BMath Bachelor of Mathematics Cheat Sheet 2026

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

1. The center Z(G) of a group G is defined as: → The set of elements that commute with every element of G
2. According to this document, multiplying by 4 can be done faster by doing what instead? → Multiplying by 2 twice
3. What kind of sequence involves using the preceding term(s) to determine each successive term? → Recursive Sequence
4. What is the iteration rule used for plotting the Mandelbrot set? → z_(n + 1) = z_n^2 + c | z_0 = 0
5. Which of the following is NOT an improper integral? → ∫[−1 to 1] x² dx
6. What is the fundamental theorem of calculus (Part 1) about? → If F(x) = ∫ₐˣ f(t) dt and f is continuous, then F'(x) = f(x)
7. Which one of the options listed below is not considered a method for solving problems? → Carry out the strategy
8. The Wronskian W(y₁, y₂) of two solutions is used to determine: → Whether the solutions are linearly independent
9. Which distribution models the number of successes in n independent Bernoulli trials with probability p? → Binomial distribution
10. Lagrange's Theorem states that for a finite group G with subgroup H: → |H| divides |G|
11. Green's theorem relates a line integral around a simple closed curve C to a double integral over the region D it encloses. It states ∮_C (P dx + Q dy) = → ∬_D (∂Q/∂x − ∂P/∂y) dA
12. Two matrices A and B are similar if: → A = P⁻¹BP for some invertible matrix P
13. In numerical linear algebra, the condition number of a matrix A is defined as: → ‖A‖·‖A⁻¹‖
14. What method does this document recommend for multiplying two-digit numbers less than twenty but more than ten together? → Apply cross multiplication
15. In modular arithmetic, 17 mod 5 equals: → 2
16. For the system x' = Ax with constant matrix A, the stability of the equilibrium x = 0 depends on: → The real parts of the eigenvalues of A
17. Which of the following sets is countably infinite? → The set of all rational numbers ℚ
18. The First Isomorphism Theorem states that if φ: G → H is a group homomorphism, then: → G/ker(φ) ≅ Im(φ)
19. The geometric distribution models: → The number of trials until the first success
20. What does the expected value E[X] of a discrete random variable X represent? → The weighted average of all possible values
21. The characteristic equation of y'' − 5y' + 6y = 0 is: → r² − 5r + 6 = 0
22. For an n×n matrix, the characteristic polynomial is of degree: → n
23. Which of the following is NOT a valid rule of inference in classical propositional logic? → Affirming the consequent: Q, P ⟹ Q ∴ P
24. Which logical connective makes 'P ⟹ Q' false only when P is true and Q is false? → Conditional (implication)
25. If f is continuous on [a, b], which theorem guarantees f attains both its maximum and minimum values? → Extreme Value Theorem
26. What method can be used to find the rule of a sequence? → Multiplying the term number by the difference
27. What is the mathematical concept used to plot fractals over real and complex domains? → Dynamical systems
28. Which of the following groups is an example of a simple group? → Z_5
29. Which of the following is a way to improve your mental math skills? → Practice regularly and consistently
30. What does the Intermediate Value Theorem guarantee for a continuous function f on [a, b] with f(a) < 0 < f(b)? → f achieves every value between f(a) and f(b)