MPT Cheat Sheet 2026

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

1. When simplifying a complex fraction like (1/2)/(3/4), the best practice is to: → Multiply by the reciprocal of the denominator: (1/2) × (4/3) = 2/3
2. A math placement test result places a student in College Algebra. What is the most productive response? → Accept the placement and commit fully to that course
3. What is the slope of the line passing through (2, 5) and (6, 13)? → 2
4. What is the slope of the line passing through (1, 3) and (4, 9)? → 2
5. Which of the following is equivalent to 5² × 5³? → 5⁵
6. If the ratio of boys to girls in a class is 3:5 and there are 24 boys, how many girls are there? → 40
7. Convert 5π/6 radians to degrees. → 150°
8. A coin is flipped and a standard die is rolled. What is the probability of getting heads and a number greater than 4? → 1/6
9. What is the value of tan(45°)? → 1
10. What role does ethics play in Core Knowledge practice? → It guides professional conduct and protects stakeholders
11. A rectangle has a length of 9 and a width of 4. What is its perimeter? → 26
12. What is the vertex of the parabola y = (x - 2)² + 5? → (2, 5)
13. What is the prime factorization of 60? → 2² × 3 × 5
14. Which inequality represents 'three less than twice a number is at most 11'? → 2n - 3 ≤ 11
15. Which of the following is the graph of y = x² - 4? → A parabola opening up with vertex at (0, -4)
16. A jar has 4 red, 3 blue, and 5 green marbles. What is the probability of randomly picking a blue marble? → 3/12
17. What are standard precautions in healthcare? → Treating all blood and body fluids as potentially infectious
18. Using the Law of Sines, if A = 30°, a = 5, and B = 45°, find side b. → 5√2/2
19. When reducing the rational expression (x²−4)/(x−2), the correct simplified form is: → x + 2, with the restriction x ≠ 2
20. On the UCF Math Placement Test, if you are unsure about a question, the best strategy is to: → Eliminate obviously wrong answers and make your best guess
21. What is the inverse of the function f(x) = (x + 4)/3? → f⁻¹(x) = 3x - 4
22. A train travels 240 km in 3 hours. At the same speed, how far does it travel in 5 hours? → 400 km
23. What is the value of x in the equation 4x - 3 = 9? → 3
24. What is the median of the data set: 7, 2, 5, 9, 3, 8, 1? → 5
25. Maria scored 78, 85, and 91 on three tests. What score does she need on a fourth test to have an average of exactly 85? → 86
26. What is the relationship between theory and practice in Technical Foundations? → Theory provides the foundation; practice applies it to real situations
27. If f(x) = 3x - 4, what is f⁻¹(x)? → (x + 4)/3
28. Simplify: (3x²y)(−2xy³) → −6x³y⁴
29. What is the midpoint of the segment connecting (2, 4) and (8, 10)? → (5, 7)
30. Which behavior demonstrates professional responsibility when taking an online proctored exam? → Ensuring your environment meets all technical and integrity requirements in advance