ACCUPLACER Math

ACCUPLACER Math Practice Test: 12 Questions Solved Step by Step

Twelve original ACCUPLACER-style math questions, four from each test, solved step by step, plus how the test works and how colleges use your score.

Professor Chacha October 9, 2026 12 min read 16 views
Young man writing in a notebook next to a laptop while studying at a desk by a brick wall

The ACCUPLACER math placement test is really three tests: Arithmetic, Quantitative Reasoning, Algebra, and Statistics (QAS), and Advanced Algebra and Functions (AAF). Each one has 20 multiple-choice questions, adjusts to your answers as you go, and is scored from 200 to 300. Your college decides which of the three you take and which score places you into which course.

Below are 12 original practice questions, four in the style of each test. Work each one out on paper before you open the solution. Every solution shows the steps and the trap that costs most students the point.

How the ACCUPLACER math test works

The College Board publishes the content of each test in its official test descriptions. Here is what each one covers:

TestWhat it covers
ArithmeticWhole number, fraction, and decimal operations; percents; comparing numbers written in different forms
Quantitative Reasoning, Algebra, and Statistics (QAS)Rational numbers, ratios and proportions, exponents, algebraic expressions, linear equations and graphs, probability and sets, descriptive statistics, basic geometry
Advanced Algebra and Functions (AAF)Linear equations and graphs, factoring, quadratics, functions, radical and rational equations, polynomial equations, exponential and logarithmic equations, geometry, trigonometry

A few facts change how you should prepare:

  • It is adaptive. The next question depends on how you answered the last one, and you have to answer every question. If you are stuck, eliminate what you can and choose the best remaining answer.
  • There is usually no time limit. The College Board says the test is untimed in most cases, but your test center confirms it. Use the time to check each answer.
  • You can't bring a calculator. Some questions show a calculator icon in the top-right corner of the screen and open an on-screen calculator. Many questions, especially arithmetic ones, have no calculator at all, so practice by hand.
  • You can't bring your own paper. Paper is on the list of items not allowed in the testing room. Ask your test center what it provides for working out problems.

Going to a public college in Texas? You will most likely take the TSIA2 instead. It runs on the same ACCUPLACER platform but has its own score scale and rules, covered in our TSI math practice test.

Arithmetic practice questions

Arithmetic questions test whether you can do the basics accurately without a calculator. Expect fractions, decimals, and percents, often inside a short word problem. For 15 more, three from each official area, try our ACCUPLACER Arithmetic practice test.

1.Subtract: \(2\tfrac{3}{4} - 1\tfrac{5}{6}\)

  1. A\(1\tfrac{1}{12}\)
  2. B\(\tfrac{11}{12}\)
  3. C\(1\tfrac{1}{2}\)
  4. D\(\tfrac{7}{12}\)
Show solution

Write both mixed numbers as improper fractions, then use the least common denominator, 12.

\[\begin{gathered}2\tfrac{3}{4} = \tfrac{11}{4} = \tfrac{33}{12} \\ 1\tfrac{5}{6} = \tfrac{11}{6} = \tfrac{22}{12}\end{gathered}\]\[\tfrac{33}{12} - \tfrac{22}{12} = \tfrac{11}{12}\]

Common trap: Subtracting the whole numbers and the fractions separately. That gives \(2 - 1 = 1\) and then \(\tfrac{3}{4} - \tfrac{5}{6}\), which is negative. Students who drop the minus sign pick \(1\tfrac{1}{12}\). Because \(\tfrac{5}{6}\) is bigger than \(\tfrac{3}{4}\), you have to borrow, and improper fractions do that for you.

Answer: B (\(\tfrac{11}{12}\))

2.A jacket costs $80. It is on sale for 25% off, and then 8% sales tax is added to the sale price. What is the total cost?

  1. A$66.40
  2. B$64.80
  3. C$60.00
  4. D$86.40
Show solution

Find the sale price first, then add tax on that price.

\[\begin{gathered}80 \times 0.75 = 60 \\ 60 \times 0.08 = 4.80 \\ 60 + 4.80 = 64.80\end{gathered}\]

In one step: \(80 \times 0.75 \times 1.08 = 64.80\).

Common trap: Combining the two percents into one: \(-25\% + 8\% = -17\%\), so \(80 \times 0.83 = 66.40\). The tax is 8% of the sale price ($60), not of the original price, so the percents can't be added.

Answer: B ($64.80)

3.Divide: \(0.36 \div 0.012\)

  1. A0.3
  2. B3
  3. C30
  4. D300
Show solution

Move the decimal point in both numbers the same number of places, until the divisor is a whole number. Here that is three places.

\[0.36 \div 0.012 = 360 \div 12 = 30\]

Check: \(30 \times 0.012 = 0.36\).

Common trap: Moving the decimal point in only one of the numbers, or a different number of places in each. That is how 3 and 0.3 appear. Always check by multiplying your answer by the divisor.

