How to Solve ACT® Math Questions
Tricks and Strategies
Discover the keys to mastering ACT® Math with our guide on clever tricks and smart strategies. Whether you're figuring out Pre-Algebra, getting the hang of Trigonometry, or exploring extra math bits, this guide is here for you. Dive into easy-to-follow techniques, practical tips, and illustrative examples to enhance your ACT Math skills and confidently tackle any question.
How to Solve ACT Math Questions
Cracking the code of ACT Math demands a solid understanding of a variety of mathematical concepts, encompassing intricate algebraic equations and geometry challenges. Our guide is designed to equip you with practical tricks and strategies, ensuring preparedness for every question type, including Multiple-Choice Questions (MCQs). To reinforce your understanding, we've incorporated valuable ACT Math sample questions, allowing you to apply the learned strategies in a practical context.
Applicability to SAT Math
The strategies outlined in this guide are not confined to ACT Math; they are also applicable to SAT Math. Whether you're preparing for the ACT or SAT, the foundational skills covered here—such as algebraic problem-solving and geometry proficiency—are integral to success.
Pre-Algebra
Pre-algebra constitutes the fundamental building blocks of the ACT Math Test, likely familiar from your middle school math classes. While not conceptually challenging, these topics may contain nuances that could have slipped from memory. Since pre-algebra questions are not generally tricky, a thorough review should suffice to ensure accuracy and success.
- ACT Math questions include 14 pre-algebra items that cover math terminology, basic number theory, and the manipulation of fractions and decimals. Strengthen your understanding of these content areas with key insights from reliable ACT Math Pre-Algebra study materials.
To discover everything you need to know about the format, syllabus, question types, and scoring of the ACT Math, check out our About ACT Math Test page.
Tricks and Strategies to ace this question type
Pre-algebra questions mainly deal with basic math like adding, subtracting, multiplying, and dividing—you know, the simple things! It's all pretty straightforward.
- Assess Your Comfort Level:
Evaluate your familiarity with pre-algebra skills, considering your math proficiency.
- Focus on Understanding:
Prioritize understanding the essence of problems rather than solely reviewing specific pre-algebra skills.
- Recognize ACT Math Patterns:
Develop your ability to recognize patterns in the wording of ACT math questions.
- Effective Problem Solving:
Practice solving ACT problems systematically, circling keywords and phrases while eliminating unnecessary information.
- Gradual Skill Enhancement:
Progress from a deliberate approach to gradually increasing your speed while problem-solving.
- Time Management:
Track your progress by timing yourself, striving to solve each practice question in an average of under one minute per problem for efficient preparation.
Pre-Algebra examples
Nora the polar bear was born in a zoo. The table below shows her weight, in pounds, each month from when she was born (birth) to age 4 months. What is the average rate of change in Nora’s weight, in pounds per month, from birth to age 4 months?
| Age (Months) | Weight (pounds) |
|---|---|
| Birth | 1.6 |
| 1 | 7.0 |
| 2 | 11.0 |
| 3 | 16.2 |
| 4 | 21.6 |
- 4.0
- 5.0
- 5.4
- 5.8
- 11.6
Ruslan recorded the temperature, in degrees Celsius, at the same time each day for 6 consecutive days. He recorded a temperature of 16°C on the 1st day and a temperature of −2°C on the 6th day. What was the change in the temperature recorded by Ruslan over the course of the 6 days?
- −18°C
- −3°C
- 3°C
- 14°C
- 18°C
The greatest common factor of 2 whole numbers is 10, and the least common multiple of these same 2 numbers is 150. What are the 2 numbers?
- 5 and 30
- 10 and 15
- 10 and 30
- 30 and 50
- 50 and 100
Elementary Algebra
In Elementary Algebra1, you'll master the basics of working with equations, solving problems with either numbers and/or expressions, and determining the value of variables. Essential skills in this content area include the ability to simplify algebraic expressions by combining like terms and understanding the relationships between numbers. Additionally, you’ll learn how to convert word problems into simple equations, solving them by isolating the variables.
- The ACT math questions incorporates ten items in elementary algebra, focusing on inequalities, linear equations, ratios, percentages, and averages.
