ACT Math Practice Test

ACT Math Practice & Test Topics

The ACT Math Practice test website offers quizzes and free practice exercises for the ACT math test.

The test topics are provided after the quiz below.

ACT Math Practice Test 1

Instructions: Each practice test contains 20 questions. You will see your score and the explanations for the answers at the end of the test.

1. What is the largest possible product of 2 even integers whose sum is 22?

 
 
 
 
 

2. A union has 12,500 members. A recent report shows that 22% of the members earn more than $100,000 per year. How many members earn more than $100,000 per year?

 
 
 
 
 

3. In a shipment of 100 mp3 players, 1% are faulty.  What is the ratio of non-faulty mp3 players to faulty mp3 players?

 
 
 
 
 

4. A company sells jeans and T-shirts. J represents jeans and T represents T-shirts in the equations below:
2J + T = $50
J + 2T = $40
Sarah buys one pair of jeans and one T-shirt. How much does she pay for her entire purchase?

 
 
 
 
 

5. A company purchases cell phones at a cost of x and sells the cell phones at four times the cost. What equation below represents the profit made on each cell phone?

 
 
 
 
 

6. Solve the following: | 15 – 23 |  = ?

 
 
 
 
 

7. Table of values for the functions f1(x) and f2(x) are given below. What is the value of f2(f1(1))?

x f1(x) x f2(x)
1 4 1 1
2 5 2 4
3 6 3 9
4 7 4 16
 
 
 
 
 

8. What is the value of the expression 3x2 – xy + y2 when x = 2 and y = –2 ?

 
 
 
 
 

9. Consider a line that crosses the  y axis at 10 and upon which lies point (6, 4). What is the slope of this line?

 
 
 
 
 

10. If one leg of a triangle is 5cm and the other leg is 12cm, what is the measurement of the hypotenuse of the triangle?

 
 
 
 
 

11. Side A of an equilateral triangle is 3 units long. What is the individual length of each of the two other sides?

 
 
 
 
 

12. If x represents a real number, what is the greatest possible value of: 4 × sin 2x

 
 
 
 
 

13. An owner of a carnival attraction draws teddy bears out of a bag at random to give to prize winners. She has 10 brown teddy bears, 8 white teddy bears, 4 black teddy bears, and 2 pink teddy bears when she opens the attraction at the start of the day. What is the probability that the first prize winner of the day will receive a pink teddy bear?

 
 
 
 
 

14. Solve the following:  106 ÷ 104 = ?

 
 
 
 
 

15. Which of the answers below is equal to the following radical expression? square root of 45

 
 
 
 
 

16. If x – 1 > 0 and y = x – 1, then y > ?

 
 
 
 

17. If a circle has a diameter of 12, what is the circumference of the circle?

 
 
 
 
 

18. A box is manufactured to contain either laptop computers or notebook computers. When the computer systems are removed from the box, it is reused to hold other items. If the length of the box is 20cm, the width is 15cm, and the height is 25cm, what is the volume of the box?

 
 
 
 
 

19. If two angles are supplementary, which of the following is true?

 
 
 
 
 

20. sin2 + cos2 = ?

 
 
 
 

Question 1 of 20

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ACT Math Topics for Pre-algebra

Details of the concepts and topics in the pre-algebra questions on the test are given in this section.

Scroll down for an overview of all of the topics on the text.

Computations with Integers

Computations with integers are extremely common on the math section of the ACT examination.

Integers are positive and negative whole numbers.

Integers cannot have decimals, nor can they be mixed numbers. In other words, they can’t contain a fraction.

Percentages

You will have to calculate percentages on the ACT math exam.

There will also be questions on using percentages to solve other types of math problems or to create equations.

Practical Calculations

Many of the questions on the ACT Math Test will ask you to do practical calculations.

For instance, you may be asked to calculate the dimensions of an object or the price of an item in a store after a discount is given.

Other common ACT math calculations might involve computations with exam scores.

You may also see data for a class of students or systems of equations.

Ratios

Ratios are expressed by using the colon. So, a ratio of 2 to 100 is expressed as 2: 100.

The number before the colon expresses one subset of the total amount of items.

The number after the colon expresses a different subset of the total.

When the number before the colon and the number after the colon are added together, we get the total amount of items.

Square Roots and Other Radicals

Square roots are also known as radicals.

Algebra questions on the ACT math exam will assess your knowledge of square roots.

You will need to know how to perform the operations of multiplication and division on radicals.

You will also see problems that have square roots with exponents.

Setting Up Basic Equations

Some problems ask you to make basic equations from the information provided.

These questions are often practical problems that involve buying or selling merchandise.

If you are told the number of groups and the amount in each group, you need to multiply when you set up the equation.

When you are told total and the number of groups or the amount in each group, you need to divide when you set up the equation.

Be sure to assign separate variables for the total, the number of groups, and the amount in each group.

Re-read the problem carefully and then express the facts in terms of an algebraic equation.

Probability

Probability problems on the ACT math test will ask you about the chance of something happening.

You can calculate probability by using a ratio or percentage.

Note that fractions are slightly different than ratios.

1/20 is the same as saying “1 in 20” (so there are 20 parts in total)

On the other hand, a ratio is expressed as follows:

1 to 34 or 1: 34

There are 35 parts in total in the above example.

Inequalities

Inequality problems have a less than or greater than sign.

There may be more than one inequality in a single problem on the math part of the test.

The second equation may have the equal sign rather than an inequality sign.

Exponent Laws

You will need to know exponent laws very well for the ACT examination.

Remember that when the base numbers are the same and you need to multiply, you can add the exponents.

However, when the base numbers are the same and you need to divide, you can subtract the exponents.

ACT Math Practice – Test Topics Part 1

The math part of the ACT test is divided into three sections:

(1) The pre-algebra and elementary algebra portion of the test includes questions on basic math.

Approximately 40 percent of the problems on the ACT math test will be in this section.

  • fractions
  • percentages
  • decimals
  • ratios
  • setting up basic algebraic expressions
  • probability
  • inequalities
  • exponents
  • operations involving square roots and radicals

ACT Math Practice – Test Topics Part 2

(2) Intermediate Algebra and Coordinate Geometry is the second part of the math test.

About 30% of the math test will cover math problems like these.

You will need preparation and practice with more complex algebraic concepts:

ACT Math Practice – Test Topics Part 3

(3) The third and final part of the math exam is plane geometry and trigonometry.

This part constitutes 30% of the ACT math exam. For this part, you will need to study the following math concepts and formulas:

Questions on the ACT Math Exam

All of the questions on the math section of the ACT test are multiple-choice.

No points are deducted as a penalty if you respond to a question incorrectly, like on the CLEP and certain other standardized tests.

So, if you are not prepared for a certain question and do not know the correct answer, it is always better to guess.

You may use a calculator during the actual ACT examination.

ACT Calculator Requirements

However, must meet certain restrictions. See the official ACT website for further information.

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