# CAST Mathematical Usage Study Guide

CAST Mathematical Usage Study Guide

## Math Basics

### Lesson 1: Operations Basics

- Addition and Subtraction
- Associative Property
- Distributive Property
- Exponents and Roots
- Integers, Decimals, and Fractions
- Multiplication and Division
- Order of Operations

### Lesson 2: Factors and Multiples

- Greatest Common Factor
- Least Common Multiple
- Multiples
- Multiples and Least Common Multiples
- Prime Numbers, Factoring, and Prime Factorization

### Lesson 3: Unit Conversions

## Fractions

### Lesson 1: Fraction Basics

- Changing Mixed Numbers to Improper Fractions
- Converting Improper Fractions to Mixed Numbers
- Fractions of a Whole
- Improper Fractions and Mixed Numbers
- Ordering Fractions

### Lesson 2: Fraction Operations

- Adding and Subtracting Fractions
- Converting Improper Fractions to Mixed Numbers and Decimals
- Converting Mixed Numbers to Decimals and Improper Fractions
- Converting Percentages to Decimals and Fractions
- Multiplying and Dividing Fractions

## Decimals

### Lesson 1: Decimal Basics

### Lesson 2: Decimal Operations

- Adding and Subtracting Decimals
- Changing a Number from Standard Form to Scientific Notation
- Converting Decimals to Fractions and Percentages
- Converting Decimals to Improper Fractions and Mixed Numbers
- Dividing Decimals
- Multiplying Decimals
- Scientific Notation

## Solving Equations

### Lesson 1: Equation Basics

- Absolute Value
- Arithmetic Sequences and their Formulas
- Solving Equations Using All Four Basic Operations
- Solving Equations Using Addition and Subtraction
- Solving Equations Using Multiplication and Division
- Solving Equations with Absolute Value

### Lesson 2: Inequalities

- Equations and Inequalities
- Graphing Solutions to Linear Inequalities
- Linear Inequalities
- Solving Absolute Value Inequalities
- Solving Inequalities Using All Four Basic Operations

### Lesson 3: Linear System of Equations

- Comparison of Methods for Solving System of Equations
- Linear Equations Basics
- System of Linear Equations
- System of Equations Basics

### Lesson 4: Graphing of Linear Equations and Functions

- Changing Constants in Graphs of Functions: Linear Functions
- Changing Constants in Graphs of Functions: Quadratic Equations
- Graphing Absolute Value Equations
- Graphing Linear Equations
- Graphing the Inverse of a Function
- Graphs of Functions
- Solutions of a Quadratic Equation on a Graph
- Using a Graph

### Lesson 5: Word Problems

- Right Triangle Word Problems
- Word Problems and Addition
- Word Problems and Division
- Word Problems and Multiplication
- Word Problems and Subtraction

## Geometry

### Lesson 1: Angle Basics

### Lesson 2: Triangles

- Area and Perimeter of a Triangle
- Measurements for Similar Triangles
- Measurements for Similar Triangles – Continued
- Proof that a Triangle is 180 Degrees
- Similar Triangles

### Lesson 3: Circles

- Area and Circumference of a Circle
- Finding Measurements for Parts of a Circle
- Unit Circles and Standard Position

### Lesson 4: Volume and Surface Area of 3D Shapes

- 3D Geometric Shapes
- Volume and Surface Area of a Cube
- Volume and Surface Area of a Pyramid
- Volume and Surface Area of a Rectangular Solid
- Volume and Surface Area of a Circular Cone
- Volume and Surface Area of a Circular Cylinder
- Volume and Surface Area of a Sphere