An InteGREATed Course for College Algebra

Here at Hawkes Learning, we’re excited about developing our new course offering, College Algebra Plus Integrated Review! Target specific remediation needs for just-in-time supplementation of foundational concepts in college algebra with these materials.

This new integrated course enhances curriculum-level math with applicable review skills to shorten the prerequisite sequence without compromising competency. If you teach a college algebra corequisite course, these materials are for you!

Table of Contents:

Chapter 0: Strategies for Academic Success

0.1 How to Read a Math Textbook
0.2 Tips for Success in a Math Course
0.3 Tips for Improving Math Test Scores
0.4 Practice, Patience, and Persistence!
0.5 Note Taking
0.6 Do I Need a Math Tutor?
0.7 Tips for Improving Your Memory
0.8 Overcoming Anxiety
0.9 Online Resources
0.10 Preparing for a Final Math Exam
0.11 Managing Your Time Effectively

Chapter 1.R: Integrated Review

1.R.1 Exponents, Prime Numbers, and LCM
1.R.2 Reducing Fraction to Lowest Terms
1.R.3 Decimals and Percents
1.R.4 Simplifying Radicals

Chapter 1: Number Systems and Fundamental Concepts of Algebra

1.1 The Real Number System
1.2 The Arithmetic of Algebraic Expressions
1.3a Properties of Exponents
1.3b Scientific Notation and Geometric Problems Using Exponents
1.4a Properties of Radicals
1.4b Rational Number Exponents
1.5 Polynomials and Factoring
1.6 The Complex Number System
Chapter 1 Review Chapter 1 Review

Chapter 2.R: Integrated Review

2.R.1 Multiplication and Division with Fractions
2.R.2 Addition and Subtraction with Fractions
2.R.3 Applications: Number Problems and Consecutive Integers
2.R.4 Proportions

Chapter 2: Equations and Inequalities of One Variable

2.1a Linear Equations in One Variable
2.1b Applications of Linear Equations in One Variable
2.2 Linear Inequalities in One Variable
2.3 Quadratic Equations in One Variable
2.4 Higher Degree Polynomial Equations
2.5 Rational Expressions and Equations
2.6 Radical Equations
Chapter 2 Review Chapter 2 Review

Chapter 3: Linear Equations and Inequalities of Two Variables

3.1 The Cartesian Coordinate System
3.2 Linear Equations in Two Variables
3.3 Forms of Linear Equations
3.4 Parallel and Perpendicular Lines
3.5 Linear Inequalities in Two Variables
3.6 Introduction to Circles
Chapter 3 Review Chapter 3 Review

Chapter 4.R: Integrated Review

4.R.1 Order of Operations with Real Numbers
4.R.2 Identifying Like Terms
4.R.3 Simplifying Expressions
4.R.4 Translating English Phrases and Algebraic Expressions

Chapter 4: Relations, Functions, and Their Graphs

4.1 Relations and Functions
4.2a Linear and Quadratic Functions
4.2b Max/Min Applications of Quadratic Functions
4.3a Other Common Functions
4.3b Direct and Inverse Variation
4.4 Transformations of Functions
4.5 Combining Functions
4.6 Inverses of Functions
Chapter 4 Review Chapter 4 Review

Chapter 5.R: Integrated Review

5.R.1 Greatest Common Factor (GCF) of a Set of Terms
5.R.2 Factoring Trinomials by Grouping
5.R.3 Review of Factoring Techniques

Chapter 5: Polynomial Functions

5.1 Introduction to Polynomial Equations and Graphs
5.2 Polynomial Division and the Division Algorithm
5.3 Locating Real Zeros of Polynomials
5.4 The Fundamental Theorem of Algebra
Chapter 5 Review Chapter 5 Review

Chapter 6.R: Integrated Review

6.R.1 Introduction to Rational Expressions
6.R.2 Special Products of Binomials
6.R.3 Special Factoring Techniques

Chapter 6: Rational Functions and Conic Sections

6.1a Rational Functions
6.1b Rational Inequalities
6.2 The Ellipse
6.3 The Parabola
6.4 The Hyperbola
Chapter 6 Review Chapter 6 Review

Chapter 7.R: Integrated Review

7.R.1 Rules for Exponents
7.R.2 Power Rules for Exponents
7.R.3 Rational Exponents

Chapter 7: Exponential and Logarithmic Functions

7.1 Exponential Functions and Their Graphs
7.2 Applications of Exponential Functions
7.3 Logarithmic Functions and Their Graphs
7.4 Properties and Applications of Logarithms
7.5 Exponential and Logarithmic Equations
Chapter 7 Review Chapter 7 Review

Chapter 8.R: Integrated Review

8.R.1 Systems of Linear Equations: Solutions by Graphing
8.R.2 Systems of Linear Inequalities

Chapter 8: Systems of Equations

8.1 Solving Systems by Substitution and Elimination
8.2 Matrix Notation and Gaussian Elimination
8.3 Determinants and Cramer’s Rule
8.4 The Algebra of Matrices
8.5 Inverses of Matrices
8.6 Linear Programming
8.7 Nonlinear Systems of Equations
Chapter 8 Review Chapter 8 Review

Chapter 9: An Introduction to Sequences, Series, Combinatorics, and Probability

9.1 Sequences and Series
9.2 Arithmetic Sequences and Series
9.3 Geometric Sequences and Series
9.4 Mathematical Induction
9.5a An Introduction to Combinatorics – Counting, Permutations, and Combinations
9.5b An Introduction to Combinatorics – The Binomial and Multinomial Theorems
9.6 An Introduction to Probability
Chapter 9 Review Chapter 9 Review

Appendix

A.1 Introduction to Polynomial Equations and Graphs (excluding complex numbers)
A.2 Polynomial Division and the Division Algorithm (excluding complex numbers)
A.3 Locating Real Zeros of Polynomials (excluding complex numbers)
A.4 The Fundamental Theorem of Algebra (excluding complex numbers)

 

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