ACCUPLACER math practice test: Arithmetic, QAS and Advanced Algebra

ACCUPLACER math is three separate Next-Generation tests of 20 questions each: Arithmetic (fractions, decimals, percents), Quantitative Reasoning, Algebra and Statistics (QAS) and Advanced Algebra and Functions (AAF). Your college picks which one you take from the course you want. Each free drill below is 12 original questions with every answer explained.

3
math tests, 20 questions each: 12
questions in each free drill: Some
questions show a calculator: QAS
the test most students get

Last checked 20 October 2026 · Test facts from College Board and college testing centers

Free math drills: pick Arithmetic, QAS or Advanced Algebra. 12 original questions each at an 18-minute practice pace, then every answer explained. No sign-up.

12
questions
18 min
time limit
Free
every answer explained

By the LifeScore Editorial Team · Updated 20 October 2026 · How we check facts · How this is scored

Which ACCUPLACER math test will I take?

The one your college assigns for the course you are aiming at: Arithmetic for basic math and some certificate programs, QAS for most students heading to college algebra or statistics, and AAF for precalculus, calculus and STEM majors.

The three math tests, from College Board and college testing-center descriptions
Test	Questions	What it covers
Arithmetic	20	Whole numbers, fractions, decimals and percents, comparing numbers and equivalents
Quantitative Reasoning, Algebra and Statistics (QAS)	20	Rational numbers, ratios, exponents, expressions, linear equations and systems, functions, probability and statistics, geometry
Advanced Algebra and Functions (AAF)	20	Linear, quadratic and polynomial functions, exponential and logarithmic, radical and rational, and trigonometry

Many colleges start you on QAS and route you to Arithmetic or AAF if your score is very low or very high. If you are not told, prepare for QAS and review the Arithmetic basics, because QAS questions lean on fractions and percents throughout.

What is on the ACCUPLACER Arithmetic test?

Twenty questions on whole numbers, fractions, decimals and percents, comparing and ordering numbers, rounding and estimation, and short word problems that use them.

Arithmetic is the most basic math test, and most people underestimate it. The questions are not hard one by one, but they are designed to catch the slips people make when they have not done fractions by hand in years: adding numerators and denominators, misplacing a decimal point, or taking a percent of the wrong number.

The rules that cover most Arithmetic questions: fractions add and subtract only over a common denominator; multiply fractions straight across; divide by multiplying by the reciprocal; line up decimal points to add; count decimal places to multiply; part = percent × whole; and percent change = change ÷ original.

What is on the ACCUPLACER QAS test?

Twenty questions across nine categories: rational numbers, ratios and proportions, exponents, algebraic expressions, linear equations, linear applications, probability and sets, descriptive statistics, and geometry.

QAS is the algebra-and-data test most students meet. It mixes pure algebra (solve 5x − 4 = 2x + 11) with applied questions (a phone plan costs $25 plus $0.10 a minute) and short statistics (mean, median, range, a simple probability). Geometry is light: area, perimeter, volume and the Pythagorean theorem.

The biggest point-losers on QAS are sign errors when moving terms across an equals sign, slope calculated as run over rise, and probability questions with a "not" in them. All three are fixed by the same habit: check your answer in the original question before you choose.

What is on the ACCUPLACER Advanced Algebra and Functions test?

Twenty questions on linear, quadratic and polynomial equations and functions, exponential and logarithmic functions, radical and rational expressions, and right-triangle and unit-circle trigonometry.

AAF decides placement into precalculus and calculus, so it assumes you are comfortable with algebra and tests how far beyond it you go. Expect factoring and the quadratic formula, function notation and composition, inverses, exponential growth and decay, the definition of a logarithm, and the special-angle values of sine, cosine and tangent.

If you are aiming at a STEM program, this is the test to prepare hardest for: placing one level below calculus can push your whole sequence of science courses back a semester.

What do ACCUPLACER math questions look like?

Short problems with four options, from one-step fraction sums to exponential models. Six examples follow, two from each test; the first and fourth are worked in full and the others open when you tap.

