# ACCUPLACER Math Practice Test Questions

Preparing for the ACCUPLACER Math test? Try these free ACCUPLACER 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 ACCUPLACER Math practice problems covering the most important math concepts on the ACCUPLACER Math test.

These ACCUPLACER Math practice questions are designed to be similar to those found on the real ACCUPLACER Math test. They will assess your level of preparation and will give you a better idea of what to study for your exam.

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**10 Sample ACCUPLACER Math Practice Questions**

1- If \(f(x) = 5 + x\) and \(g(x) = – x^2 – 1 – 2x\), then find \((g – f)(x)\)?

A. \(x^2 – 3x – 6\)

B. \(x^2 – 3x + 6\)

C. \(-x^2 – 3x + 6\)

D. \(-x^2 – 3x – 6\)

2- \(\frac{|3+x|}{7} ≤ 5\), then \(x =\) ?

A. \(–38 ≤ x ≤ 35\)

B. \(–38 ≤ x ≤ 32\)

C. \(–32 ≤ x ≤ 38\)

D. \(–32 ≤ x ≤ 32\)

3- \(tan (– \frac{π}{6})\) = ?

A. \(\frac{\sqrt{3}}{3}\)

B. \(-\frac{\sqrt{2}}{2}\)

C. \(\frac{\sqrt{2}}{2}\)

D. \(-\frac{\sqrt{3}}{3}\)

4- \(\frac{\sqrt{32a^5 b^3}}{\sqrt{2ab^2}}=?\)

A. \(4a^2 \sqrt {b}\)

B. \( 2b^2 \sqrt {a}\)

C. \( 4b^2 \sqrt {a}\)

D. \(-4a^2 \sqrt {b}\)

5- The cost, in thousands of dollars, of producing \(x\) thousands of textbooks is \(C (x) = x^2 + 10x + 30\). The revenue, also in thousands of dollars, is \(R(x) = 4x\). Find the profit or loss if 3,000 textbooks are produced. (\(profit = revenue – cost\))

A. $21,000 loss

B. $57,000 profit

C. $3,000 profit

D. $57,000 loss

6- Suppose a triangle has the dimensions indicated below:

Then Sin \(B =\) ?

A. \(\frac{3}{5}\)

B. \(\frac{4}{5}\)

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

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

7- Find the slope-intercept form of the graph \(6x – 7y = – 12\)

A. \(y = – \frac{7}{6} x – \frac{12}{7}\)

B. \(y = – \frac{6}{7} x + 12\)

C. \(y = \frac{6}{7} x + \frac{12}{7}\)

D. \(y = \frac{7}{6}x – 12\)

8- Ella (E) is 4 years older than her friend Ava (A) who is 3 years younger than her sister Sofia (S). If E, A, and S denote their ages, which one of the following represents the given information?

A. \(E=A+4\)

\(S=A-3\)

B. \(E=A+4\)

\(A=S+3\)

C. \(A=E+4\)

\(S=A-3\)

D. \(E=A+4\)

\(A=S-3\)

9- Which of the following point is the solution of the system of equations?

\(5x + y = 9\)

\(10x-7y= -18\)

A. \((2, 4)\)

B. \((2, 2)\)

C. \((1, 4)\)

D. \((0, 4)\)

10- Find the Center and Radius of the graph \((x – 3)^2 + (y + 6)^2 = 12\)

A. \((3, 6), \sqrt{3}\)

B. \((3, –6), 2\sqrt{3}\)

C. \((–3, 6), 2\sqrt{3}\)

D. \((3, –6), \sqrt{3}\)

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## Answers:

1- **D**

\((g – f)(x) = g(x) – f(x) = (– x^2 – 1 – 2x) – (5 + x)\)

\(– x^2 – 1 – 2x – 5 – x = – x^2 – 3x – 6\)

2- **B**

\(\frac{|3+x|}{7} ≤5⇒|3+x|≤35⇒-35≤3+x≤35⇒-35-3≤x≤35-3⇒

-38≤x≤32 \)

3-** D**

\((– \frac{π}{6}) = -\frac{\sqrt 3}{3}\)

4- **A**\(\frac{\sqrt{32a^5 b^3}}{\sqrt{2ab^2}}=\frac{4a^2 b\sqrt{2ab}}{b\sqrt{2a}}= 4a^2 \sqrt b\)

5- **D**

\( c(3)=(3)^2+10(3)+30=9+30+30=69\)

\(4×3=12⇒12-69=-57⇒57,000 \space\) loss

6- **B**

\(sinB=\frac{the \space length \space of \space the \space side \space that \space is \space opposite \space that \space angle}{the \space length \space of \space the \space longest \space side \space of \space the \space triangle} =\frac{4}{5}\)

7- **C**

\(-7y=-6x-12⇒y=\frac{-6}{-7}x-\frac{12}{-7}⇒y=\frac{6}{7}x+\frac{12}{7}\)

8- **D**

\(E = 4 + A\)

\(A = S – 3\)

9- **C**

\(5x + y = 9\)

\(10x-7y= -18\)

⇒ Multiplication \((–2)\) in first equation ⇒

\(-10x- 2y = -18 \)

\(10x-7y= -18\)

Add two equations together \(⇒ –9y = –36 ⇒ y = 4\) then: x = 1\)

10- **B**

\((x – h)^2 + (y – k)^2 = r^2 \) ⇒ center: \((h,k)\) and radius: \(r\)

\((x – 3)^2 + (y + 6)^2 = 12 \)⇒ center: \((3,-6)\) and radius: \(2\sqrt {3}\)

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