ACT Math

Looking for free ACT Math help?

We have a collection of videos, games, activities and worksheets that are suitable for the ACT Math Section. The topics covered are: Pre-Algebra, Elementary Algebra, Intermediate Algebra, Coordinate Geometry, Plane Geometry, and Trigonometry.

In our lessons here, we shall look at

  • Tips and strategies for the ACT.
  • Worked solutions for some ACT practice tests.
  • Concepts that you will need to know for the ACT Math sections.

Related Topics: More ACT Tips and Prep

What is the ACT?

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 of pre-algebra 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 of elementary algebra 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 of intermediate algebra 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 of coordinate geometry 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 line
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 circles

Equations of curves

Graphing inequalities
Conics

ACT Questions - Coordinate Geometry



Plane Geometry (23%)

Questions in this content area of plane geometry 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

ACT Questions - Plane Geometry



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 Problems
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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