ACT Math

What is the ACT?

ACT Tips and Strategies I
ACT Tips and Strategies II
Can I use a calculator in the ACT?

ACT vs SAT
Planning Your Testing Calender
College Admission

Free preparation Booklet from the ACT Official Site

Preparing for the ACT - Download a free student preparation booklet —includes test information, complete practice tests with scoring keys, and a writing prompt with sample essays. (also available from most high schools and colleges)

Free Practice Test Questions from the ACT Official Site

Five Sets of Sample English Test Questions
Five Sets of Sample Mathematics Test Questions
Four Sets of Sample Reading Test Questions
Seven Sets of Sample Science Test Questions
Six Sets of Sample Writing Prompts and Responses

ACT Tips: English and Reading
ACT Tips: Reading Comprehension I
ACT Tips: Reading Comprehension II

ACT Tips: Essay Writing
ACT Tips: Writing I
ACT Tips: Writing II
ACT Tips: Science

Content Covered by the ACT Mathematics Test

The ACT Mathematics Test covers six content areas: pre-algebra, elementary algebra, intermediate algebra, coordinate geometry, plane geometry, and trigonometry.

Pre-Algebra (23%)

Questions in this content area are based on

Basic operations on whole numbers, decimals, fractions and integers
Place value for whole numbers and decimals
Order of Operations

Rational Numbers
What are Rational Numbers?
Comparing & Ordering Rational Numbers
Multiplying & Dividing Rational Numbers

Square roots and Approximations
Simplifying square roots
Approximating square roots
The concept of exponents

Scientific Notation
Convert from Scientific Notation to Standard Notation
Convert from Standard Notation to Scientific Notation

Factors
Factors, Divisibility Tests, Prime Factorization

Ratio, Proportion and Percents
Ratio and proportion
Percents, Decimals and Fractions
Percent of a Number
Percent Word Problems

Linear Equations
Linear equations in one variable
Linear equations with fractions and decimals
Equations with Infinitely Many Solutions or No Solutions

Absolute Value
Absolute value
Ordering numbers by value

Elementary Counting Techniques and Simple Probability
Elementary counting techniques
Simple probability
Complementary Events

Data collection
Data representation and interpretation (Charts and Graphs)
Line Graphs
Bar Graphs
Circle Graphs
Interpret Line Graphs
Interpret Circle Graphs
Understanding simple descriptive statistics (Mean, Median, Mode)

ACT Questions - Pre-Algebra

Elementary Algebra (17%)

Questions in this content area are based on

Properties of exponents and square root
Positive, Zero and Negative Exponents
Exponent Rules
Fractional Powers, Fractional Exponents, Rational Exponents

Algebraic Expressions
Evaluation of algebraic expressions through substitution

Using variables to express functional relationships
Understanding algebraic operations

The solution of quadratic equations by factoring
Solve Quadratic Equations by Factoring

ACT Questions - Elementary Algebra

Intermediate Algebra (15%)

Questions in this content area are based on

An understanding of the quadratic formula
Solve Quadratic Equations using the Quadratic Formula

Rational expressions
Simplifying Rational Expressions
Adding and Subtracting Rational Expressions
Multiplying and Dividing Rational Expressions

Radical expressions
Simplifying Radicals and Square Roots
Adding and Subtracting Radicals
Multiplying Radicals
Dividing Radicals

Absolute value equations and inequalities
Solving Absolute Value Equations
Solving and Graphing Absolute Value Inequalities

Sequences and patterns
Arithmetic Sequence
Geometric Sequence

Systems of equation
Solving Systems of Equations by Substitution
Solving Systems of Equations by Addition or Elimination
Solving Systems of Equations Graphically
Solving Systems of Equations with Fractions or Decimals

Quadratic inequalities
Solving Quadratic Inequalities

Functions
Function Notation
Composite Functions
Inverse Functions
Exponential and Logarithmic Functions

Modeling

Matrices
Introduction to Matrices
Matrix Addition and Subtraction
Matrix Scalar Multiplication
Matrix Multiplication

Polynomials
Roots of polynomials

Complex numbers
Introduction to Complex Numbers
Adding and Subtracting Complex Numbers
Multiplying Complex Numbers
Dividing Complex Numbers

ACT Questions - Intermediate Algebra

Coordinate Geometry (15%)

Questions in this content area are based on

Graphing and the relations between equations and graphs
including points, lines, polynomials, circles, and other curves
Plotting points on graphs

Equations of lines
Graphing Lines by Plotting Points
Graphing Horizontal and Vertical Lines
Graphing Lines using the x-intercept and y-intercept

Slope and Equations
Finding the Slope of a Line
Convert a linear equation from standard form to slope-intercept form
Graphing Lines by Slope Intercept Method
Find the equation of a line using the Point Slope Form
Graphing Linear Equations

Parallel and perpendicular lines
Equations for Parallel and Perpendicular Lines

Distance and Midpoint Formula
Distance Formula
Midpoint Formula

Equations of polynomials
Equations of cicles
Equations of curves

Graphing inequalities

Conics

ACT Questions - Coordinate Geometry

Plane Geometry (23%)

Questions in this content area are based on

Properties and relations of plane figures, including angles
Rectangles, Parallelograms, Triangles
Trapezoids, Regular Polygons, Circles
Interior and Exterior Angles of Polygons

Relations among perpendicular and parallel lines
Adjacent, Complementary, Supplementary and Vertical Angles
Corresponding Angles
Alternate Interior Angles
Co-Interior Angles
Corresponding and Alternate Angles
Problems involving Parallel Lines and Transversal

Properties of circles, triangles, rectangles, parallelograms, and trapezoids
Triangles, Circles
Rectangles, Parallelograms, Trapezoids

Volume
Volume of a Cube
Volume of a Rectangular Prism
Volume of Triangular Prisms
Volume of Prisms
Volume of a Cylinder
Volume of a Cone
Volume of a Pyramid

Applications of geometry to three dimensions
Volume Word Problems
Volume of Prisms – Applications

Transformations
Introduction to Transformation
Reflection
Rotation
Translation

Concept of proof and proof techniques
Two Column Proofs
CPCTC

Trigonometry (7%)

Questions in this content area are based on

Understanding trigonometric relations in right triangles
Using the Trigonometry Formula - SOH-CAH-TOA

Values and properties of trigonometric functions

Graphing trigonometric functions
Sine and Cosine Graphs
Tangent Graphs

Modeling using trigonometric functions
Solving Triangles using Trigonometry
Trigonometry ProblemsI
Angles of Elevation and Depression

Use of trigonometric identities
Solving trigonometric equations
Trigonometric Functions - Sin, Cos, Tan, Csc, Sec and Cot
Trig Identities - cofunctions, reciprocal, quotient, ratio, Pythagorean, and even/odd
Simplifying Trigonometric Expressions
Trigonometric Identities I
Trigonometric Identities II

Inverse Trigonometric Functions

ACT Questions - Trigonometry

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