ch 8
    Ch 9


    Chapter 1 Functions

    Chapter 2 Linear and Quadratic Functions

    Chapter 3 Polynomial and Rational Functions

    Chapter 4 Exponential and Logarithmic Functions

    Chapter 5 Trigonometry and the Circular Functions

    Chapter 6 Trigonometric Equations and Applications

    Chapter 7 Polar Coordinates and Parametric Equations

    Chapter 8 Conic Sections and Quadric Surfaces

    Chapter 9 Matrices, Determinants, and Vectors


    All of these exams, as with all of the material at this Precalculus web site, are copyrighted. The material is presented here for your personal use.

    Tom Duran & Craig Lykins

    Select Chapter 1 - 9

    Ch 1
    Ch 2
    Ch 3
    Ch 4
    Ch 5
    Ch 6
    Ch 7
    Ch 8
    Ch 9

    The links below present opportunities to explore the concepts from Precalculus using information that is available from World Wide Web sites, with data that is up to date. Here you will see Precalculus in Action!

    Chapter 1 Functions


    Chapter 2 Linear and Quadratic Functions

    Chapter 3 Polynomial and Rational Functions


    Chapter 4 Exponential and Logarithmic Functions

    Chapter 5 Trigonometry and the Circular Functions


    Chapter 6 Trigonometric Equations and Applications

    Chapter 7 Polar Coordinates and Parametric Equations


    Chapter 8 Conic Sections and Quadratic Surfaces

    Chapter 9 Matrices, Determinants, and Vectors

     

     

    Date Homework

    Section

    Topics

    1

    1/10  

    P.5

    Syllabus, Policy Statement, the Cartesian Plane

    2

     

    1/12 p. 82
    # 1-69 eoo
    p. 94
    # 11-43 eoo

    1.1

    1.2 (read)

    Graphs of Equations; graphs of equations

    (Lines in the plane)

    3

    1/14 p. 107
    # 1-67 eoo

    1.3

    Functions; functions; piecewisefunctions;

    4

    1/19 p. 121
    # 1-71 eoo

    1.4

    Graphs of Functions; increasing&decreasing; even&odd;

    5 1/21   1.4 (cont'd)  

    6

    1/24 p. 131
    #1-69 eoo

    1.5

    Shifting, Reflecting and Stretching Graphs; shifting graphs;

    7

    1/26 p. 141
    #1-79 eoo

    1.6

    Combinations of Functions; operations on functions

    8

    1/28 p. 152
    #1-83 eoo

    1.7

    Inverse Functions; inverse functions

    9

    2/1 p. 160
    Chapter Test

    Review
    Practice Test

    P.5 and Chapter 1
    AnswerKey

    10

    2/2  

    TEST 1

     

    11

    2/4 p. 32
    #1-149e-o-o
    157,159

    P.3

    Polynomials and Factoring
    FactoringPolynomials

    12

    2/7 p. 168
    #1-43e-o-o

    2.1(read)

    Linear Equations and Problem Solving
    EquationsOfLines

    13

    2/9 p. 179
    #1-49e-o-o
    53,67,69,73,75

    2.2

    Solving Equations Graphically

    14

    2/11 p. 189
    #1-71e-o-o
    79,80

    2.3

    Complex Numbers
    ComplexNumbers

    15

    2/14 p. 205
    #1-107e-o-o

    2.4

    Solving Equations Algebraically
    QuadraticFormEquations; RadicalEquations

    16

    2/16 p. 219
    #1-63 e-o-o

    2.5

    Solving Inequalities Algebraically and Graphically
    InequalitiesPolynomial&Rational

    17

    skip p. 227
    #1-11 odd

    2.6

    Linear Models
    data analysis

    18

    2/18 p. 32
    #37-67e-o-o
    119-149e-o-o
    p. 236
    #1-23

    Review

    P.3 and Chapter 2
    P3 review; chp2 review

    19

    2/23  

    TEST 2

     

    20

    2/25 p. 247
    #1-65 e-o-o

    3.1

    Quadratic Functions
    quadratic functions

    21

    2/28 p. 260
    #1-83 e-o-o

    3.2

    Polynomials of Higher Degree
    polynomial functions

    22

    3/2 p. 275
    # 1-23, 31-55 e-o-o

    3.3

    Real Zeros of Polynomial Functions
    real zeros of functions

    23

    3/4 p. 284
    #1-57 e-o-o

    3.4

    The Fundamental Theorem of Algebra
    complex zeros

    24

    3/7 p. 44
    #1-69 e-o-o

    P.4

    Rational Expressions

    25

    3/9 p. 292
    #1-35, 39 odd

    3.5

    Rational Functions and  Asymptotes
    rational functions

    26

    3/11 p. 301
    #1-63, 69
    e-o-o

    3.6

    Graphs of Rational Functions
    rational functions graphs

    27

    3/18  

    3.7

    Quadratic Models

    28

    3/14 p. 313
    #1-27, 33-59, 65-115 e-o-o

    Review

    P.4 and Chapter 3

    29

    3/16 p. 318
    #1-16

    TEST 3

     

