ACT Math Practice Test Questions

Preparing for the ACT Math test? Try following FREE ACT Math Practice Questions. Reviewing practice questions is the best way to brush up on your Math skills. Here, we walk you through solving 10 common ACT Math practice problems covering the most important math concepts on the ACT Math test. For additional educational resources, visit the U.S. Department of Education website.

These ACT Math practice questions are designed to be similar to those found on the real ACT Math test. They will assess your level of preparation and will give you a better idea of what to study for your exam. For additional educational resources, visit the U.S. Department of Education website.

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A. \(72 \%\)

B. \(120 \%\)

C. \(140 \%\)

D. \(160 \%\)

E. \(180 \%\)

6- If \(x\) is a real number, and if \(x^3+18=130\), then \(x\) lies between which two consecutive integers?

A. 1 and 2

B. 2 and 3

C. 3 and 4

D. 4 and 5

E. 5 and 6

7- if \(\frac{3x}{16} = \frac{x – 1}{4}\) =?

A. \(\frac{1}{4}\)

B. \(\frac{3}{4}\)

C. 3

D. 4

E. \(\frac{9}{4}\)

8- If \((x-2)^3=27\) which of the following could be the value of \((x-4)(x-3)\)?

A. 1

B. 2

C. 6

D. \(-1\)

E. \(-2\)

9- Simplify \((–5 + 9i)(3 + 5i)\)?

A. \(6 – 2i\)

B. \(60 – 2i\)

C. \(6 +2i\)

D. \(-60 +2i\)

E. \(2i\)

10- If tan \(\theta = 5/12\) and sin \(\theta > 0\), then cos \(\theta\) =?

A. \(-\frac{5}{13}\)

B. \(\frac{12}{13}\)

C. \(\frac{13}{12}\)

D. \(-\frac{12}{13}\)

E. 0

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Answers:

2- C
\(5^{\frac{7}{3}}× 5^{\frac{2}{3}} = 5 ^{\frac{7}{3} + \frac{2}{3}}= 5^{\frac{9}{3}}= 5^3\) For education statistics and research, visit the National Center for Education Statistics.

3- B
\(2x^2+3y^5-x^2+2z^3-2y^2+2x^3-2y^5+5z^3=2x^2-x^2+2x^3-2y^2+3y^5-2y^5+2z^3+5z^3=x^2+2x^3-2y^2+y^5+7z^3\) For education statistics and research, visit the National Center for Education Statistics.

4- C
Add the first 5 numbers. \(40 + 45 + 50 + 35 + 55 = 225\)
To find the distance traveled in the next 5 hours, multiply the average by number of hours.
\(Distance = Average × Rate = 50 × 5 = 250\)
Add both numbers. \(250 + 225 = 475\) For education statistics and research, visit the National Center for Education Statistics.

5- C
The question is this: 1.75 is what percent of 1.25?
Use percent formula:
\(part = \frac{percent}{100}× whole \)
\(1.75 = \frac{percent}{100}× 1.25 ⇒ 1.75 = \frac{percent ×1.25}{100}⇒175 = percent ×1.25 ⇒ percent =\frac{175}{1.25}= 140\) For education statistics and research, visit the National Center for Education Statistics.

6- D
Solve for \(x\).
\(x^3+18=130\)
\(x^3=112\)
Let’s review the options.
A. 1 and \(2. 1^3 = 1\) and \(2^3 = 8\), 112 is not between these two numbers.
B. 2 and 3. \(2^3 = 8 \space and \space 3^3 = 27\), 112 is not between these two numbers.
C. 3 and 4. \(3^3 = 27\) and \(4^3 = 64\), 112 is not between these two numbers.
D. 4 and 5. \(4^3 = 64 \) and \(5^3 = 125\), 112 is between these two numbers.
E. 5 and 6. \(5^3 = 125\) and \(6^3 = 216\), 112 is not between these two numbers. For education statistics and research, visit the National Center for Education Statistics.

7- D
Solve for \(x\).\(\frac{3x}{16} = \frac{x – 1}{4}\)
Multiply the second fraction by 4.
\(\frac{3x}{16}=\frac{4(x-1)}{4×4}\)
\(3x=4x-4\)
\(0=x-4\)
\(4=x\) For education statistics and research, visit the National Center for Education Statistics.

8- B
\((x-2)^3=27→x-2=3→x=5
→(x-4)(x-3)=(5-4)(5-3)=(1)(2)=2\) For education statistics and research, visit the National Center for Education Statistics.

9- D
We know that: \(i=√(-1)⇒i^2=-1\)
\( (-5+9i)(3+5i)=-15-25i+27i+45i^2=-15+2i-45=2i-60\) For education statistics and research, visit the National Center for Education Statistics.

10- B
\(tanθ=\frac{opposite}{adjacent}\)
\(tanθ=\frac{5}{12}\)⇒ we have the following right triangle. Then
\(c=√(5^2+12^2 )=√(25+144)=√169=13\)
\(\frac{adjacent}{hypotenuse}=\frac{12}{13}\) For education statistics and research, visit the National Center for Education Statistics.

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