# High School Books

## Theory & Problems for Foundations of Mathematics and Pre-Calculus 10

**TABLE OF CONTENTS **

** **

**Chapter 1 - Measuring Systems, Surface Area, and Volume **

1.1 Metric Systems

1.2 Imperial Systems

1.3 Converting Metric and Imperial Systems

1.4 Surface Area and Volume of Prisms

1.5 Surface Area and Volume of Pyramids

1.6 Surface Area and Volume of Cylinders, Cones, and Spheres

1.7 Chapter Review

**Chapter 2 - Radicals **

2.1 Number Systems

2.2 Greatest Common Factor and Least Common Multiple

2.3 Squares and Square Roots

2.4 Rational and Irrational Numbers

2.5 Simplifying Radicals

2.6 Exponential Notation

2.7 Chapter Review

**Chapter 3 - Polynomials **

3.1 Classifying Polynomials

3.2 Multiplying Polynomials

3.3 Removing Common Factors

3.4 Factoring x bx c 2 + +

3.5 Factoring ax bx c 2 + +

3.6 Special Factors

3.7 Chapter Review

**Chapter 4 - Relations and Functions **

4.1 Relations

4.2 Functions

4.3 Linear Equations

4.4 Non-Linear Equations

4.5 Graphing with a Calculator

4.6 Chapter Review

**Chapter 5 - Linear Functions **

5.1 Slope

5.2 Rate of Change

5.3 Graphing Linear Functions

5.4 Parallel and Perpendicular Lines

5.5 Applications of Linear Relations

5.6 Chapter Review

**Chapter 6 - Linear Equations **

6.1 Different Forms of Linear Equations

6.2 Special Cases of Linear Equations

6.3 Equations of Parallel and Perpendicular Lines

6.4 Linear Applications and Modelling

6.5 Function Notation

6.6 Chapter Review

**Chapter 7 - Solving Linear Systems **

7.1 Solving Linear Systems by Graphing

7.2 Solving Linear Systems by Addition

7.3 Solving Linear Systems by Substitution

7.4 Problem Solving with Two Variables

7.5 Chapter Review

**Chapter 8 – Trigonometry**

8.1 Sine, Cosine, and Tangent for Right Triangles

8.2 Relationships Between Sine, Cosine, and Tangent

8.3 Special Angles

8.4 Applications of Trigonometry

8.5 Compound Trigonometry Applications

8.6 Chapter Review

## Theory & Problems for Pre-Calculus 11

**TABLE OF CONTENTS **

**Chapter 1 - Absolute Value and Radicals **

1.1 Absolute Value

1.2 Radical Operations

1.3 Simplifying Radicals

1.4 Adding and Subtracting Radical Expressions

1.5 Multiplying and Dividing Radical Expressions

1.6 Radical Equations

1.7 Chapter Review

**Chapter 2 - Rational Expressions **

2.1 Properties of Rational Expressions

2.2 Multiplication and Division of Rational Expressions

2.3 Sums and Differences of Rational Expressions

2.4 Mixed Operations

2.5 Rational Equations

2.6 Applications of Rational Equations

2.7 Chapter Review

**Chapter 3 - Trigonometry **

3.1 Angles and Their Measure

3.2 The Three Trigonometric Functions

3.3 Special Angles

3.4 Oblique Triangles

3.5 Law of Sines

3.6 Law of Cosines

3.7 Chapter Review

**Chapter 4 - Factoring and Functions **

4.1 Factoring x bx c 2 + +

4.2 Factoring ax bx c 2 + +

4.3 Absolute Value Functions

4.4 Solving Absolute Value Equations

4.5 Rational Functions

4.6 Reciprocal Functions

4.7 Chapter Review

**Chapter 5 - Quadratic Functions **

5.1 Properties of Quadratic Functions

5.2 The Standard Form of a Quadratic Function

5.3 Finding the Equation of a Parabola

5.4 General Form to Standard Form

5.5 Vertex of a Parabola

5.6 Applications of Quadratic Functions

5.6 Chapter Review

**Chapter 6 - Quadratic Equations **

6.1 Solving Quadratic Equations by Factoring

6.2 Completing the Square and Square Root Property

6.3 The Quadratic Formula

6.4 Graphing Calculator and the Discriminant

6.5 Applications of Quadratic Equations

6.6 Chapter Review

**Chapter 7 - Systems of Equations **

7.1 Graphing Non-Linear Systems of Equations

7.2 Solving Non-Linear Systems Algebraically

7.3 Graphing Linear Inequalities

7.4 Graphing Non-Linear Inequalities in Two Variables

7.5 Chapter Review

**Chapter 8 - Sequence and Series **

8.1 Arithmetic Sequences

8.2 Arithmetic Series

8.3 Geometric Sequences

8.4 Geometric Series

8.5 Infinite Geometric Series

8.6 Chapter Review

## Theory & Problems for Pre-calculus 12

**TABLE OF CONTENTS **

**Chapter 1 – Transformations**

1.1 Functions and Relations

1.2 Arithmetic Combinations of Functions

1.3 Composite Functions

1.4 Transformations of Graphs

1.5 Inverse Functions

1.6 Combined Transformations

1.7 Chapter Review

**Chapter 2 - Polynomials **

2.1 Polynomials

2.2 Graphing Polynomial Functions

2.3 Division of Polynomials

2.4 The Remainder and Factor Theorems

2.5 Polynomial Applications

2.6 Chapter Review

**Chapter 3 - Radicals and Rational Functions **

3.1 Radicals

3.2 Graphing and Solving Radical Equations

3.3 Rational Functions

3.4 Graphing Rational Functions

3.5 Chapter Review