Tricks and Strategies to ace this question type
Algebra expresses equations symbolically using variables like 'a,' 'b,' or 'x.' Unlike regular arithmetic, algebra allows for unknowns in expressions, introducing concepts like "a + b = c." The ACT Math test often includes algebra questions, which test your ability to work with symbolic expressions. Solving algebraic equations, such as "x + 6 = 16," involves finding the numeric value of 'x' that makes the equation true—this value is the solution. The ACT Math test frequently features algebra questions, testing your ability to work with these symbolic expressions.
- Solving Expressions With Substitution
- Master manipulating equations and effectively solving problems with given expressions.
- Develop confidence in substituting numbers as a fundamental skill in algebra.
- Simplifying Algebraic Expressions
- Combine like terms and factorize expressions using basic math properties.
- Apply the associative and distributive properties for practical simplification.
- Writing/Solving Expressions and Equations
- Convert word problems into simple linear equations or expressions for solving.
- Solve equations by isolating the variable on one side and the numbers on the other.
- Multiplying Binomials
- Employ the FOIL method (First, Outer, Inner, Last) when dealing with binomials.
- Recognize the significance of FOIL for efficient multiplication.
- Inequalities
- Treat inequalities like equations, but be mindful of sign changes when multiplying or dividing both sides by a negative number.
- Understand the nuances of inequalities and their solutions for accurate problem-solving.
Elementary Algebra examples
Which of the following polynomials is a factor of x2 + bx − 15, given that x = −3 is a solution to the equation x2 + bx − 15 = 0 ?
- x − 5
- x − 3
- x − 2
- x + 2
- x + 5
Given that (x + 4) and (x − 3) are factors of the quadratic expression x2 + ax + a + b, what is the value of b ?
- 13
- 11
- 1
- −11
- −13
One of the following quadratic equations has the complex number as a solution. Which one?
- x2 + 3 = 0
- x2 − 3x + 3 = 0
- x2 + 3x + 3 = 0
- x2 − 6x + 12 = 0
- x2 + 6x − 12 = 0
Intermediate Algebra
Intermediate Algebra delves into quadratic equations, like, x² – 5x + 6. Learning to factor involves setting up parentheses based on coefficients. The roots, or solutions, are determined by finding the numbers that add to the middle term and multiply by the third term. This foundational skill prepares you for more intricate algebraic problem-solving in the Intermediate Algebra section.
- The ACT Math problems features nine intermediate algebra questions that revolve around exponents, roots, simultaneous equations, and quadratic equations.
Tricks and Strategies to ace this question type
- Mastering Quadratic Equations
- Understand the standard form ax² + bx + c.
- Effectively factorize examples like x² – 5x + 6.
- Apply rules for adding, multiplying, and determining roots.
- Tackling Systems of Equations
- Follow the "n equations with n variables rule" for multi-variable equations.
- Apply substitution and combination methods for efficient problem-solving.
- Unlocking Functions
- Visualize (x, f(x)) as (x, y) and use “pick numbers” for problem-solving.
- Apply “pick numbers” to analyze and compare given functions.
- Demystifying Logarithms
- Recognize logarithms as an exponent alternative.
- Grasp the core concept: logx(y) = a, and refer to a comprehensive list of logarithm rules if needed.
Intermediate Algebra Examples
The function f that is defined as f(x) = 7 − 5x has domain {−1, 0, 3}. What is the range of f ?
- {−8, 2, 12}
- {−8, 7, 12}
- {−2, 0, 6}
- {2, 7, 12}
- {2, 7, 22}
Which of the following expressions is equivalent to for all nonzero values of x and y ?
Rodney rides a skateboard at a constant rate along a straight line past his friends Alana, Bucky, Chad, Daewon, and Elissa. His friends record the time t, in seconds, that it takes Rodney to reach them and the distance d, in feet, he is from a reference point. The results are shown in the table below.
If Rodney is a distance of d = 13 feet from his reference point at time t = 0, which of the equations below represents the relationship between d and t ?
- d = t + 13
- d = t + 16
- d = 3t + 10
- d = 3t + 13
- d = 13t + 3
Coordinate Geometry
Coordinate geometry requires a thorough understanding of its various aspects to navigate the diverse questions on the test. Fortunately, once you grasp the fundamentals, coordinate geometry becomes easy to visualize and comprehend. Coordinate geometry involves working with line graphs on the (x, y) coordinate plane.