ACCUPLACER-style question 1 · Fractions
What is 3/4 − 1/6?
1. A7/12
2. B1/3
3. C1/2
4. D5/12
Worked answer
A: 7/12. Use 12 as the common denominator: 3/4 = 9/12 and 1/6 = 2/12, so the difference is 7/12.
1. The smallest number both 4 and 6 divide into is 12.
2. 3/4 = 9/12 and 1/6 = 2/12.
3. 9/12 − 2/12 = 7/12, which does not simplify.
The trap: Subtracting tops and bottoms (3 − 1 over 4 − 6) gives nonsense. Fractions only subtract over a common denominator.
ACCUPLACER-style question 2 · Percent
A jacket is on sale for $63 after a 30% discount. What was the original price?
1. A$90
2. B$81.90
3. C$93
4. D$84
Show the worked answer
A: $90. After a 30% discount you pay 70% of the original, so 0.7 × price = 63 and the price is 63 ÷ 0.7 = $90.
1. The sale price is 100% − 30% = 70% of the original.
2. 0.7 × original = 63.
3. Original = 63 ÷ 0.7 = 90.
The trap: Adding 30% of $63 back ($81.90) is the classic slip: the 30% was taken from the original, not from the sale price.
ACCUPLACER-style question 3 · Linear equation
Solve for x: 5x − 4 = 2x + 11
1. A5
2. B7/3
3. C15
4. D3
Show the worked answer
A: 5. Subtract 2x from both sides: 3x − 4 = 11. Add 4: 3x = 15. Divide by 3: x = 5.
1. Collect the x terms: 5x − 2x = 3x, so 3x − 4 = 11.
2. Add 4 to both sides: 3x = 15.
3. x = 5. Check: 5(5) − 4 = 21 and 2(5) + 11 = 21.
The trap: Stopping at 3x = 15 and choosing 15. Always finish by dividing, then check in the original.
ACCUPLACER-style question 4 · Probability
A bag holds 4 red, 5 blue and 3 green marbles. One marble is drawn at random. What is the probability that it is not blue?
1. A7/12
2. B5/12
3. C7/5
4. D1/3
Worked answer
A: 7/12. There are 12 marbles and 7 that are not blue (4 red + 3 green), so the probability is 7/12.
1. Total: 4 + 5 + 3 = 12 marbles.
2. Not blue: 4 + 3 = 7.
3. Probability = 7/12.
The trap: 5/12 is the probability that it IS blue. Read "not" twice.
ACCUPLACER-style question 5 · Quadratic
What are the solutions of 2x² − 7x + 3 = 0?
1. Ax = 3 and x = 1/2
2. Bx = −3 and x = −1/2
3. Cx = 3 and x = 2
4. Dx = 6 and x = 1
Show the worked answer
A: x = 3 and x = 1/2. Factor: (2x − 1)(x − 3) = 0, because 2x × x = 2x², −1 × −3 = 3 and −6x − x = −7x. So x = 1/2 or x = 3.
1. Look for factors (2x + a)(x + b) with a × b = 3 and 2b + a = −7: a = −1, b = −3.
2. 2x² − 7x + 3 = (2x − 1)(x − 3).
3. Each factor can be zero: 2x − 1 = 0 gives x = 1/2, and x − 3 = 0 gives x = 3.
The trap: Flipping the signs (x = −3 and −1/2). The factor (x − 3) gives the solution +3, and (2x − 1) gives +1/2.
ACCUPLACER-style question 6 · Exponential
A town of 8,000 people grows by 5% a year. Which expression gives its population after t years?
1. A8,000(1.05)ᵗ
2. B8,000(0.05)ᵗ
3. C8,000 + 0.05t
4. D8,000(1.5)ᵗ
Show the worked answer
A: 8,000(1.05)ᵗ. Growing by 5% multiplies the population by 1.05 each year, so after t years it is 8,000 × 1.05ᵗ.
1. Each year the population is 100% + 5% = 105% of the year before.
2. 105% as a decimal is 1.05.
3. After t years: 8,000 × (1.05)ᵗ.
The trap: Using 0.05 as the base shrinks the town to almost nothing. The base is the growth factor, 1 + rate.