**Chapter 4 - Logarithms **

4.1 Exponents

4.2 Logarithmic Functions and Their Graphs

4.3 Properties of Logarithms

4.4 Exponential and Logarithmic Equations

4.5 Applications of Exponential and Logarithmic Equations

4.6 Chapter Review

**Chapter 5 - Trigonometry, Part I **

5.1 Angles and Their Measure

5.2 Trigonometric Functions of Acute Angles

5.3 Trigonometric Functions - General and Special Angles

5.4 Graphing Basic Trigonometric Functions

5.5 Applications of Periodic Functions

5.6 Chapter Review

**Chapter 6 - Trigonometry, Part II **

6.1 Trigonometric Identities and Equations

6.2 Verifying Trigonometric Identities

6.3 Trigonometric Equations

6.4 Sum and Difference Identities

6.5 Double Angle Identities

6.6 Chapter Review

**Chapter 7 - Combinatorics **

7.1 Fundamental Counting Principle

7.2 Permutations

7.3 Combinations

7.4 Binomial Theorem

7.5 Pathway Problems

7.6 Chapter Review

## Theory and Problems for Mathematics 8

**TABLE OF CONTENTS**

**Chapter 1 - Fractions **

1.1 Simplifying Fractions

1.2 Multiplying Fractions

1.3 Multiplying Mixed Fractions

1.4 Dividing Fractions

1.5 Dividing Mixed Fractions

1.6 Adding and Subtracting Fractions

1.7 Chapter Review

**Chapter 2 - Integers **

2.1 The Number Line

2.2 Multiplication of Integers

2.3 Division of Integers

2.4 Order of Operations

2.5 Chapter Review

**Chapter 3 - Geometry **

3.1 Three Dimensional Figures

3.2 Surface Area of Prisms

3.3 Volume of Prisms

3.4 Surface Area of a Cylinder

3.5 Volume of a Cylinder

3.6 Parallels and Transversals

3.7 Congruency and Similarity

3.8 Chapter Review

**Chapter 4 - Percents, Ratios, and Proportions **

4.1 Ratios, Rates, and Unit Rates

4.2 Proportions

4.3 Relating Percents, Decimals, and Fractions

4.4 Percent Problems

4.5 Compound Percent and Reasoning Problems

4.6 Chapter Review

**Chapter 5 - Linear Equations **

5.1 Algebraic Expressions

5.2 Addition and Subtraction of Polynomials

5.3 Addition and Subtraction Equations

5.4 Multiplication and Division Equations

5.5 Combined Operations

5.6 Linear Relations

5.7 Linear Models

5.8 Chapter Review

**Chapter 6 - Square Roots and the Pythagorean Theorem **

6.1 Square Roots

6.2 Modelling Square Roots

6.3 Non-Perfect Square Roots

6.4 The Pythagorean Theorem

6.5 Applications of the Pythagorean Theorem

6.6 Chapter Review

**Chapter 7 - Data Analysis and Probability **

7.1 Tables

7.2 Interpreting Graphs

7.3 Constructing Graphs

7.4 Misleading Graphs

7.5 Measure of Central Tendency

7.6 Probability

7.7 Independent and Dependent Events

7.8 Chapter Review

**Chapter 8 - Geometric Patterns **

8.1 Isometric Drawings

8.2 Rotating Cubes

8.3 Tessellations

8.4 Transformations

8.5 Creating Tessellations

8.6 Chapter Review

## Theory and Problems for Mathematics 9

**TABLE OF CONTENTS **

**Chapter 1 - Square Roots, Powers, and Exponent Laws **

1.1 The Real Number System

1.2 Square Roots

1.3 Square Roots of Non-Perfect Squares

1.4 Defining a Power

1.5 Orders of Operations

1.6 Exponent Laws

1.7 Power Rules

1.8 Chapter Review

**Chapter 2 - Finance **

2.1 Income

2.2 Simple Interest

2.3 Compound Interest

2.4 Budget

2.5 Chapter Review

**Chapter 3 - Rational Numbers **

3.1 Defining Rational Numbers

3.2 Adding and Subtracting Rational Numbers

3.3 Adding and Subtracting Using Fraction Notation

3.4 Multiplying and Dividing Rational Numbers

3.5 Chapter Review

**Chapter 4 - Linear Relations **

4.1 Patterns

4.2 Linear Systems

4.3 Graphing Equations in the Form Ax + By = C

4.4 Matching Equations of Graphs

4.5 Chapter Review

**Chapter 5 – Polynomials**

5.1 Defining Polynomials

5.2 Adding and Subtracting Polynomials

5.3 Multiplying Polynomials

5.4 Dividing Polynomials

5.5 Chapter Review

**Chapter 6 - Linear Equations **

6.1 Understanding Linear Equations

6.2 Removing Fractions, Decimals and Parentheses

6.3 Linear Inequalities

6.4 Adding and Subtracting Linear Inequalities

6.5 Multiplying Linear Inequalities

6.6 Applications of Linear Equations

6.7 Chapter Review

**Chapter 7 - Reasoning **

7.1 Inductive Reasoning to Find a Specific Term

7.2 Inductive Reasoning to Find the nth Term

7.3 Deductive Reasoning

7.4 Puzzles and Games of Strategy

7.5 Chapter Review

**Chapter 8 - Probability and Statistics **

8.1 Population Versus Sample in Statistics

8.2 When to use a Population or a Sample in Statistics

8.3 Measure of Central Tendency in Statistics

8.4 Misleading Graphs

8.5 Probability Part I

8.6 Probability Part II

8.7 Chapter Review

**Chapter 9 - Similarity and Scale Factors **

9.1 Scale Factor

9.2 Similar Triangles

9.3 Similar Polygons

9.4 Reflection and Symmetry

9.5 Rotation

9.6 Chapter Review