Practice Makes Perfect Algebra - Carolyn Wheater [1]
Mixture problems: coffee, coins, cars, and chemicals
3 Linear inequalities
Simple inequalities
Compound inequalities
Absolute value inequalities
4 Coordinate graphing
The coordinate plane
Distance
Midpoints
Slope and rate of change
Graphing linear equations
Vertical and horizontal lines
Graphing linear inequalities
Graphing absolute value equations
Writing linear equations
Parallel and perpendicular lines
5 Systems of linear equations and inequalities
Graphing systems of equations
Graphing systems of inequalities
Solving systems of equations by substitution
Solving systems of equations by combination
Combinations with multiplication
Dependent and inconsistent systems
6 Powers and polynomials
Rules for exponents
More rules
Monomials and polynomials
Adding and subtracting polynomials
Multiplying polynomials
Dividing polynomials
7 Factoring
Greatest common monomial factor
Factoring x2 + bx + c
Factoring ax2 + bx + c
Special factoring patterns
8 Radicals
Simplifying radical expressions
Adding and subtracting radicals
Solving radical equations
Graphing square root equations
9 Quadratic equations and their graphs
Solving by square roots
Completing the square
The quadratic formula
Solving by factoring
Graphing quadratic functions
10 Proportion and variation
Using ratios and extended ratios
Solving proportions
Variation
Joint and combined variation
11 Rational equations and their graphs
Simplifying rational expressions
Multiplying rational expressions
Dividing rational expressions
Adding and subtracting rational expressions
Complex fractions
Solving rational equations
Graphing rational functions
Work problems
12 Exponential growth and decay
Compound interest
Exponential growth and decay
Graphing the exponential functions
13 Matrix algebra
Rows and columns
Addition and subtraction
Scalar multiplication
Matrix multiplication
Determinants
Inverses
Solving systems with matrices
Answers
Introduction
An old joke tells of a tourist, lost in New York City, who stops a passerby to ask, “How do I get to Carnegie Hall?” The New Yorker’s answer comes back quickly: “Practice, practice, practice!” The joke may be lame, but it contains a truth. No musician performs on the stage of a renowned concert hall without years of daily and diligent practice. No dancer steps out on stage without hours in the rehearsal hall, and no athlete takes to the field or the court without investing time and sweat drilling on the skills of his or her sport.
Math has a lot in common with music, dance, and sports. There are skills to be learned and a sequence of activities you need to go through if you want to be good at it. You don’t just read math, or just listen to math, or even just understand math. You do math, and to learn to do it well, you have to practice. That’s why homework exists, but most people need more practice than homework provides. That’s where Practice Makes Perfect Algebra comes in.
When you start your formal study of algebra, you take your first step into the world of advanced mathematics. One of your principal tasks is to build the repertoire of tools that you will use in all future math courses and many other courses as well. To do that, you first need to understand each tool and how to use it, and then how to use the various tools in your toolbox in combination.
The almost 1000 exercises in this book are designed to help you acquire the skills you need, practice each one individually until you have confidence in it, and then combine various skills to solve more complicated problems. Since it’s also important to keep your tools in good condition, you can use Practice Makes Perfect Algebra to review. Reminding yourself of the tools in your toolbox and how to use them helps prepare you to face new tasks that require you to combine those tools in new ways.
With patience and practice, you’ll find that you’ve assembled an impressive set of tools