Loyola University Chicago

Mathematics and Statistics

MATH 100: Intermediate Algebra

Course Details
Credit Hours: 3
Prerequisites: None
Description:  Fundamentals of algebra. Graphs of linear equations, polynomials and factoring, first and second-degree equations and inequalities, radicals and exponents, and systems of equations. Word problems emphasized throughout the course.

McCallum, Connally, Hughes-Hallett et al. Algebra: Form and Function. 2nd edition. (with WileyPlus ebook)

Instructions for students to obtain the e-book and to use WileyPlus: Use your Loyola email address to create a WileyPlus account. Your professor will include details on WileyPlus in the syllabus.

Chapter 1: Functions and Algebraic Structure
   1.1  What Is A Function?
   1.2  Functions and Expressions
   1.3  Functions and Equations
   1.4  Functions and Change
   1.5  Functions, Modeling, and Proportionality

Chapter 2: Linear Functions
   2.1  Introduction to Linear Functions
   2.2  Linear Expressions
   2.3  Linear Equations
   2.4  Equations for Lines in The Plane
   2.5  Modeling with Linear Functions
   2.6  Systems of Linear Equations

Chapter 3: Quadratic Functions
   3.1  Introduction to Quadratic Functions
   3.2  Quadratic Expressions
   3.3  Converting to Factored and Vertex Form
   3.4  Quadratic Equations
   3.5  Factoring Hidden Quadratics

Chapter 4: Power Functions
   4.1  Power Functions: Positive Exponents
   4.2  Power Functions: Negative Exponents
   4.3  Power Functions and Expressions
   4.4  Power Functions and Equations
   4.5  Modeling with Power Functions

Chapter 5: More on Functions
   5.1  Domain and Range
   5.2  Composing and Decomposing Functions
   5.3  Shifting and Scaling
   5.4  Inverse Functions

Appendix A: Expressions  

A.1 Reordering and Regrouping
   1-2, 7, 8, 10, 12, 13, 15, 18, 22, 24, 26, 30, 32

A.2 The Distributive Law 
   3, 4, 7, 14, 18, 19, 24, 30, 38, 39, 41, 45, 51, 57, 59

Appendix B: Equations

B.1 Using the Operations of Arithmetic to Solve Equations

   5, 20, 26, 36, 41, 48, 54

Appendix C: Inequalities

C.1 Solving Inequalities

   5, 9, 18, 31, 37, 40, 42

Chapter 1: Functions and Algebraic Structure

1.1 What Is A Function?

   1, 3, 9, 11, 12, 18, 21, 25, 26, 28, 30, 39, 44, 47

1.2 Functions and Expressions

   1-2, 6-7, 17, 18, 28, 29, 30, 38, 42, 45, 47, 51

1.3  Functions and Equations

   15, 16, 19, 21, 22, 25, 27, 28, 30, 41, 48, 52, 58, 64

1.4  Functions and Change

   1-2, 3-4, 5, 6, 9, 15, 18, 22, 24, 26, 31

1.5  Functions, Modeling, and Proportionality

   1, 8, 10, 12, 17, 18, 20, 23, 25, 27, 36, 41, 49

Chapter 2: Linear Functions

2.1  Introduction to Linear Functions

   15, 18, 27, 30, 37, 40, 42, 47, 50

2.2  Linear Expressions

   5, 15, 18, 26, 28, 38, 46, 49, 51, 54, 59, 63, 84

2.3  Linear Equations

   1, 8, 10, 11, 30, 33, 47, 51, 74

2.4  Equations for Lines in The Plane

   2, 13, 18, 24, 39, 45, 53, 56, 61, 62, 70

2.5  Modeling with Linear Functions

   2, 5, 8, 15, 20, 23, 26

2.6  Systems of Linear Equations

   4, 9, 18, 21, 23, 32, 41, 46, 59, 61

Appendix D: Quadratics

D.1 Quadratic Expressions

   3, 9, 18, 23, 28, 32, 35, 37, 44, 46, 50, 56

D.2 Solving Quadratic Equations

   4, 6, 9, 12, 13, 15, 16

Chapter 3: Quadratic Functions

3.1  Introduction to Quadratic Functions

   2, 6, 7, 12, 13, 23, 25, 27

3.2  Quadratic Expressions

   1, 6, 9, 13, 15, 17, 18, 20, 21, 22, 25, 27, 30, 38, 41, 45, 58 

3.3  Converting to Factored and Vertex Form

   4, 8, 13, 17, 19, 26, 27, 34, 36, 37, 39, 42, 43, 45

3.4  Quadratic Equations

   3, 11, 13, 14, 18, 23, 25, 29, 35, 36, 38, 44, 46, 52, 57, 58, 60, 62, 69, 71, 75

3.5  Factoring Hidden Quadratics

   8, 14, 16, 20, 21, 26, 31, 34, 38, 40, 46

Appendix G: Exponents

G.1 Exponents with Integer Powers

   2, 5, 16, 17, 23, 26, 30, 32, 37, 42, 50, 58, 60, 61, 68, 75, 80, 88, 105

G.2 Exponents with Fractional Powers

   3, 6, 8, 13, 14, 17, 18, 23, 24, 34, 37

Chapter 4: Power Functions

4.1  Power Functions: Positive Exponents

   1, 6, 12, 15, 17, 23, 26, 28

4.2  Power Functions: Negative Exponents

   1, 7, 11, 13, 14, 16, 20, 24, 26, 27

4.3  Power Functions and Expressions

   3, 5, 8, 10, 13, 19, 25, 26, 31, 36, 37, 42, 48, 50, 54, 56, 61, 64

4.4  Power Functions and Equations

   3, 9, 11, 12, 17, 20, 22, 26, 28, 34, 41, 45, 49, 55, 62

4.5  Modeling with Power Functions

   2, 6, 10, 14, 15, 16, 19, 22, 25, 33, 35

Chapter 5: More on Functions

5.1  Domain and Range

   14, 15, 17, 24, 26, 29, 38, 41, 44, 59, 61, 62, 63, 65

5.2  Composing and Decomposing Functions

   1, 2, 5, 9, 10, 12, 13, 16, 17, 20, 21, 26, 34, 38, 41

5.3  Shifting and Scaling

   1, 3, 6, 9, 12, 14, 15, 17, 18, 21, 25, 27, 36, 42, 45

5.4  Inverse Functions

   1, 2, 3, 4, 6, 8, 10, 13, 15, 18, 23, 24, 25, 27, 30

See Course Page for additional resources.