ACCUPLACER Math

ACCUPLACER QAS Practice Test: 15 Questions Solved Step by Step

Fifteen original ACCUPLACER QAS questions covering all nine official areas, from ratios to probability, solved step by step.

Professor Chacha October 9, 2026 6 min read 5 views
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Quantitative Reasoning, Algebra, and Statistics (QAS) is the middle ACCUPLACER math test. It covers pre-algebra and Algebra 1 plus some data and geometry, and most community college students who place into a credit math course do it through this test. Below are 15 original QAS-style questions, solved step by step, covering every area on the official list.

What QAS covers

The College Board's test specifications list nine content areas for QAS, with 1 to 4 questions from each on a 20-question test:

Area Questions here
Rational numbers 1, 2
Ratio and proportional relationships 3, 4
Exponents 5, 6
Algebraic expressions 7, 8
Linear equations 9
Linear applications and graphs 10, 11
Probability and sets 12, 13
Descriptive statistics 14
Geometry concepts 15

Some QAS questions show an on-screen calculator; many don't. Practice these by hand first. If you want the big picture of all three ACCUPLACER math tests and how scores work, start with our ACCUPLACER math practice test, which also has four more QAS questions.

Numbers, ratios, and exponents

1.Divide: \(-\tfrac{2}{3} \div \tfrac{4}{9}\)

  1. A\(-\tfrac{3}{2}\)
  2. B\(-\tfrac{8}{27}\)
  3. C\(\tfrac{3}{2}\)
  4. D\(-\tfrac{2}{3}\)
Show solution \[-\tfrac{2}{3} \times \tfrac{9}{4} = -\tfrac{18}{12} = -\tfrac{3}{2}\]

Common trap: Multiplying straight across, \(-\tfrac{2}{3} \times \tfrac{4}{9} = -\tfrac{8}{27}\). Dividing by a fraction means multiplying by its reciprocal.

Answer: A (\(-\tfrac{3}{2}\))

2.Evaluate: \(-5 - (-8) + (-3)\)

  1. A\(-16\)
  2. B6
  3. C0
  4. D\(-6\)
Show solution

Subtracting a negative is adding a positive.

\[-5 + 8 - 3 = 0\]

Common trap: Treating \(-(-8)\) as \(-8\), which leads to \(-16\). Two negatives next to each other make a plus.

Answer: C (0)

3.On a map, 1 inch represents 25 miles. Two towns are 3.6 inches apart on the map. How far apart are they in real life?

  1. A25 miles
  2. B90 miles
  3. C1.44 miles
  4. D75 miles
Show solution \[3.6 \times 25 = 90 \text{ miles}\]

Common trap: Dividing instead of multiplying: \(3.6 \div 25 = 0.144\). Each inch stands for 25 miles, so more inches mean more miles.

Answer: B (90 miles)

4.The ratio of boys to girls in a class is 3 to 5. There are 40 students. How many are boys?

  1. A24
  2. B25
  3. C8
  4. D15
Show solution

The ratio 3 : 5 splits the class into \(3 + 5 = 8\) equal parts. Each part is \(40 \div 8 = 5\) students.

\[\text{boys} = 3 \times 5 = 15\]

Common trap: Using \(\tfrac{3}{5}\) of 40, which gives 24. The ratio compares boys to girls, not boys to the whole class, so the total number of parts is 8.

Answer: D (15)

5.Simplify: \((2x^3)^2\)

  1. A\(4x^6\)
  2. B\(2x^6\)
  3. C\(4x^5\)
  4. D\(2x^5\)
Show solution

Square both the 2 and the \(x^3\). A power of a power multiplies the exponents.

\[(2x^3)^2 = 2^2 \cdot (x^3)^2 = 4x^6\]

Common trap: Squaring only the \(x\)-part and leaving the 2 alone, which gives \(2x^6\). The exponent applies to everything inside the parentheses.

Answer: A (\(4x^6\))

6.What is the value of \(3^{-2}\)?

  1. A\(-9\)
  2. B\(-6\)
  3. C\(\tfrac{1}{9}\)
  4. D\(-\tfrac{1}{6}\)
Show solution

A negative exponent means "one over" the positive power.

\[3^{-2} = \tfrac{1}{3^2} = \tfrac{1}{9}\]

Common trap: Thinking a negative exponent makes the answer negative. It flips the number into a fraction; the sign stays positive.

Answer: C (\(\tfrac{1}{9}\))

Expressions and equations

7.Simplify: \(3(2x - 5) - (x - 4)\)

  1. A\(5x - 19\)
  2. B\(5x - 11\)
  3. C\(7x - 11\)
  4. D\(5x + 1\)
Show solution

Distribute the 3, then distribute the minus sign to both terms in the second parentheses.

\[6x - 15 - x + 4 = 5x - 11\]

Common trap: Writing \(-(x - 4)\) as \(-x - 4\). The minus sign changes the sign of every term inside, so \(-4\) becomes \(+4\).

Answer: B (\(5x - 11\))

8.Evaluate \(a^2 - 2ab\) when \(a = -3\) and \(b = 2\).

  1. A21
  2. B\(-3\)
  3. C\(-21\)
  4. D3
Show solution \[(-3)^2 - 2(-3)(2) = 9 + 12 = 21\]

Common trap: Writing \((-3)^2\) as \(-9\), which gives 3. Put every substituted negative number in parentheses.