- ACT Math question types include nine coordinate geometry problems that focus on slope, distance, midpoint, parallel and perpendicular lines, points of intersection, and graphing.
Tricks and Strategies to ace this question type
Coordinate plane questions assess your comprehension of its mechanics, focusing on how to manipulate points and lines. These questions may test your understanding of the coordinate plane’s infinite expanse, your grasp of negative and positive x and y coordinate values, and your ability to visualize the movement of points across the coordinate plane.
- Note Down Given Information
- Resist the temptation to solve coordinate geometry problems mentally.
- Avoid mistakes by writing down given information, especially with negatives or absolute values.
- When a diagram lacks coordinates, jot down the information to organize your thoughts.
- Visualize with Drawings
- Sketch scenarios, even creating your own diagrams when none are provided.
- Mark details on sketches to help manage information effectively.
- Invest a small amount of time in drawing, saving energy and preventing mental overload.
- Select Formulas Wisely
- Decide which formulas to use beforehand, preventing last-minute confusion.
- If comfortable, memorize additional formulas, but ensure accuracy through practice.
- Focus on key formulas, such as the Pythagorean theorem, and prioritize quality over quantity.
Coordinate Geometry Examples
The bar graph below shows the number of children enrolled in the after-school program from the 7 classes at Sunshine Children’s Learning Center. What is the probability that a child selected at random from the after-school program is from Class 2 ?
Which of the following is an equation of a parabola that passes through the points labeled in the standard (x,y) coordinate plane below?
In the standard (x,y) coordinate plane, the graph of has a vertical asymptote at:
- x = 2
- x = 3
- x = 5
- x = 10
- x = 30
Plane Geometry
Although you might manage the ACT without a strong grasp of trigonometry or intermediate algebra, a solid understanding of plane geometry is indispensable. This is crucial as geometry questions make up a substantial portion of the test.
- The ACT Math questions features 14 plane geometry items based on angles, lengths, triangles, quadrilaterals, circles, perimeter, area, and volume.
Tricks and Strategies to ace this question type
Plane geometry problems rank among the most challenging questions on the ACT math section, typically requiring more time and completion in multiple steps. Use this awareness to prioritize your study efforts in the most productive areas.
- Clarify the Problem
- Identify the specific information the problem seeks for solids like cubes or spheres.
- Understand whether you're asked to find volume, surface area, or both.
- Recognize the relevant formulas and elements of the geometric solid(s) involved.
- Visualize with Drawings
- Draw a sketch when the problem describes a solid without a provided image.
- Improve your understanding by visualizing the information and its application to the question.
- Apply Formulas Efficiently
- Apply the identified formulas by plugging in the provided information.
- If formulas escape memory, resort to alternative methods like the Pythagorean theorem.
- Ensure Clarity and Accuracy
- Label your work meticulously to avoid falling into trap answers.
- Double-check your solution for consistency and correctness, especially in a high-stress setting.
Plane Geometry Examples
In the figure below, ABCD is a trapezoid with perpendicular to is 8 inches long; and is 22 inches long. If the area of right triangle △BCE is 40 square inches, what is the area, in square inches, of trapezoid ABCD?
- 88
- 108
- 120
- 128
- 150
What is the area, in square centimeters, of a right triangle with side lengths of 6 cm, 10 cm, and 8 cm ?
- 24
- 30
- 40
- 48
- 60
In the circle below, radius and radius each have a length of 6 inches, and the measure of is 170°. The shaded sector is bounded by these radii and minor arc What is the area, in square inches, of the shaded sector of the circle?
Trigonometry
Trigonometry studies the relationships between the sides and angles of right triangles. The ratios between the measures of the sides of a right triangle and the measures of its angles are consistent, no matter how large or small the triangle.
- ACT Math problems includes four questions based on basic sine, cosine, tangent functions, trig identities, and graphing.
Tricks and Strategies to ace this question type
- Understand Basic Trigonometric Concepts
- Master fundamental concepts such as sine, cosine, tangent, and reciprocal functions.
- Familiarize Yourself with Trigonometric Identities
- Grasp essential trigonometric identities to simplify expressions and solve problems efficiently.
