ACT Math Section Breakdown: Topics and Question Types

The ACT Math section tests your knowledge of mathematical concepts typically covered through Algebra II, with some trigonometry. Understanding the breakdown of topics and question types helps you prepare strategically, identify your strengths and weaknesses, and maximize your score. This comprehensive guide covers everything you need to know about the ACT Math section.

ACT Math Section Overview

The ACT Math section consists of 60 multiple-choice questions to be completed in 60 minutes, giving you exactly one minute per question. The section covers content from pre-algebra through trigonometry, with questions ranging from basic arithmetic to advanced problem-solving.

Key Characteristics:

• All questions are multiple-choice with five answer choices
• Questions generally increase in difficulty throughout the section
• Calculators are permitted (with some restrictions)
• Questions test both mathematical knowledge and problem-solving skills

Content Breakdown by Topic Area

The ACT Math section covers six main content areas:

1. Pre-Algebra (20-25% of questions)

This foundational area includes:

• Basic operations with whole numbers, fractions, and decimals
• Exponents and square roots
• Scientific notation
• Factors and multiples
• Ratios, proportions, and percentages
• Linear equations with one variable
• Absolute value
• Basic probability

Example Topics:

• Calculating percentages and finding percent changes
• Working with ratios and proportions
• Solving simple linear equations
• Understanding number properties (prime numbers, factors, etc.)

2. Elementary Algebra (15-20% of questions)

Covers fundamental algebraic concepts:

• Substitution and simplifying expressions
• Solving linear equations and inequalities
• Factoring
• Working with variables and expressions
• Understanding algebraic relationships

Example Topics:

• Solving for x in equations like 3x + 7 = 22
• Simplifying expressions such as (2x + 3)(x - 4)
• Understanding linear relationships and slopes
• Working with inequalities

3. Intermediate Algebra (15-20% of questions)

More advanced algebraic concepts:

• Quadratic equations and factoring
• Radical and rational expressions
• Systems of equations
• Functions and function notation
• Logarithms
• Complex numbers (basic)

Example Topics:

• Solving quadratic equations using factoring or quadratic formula
• Working with functions f(x) and understanding domain and range
• Solving systems of linear equations
• Simplifying radical expressions

4. Coordinate Geometry (15-20% of questions)

Graphing and coordinate plane concepts:

• Graphing equations and inequalities
• Slope and distance formulas
• Midpoint formula
• Parallel and perpendicular lines
• Conic sections (circles, parabolas, ellipses)
• Coordinate plane transformations

Example Topics:

• Finding the slope of a line given two points
• Graphing linear equations
• Finding the distance between two points
• Understanding how changes to equations affect graphs

5. Plane Geometry (20-25% of questions)

Properties of shapes and figures:

• Properties of triangles, quadrilaterals, circles
• Area and perimeter formulas
• Volume and surface area
• Similarity and congruence
• Angles and parallel lines
• Circles: arcs, chords, tangents

Example Topics:

• Calculating the area of various shapes
• Finding missing angles using geometric properties
• Understanding triangle properties (Pythagorean theorem, special triangles)
• Working with circles (circumference, area, arc length)

6. Trigonometry (5-10% of questions)

Basic trigonometric concepts:

• Right triangle trigonometry (SOH-CAH-TOA)
• Trigonometric identities
• Graphing trigonometric functions
• Inverse trigonometric functions
• Unit circle concepts

Example Topics:

• Using sine, cosine, and tangent to solve right triangles
• Understanding trigonometric ratios
• Working with special angles (30°, 45°, 60°)
• Applying trigonometry to solve geometric problems

Question Types and Formats

ACT Math questions appear in several formats:

1. Direct Calculation Questions

These questions require straightforward mathematical computation:

• "What is 15% of 240?"
• "Solve for x: 2x + 5 = 17"

Strategy: These are usually quick points if you know the concept. Work carefully and check your arithmetic.

2. Word Problems

Real-world scenarios requiring mathematical solutions:

• "A store discounts an item by 25%, then applies an additional 10% discount. What is the final price?"
• "If a train travels 60 miles in 45 minutes, how long will it take to travel 120 miles?"

Strategy: Translate the words into mathematical expressions. Identify what you're solving for and set up equations systematically.

3. Geometry Diagram Questions

Questions accompanied by geometric figures:

• Triangles with labeled sides and angles
• Circles with chords, tangents, or inscribed angles
• Complex figures requiring multiple calculations

Strategy: Use the diagram to visualize the problem. Label what you know and what you need to find. Apply geometric formulas systematically.

4. Function Questions

Questions involving function notation and properties:

• "If f(x) = 2x + 3, what is f(5)?"
• "What is the domain of f(x) = √(x - 4)?"

Strategy: Understand function notation and properties. Substitute values carefully and consider restrictions (like square roots of negative numbers).

