ACT Math Problems

ACT Math Problems for the Exam

Instructions: This practice test contains 20 questions. You will see your score and the answers to all of the questions when you have completed the test.

1. A class has 312 students. Thirty-nine of the students in the class participate in marching band. What is the percentage of the students in the class that participate in marching band?

 
 
 
 
 

2. The owner of a carnival attraction launches toy boats of different colors. There are 15 boats in total: 5 are blue, 3 are red, and 7 are green. If the first boat launched is green, and the next boat launched is selected at random, what is the probability that the next boat is blue?

 
 
 
 
 

3. Consider a class which has n students. In this class, t% of the students subscribe to digital TV packages. Which of the equations represents the number of students who do not subscribe to any digital TV package?

 
 
 
 
 

4. In the equations below, x represents the cost of one online game and y represents the cost of one discounted movie ticket.
x – 2 > 5
y = x – 2
The cost of 2 discounted movie tickets is greater than which one of the following?

 
 
 
 
 

5. Solve the following: 115 × 113 = ?

 
 
 
 
 

6. What is the product of 20 and the square root of 144?

 
 
 
 
 

7. How many solutions exist for the following equation?
x2 + 8 = 0

 
 
 
 
 

8. Consider the following matrices:
matrices-1
What is A + B?

 
 
 
 
 

9. Consider a grocery store and a pizza place in a town.  The grocery store is represented by the coordinates (-4, 2) and the pizza place is represented by the coordinates (2,-4). If the grocery store and the pizza place are connected by a line segment, what is the midpoint between the two locations?

 
 
 
 
 

10. Consider the isosceles triangle in the diagram below:
angle measurement 1
What is the measurement of angle B?

 
 
 
 
 

11. A football field is 100 yards long and 30 yards wide. What is the area of the football field in square yards?

 
 
 
 
 

12. Angle A and angle B each have measurements between 0° and 45°. If cos A = sin B, what is the sum in degrees of Angle A + Angle B ?

 
 
 
 
 

13. Solve the following:  -| 21 – 32 | = ?

 
 
 
 
 

14. What is the volume of a cylinder that has a radius of 6 and a height of 10?

 
 
 
 
 

15. If a circle with center (-6, 6) is tangent to the x axis in the standard (x, y) coordinate plane, what is the diameter of the circle?

 
 
 
 
 

16. In the figure below, angle Y is a right angle and angleX = 60°.
If line segment YZ is 5 units long, then how long is line segment XY?

hypotenuse length 1

 
 
 
 
 

17. Marta has just bought a new pair of tennis shoes. She wants to wear the new running shoes to run up and down a hill near her house. The measurements to find the slope of the hill can be placed on a two dimensional linear graph on which x = 5 and y = 165. If the line crosses the y axis at 15, what is the slope of this hill?

 
 
 
 
 

18. For the following equation, i represents an imaginary number. Simplify the equation:
(1 – i) – (3 – 2i)

 
 
 
 
 

19. For the functions f2(x) listed below, x and y are integers greater than 1. If f1(x) = x2, which of the functions below has the greatest value for f1(f2(x))?

 
 
 
 
 

20. If the first term of an arithmetic sequence is 5, and we can find subsequent terms by adding 8, what equation can be used to find the nth term of the sequence?

 
 
 
 
 

Question 1 of 20

This page provides ACT math problems for the examination.

You will find problems and formulas for all of the parts of the math test.

Geometry exercises

Trigonometric functions

ACT Math Problems for Algebra

The algebra questions on the exam cover basic algebraic concepts such as:

  • mean (arithmetic average)
  • median
  • mode
  • range
  • algebraic fractions
  • absolute values
  • square roots
  • factoring and simplifying polynomials
  • algebraic inequalities, expressions, and equations
  • rational and radical expressions

You will encounter combinations of these concepts in certain math problems on the intermediate algebra part on the test.

So you will often need more than one type of math formula to solve these questions.

For instance, you may see a question that has a fraction that contains another fraction in its numerator or denominator.

Another common type of problem is where an erroneous result is given.

Then you have to use the data provided in order to correct the result.

For example, an average grade may have been calculated for a class, but the score for one student was omitted.

In these problems, you will be given the erroneous average and the omitted score.

Then you will have to calculate the correct average.

ACT – Geometry

The geometry questions page gives you the math formulas that you need for the test.

On our geometry page, you will learn how to solve coordinate geometry problems, like midpoints, slope, and distance.

Our geometry  page also gives you common formulas for plane geometry.

You will see all of the formulas for figures like circles, triangles, squares, rectangles, and cones.

On the geometry page, you will also see formulas for the circumference of circles.

Formulas are also given for the area, angles, perimeter, and volume of various geometric figures.

ACT – Trigonometry

You will also see the equations that you need in order to calculate trigonometric functions on the math test.

The trigonometry section illustrates the concepts of sine, cosine, and tangent.

It also gives you the math formulas that you need for these trigonometric relationships.

More ACT Math Problems

Need more math problems? If so, click on these links:

Types of ACT Math Problems

ACT Math Problems – Test 1

More ACT Math Problems