- Recall the SOHCAHTOA acronym
- Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent.
- Right Triangle Trigonometry
- Apply trigonometric principles to right-angled triangles for problem-solving.
- Recognize the relationships between angles and sides in a right triangle.
- Practice Problem-Solving
- Regularly practice solving diverse trigonometry problems to enhance proficiency.
- Review Special Trigonometric Values
- Memorize special values for common angles for quick calculations.
- Manage Time Effectively
- Develop time-management skills to allocate appropriate time to each trigonometry question.
- Utilize Calculator Functions Wisely
- Leverage calculator2 functions effectively, but ensure a solid understanding of concepts without over-reliance.
- Stay Calm and Focused
- Maintain composure during the test and stay focused on applying trigonometric concepts strategically.
- Review Mistakes for Improvement
- Improve your trigonometry skills continuously by learning from mistakes made on practice tests.
Trigonometry examples
A mail sorting facility uses a conveyor belt to move boxes. An inclined section of the conveyor moves boxes from a horizontal belt upward to another horizontal belt 15 feet higher, as shown below. The inclined section is 39 feet long and covers a horizontal distance of 36 feet. Which of the following expressions gives the measure of the angle between the inclined section of the conveyor and the horizontal?
In the right scalene triangle shown below, one angle measure and 2 side lengths, in meters, are given. In terms of a and b, what is cos θ?
A vertical flagpole has a 25-foot wire attached as shown in the figure below. The wire forms an angle of 47° with the level ground. The distance along the pole, in feet, between the ground and the top of the wire is equal to which of the following expressions?
Additional Topics in Math
The ACT Math test covers a broad range of topics, including additional math concepts that go beyond the traditional high school curriculum. Within the test, you'll encounter various ACT Math question types designed to assess your proficiency in different areas of mathematics.
- Complex Numbers:
- Work with complex numbers, understanding their properties and operations.
- Matrices and Vectors:
- Apply matrix and vector operations, including addition, multiplication, and transformations.
- Logarithmic and Exponential Functions:
- Review logarithmic and exponential functions, along with their applications.
- Conic Sections:
- Understand conic sections, including circles, ellipses, hyperbolas, and parabolas.
- Sequences and Series:
- Analyze sequences and series, recognizing patterns and calculating sums.
- Probability and Statistics:
- Apply advanced probability and statistics concepts, including conditional probability and statistical inference.
- Fundamental Calculus Concepts:
- Grasp fundamental calculus concepts without digging into extensive topics.
Additional topics in Math examples
The 1st term in the geometric sequence below is 4. If it can be determined, what is the 5th term?
4, −12, 36,−108, ⋯
- −324
- −144
- 144
- 324
- Cannot be determined from the given information
Max is playing a game involving 3 fair 6-sided cubes with the digits 1 through 6 on its faces, 1 digit per face. He will roll 3 cubes at the same time and will be awarded 4 points for each cube that has an odd number on its top face. Let the random variable X represent the total number of points awarded on any 1 roll. What is the expected value of X ?
- 2
- 6
- 12
- 24
- 36
One of the following matrices is equal to the matrix product . Which one?
Key Takeaways
Understanding the complexities of ACT Math is like untangling a web of mathematical concepts. Our guide, enriched with sample questions, can help you decode everything from algebraic equations to geometry challenges, providing practical tips and ACT math strategies for every question type. UWorld, a premier test prep resource, gives you access to unlimited exam-level practice, including a comprehensive collection of ACT Math sample questions, to boost your skills. Dive into detailed explanations that shed light on the reasoning behind each answer, helping you understand why certain solutions are correct. With these resources at your fingertips, you'll be well-equipped to tackle the ACT Math section with confidence and precision, setting the stage for a successful test-taking experience.
References
1(2024). Mathematics Test Description for the ACT. Act.org. Retrieved January 5, 2024, from https://www.act.org/content/act/en/products-and-services/the-act/test-preparation/description-of-math-test.html
2(2024). Math Test Tips. Act.org. Retrieved January 5, 2024, from
https://www.act.org/content/act/en/students-and-parents/high-school-success/testing-advice-for-the-act/act-math-test-tips.html