Answer: C (30)

4.Which of these numbers is the greatest?

  1. A\(\tfrac{5}{8}\)
  2. B0.6
  3. C62%
  4. D0.615
Show solution

Write every number as a decimal with the same number of places.

\[\begin{gathered}\tfrac{5}{8} = 0.625 \\ 0.6 = 0.600 \\ 62\% = 0.620 \\ 0.615\end{gathered}\]

The greatest is 0.625, which is \(\tfrac{5}{8}\).

Common trap: Picking 0.615 because it has more digits. Line the numbers up to three decimal places and compare them digit by digit.

Answer: A (\(\tfrac{5}{8}\))

Quantitative Reasoning, Algebra, and Statistics practice questions

QAS mixes pre-algebra and Algebra 1 with data. Linear equations and their graphs show up the most, along with ratios and basic statistics. Our ACCUPLACER QAS practice test has 15 more questions covering all nine QAS areas.

5.Solve for \(x\): \(3(x - 4) = 2x + 5\)

  1. A1
  2. B9
  3. C\(-7\)
  4. D17
Show solution

Distribute the 3 to both terms inside the parentheses, then get \(x\) alone.

\[\begin{gathered}3x - 12 = 2x + 5 \\ \Rightarrow\; 3x - 2x = 5 + 12 \\ \Rightarrow\; x = 17\end{gathered}\]

Check: \(3(17 - 4) = 39\) and \(2(17) + 5 = 39\).

Common trap: Multiplying only the \(x\) by 3 and writing \(3x - 4\). That leads to \(x = 9\). The 3 multiplies everything inside the parentheses.

Answer: D (17)

6.A pancake recipe uses 3 cups of flour for 4 servings. How many cups of flour are needed for 10 servings?

  1. A\(7\tfrac{1}{2}\)
  2. B9
  3. C\(13\tfrac{1}{3}\)
  4. D12
Show solution

Find the flour for one serving, then multiply by 10.

\[\begin{gathered}\tfrac{3}{4} \text{ cup per serving} \times 10 \\ = \tfrac{30}{4} = 7\tfrac{1}{2} \text{ cups}\end{gathered}\]

As a proportion: \(\tfrac{3}{4} = \tfrac{c}{10}\), so \(4c = 30\) and \(c = 7.5\).

Common trap: Two traps here. Adding instead of scaling: 6 more servings means 6 more cups, so 9. Or writing the proportion upside down, \(\tfrac{4}{3} = \tfrac{c}{10}\), which gives \(13\tfrac{1}{3}\). Keep the same units on top in both fractions: cups over servings.

Answer: A (\(7\tfrac{1}{2}\))

7.Five students scored 72, 90, 68, 85, and 85 on a quiz. What is the median minus the mean?

  1. A5
  2. B12
  3. C17
  4. D0
Show solution

The mean is the total divided by 5:

\[\tfrac{72 + 90 + 68 + 85 + 85}{5} = \tfrac{400}{5} = 80\]

For the median, put the scores in order first: 68, 72, 85, 85, 90. The middle score is 85.

\[85 - 80 = 5\]

Common trap: Taking the middle of the list without sorting it. The middle of 72, 90, 68, 85, 85 is 68, and \(80 - 68 = 12\). The median only makes sense after the numbers are in order.

Answer: A (5)

8.Which equation describes the line that passes through the points \((-2, 1)\) and \((4, 4)\)?

  1. A\(y = 2x + 5\)
  2. B\(y = \tfrac{1}{2}x + 2\)
  3. C\(y = \tfrac{1}{2}x - 4\)
  4. D\(y = -\tfrac{1}{2}x\)
Show solution

The slope is the change in \(y\) divided by the change in \(x\):

\[m = \tfrac{4 - 1}{4 - (-2)} = \tfrac{3}{6} = \tfrac{1}{2}\]

Put one point into \(y = mx + b\) to find \(b\):

\[\begin{gathered}1 = \tfrac{1}{2}(-2) + b \\ \Rightarrow\; 1 = -1 + b \\ \Rightarrow\; b = 2\end{gathered}\]

So \(y = \tfrac{1}{2}x + 2\). Check the other point: \(\tfrac{1}{2}(4) + 2 = 4\).

Common trap: Dividing run by rise and getting a slope of 2. The line \(y = 2x + 5\) does pass through \((-2, 1)\), which makes it look right, but it misses \((4, 4)\). Check your equation with both points.

Answer: B (\(y = \tfrac{1}{2}x + 2\))

Advanced Algebra and Functions practice questions

AAF is the test for students placing into college algebra, precalculus, or higher. It assumes Algebra 1 is solid and moves on to quadratics, functions, exponents, and radicals. Factoring comes up often; our lesson on how to factor trinomials covers it step by step.

