College Math Placement Test Cheat Sheet 2026

The 30 highest-yield College Math Placement Test facts, distilled from real exam questions. Print it, save it as a PDF, or study it here — free, no sign-up.

1. What is the prime factorization of 72? → 2³ × 3²
2. What is the slope of the line through (−2, 5) and (4, −1)? → −1
3. If the steam cleaners charge 10 cents per square foot, how much would it cost in dollars to steam clean a room that is W yards wide and L yards long? → 0.9WL
4. If the scale on a blueprint is 1 cm = 2.5 meters, what does an area of 4 cm² on the blueprint represent in real life? → 25 m²
5. A temperature drops from 14°F to −8°F. By how many degrees did it drop? → 22°
6. What is the y-intercept of the line 3x + 2y = 12? → 6
7. Solve for x: 2(x - 3) = 4x + 6 → x = -6
8. Which number is NOT a multiple of 7? → 90
9. Simplify: (3/4 + 1/6) × 12 → 11
10. What are the roots of x² − 5x + 6 = 0? → x=2 and x=3
11. How long will it take Jessica and Johnny to paint the same house together if Jessica can do it in four hours and Johnny can do it in six? → 2 hours and 24 minutes
12. In College Math Placement Test preparation, which mathematical concept is foundational for problem-solving? → Understanding order of operations and algebraic reasoning
13. Which of the following is a factor of x² − 9? → (x − 3)(x + 3)
14. A bag contains 4 red, 3 blue, and 5 green marbles. What is the probability of drawing a blue marble? → 3/12
15. What is the slope of the line y = −4x + 7? → −4
16. What is the sum of the solutions of x² − 6x + 8 = 0? → 6
17. Which data representation is most appropriate for showing trends over time? → Line graph
18. Convert 2 3/4 to an improper fraction. → 11/4
19. Which of the following is equivalent to (x² − 9)/(x² − x − 6)? → (x + 3)/(x + 2)
20. In a right triangle, if one acute angle is θ, then the other acute angle is → 90° − θ
21. Which value of x satisfies 5x + 3 > 18? → x = 4
22. What are the x-intercepts of f(x) = x² + 2x − 15? → x = 3 and x = −5
23. A car travels 240 miles in 4 hours. At the same speed, how far will it travel in 7 hours? → 420 miles
24. A polynomial has roots x = 2 (multiplicity 2) and x = -1. What is the lowest-degree polynomial with these roots? → x³ - 3x² + 4
25. What is the horizontal asymptote of f(x) = (3x² + 2) / (x² - 5)? → y = 3
26. Which approach best demonstrates mastery of trigonometry in College Math Placement Test practice? → Applying principles to novel situations with sound judgment
27. A rectangular prism has length 5, width 4, and height 3. What is its surface area? → 94
28. Simplify: 3x − 2(4 − x) + 7 → 5x + 3
29. What is the equation of a circle centered at (3, −2) with radius 7? → (x−3)² + (y+2)² = 49
30. How many positive divisors does 100 have? → 9