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!

Below is the table of contents.

College Algebra Plus Integrated Review

Chapter 1.R: Integrated Review
1.R.1 Exponents, Prime Numbers, and LCM
1.R.2 Reducing Fractions
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 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 Solving Equations: Ratios and 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 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 4.R: Integrated Review
4.R.1 Order of Operations
4.R.2 Variables and Algebraic Expressions
4.R.3 Simplifying Expressions
4.R.4 Translating Phrases into 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 5.R: Integrated Review
5.R.1 Greatest Common Factor of Two or More Terms
5.R.2 Factoring Trinomials by Grouping
5.R.3 Additional Factoring Practice
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 6.R: Integrated Review
6.R.1 Defining Rational Expressions
6.R.2 Special Products
6.R.3 Special Factorizations – Squares
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 7.R: Integrated Review
7.R.1 Simplifying Integer Exponents I
7.R.2 Simplifying Integer Exponents II
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 8.R: Integrated Review
8.R.1 Solving Systems of Linear Equations 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 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 A: 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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