TMUA Cheat Sheet 2026

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

1. If a = 3 and b = 4, what is the value of √(a² + b²)? → 5
2. What is the most effective strategy for solving word problems in TMUA assessments? → Identify given information, determine what is asked, and set up equations
3. The first three terms of a geometric sequence are x+2, 3x, and 5x+4. What is the common ratio? → 2
4. Solve for x in [0, 2π]: 2cos(x) - 1 = 0. → x = π/3 or x = 5π/3
5. The function f(x) = 2x³ − 9x² + 12x has stationary points at which x-values? → x = 1 and x = 2
6. lim_{h→0} [f(x+h) − f(x)]/h defines: → The derivative f′(x)
7. Which rule of inference is: 'P ∨ Q, ¬P ⊢ Q'? → Disjunctive syllogism
8. The graph of y = sin(x) is translated π/4 to the right. What is the new equation? → y = sin(x - π/4)
9. Which of the following is the contrapositive of the statement 'If n is divisible by 6, then n is divisible by 2'? → If n is not divisible by 2, then n is not divisible by 6
10. A function f is such that f(2x+1) = 4x² + 4x + 3. What is f(5)? → 23
11. Which of the following statements about proof by induction is correct? → You assume the statement holds for n=k and prove it for n=k+1
12. Three consecutive terms of an arithmetic sequence sum to 30 and their product is 750. What is the middle term? → 10
13. Which of the following is a valid statement of Wilson's Theorem? → (p−1)! ≡ −1 (mod p) for all primes p
14. In TMUA practice, what is the best approach to quality improvement in problem solving? → Use data-driven methods with measurable outcomes
15. A right triangle has hypotenuse 10 and one angle of 30°. What is the length of the side opposite the 30° angle? → 5
16. In a geometric sequence, the sum of the 3rd and 4th terms equals 12 times the first term. What is the common ratio? → 2
17. Prove by contradiction: if n² is even, then n is even. Which step is essential? → Assuming n is odd and showing n² is odd
18. What is the PRIMARY purpose of obtaining TMUA certification in Test of Mathematics for University Admission? → To demonstrate verified competency and adherence to professional standards
19. In a circle, a chord of length 16 cm is 6 cm from the center. What is the radius? → 10 cm
20. What is the range of values of k for which the equation x² − kx + k + 3 = 0 has no real roots? → −2 < k < 6
21. A data set consists of values 3, 7, 7, 9, 12, 15, 15, 15, 20. What is the mode? → 15
22. A sample of 5 values has mean 8 and variance 4. What is Σx²? → 340
23. A TMUA certified professional is asked to provide services outside their scope of competence. The CORRECT ethical response is to: → Decline and refer to a qualified professional
24. How does the TMUA body of knowledge relate to daily professional practice? → It provides the foundational framework that guides decision-making and standard practices
25. A cone has base radius 3 cm and slant height 5 cm. What is its total surface area? → 24π cm²
26. If x + y = 5 and xy = 4, find x³ + y³. → 65
27. Which scenario represents a violation of the Test of Mathematics for University Admission code of professional conduct? → Misrepresenting qualifications or certification status
28. What is the last two digits (i.e. the value mod 100) of 7^400? → 01
29. What does the mean of a data set represent in TMUA quantitative analysis? → The arithmetic average of all values
30. What is the value of x in the equation 5x - 10 = 0? → 2