# ACT Mathematics Test Format: How To Navigate The Test

ACT Mathematics Test Format in this blog post is simplified and well explained for students to be able to grab and pass the ACT Mathematics test with ease. The ACT Mathematics Test format includes topics in algebra, geometry, trigonometry, statistics, and probability.

In this lesson, we will take a closer look at exactly what topic you should study as well as the ACT Mathematics test format and other useful information such as the structure of the test, scoring, the breakdown of topics, and the question format. The ACT math test covers the following broad areas of mathematics:

### Preparing for Higher Math (57%–60% of all questions)

- Number and Quantity (7%–10%)
- Algebra (12%–15%)
- Functions (12%–15%)
- Geometry (12%–15%)
- Statistics and Probability (8%–12%)
- Integrating Essential Skills (40%–43% of all questions)
- Within these categories, about 25% will test your modeling skills.

Let’s now look at each of these a little closer so that you know what kinds of questions you may encounter. This category consists of the following topics:

#### Number and Quantity (7%–10%)

Number and Quantity questions will ask you to recognize and apply properties of real and complex numbers; this will include computations involving whole numbers, integers, rational numbers (fractions, decimals, and mixed numbers), irrational numbers, and complex numbers. You will be asked to apply your knowledge of place value, rounding, factors and multiples, exponents, vectors, and matrices.

An understanding of number properties and quantities will provide you with a solid foundation to build your algebra, geometry, statistics, and probability skills.

#### Algebra (12%–15%)

Algebra questions will span a variety of topics you have learned in pre-algebra, algebra I or II, and other more advanced algebra classes. You will be asked to solve real-world applications that involve solving one- and multi-step arithmetic problems, as well as problems that involve linear, quadratic, polynomial, radical, and exponential equations or relationships.

You will need to be able to represent models graphically and interpret these models within the context of a given problem. Other topics that you may see include systems of equations/inequalities, simplifying and manipulating algebraic expressions, working with rational expressions and equations, absolute value expressions and equations, using matrices, and analyzing problems and graphical models to form reasonable conclusions.

#### Functions (12%–15%)

Functions are an extension of algebraic topics and will focus on patterns, graphical relationships, and modeling using function notation, expression, equations, graphical representations, and other real-world applications. Questions will assess your understanding and ability to apply your knowledge of linear, quadratic, polynomial, radical, exponential, logarithmic, piecewise, and trigonometric functions.

#### Geometry (12%–15%)

Geometry questions will include topics such as measurement conversions; angles and their properties; the properties of basic shapes including concepts of similarity and congruence; geometric formulas including area and volume; coordinate geometry topics such as parallel and perpendicular lines, midpoint, and distance calculations; and transformations in the plane. Some questions may require you to be somewhat familiar with the basic idea of proof in geometry, but this will be more about reasoning skills than anything specific.

This area may also incorporate trigonometry topics such as solving trig functions concerning right triangles, using trig identities, solving basic trig equations, and understanding trigonometric graphs (and transformations on these graphs) and how they are used to model real-world phenomena.

#### Statistics and Probability (8%–12%)

Statistics and Probability questions will assess your understanding of data collection, data summary methods, visual representations of data, and analysis of data to conclude. Topics will include measures of central tendency and spread of distributions; surveys, observational studies, and experiments; modeling relationships of data; calculating probabilities; averages; interpreting tables, charts, and other graphical displays; and techniques in statistical modeling.

#### Integrating Essential Skills (40%–43%)

The Integrating Essential Skills category will focus on your ability to use skills you may have learned in elementary or middle school that continue to be important in advanced math classes. This can include topics such as rates, ratios, and proportions; geometric formulas and relationships such as area, perimeter, surface area, and volume; statistics concepts like mean, median, mode, and range; and expressing numbers and equations in different ways.

Questions may incorporate multiple essential skills and topics and ask you to make connections in different contexts. It is important to be able to work through problems that are not “typical” and use a variety of skills to work toward a solution.

#### Modeling (>25%)

This category evaluates your overall ability to use modeling skills across different topic areas and types of problems. You will be asked to create, interpret, analyze, evaluate, and recreate models. As you dig into each of the specific topic areas, pay attention to aspects of problems that require you to use or work through a model.

As you can see, the ACT covers a broad range of topics. In the end, the goal is to have a very solid foundation in algebra/pre-algebra and then build from there. That’s exactly what we will do in this tutorial!

## ACT Mathematic Test Format

The 60-minute ACT math test contains 60 multiple-choice questions from six categories of subjects taught in most high schools up to the start of 12th grade.

Each question has five possible answer choices. Unlike on the SAT, you are not given a reference sheet of formulas. This is because the ACT math exam tests your reasoning skills. You will not need to memorize advanced formulas, although you should know the basic ones, which we will cover later in this course.

You may use a calculator, but as you will see in the following lessons, you can solve many questions more quickly without one.

Essentially, the ACT math test evaluates your ability to reason through math problems. You will have to interpret data based on the information given and on your existing knowledge of math. The questions are meant to evaluate critical thinking ability by asking you to correctly interpret the problem, analyze the data, reason through possible conclusions, and determine the correct answer—the one supported by the data presented in the question.

## ACT Mathematics Test Scoring: How To Calculate Your Score

When you take the ACT math test, you will receive separate scores for the following categories:

- Number and Quantity
- Algebra
- Functions
- Geometry
- Statistics and Probability
- Integrating Essential Skills

This includes topics such as ratios, proportions, percentages, area, volume, averages, and number sense.

Both of the above sections will contain modeling questions that ask you to work with and analyze mathematical models.

You will also receive an overall score, which is given on a scale of 1–36 and based on how many of the 60 questions you answered correctly. Your full ACT test score is then determined by averaging this math score with the other section scores.

## General Test-Taking Strategies

As you prepare for the ACT math test, remember these test-taking strategies:

- The math questions start easy and get harder.
- Pace yourself accordingly.
- There is no penalty for wrong answers.
- Make sure that you answer all of the questions, even if some answers are only a guess.
- If you are not sure of an answer, take your best guess.
- The entire ACT math test is comprised of multiple-choice questions, so the correct answer is always there. Try to eliminate a couple of the answer choices.
- If you skip a question, leave that question blank on the answer sheet and return to it when you are done.
- Often a question later in the test will spark your memory about the answer to a question that you skipped.
- Read carefully!
- Make sure you understand what the question is asking.
- Keep your work organized.
- Number your work on your scratch paper so that you can refer back to it while checking your answers.
- Look for easy solutions to difficult problems.
- For example, the answer to a problem that can be solved using a complicated algebraic procedure may also be found by “plugging” the answer choices into the problem.
- Know basic formulas, such as those for the area of triangles, rectangles, and circles. The Pythagorean theorem and basic trigonometric functions and identities are also useful and not that difficult to remember.