Make math the part you place high on

One drill shows the gap. Four more drills per math test and eight full mocks close it.

The ACCUPLACER Pass Pack gives you 8 full mocks on the real clock, 20 drills of 12 questions for the sections that cost you points, and a predictor that turns your mocks into the odds of reaching your target. One payment, no subscription, and your free score stays free.

Prep courses for these tests usually cost $19 to $129. The ACCUPLACER Pass Pack is US$39 (£29), once.

See the ACCUPLACER Pass Pack How our questions are built and checked

8
timed mocks: 20
topic drills: 1
score predictor

What formulas do I need for ACCUPLACER math?

The test gives you no formula sheet for most questions, so know these by heart: percent, percent change, slope, the Pythagorean theorem, the circle and rectangle formulas, the quadratic formula and the exponent and log rules.

Our study list, with the test each formula matters most on
Formula	What it says	Test
Percent	part = percent × whole	Arithmetic, QAS
Percent change	(new − old) ÷ old	Arithmetic, QAS
Slope	(y₂ − y₁) ÷ (x₂ − x₁)	QAS, AAF
Line	y = mx + b (m is slope, b is the y-intercept)	QAS, AAF
Mean	sum of values ÷ number of values	QAS
Pythagorean theorem	a² + b² = c²	QAS
Circle	area = πr², circumference = 2πr	QAS
Quadratic formula	x = (−b ± √(b² − 4ac)) ÷ 2a	AAF
Exponent rules	xᵃ · xᵇ = xᵃ⁺ᵇ, (xᵃ)ᵇ = xᵃᵇ	QAS, AAF
Logarithm	log_b(x) = y means bʸ = x	AAF
Growth model	amount = start × (1 + rate)ᵗ	AAF

Can I use a calculator on ACCUPLACER math?

Only the calculator the test itself shows, and it appears on some questions only; you cannot bring your own. Practise without one.

The pop-up calculator appears where College Board judges the arithmetic is not the point of the question. Everywhere else you work by hand on scratch paper, which is why fractions, negatives and exponents done by hand are worth an evening of review even for strong students. Our drills assume no calculator.

How should I study for ACCUPLACER math in a week?

Spend the first two days on fractions, decimals and percents, the next three on equations and your target test's topics, and the last two on full practice under exam habits.

Our plan, about 40 minutes a day

Day 1
40 min
Take the free drill for your target test. Write down every question type you missed.
Day 2
40 min
Fractions and percents by hand: 20 problems, checking each by estimating first.
Day 3
40 min
Linear equations and word problems: write one equation per problem before solving.
Day 4
40 min
Your target test's topics: statistics and geometry for QAS, factoring and functions for AAF.
Day 5
40 min
Exponents, roots and (for AAF) logarithms. Make a one-page formula card.
Day 6
45 min
Take the full [ACCUPLACER practice test](/accuplacer-practice-test) and review every miss.
Day 7
30 min
Redo the questions you missed, then rest. Sleep matters more than one more hour.

Frequently asked questions

How many math questions are on the ACCUPLACER?

Each math test has 20 questions. Most students take one math test; some colleges give two.

What is the hardest ACCUPLACER math test?

Advanced Algebra and Functions. It covers logarithms, trigonometry and function composition, and places students into precalculus and calculus.

What is a good ACCUPLACER math score?

It depends on the course and college. Valencia College, for example, lists QAS 276+ for college algebra. See ACCUPLACER scores for more charts.

Is the math adaptive?

Yes. Each answer affects the difficulty of the next question, so accuracy on the early questions matters.

Is there geometry?

A little, mainly on QAS: area, perimeter, volume and right triangles. AAF adds right-triangle trigonometry.

Place into the math course you want

Four drills for each math test, eight full five-part mocks and every answer worked step by step, in one payment.