ACT Math Test
There are 60 questions in the math section of the ACT, and 60 minutes are allotted to complete them. The topics that may be addressed in this portion of the test include algebra (pre-algebra, elementary, and intermediate), coordinate geometry, plane geometry, and trigonometry. Even though there are only six main topics, there are a significant number of question types that may be asked. They include questions dealing with linear equations, absolute value, exponents, factoring, inequalities, volume, and right triangles.*Tips: Many types of calculator are prohibited from use during the ACT. Make sure your calculator is on the "acceptable" list before you go to take the test. If you are caught with a prohibited calculator, you will be asked to leave the test room and your answer sheet will not be scored. Since you have only a minute to complete each question, it's important to work quickly. Don't let yourself get stuck on a question - you'll risk running out of time.
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ACT Math Test Questions
1. Simplify the following expression
(6x88 ÷ x2 )+ x3
A. 6x7
B. 6x9
C. 6x4 + x3
D. 6x6 + x3
2. What is the value of the following expression if m = -3 3m + 2m2 - 36
A. -63
B. -45
C. -27
D. -9
3. Solve for p using the following system of equations.
2p - 5k = 20
3p - 20k = 75
A. p = -1
B. p = 1
C. p = 5
D. p = -5
4. What is the midpoint of points D (5, -2) and E (26, 9)?
A. (1, 17.5)
B. (3.5, 15.5)
C. (17.5, 1)
D. (15.5, 3.5)
5. A square has a perimeter of 24cm. If a diagonal line is drawn through the square in such a way that two identical right triangles are produced, what is the length of the diagonal line?
A. 3.46 cm
B. 6 cm
C. 8.49 cm
D. 24 cm
ACT Math Test Questions - Answer Key:
1. Correct Answer: D
Explanation: To solve this problem, it is necessary to observe the law of exponents which states that xm/xn = xm-n.
Therefore, 6x8/x2 = 6x8-2, or 6x6
Since we cannot add x3 to this value, the expression cannot be simplified any further.
2. Correct Answer: C
Explanation: To solve this problem, it is necessary to substitute the provided value of m (-3) into the expression where m is used to represent the number:
3 (-3) + 2 (-3)2 - 36
Keep in mind that when negative numbers are squared, they become positive.
-9 + 2*9 - 36
-9 + 18 - 36
-27
3. Correct Answer: B
Explanation:
2p - 5k = 20
3p - 20k = 75
To solve for a variable using a system of equations, one of the variables must be cancelled out. To eliminate k from these equations, first multiply the top equation by -4.
-4(2p - 5k = 20)
-8p + 20k = -80
Then, add the two equations to eliminate k.
-8p + 20k = -80
+3p - 20k = 75
-5p = -5
Solve for p.
-5p = -5
p = -5/-5
p = 1
4. Correct Answer: C
Explanation: To find a midpoint, simply calculate the average of the two sets of points.
For x, the midpoint is calculated in the following manner:
(5 + 26)/2 = 15.5
For y, the midpoint is calculated in the following manner:
(-2 + 9)/2 = 3.5
The midpoint is (15.5, 3.5)
5. Correct Answer: D
Explanation: We know the figure is a square, meaning each of its sides is the same length. To find the length of each side, simply divide the perimeter by 4: 24 / 4 = 6cm
When a diagonal line is drawn through the square, two right triangles are formed.
Since we know the length of two of the triangle's sides (6cm), we can find the length of the third side by using the Pythagorean Theorem.
a2 + b2 = c2
62 + 62 = c2
36 + 36 = c2
72 = c2
v72 = vc2
8.49 = c
The length of the diagonal line is 8.49cm.
