College Math Placement Practice Questions with Answers: Arithmetic to Precalculus

College math placement practice questions with full answers — from arithmetic and fractions through algebra, functions, and precalculus topics, designed for placement exam review.

College math placement tests determine which math course you start with — and starting in the right course matters. Placing into a remedial math course can add one or two semesters (and thousands of dollars in tuition) before you reach the course your program requires. Placing too high and finding yourself underprepared wastes similar time and money.

This page provides a representative set of practice questions organized by topic — from basic arithmetic through precalculus — with complete answers. Use these questions to assess where you are strong and where you need focused review before your placement test.

ViewMath is not affiliated with or endorsed by the College Board (ACCUPLACER), ACT, or any college or university placement testing program. Placement test formats vary by institution. Always confirm the specific topics and format of your placement test with your college’s testing center.

Section 1: Arithmetic and Number Sense

Questions in this area test basic computation, fractions, decimals, ratios, and percent — without a calculator.

  1. Compute: 3/4 + 2/3. (Answer: 9/12 + 8/12 = 17/12 = 1 5/12)
  2. Compute: 5/6 ÷ 2/3. (Answer: 5/6 × 3/2 = 15/12 = 5/4 = 1 1/4)
  3. Order from least to greatest: 0.75, 5/8, 3/4, 0.625. (Answer: 5/8 = 0.625, 0.625, 0.75 = 3/4, 0.75 → 0.625, 0.625, 0.75, 0.75. So: 5/8 = 0.625 < 3/4 = 0.75; all four values: 0.625 = 5/8 = 0.625, 0.75 = 3/4 = 0.75 → order: 5/8, 0.625 (tie), then 3/4, 0.75 (tie). Simplified: 0.625, 0.625, 0.75, 0.75.)
  4. A store marks up a $40 item by 35%. What is the selling price? (Answer: $40 × 1.35 = $54.00)
  5. Convert 0.045 to a fraction in lowest terms. (Answer: 45/1000 = 9/200)
  6. What is 15% of 280? (Answer: 0.15 × 280 = 42)
  7. A car travels 240 miles on 8 gallons of gas. What is the car’s fuel efficiency in miles per gallon? (Answer: 240 ÷ 8 = 30 mpg)

Section 2: Pre-Algebra and Integers

  1. Compute: −7 + (−3) × 2. Use order of operations. (Answer: −7 + (−6) = −13)
  2. Simplify: |−9| − |4|. (Answer: 9 − 4 = 5)
  3. Evaluate: 2³ − 4 × 2 + 6. (Answer: 8 − 8 + 6 = 6)
  4. A temperature drops 12°F per hour. If it starts at 7°F, what is the temperature after 3 hours? (Answer: 7 − 36 = −29°F)
  5. Simplify: −4(−3 + 7). (Answer: −4 × 4 = −16)

Section 3: Elementary Algebra

Placement tests often have a dedicated elementary algebra section covering linear equations, inequalities, and basic polynomial operations.

  1. Solve for x: 4x − 7 = 17. (Answer: 4x = 24, x = 6)
  2. Solve for y: 3(y + 2) = 2y − 4. (Answer: 3y + 6 = 2y − 4, y = −10)
  3. Solve the inequality: 5 − 2x > 11. (Answer: −2x > 6, x < −3)
  4. Simplify: (3x² + 5x − 2) + (x² − 3x + 7). (Answer: 4x² + 2x + 5)
  5. Multiply: (2x − 3)(x + 4). (Answer: 2x² + 8x − 3x − 12 = 2x² + 5x − 12)
  6. Factor: x² + 7x + 12. (Answer: (x + 3)(x + 4))
  7. Solve the system: 2x + y = 10 and x − y = 2. (Answer: Add equations: 3x = 12, x = 4; then y = 10 − 8 = 2. Solution: (4, 2))

Section 4: Intermediate Algebra

  1. Simplify: (x³y²)/(xy⁴). (Answer: x²/y²)
  2. Solve: x² − 5x + 6 = 0. (Answer: (x − 2)(x − 3) = 0, x = 2 or x = 3)
  3. Simplify: √(50). (Answer: 5√2)
  4. Rationalize the denominator: 3/√5. (Answer: 3√5/5)
  5. Solve: 2x² = 18. (Answer: x² = 9, x = ±3)
  6. Write the equation of the line through (2, 3) with slope −1/2. (Answer: y − 3 = −1/2(x − 2), or y = −x/2 + 4)
  7. The vertex of y = (x − 3)² + 5 is at what point? (Answer: (3, 5))

Section 5: Precalculus and College Algebra

  1. Find f(3) if f(x) = 2x² − 4x + 1. (Answer: 2(9) − 4(3) + 1 = 18 − 12 + 1 = 7)
  2. What is the domain of f(x) = 1/(x − 4)? (Answer: All real numbers except x = 4)
  3. Simplify: log₂(32). (Answer: 2⁵ = 32, so log₂(32) = 5)
  4. Convert 150° to radians. (Answer: 150 × π/180 = 5π/6)
  5. If sin θ = 3/5 and θ is in the first quadrant, find cos θ. (Answer: Using Pythagorean identity, cos θ = 4/5)
  6. Find all values of x in [0, 2π) where cos x = −1. (Answer: x = π)
  7. The exponential equation e^x = 7 solved for x is x = ___. (Answer: x = ln 7)

How to Use These Practice Questions

Work through each section without a calculator first (most placement tests restrict calculator use for the arithmetic and algebra portions). Mark every question you are unsure about, even if you eventually wrote an answer. After finishing a section, review all marked questions before checking the answers.

Sort your results into three categories:

  • Mastered: Answered correctly and confidently. Brief review only.
  • Shaky: Got it right but slowly or unsurely. Practice 5–10 more of this type.
  • Not yet: Wrong or left blank. Find a resource (textbook, Khan Academy, tutoring) and address the gap before the test.

Most students need 2–4 weeks of focused review to move up one placement level. Targeted, daily practice on the weakest areas is more effective than reviewing everything at random.

ViewMath College Math Resources

ViewMath offers practice books for college math placement tests and related assessments. Browse the college math catalog using the sidebar below.

ViewMath is an independent publisher. Our materials are designed for practice and review and are not official placement test preparation materials from any college or testing organization.

Related Posts:

© 2026 ViewMath Math Made Easy