### What are your chances of acceptance?

Duke University
UCLA
Unweighted GPA: 3.7
1.0
4.0
SAT: 720 math
200
800
| 800 verbal
200
800

#### Extracurriculars

Low accuracy (4 of 18 factors)
8 ACT Info and Tips

# A Guide to the Math Section of the ACT

## What’s Covered:

The math section of the ACT assesses the mathematical skills that students generally have acquired by the beginning of 12th grade. Many students consider the math section to be one of the ACT’s most challenging, as when you’re tackling problems with many moving parts, while under the ACT’s infamous time pressure, you can easily slip up and make a silly mistake.

Familiarizing yourself with the format, scoring, and content of the math section of the ACT is a great way of avoiding such mistakes, and ensuring that your score accurately reflects your mathematical knowledge.

## What Is the Format of the Math Section of the ACT?

The math section of the ACT consists of 60 questions and is 60 minutes long. It’s the second section of the test, which means it follows the English section and precedes the 10-minute break. For some students, the first challenge of the math section is shifting gears from humanities-based thinking to computational thinking.

If this is the case for you, experiment with mind-clearing strategies during your practice tests, and if they work for you, make sure to employ them on the day of the real ACT. For example, try taking several deep, meditative breaths while rolling your shoulders or arching/relaxing your back.

Doing these simple relaxation tricks while taking practice tests in your bedroom may feel silly. But if you get in the habit, you’ll have a mental cue that helps you shift gears quickly on test day. Make sure that you choose quick, simple actions that you can easily do as the test proctor reads the instructions.

With your mind clear of all the thinking you just did for the English section, you’re ready to get started on math. The 60 questions are not arranged by subject area or topic; however, they’re generally ordered by level of difficulty. So, the questions at the beginning of the section will be easier, and they will get harder and more complex as you proceed.

Of course, this is just an overall trend–how hard you find a particular question depends on your own strengths. Even well-prepared, mathematically strong students might find a few of the earlier questions difficult or a few of the later questions easier. So, if you find an early question that seems tricky, don’t feel bad–just circle it and come back to it later.

Calculators are allowed on the ACT, but the test makers note that all questions can be solved without a calculator. In other words, you should treat your calculator as a tool to help you solve questions more efficiently, or check your work with, but not as something that will paper over any gaps in your mathematical knowledge.

Make sure to review the ACT calculator policy well before exam day, as not all calculators are allowed. For example, the popular TI-89 calculator is not permitted. In fact, trying to use a TI-89 is one of the most common reasons students are dismissed from the ACT.

Also know that the ACT, unlike the SAT, does not provide any references, which means you’ll need to know all the common math formulas by heart. These generally include y = mx + b, the area formula, the quadratic formula, and others, but nothing too complex. Learn more about which formulas you’ll for sure want to memorize in our strategy section below.

## How Is the Math Section of the ACT Scored?

Like the other sections of the ACT, your score report for the ACT math section will not state the number of questions that you got correct. Rather, this “raw score” is equated to a scaled score between 1-36.

The ACT scaling process is different from grading on a curve, as it doesn’t account for the performance of other students taking the same test as you. Rather, it ensures that from one test sitting to the next, students with the same mastery of the material will earn the same score, regardless of any slight variations in difficulty between exams.

Below is a table showing how many questions you need to get right on the math section of the ACT to earn a certain scaled score. Keep in mind that this scale is for a particular practice test and the exact numbers may vary slightly between different visions of the exam.

 Scaled Score Questions Answered Correctly 36 59-60 35 57-58 34 55-56 33 54 32 53 31 51-52 30 49-50 29 47-48 28 45-46 27 42-44 26 39-41 25 37-38 24 34-36 23 32-33 22 31 21 29-30 20 27-28 19 25-26 18 22-24 17 19-21 16 16-18 15 13-15 14 10-12 13 8-9 12 7 11 5-6 10 4 9 – 8 3 7 – 6 2 5 – 4 1 3 – 2 – 1 0

## What Skills Does the Math Section of the ACT Assess?

The math section of the ACT covers a lot of specific mathematical topics, and thus lends itself well to straightforward, rote studying. The content is divided into three categories: preparing for higher math, integrating essential skills, and modeling.

### Preparing for Higher Math

Preparing for higher math covers the bulk of mathematics typically found in high school curricula, beginning with algebra. This category can be further broken down into five subcategories:

• Number and quantity (7-10%): Asks you to demonstrate your knowledge of real and complex numbers and your ability to understand and use numerical quantities in forms like integer and rational exponents, vectors, and matrices.

•  Algebra (12-15%): Assesses your ability to solve, graph, and model expressions employing equations like linear, polynomial, radical, and exponential relationships.

• Functions (12-15%): Evaluates your understanding of function definition, notation, representation, and application with questions on topics such as linear, radical, piecewise, polynomial, and logarithmic functions.

• Geometry (12-15%): Tests your knowledge of topics related to shapes and solids, such as congruence and similarity relationships or surface area and volume measurements, along with your ability to understand the composition of objects and solve for missing values in triangles, circles, and other figures.

• Statistics and probability (8-12%): Tests your knowledge of center and spread of distributions and your ability to apply and analyze data collection methods, understand and model relationships in bivariate data, and calculate probabilities.

### Integrating Essential Skills

Integrating essential skills evaluates your ability to apply your knowledge and skills to solve complex problems. The questions cover topics such as:

• Rates and percentages
• Proportional relationships
• Area
• Surface area
• Volume
• Average and median values
• Different methods of expressing numbers

You’ll need to solve unconventional problems by using different skills to solve different parts of a problem and applying skills in non-standard ways, to demonstrate your understanding of the connections between concepts and broader problem-solving fluency.

