ACCUPLACER Arithmetic Test: The Five Skill Areas and Worked Examples

What the Arithmetic test covers

Arithmetic is the foundation of the three ACCUPLACER math tests. College Board says it measures fluency with and understanding of basic arithmetic, and that questions may be pure computation or a real-life situation you have to turn into math. Every question stands alone.

You may take Arithmetic because your college assigns it, or because a low score on Quantitative Reasoning, Algebra, and Statistics (QAS) branches you down to it. Either way, these skills also carry QAS, so time spent here isn't wasted. Start by working fraction, decimal, and percent problems with every step shown → until the procedures feel automatic.

What each score band expects

College Board's Skills Insight statements for Arithmetic make a clear ladder. Each band adds to the ones below it:

Notice where percents sit: the middle and upper bands are mostly about percents and fractions. If your college's Arithmetic cutoff is in the 250s or 260s, percent fluency is the skill to build.

Worked examples (original, not from the test)

1. Dividing by a number between 0 and 1. What is 4.5 ÷ 0.3?

Move the decimal one place in both numbers: 45 ÷ 3 = 15. Sanity check: dividing by something smaller than 1 makes the result larger, so an answer below 4.5 must be wrong. That check alone eliminates two choices on many questions.

2. Percent increase. A bus pass rises from $40 to $46. What is the percent increase?

The change is $6. Divide by the original price, not the new one: 6 ÷ 40 = 0.15, so 15%. Dividing by the new price (6 ÷ 46) is a classic mistake, so expect to see its result among the choices.

3. Comparing mixed formats. Which list is in order from least to greatest: 0.6, 5/8, 62%?

Convert everything to decimals: 0.6 = 0.600, 5/8 = 0.625, 62% = 0.620. So the order is 0.6, 62%, 5/8. Writing all three with three decimal places makes the comparison mechanical.

4. Order of operations with mixed numbers. Evaluate 2 1/2 + 3/4 × 2.

Multiply first: 3/4 × 2 = 6/4 = 1 1/2. Then add: 2 1/2 + 1 1/2 = 4. Adding first gives (2 1/2 + 3/4) × 2 = 6 1/2, a classic distractor.

5. Percents over 100%. A small business made 180% of last year's sales. Last year's sales were $25,000. What were this year's sales?

180% = 1.8, and 1.8 × 25,000 = 45,000. "180% of" means the whole amount, not an increase of 180%, which would give $70,000.

Mistakes that cost the most points

• Percent of the wrong base. Increase and decrease use the original value as the denominator.
• Reading "of" as add. "Percent of" means multiply.
• Mixed-number shortcuts. Convert mixed numbers to improper fractions before multiplying or dividing; never multiply the whole numbers and fractions separately.
• Skipping the size check. Before choosing, estimate. If 0.48 × 19 is "about half of 20," the answer is near 9, not 91.
• Rounding too early. Round once, at the end, to the place the question asks for.

Practice without a calculator

You can't bring a calculator. Some math questions provide an on-screen one through a calculator icon, but not all do, and College Board offers one only where it doesn't give the answer away. Because much of Arithmetic is about doing the operation, plan on working most questions by hand.

A useful drill: write ten mixed problems per session (two of each skill area), solve them on paper, and check them with a calculator only afterward. Track which area produces errors, then focus your next sessions on the Arithmetic skill area that keeps costing points →.

The free ACCUPLACER practice questions include Arithmetic items with full explanations, and College Board's free Arithmetic sample questions come with a rationale for each choice. When Arithmetic feels solid, look at the QAS guide, because a strong Arithmetic score can branch you up to QAS at some colleges.