9.Solve: \(x^2 - 5x - 14 = 0\)

  1. A\(x = -7\) or \(x = 2\)
  2. B\(x = 7\) or \(x = -2\)
  3. C\(x = 14\) or \(x = -1\)
  4. D\(x = -14\) or \(x = 5\)
Show solution

Look for two numbers that multiply to \(-14\) and add to \(-5\): they are \(-7\) and \(2\).

\[\begin{gathered}(x - 7)(x + 2) = 0 \\ \Rightarrow\; x = 7 \text{ or } x = -2\end{gathered}\]

Common trap: Stopping at the factors and keeping their signs. The factor \(x - 7\) is zero when \(x = 7\), so each solution has the opposite sign of the number in its factor.

Answer: B (\(x = 7\) or \(x = -2\))

10.If \(f(x) = 2x^2 - 3x + 1\), what is \(f(-2)\)?

  1. A3
  2. B\(-1\)
  3. C11
  4. D15
Show solution

Replace every \(x\) with \((-2)\), keeping the parentheses.

\[\begin{gathered}f(-2) = 2(-2)^2 - 3(-2) + 1 \\ = 2(4) + 6 + 1 \\ = 15\end{gathered}\]

Common trap: Two sign mistakes lead to the wrong choices. Writing \((-2)^2\) as \(-4\) gives \(-1\). Writing \(-3(-2)\) as \(-6\) gives 3. Put the number in parentheses every time you substitute.

Answer: D (15)

11.Solve for \(x\): \(3^{x + 1} = 81\)

  1. A4
  2. B3
  3. C26
  4. D27
Show solution

Write 81 as a power of 3, then set the exponents equal.

\[\begin{gathered}81 = 3^4 \\ \Rightarrow\; x + 1 = 4 \\ \Rightarrow\; x = 3\end{gathered}\]

Common trap: Finding that the exponent is 4 and stopping there. The exponent is \(x + 1\), so \(x\) is 3. Another common slip is dividing 81 by 3 and choosing 27.

Answer: B (3)

12.Solve: \(\sqrt{x + 7} = x - 5\)

  1. A\(x = 2\) only
  2. B\(x = 2\) and \(x = 9\)
  3. C\(x = 9\) only
  4. DNo solution
Show solution

Square both sides, then solve the quadratic.

\[\begin{gathered}x + 7 = (x - 5)^2 \\ x + 7 = x^2 - 10x + 25\end{gathered}\]\[\begin{gathered}x^2 - 11x + 18 = 0 \\ \Rightarrow\; (x - 9)(x - 2) = 0 \\ \Rightarrow\; x = 9 \text{ or } x = 2\end{gathered}\]

Now check both in the original equation. For \(x = 9\): \(\sqrt{16} = 4\) and \(9 - 5 = 4\). It works. For \(x = 2\): \(\sqrt{9} = 3\) but \(2 - 5 = -3\). It does not work.

Common trap: Keeping both answers from the quadratic. Squaring both sides can create an extra answer that does not satisfy the original equation, so a radical equation always needs a final check.

Answer: C (\(x = 9\) only)

Answer key

Click a number to go back to that question.

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

Teacher's note: The habit I push hardest with students preparing for an entrance exam is simple: put your answer back into the problem before you move on. It takes seconds, and it catches the slips behind most of the traps above, from a decimal in the wrong place to a solution that does not really work. On an untimed test like ACCUPLACER, there is no reason to skip it.

Read nextGED Math Practice Test: 12 Questions Solved Step by StepRead nextPercent Word Problems: How to Solve Them, With Practice

What your ACCUPLACER math score means

Scores run from 200 to 300. There is no single passing score: each college decides which scores place you into which course, so the score you need depends on the school and the class you want. Ask your advisor or check your college's placement page before test day.

The College Board describes what students in each score range can usually do, using seven score bands:

Score band
200 to 220
221 to 230
231 to 240
241 to 250
251 to 260
261 to 270
271 to 300

Your score report links to these descriptions. Reading the band just above yours tells you exactly which skills to work on before a retest.

A two-week plan before test day

  1. Day 1: Take the free official practice test. You need to create an account on the ACCUPLACER site to use it. Write down every topic you missed.
  2. Days 2 to 10: Study one weak topic per day. Do the problems by hand, then check each answer. Most points are lost on fractions, percents, and linear equations, so start there unless your practice test says otherwise.
  3. Days 11 and 12: Redo the questions on this page and the official practice test without looking at your notes.
  4. Day 13: Confirm the time, place, and ID you need with your test center. Ask whether you can retake the test and how long you would have to wait.
  5. Day 14: Rest. A clear head is worth more than one more night of cramming.

Remember that you can take your time on test day. On an untimed test, the students who check every answer are the ones who move up a course.

Tags: ACCUPLACER Algebra Fractions Percents Practice test
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.

Keep practicing

Comments (0)

Be the first to comment.

Leave a comment