### Modeling

Modeling questions are located in both the preparing for higher math and integrating essential skills categories, and include all questions related to producing, interpreting, understanding, evaluating, and improving models.

## Strategies for the Math Section of the ACT

### 1. Save Time for the Harder Questions

It’s easy to think of the pace of the math section of the ACT as one minute per question, since you have 60 minutes to answer 60 questions. However, since the test generally gets more difficult as you go, you’ll want to reach the midpoint of the test in much less than 30 minutes.

Try to answer the first 30-40 questions in 20-30 minutes, so that you’ll have extra time for the last 20 questions, which are generally more complex and thus require more time to untangle.

One strategy to stay on pace is to skip over questions that initially seem very difficult. If you’ve spent 10 seconds thinking about a question and still have no idea how to solve it, write down your best guess, circle the question number, and move on. If you get totally bogged down on a particular question, you’ll be rushed on the others, and might make errors that you wouldn’t otherwise.

At the end of the section, if you have time left, you can revisit the questions you skipped. If you run out of time, at least you’ve already guessed, and have a 25% chance of getting the question right.

### 2. Break Down Word Problems

Word problems can be challenging for even the most savvy math students, as they often include irrelevant information and sometimes the actual question isn’t clear. What they’re testing is your ability to use your mathematical knowledge in context, so being able to sift through them and find the pieces that matter is an essential test strategy.

One popular method for breaking down word problems is to underline figures that indicate numerical value, cross out irrelevant numbers, and circle words that indicate function—for example, words like per, each, and every usually indicate a rate, which means you’ll likely need to use multiplication or division to arrive at your answer. Another popular technique is to draw a quick sketch of the scenario to help you envision what’s being described.

### 3. Know When to Use Your Calculator

Remember, you can complete the entire math section of the ACT without a calculator. Consider your calculator as a helpful tool rather than a crutch–relying on it too much can signal a gap in your knowledge, and eventually cost you on test day.

As you practice, start by using mental math. Only turn to your calculator when necessary, and take note of the questions where you need to do so. While there’s nothing wrong with using your calculator, if you’re using it a disproportionate amount on certain kinds of questions, that could be a sign that you need to concentrate your studying on particular topics.

On the other hand, if you find yourself using it for every question or most questions, especially at the beginning when the questions are less complex, you should be honest with yourself about why you feel reliant on it. Self-confidence is also key to the math section of the ACT, as checking every single answer on your calculator will eat into your precious time during the real exam.

### 4. Backsolve From Answer Choices

Backsolving from the answer choices is a particularly helpful strategy for algebra questions. Rather than trying to solve for an unknown variable, take the answer choices, plug them into the equation, and see which works.

Increase your efficiency by starting with the value that seems most probable, or the middle value if you have no idea. If that doesn’t work, progress through the remaining answer choices, moving from most to least likely to be correct. Even if the problem is beyond your algebra skills, backsolving will allow you to arrive at the correct answer fairly efficiently.

Backsolving is trickier to do with word problems or other kinds of questions, but if you can set up a formula that you’re confident represents the question being asked, backsolving is definitely a tool you have at your disposal.

### 5. Familiarize Yourself With the Content Covered

As noted earlier, there’s no reference sheet provided for the math section of the ACT. Consequently, there’s a handful of mathematical formulas that you want to have down cold, including:

• Slope-intercept formula
• Area of triangles
• Pythagorean theorem
• Special types of triangles (30-60-90, isosceles, equilateral, etc.)
• Area of a circle
• Circumference
• Area of a sector
• Area of a rectangle
• Area of a parallelogram
• Area of trapezoid
• Trigonometry functions (sin, cos, tan, SOHCAHTOA)

Creating flashcards, making your own Quizlet, and taking turns quizzing friends are all good ways to commit these formulas to memory. Some students find the simple act of writing each equation out an effective memorization tool as well.

### 6. Write Down at Least Part of Your Calculations

There are some questions that you will know the answer to immediately or can solve quickly, either in your head or with your calculator. On these questions, you might be tempted to answer as quickly as possible and move on, but you should write down at least a quick note to yourself of what you did, whether mentally or on your calculator, to arrive at your answer.

While you generally want to trust your gut on standardized tests like the ACT, if you’re checking your answers and realize one of them doesn’t make sense, referring to your notes can help you identify where you went wrong, rather than needing to start at the beginning.

## Free ACT Study Resources

Many free resources are available online to students studying for the ACT, including:

ACT prep books are a more analog study aid. Ask your family or friends if they have any prep books from when they took the test. Because most people don’t need prep books after they’ve taken the test, Little Free Libraries are often a good source for prep books.

## How Will the ACT Impact Your Chances of Acceptance?

Despite the expansion of test-optional policies, standardized tests like the ACT (or SAT) continue to play a major role in the college admissions process, especially at highly selective schools. However, test scores aren’t the only factor considered—your GPA, course rigor, extracurriculars, essays, letters of recommendation, and so on are also crucial.

If you’re wondering how your overall profile will stack up at the colleges you’re considering, check out CollegeVine’s free chancing engine, which evaluates all quantifiable aspects of your application, including grades, course rigor, extracurriculars, and, yes, standardized test scores to estimate your odds of being accepted at over 1,600 schools across the country.

Our admissions calculator can also give you suggestions for how to boost your chances of acceptance—for example, by raising your ACT score.

Short Bio
A graduate of Northeastern University with a degree in English, Tim Peck currently lives in Concord, New Hampshire, where he balances a freelance writing career with the needs of his two Australian Shepherds to play outside.