Answer: A (21)

9.Solve for \(x\): \(5 - 2(x + 1) = 11\)

  1. A4
  2. B\(-7\)
  3. C7
  4. D\(-4\)
Show solution \[\begin{gathered}5 - 2x - 2 = 11 \\ \Rightarrow\; 3 - 2x = 11 \\ \Rightarrow\; -2x = 8 \\ \Rightarrow\; x = -4\end{gathered}\]

Common trap: Subtracting 5 and 2 in the wrong order, or dropping the sign when dividing by \(-2\). Check: \(5 - 2(-4 + 1) = 5 + 6 = 11\).

Answer: D (\(-4\))

10.Where does the line \(y = -2x + 6\) cross the \(x\)-axis?

  1. A\((0, 6)\)
  2. B\((3, 0)\)
  3. C\((-3, 0)\)
  4. D\((6, 0)\)
Show solution

On the \(x\)-axis, \(y = 0\).

\[\begin{gathered}0 = -2x + 6 \\ \Rightarrow\; 2x = 6 \\ \Rightarrow\; x = 3\end{gathered}\]

Common trap: Choosing \((0, 6)\), which is where the line crosses the \(y\)-axis. The \(x\)-intercept is where \(y\) is zero.

Answer: B (\((3, 0)\))

11.A one-day car rental costs $35 plus $0.20 per mile. Your budget for the day is $95. What is the greatest number of miles you can drive?

  1. A475
  2. B175
  3. C300
  4. D400
Show solution \[\begin{gathered}35 + 0.20m \le 95 \\ \Rightarrow\; 0.20m \le 60 \\ \Rightarrow\; m \le 300\end{gathered}\]

Common trap: Dividing the whole budget by $0.20 and getting 475. The $35 daily charge comes out first.

Answer: C (300)

Probability, statistics, and geometry

12.A fair six-sided die is rolled once. What is the probability of rolling an even number or a number greater than 4?

  1. A\(\tfrac{2}{3}\)
  2. B\(\tfrac{5}{6}\)
  3. C\(\tfrac{1}{2}\)
  4. D\(\tfrac{1}{3}\)
Show solution

List the outcomes that work: even numbers are 2, 4, 6; numbers greater than 4 are 5, 6. Together that is 2, 4, 5, 6.

\[P = \tfrac{4}{6} = \tfrac{2}{3}\]

Common trap: Adding \(\tfrac{3}{6} + \tfrac{2}{6} = \tfrac{5}{6}\). That counts the 6 twice, because it is both even and greater than 4.

Answer: A (\(\tfrac{2}{3}\))

13.In a class of 30 students, 18 play a sport, 12 play an instrument, and 5 do both. How many students do neither?

  1. A0
  2. B10
  3. C25
  4. D5
Show solution

Students who do at least one: \(18 + 12 - 5 = 25\). The 5 is subtracted because those students were counted in both groups.

\[30 - 25 = 5\]

Common trap: Adding 18 and 12 to get 30 and concluding that nobody is left. The students who do both were counted twice.

Answer: D (5)

14.The mean of five numbers is 12. Four of the numbers are 10, 14, 9, and 11. What is the fifth number?

  1. A11
  2. B16
  3. C12
  4. D44
Show solution

The five numbers must add up to \(5 \times 12 = 60\).

\[\begin{gathered}60 - (10 + 14 + 9 + 11) \\ = 60 - 44 = 16\end{gathered}\]

Common trap: Answering 12, as if the missing number had to equal the mean. The other four average 11, so the fifth must be higher to pull the mean up.

Answer: B (16)

15.A rectangle has a perimeter of 46 cm and a length of 15 cm. What is its area?

  1. A\(345 \text{ cm}^2\)
  2. B\(690 \text{ cm}^2\)
  3. C\(120 \text{ cm}^2\)
  4. D\(64 \text{ cm}^2\)
Show solution

First find the width from the perimeter, \(P = 2l + 2w\).

\[\begin{gathered}46 = 2(15) + 2w \\ \Rightarrow\; 2w = 16 \\ \Rightarrow\; w = 8\end{gathered}\]\[A = 15 \times 8 = 120 \text{ cm}^2\]

Common trap: Using \(46 - 15 = 31\) or half the perimeter, 23, as the width. The perimeter includes each side twice.

Answer: C (\(120 \text{ cm}^2\))

Answer key

  1. 1 A
  2. 2 C
  3. 3 B
  4. 4 D
  5. 5 A
  6. 6 C
  7. 7 B
  8. 8 A
  9. 9 D
  10. 10 B
  11. 11 C
  12. 12 A
  13. 13 D
  14. 14 B
  15. 15 C

What to study next

  • Missed 3 or 4? Lines are worth a review: see how to find slope, which covers intercepts too.
  • Missed 11 or 14? Both are "take out the fixed part first" problems, the same skill as in our lesson on percent word problems.
  • Got almost everything right? Your college may let you take the harder Advanced Algebra and Functions test. The AAF questions in the main practice test show what it looks like.

Teacher's note: On QAS, the sign errors cost more points than the hard ideas. My advice is to slow down at one specific moment: every time a minus sign sits in front of parentheses or in front of a negative number. Pause, rewrite that piece with the sign handled, then continue. Questions 2, 7, 8, and 9 above all turn on that moment.

Tags: ACCUPLACER Algebra Probability QAS Statistics
Professor Chacha
Professor Chacha Math teacher and educational psychologist

Math teacher and educational psychologist with more than 20 years of classroom experience. He writes every practice question on this site from scratch and solves it step by step, the way he explains it to his own students.

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