5. Data Interpretation Questions

Questions using tables, graphs, or charts:

• Reading information from scatter plots
• Interpreting data from tables
• Understanding trends from line graphs

Strategy: Read graphs and tables carefully. Pay attention to axes labels and units. Extract the relevant information for your calculation.

Difficulty Progression

ACT Math questions generally increase in difficulty throughout the section:

Questions 1-20: Typically easier, testing fundamental concepts

• Basic arithmetic and pre-algebra
• Straightforward calculations
• Simple word problems

Questions 21-40: Moderate difficulty

• More complex algebraic manipulations
• Multi-step problems
• Coordinate geometry and plane geometry

Questions 41-60: Most challenging

• Advanced algebra and trigonometry
• Complex multi-step problems
• Questions requiring multiple concepts

Strategy: Don't spend too much time on early questions—they should be relatively quick. Save time for the more challenging questions at the end. However, don't assume early questions are always easy; some difficult concepts can appear early.

Calculator Usage and Restrictions

The ACT allows calculators, but with important restrictions:

Permitted Calculators:

• Most graphing calculators
• Scientific calculators
• Four-function calculators

Prohibited Calculators:

• Calculators with computer algebra systems (CAS)
• Calculators with QWERTY keyboards
• Calculators with paper tape
• Calculators that make noise or require an outlet
• Apps on phones or tablets

Calculator Strategy:

• Use your calculator for complex calculations, but don't rely on it for basic arithmetic
• Practice mental math for simple calculations to save time
• Know how to use your calculator efficiently (store values, use memory functions)
• Don't forget that you can still make mistakes with a calculator—double-check critical calculations

Common Problem-Solving Strategies

1. Plug In Numbers

When questions involve variables, try plugging in specific numbers:

• Useful for questions like "If x > 3, which expression is always positive?"
• Choose numbers that make calculations easy (like 0, 1, or -1)

2. Use Answer Choices

Sometimes it's faster to work backwards from answer choices:

• Plug answer choices into equations or formulas
• Start with the middle value if answers are numerical
• Eliminate obviously wrong answers first

3. Draw Diagrams

For geometry problems, drawing your own diagram can help:

• Visualize the problem more clearly
• Label what you know
• Identify relationships between elements

4. Eliminate Wrong Answers

Narrow down choices by eliminating obviously incorrect options:

• Answers that are too large or too small
• Answers with incorrect units
• Answers that don't make logical sense

5. Look for Patterns

Many ACT Math questions test pattern recognition:

• Sequences and series
• Functions with repeating patterns
• Geometric progressions

Time Management Tips

With 60 questions in 60 minutes, time management is crucial:

Target Pacing:

• Questions 1-20: 15-20 minutes
• Questions 21-40: 20-25 minutes
• Questions 41-60: 20-25 minutes
• Buffer time: 5-10 minutes for review

Efficiency Strategies:

• Skip questions that are taking too long (mark and return)
• Answer easy questions quickly to save time for hard ones
• Use calculator shortcuts for repetitive calculations
• Don't overthink simple questions

Study Plan Recommendations

Identify Weak Areas:

• Take a practice test to see which topics cause the most difficulty
• Focus extra study time on your weakest content areas
• Don't neglect your strengths—maintain proficiency

Practice by Topic:

• Work through practice problems organized by topic
• Master fundamental concepts before moving to advanced topics
• Build from pre-algebra up through trigonometry

Practice Under Time Pressure:

• Take timed practice sections regularly
• Simulate test conditions as closely as possible
• Track your improvement over time

Common Mistakes to Avoid

Mistake 1: Calculation Errors

Simple arithmetic mistakes can cost points. Double-check your work, especially on multi-step problems.

Mistake 2: Misreading Questions

Read questions carefully, especially word problems. Pay attention to what you're solving for.

Mistake 3: Not Showing Work

While you don't need to show work on the ACT, doing calculations on paper helps prevent errors and allows you to review your steps.

Mistake 4: Overusing Calculator

Relying too heavily on your calculator wastes time. Use mental math when possible.

Mistake 5: Giving Up Too Early

Even if a problem seems difficult, try working through it systematically. You might find it's simpler than it appears.

Conclusion

Understanding the ACT Math section breakdown helps you prepare strategically and maximize your score. Focus on mastering fundamental concepts, practicing under time pressure, and developing efficient problem-solving strategies. With consistent practice and targeted study, you can achieve your target ACT Math score.

Remember that improvement takes time and patience. Track your progress, identify your weaknesses, and dedicate regular practice time to each content area. Use our ACT Score Calculator to see how improving your Math section score affects your composite score, and explore our guide on ACT Science Reasoning Strategies for tips on another section.

Sources

• ACT, Inc. – Official ACT Mathematics test content specifications and question types
• Mathematical Association of America – ACT Math content guidelines and standards