How to Ace the ACT Math Section

The ACT is one of the standardized tests commonly used for college admissions. But because of COVID, many colleges have stopped requiring these college entrance exams. However, many colleges still require the SAT and the ACT for admission. The ACT can still be a useful test to boost your college application or qualify for scholarships. Therefore, doing well on the exam can be important for your future!

Format of the ACT

The ACT consists of four multiple-choice sections and an optional essay. Here is a breakdown of the multiple-choice sections:

English

  • 75 questions, 45 minutes

  • Covers grammar, punctuation, sentences, and rhetorical skills

Math

  • 60 questions, 60 minutes

  • Covers a variety of math topics

Reading

  • 40 questions, 35 minutes

  • Four passages (fiction, social studies, humanities, sciences), 10 questions in each passage

Science

  • 40 questions, 35 minutes

  • Science passages with graphs, charts, and tables

This blog will detail how to ace the math section of the ACT specifically. However, UPchieve has many other resources to help you study and prepare for the other sections of this exam!

How UPchieve Can Help You Study

Understand basic test-taking strategies: We’ll review basic test-taking strategies for the ACT with you! We recommend that students familiarize themselves with these before taking practice tests. We’ll cover some of these strategies throughout this blog.

Help you build a schedule to take at least 3 timed, full-length practice tests: Studies have shown that familiarizing oneself with the format, content, and timing of the test is very helpful in increasing your score. UPchieve coaches will help you find time in your schedule to take at least 3 practice tests before the date of your exam and time to review your answers with a coach.

Review each incorrect answer: We recommend students request 1:1 coaching sessions to review their incorrect answers with an UPchieve coach!

ACT Test-Taking Strategies

1. Know what to bring: From printouts of admissions tickets to the right calculator, make sure you don’t forget any important items on the day of the test, so you aren’t forced to sit out of the exam.

2. Read each question carefully: Questions often have multiple steps or present familiar math in unfamiliar ways, so it’s important to notice what is being asked.

3. Consider all the steps: Note if the question is asking you to perform multiple steps or operations.

4. Answer every question: No points are taken away for incorrect answers, so fill in each bubble.

5. Guess strategically:

  • Try to eliminate answers. Some answers will be clearly wrong.

  • Pick one letter to guess on questions when you don’t have time to read or are unable to eliminate answer choices. This will statistically improve the chance of getting these answers correct.

6. Pace yourself: You should spend an average of 1 minute per question.

7. Do the easy problems first: This increases your confidence and gives you more time for more challenging questions.


ACT Math Section Content

In the math section of the ACT, there are 60 mostly “self-contained” multiple-choice questions. The best part is that calculators are allowed for all math problems!

Here is the breakdown of the topics in the math section, and the percentages of how many questions are in each topic:

  • Number and Quantity: 7-10% of questions

  • Algebra: 12-15%

  • Functions: 12-15%

  • Geometry: 12-15%

  • Statistics & Probability: 8-12%

  • Integrating these skills in complex problems: 40-43%


ACT Math Section Formulas and Concepts

Now, here are formulas and concepts you should know to ace this section:

Numbers and Quantities

  • Order of Operations: PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction)

  • Prime numbers: Numbers only divisible by 1 and itself (examples: 2, 7, 13)

  • Prime factorization: Determining the prime numbers that multiply together to give a certain original number

  • Greatest common factor: Identify the largest number that divides both numbers given without leaving a remainder

  • Relationship between percents, fractions, and decimals: 50% = ½ = .5

  • Exponents (including i² = -1)

  • Square roots: Solve, simplify, add, subtract, multiply or divide

Graphing Concepts

  • Quadratic Formula: x = (-b ± √(b² - 4ac)) / 2a

  • Factoring Quadratics: (x - a)(x - b) = 0

  • Slope-Intercept Form: y = mx + b

  • Point-slope form: y - y₁ = m(x - x₁)

  • Slope formula: m = (y₂ - y₁)/(x₂ - x₁)

  • Distance Formula: √((x₂ - x₁)² + (y₂ - y₁)²)

  • System of equations using substitution or elimination

  • Matrices

Functions

  • Solving functions and basic concepts (domain, range, etc.)

  • Quadratic Functions in various forms

  • Polynomial Functions and Factorization

  • Exponential and Logarithmic Functions

  • Composite and Inverse Functions

Geometry

Area Formulas

  • Triangle: 0.5 * base * height

  • Rectangle: length * width

  • Circle: πr²

Volume Formulas

  • Cylinder: πr²h

  • Sphere: 4/3 * πr³

  • Cone: 1/3 * πr²h

Unit Circle: Angles and their corresponding trigonometric values on the unit circle

  • The sum of central angle measures in a circle is 360°.

  • Since all radii have the same length, any triangle that contains two radii is an isosceles triangle.

Triangles

  • Pythagorean Theorem: a² + b² = c²

  • Special right triangles

  • SOHCAHTOA

Statistics and Probability

  • Mean, median, mode, and range

  • Understanding of histograms, box plots, scatter plots, bar graphs, and line graphs

  • Recognizing trends, outliers, and other features in data

  • Understand and interpret data distributions

  • Basic understanding of sampling and experiments

  • Probability of an event: P(A)= number of favorable outcomes/total outcomes

  • Complementary events: P(A’) = 1 - P(A), where A’ is the complement of event A

  • Compound events

    • Independent events: P(A and B) = P(A) x P(B)

    • Exclusive events P(A or B) = P(A) + P(B)

  • Dependent Events

    • P(A and B) = P(A) x P(A|B)

  • Permutations (nPr): when order matters, like arranging 3 books out of 5 on a shelf

  • Combinations (nCr): when order doesn't matter, like selecting 3 books out of 5 to take on a trip


Best Strategies to Ace the ACT Math Section

1. Change words to math actions: Look for keywords that indicate mathematical concepts and write them in the problem.

2. Plug in answer choices: Plugging your answer back into the question, if possible, can guarantee that your answer is correct. Plugging multiple-choice answers into an equation can also help eliminate answers that are clearly wrong.

3. Replace abstract values with concrete ones: For example, if a question were to ask which statements are true for all negative values of x, try plugging in -2 to determine if the statement is correct.

4. Draw and label diagrams: Instead of keeping information in your mind, draw visual representations to solve a problem.

5. Use your calculator: Be familiar with your calculator features. This can help you solve problems and save a lot of time when answering questions.


Resources and Final Thoughts on the ACT Math Section

Keep in mind that there are a ton of resources at your disposal!

While the math section is just a part of the ACT, acing it can increase your overall score. A great ACT score creates opportunities for potential scholarships or programs. Therefore, preparing and studying for the ACT is crucial.

UPchieve is a great tool to prepare for the ACT because you can meet one-on-one with tutors who can help you with any of the listed math topics. UPchieve tutors can also help you create healthy study habits and build study schedules! 

Good luck!

College & Career Advice, Student TipsAvani Chaudhry