# Free ACT Math Diagnostic Tests

Take the Varsity Learning Tools free diagnostic test for ACT Math to determine which academic concepts you understand and which ones require your ongoing attention. Each ACT Math problem is tagged down to the core, underlying concept that is being tested. The ACT Math diagnostic test results highlight how you performed on each area of the test. You can then utilize the results to create a personalized study plan that is based on your particular area of need.

### All ACT Math Resources

Our free ACT Mathematics Practice Tests are each a selection of 10 to 12 questions, which will give you a cross-section of topics from the Mathematics section of the official ACT. You might think of them as little quizzes, which you can use to hone your skills. Whether you need top ACT Math tutors in AtlantaACT English tutors in Houston, or top ACT Math tutors in San Francisco, working with a pro may take your studies to the next level.

ACT Mathematics Section

What does the ACT Mathematics section cover?

The ACT Mathematics section tests six areas of mathematics that students are expected to be familiar with after completing 11th grade. These sections are pre-algebra, elementary algebra, intermediate algebra, coordinate geometry, plane geometry, and some trigonometry.

Questions drawn from each of these sections appear in the following ratios and test the following material:

Pre-Algebra (23%): Pre-Algebra ACT Mathematics questions test concepts such as performing basic operations, understanding place value, understanding absolute value, understanding ratio, proportion, and percent, solving simple single-variable equations, and understanding probability.

Elementary Algebra (17%): Elementary Algebra ACT Mathematics questions test concepts such as using exponents and square roots, using substitution and elimination to solve pairs of two-variable equations, and factoring equations.

Intermediate Algebra (15%): Intermediate Algebra ACT Mathematics questions test concepts such as using the quadratic formula, solving equations that involve absolute values and inequalities, solving equations that both use inequalities and require the quadratic formula, modeling story problems with equations, solving functions, finding the roots of polynomials, and understanding matrices, complex numbers, and radical and rational expressions.

Coordinate Geometry (15%): Coordinate Geometry ACT Mathematics questions test concepts based on the coordinate plane, so questions in this category concern graphing points, lines, inequalities, polynomials, circles, and curves, as well as understanding the equations that produce them. Features of those graphed equations such as slope, parallel and perpendicular lines, distance, midpoints and conics are also tested.

Plane Geometry (23%): Plane Geometry ACT Mathematics test questions concern the area and volume of plane figures and three-dimensional shapes. These questions also test a student’s understanding of angles and relationships created by parallel and perpendicular lines, properties of figures of different shapes, transformations, and the idea of proof and proof techniques.

Trigonometry (7%): A complete understanding of all of trigonometry is not necessary for doing well on the ACT Mathematics section. ACT Mathematics Trigonometry questions test understanding properties of right triangles, understanding trigonometric functions’ values and properties, graphing and modeling using those functions, using trigonometric identities, and solving trigonometric equations.

How many problems are on the Mathematics section, and how much time do I have to complete them?

Each ACT Mathematics section consists of 60 multiple-choice questions, and you are given 60 minutes to complete the section. While you might be worried to find that you only have one minute per question, questions of varying difficulty levels are asked, so certain questions will take you less than a minute to solve, while other questions will take longer.

How many multiple choice answers are there on an ACT Mathematics question?

Unlike other sections of the ACT, which consist of multiple-choice questions that have four possible answers choices, the Mathematics Section of the ACT consists of multiple-choice questions that each have five possible answer choices.

Can I use a calculator on the ACT Mathematics section?

Yes! Students should bring their own calculator—scientific, graphing, or basic four-function calculators are permitted. While calculators can be useful to solve some questions, they may slow you down on other questions where simplifying or estimating may be a better choice.

What kind of calculator can I use on the ACT Mathematics section?

Certain calculators are not permitted by the ACT, and if you bring one of those calculators to the ACT, you will not be allowed to test.

While the ACT allows you to use a four-function, scientific, or graphing calculator, your calculator may not include any of the following features:

- built-in computer algebra systems

- tablet or laptop computers (i.e. PDAs)

- electronic pen-input devices or writing pads

- calculators with any kind of built-in communication device (i.e. calculators on cell phones or smartphones)

- calculators with a typewriter keypad in QWERTY format (letters keys not in this format are permitted)

The following types of calculators are permitted only with these modifications:

- Calculators with paper tape are permitted if the student removes the tape.

- Calculators that emit noise are permitted if the student mutes the noise so that the calculator makes no sound.

- Calculators with infrared data ports are permitted if the student completely covers the infrared data port with duct tape or electrician’s tape.

- Calculators that have power cords are permitted if the student removes all such cords.

Do I need to memorize formulas for the ACT Mathematics section?

The Mathematics section requires knowledge of basic formulas, including how to find the areas of circles, quadrilaterals, triangles, and basic three-dimensional figures.

Can I guess if I don’t know the answer?

Yes! Unlike the SAT, which calculates test scores based on how many questions you answer incorrectly, the ACT calculates test scores based on how many answers you got right. In other words, there is no penalty for guessing on the ACT; even if you get the question incorrect, it will not hurt your score. You will have better odds at guessing if you can eliminate at least one of the answer choices that you are certain is incorrect, and guess between the remaining answers.

What type of questions appear on the ACT Mathematics section?

The ACT tests six different areas of mathematics, and asks a variety of different question types; however, there are basically two overarching types of questions on the ACT Mathematics section: equation problems and word problems. The equation problems present an equation for you to solve, and often require a fair bit of computation. The word problems often—but not always—involve less calculation, but require translation: you’ll have to read the story and figure out how to translate words into an equation. For both types of questions, it’s important to read the instructions carefully, draw graphs and illustrations if needed, and eliminate wrong answers as you go along.

Can I write out my work on the ACT Mathematics section?