Contents

Introduction

1   Functions: An introduction

Relations and inverses

Functions

Function notation

Arithmetic of functions

Transformation of functions

Inverse of a function

Graphical representation of functions

2   Linear equations and inequalities

Simple linear equations

Linear inequalities

System of linear equations—graphical

System of linear equations—substitution

System of linear equations—elimination

System of linear equations—three variables

System of linear equations—matrix

System of linear equations—application

System of linear inequalities

Absolute value equations

Absolute value inequalities

3   Quadratic relationships

The parabola

Special factoring formulas

Trial and error

Completing the square

Quadratic formula

Applications

Square root function

Circles

Ellipses

Hyperbolas

Systems of equations

4   Complex numbers

Powers of i

Arithmetic of complex numbers

The discriminant and nature of the roots of a quadratic equation

Sum and product of roots of a quadratic equation

5   Polynomial functions

Even and odd functions

Inverse functions

End behavior

Factor theorem

6   Rational and irrational functions

Rational functions

Multiplying and dividing rational expressions

Adding and subtracting rational expressions

Solving rational equations

Irrational functions

Simplifying irrational expressions

Solving irrational equations

7   Exponential and logarithmic functions

Properties of exponents

Exponential and logarithmic functions

Properties of logarithms

Solving exponential and logarithmic equations

8   Sequences and series

Summation notation

Recursion

Arithmetic sequences

Arithmetic series

Geometric sequences

Geometric series

9   Introduction to probability

Fundamental theorem of counting

Permutations

Combinations

Binomial expansions

Conditional probability

Binomial probability/Bernoulli trial

10   Introduction to statistics

Measures of central tendency

Measures of dispersion

Normal distribution

Regressions

11   Inferential statistics

Basics

Central limit theorem and standard error

Standardized (z) scores

The basics of inferential statistics

Confidence intervals

Tests of hypotheses

Simulation

12   Trigonometry: Right triangles and radian measure

Right triangle trigonometry

Special right triangles

The unit circle: First quadrant

The unit circle—beyond the first quadrant

Radian measure

Basic trigonometric identities

Area of a triangle

Law of sines

Ambiguous case

Law of cosines

13   Graphs of trigonometric functions

Amplitude and period

Graphing trigonometric functions

Inverse trigonometric functions

Solving trigonometric equations

Answer key