    30

    3/28 p. 329 #1-69eoo

    4.1

    Exponential Functions and Their Graphs

    exponential functions

    31

    3/30 p. 339 #1-33odd

    4.2

    Logarithmic Functions and Their Graphs

    logarithmic functions

    32 4/1 p. 378 #1,9,11,15,19 4.6 Models (linear, quadratic, logarithmic, and exponential)
    http://www.prenhall.com/divisions/esm/app/calc_v2/
     
    33 4/4 p.339 #35-75eoo 4.2 (cont'd) Logarithmic Functions and their Graphs, cont'd

    34

    4/6 p. 347 #1-79eoo

    4.3

    Properties of Logarithms

    35

    4/8 p.357 #1-93eoo 97,103,
    111

    4.4

    Solving Exponential and Logarithmic Equations

    36

    4/11 p.368 #1-6, 15, 23, 29, 35, 39, 41,43

    4.5

    Exponential and Logarithmic Models

    37

    4/13 p. 388 #1-22

    Review

    Chapter 4

    38

    4/15  

    TEST 4

     

    39

    4/18 p.599 #1,5,9,63-77odd
    p. 610 #45-51, 61-67odd

    8.1, 8.2

    Solving Systems of Equations

    40

    4/20 p.639 #1-13,23-27,31-37,73,75,79
    p.654 #1-41odd

    8.4, 8.5

    Matrices and Systems of Equations
    Operations with Matrices

    41

    4/22 p.665 #1-61odd

    8.6, 8.7

    The Inverse of a Square Matrix
    The Determinants of a Square Matrix

    42

    4/25 p.684 #1-33

    8.8

    Solving Systems of Equations with Matrices
    Applications of Matrices and Determinants

    43

    4/27 p.694 #1-17odd

    Review

    Chapter 8

    44

    4/30  

    TEST 5

     

    45

    5/2 p.389 #1-43

    Review

    Review for final exam

     

    5/4
    5/9
    section102
    section103

    FINAL EXAM

    COMPREHENSIVE FINAL EXAM

    Precalculus Pretest


    1. Solve the linear equation
    12 - 2(x - 14) = 6(x + 5)

    2. Solve the pair of linear equations

    4x + 3y = 4
    5x - 7y = -38

    3. Solve the quadratic equation

    (3x - 12)2 = 144

    4. Solve the quadratic equation

    3x2 - 4x -1 = 0

    5. Solve the equation involving radicals

     


    6. Solve the equation involving rational expressions

     

    7. Find three linear inequalities that describe the shaded region below.

     

    8. Match each line with its equation. (Not all equations are used.)

     

    9. Match each parabola with its equation. (Not all equations are used.)

     

    10. You have $5000 in the bank and are saving $425/mo. Your friend has $8400 and is spending $275/mo. As soon as you have the same amount of cash, you are heading for Greece. How long before you leave?

    Answers


     

    Exploring Precalculus

    William Mueller



    Description of Materials


    0. What Is Precalculus?

    1. Functions and Their Changes

    2. Functions as Models

    3. Families of Functions

    4. Functions Defined by Data

    5. New Functions From Old

    6. Advanced Numbers & Functions


    The Number e (from 3.)


    Am I Ready for Calculus?

     

    Prerequisite Material

    A
    Absolute Value


    B
    Binomial Expressions


    C
    Complex Numbers


    D
    Dimensional Analysis

    E
    Exponential Expressions (Simplifying)
    Exponential Expressions (Combining)


    F
    Factoring Binomial Expressions
    Factoring Trinomial Expressions
    Factoring to Solve Quadratic Equations

    G

    H
    Binomial Expressions


    I
    Imaginary Nuumbers






    L
    Linear Equations (Solving)
    Linear Equations (Checking)
    Linear Equations (Solving Systems)
    Linear Inequalities (Solving)






    O
    Order of Operations





    Q
    Quadratic Equations (Factoring)
    Quadratic Equations (The Quadratic Formula)
    Quadratic Equations (Completing the Square)
    Quadratic Equations (Extracting Roots)
    Quadratic Inequalities


    R
    Radical Equations
    Rational Equations
    Rational Expressions


    S
    Solving Linear Equations
    Solving Systems of Linear Equations
    Solving Linear Inequalities
    Solving Quadratic Equations (Factoring)
    Solving Quadratic Equations (The Quadratic Formula)
    Solving Quadratic Equations (Completing the Square)
    Solving Quadratic Equations (Extracting Roots)
    Solving Quadratic Inequalities
    Solving Quadratic-in-Form Equations
    Solving Rational Equations
    Solving Radical Equations