A-LEVEL Cheat Sheet 2026

The 30 highest-yield A-LEVEL 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 general solution of the differential equation dy/dx = ky, where k is a constant? → y = Ae^(kx)
2. What is the area enclosed between the curve y = x² and the line y = 4? → 32/3
3. What is the value of ∫₀² x² dx? → 8/3
4. A simple pendulum has period T = 2π√(L/g). If L is quadrupled, how does T change? → T doubles
5. Why does HF have a higher boiling point than HCl despite having a lower molar mass? → HF has stronger hydrogen bonding due to the high electronegativity of fluorine
6. What is 'moral hazard' in economics? → When one party takes more risks because another party bears the cost or consequences
7. Find the equation of the circle with centre (3, -1) and radius 5. → (x-3)² + (y+1)² = 25
8. What is a 'negative externality'? → A cost imposed on third parties not involved in a transaction
9. A random variable X ~ N(50, 16). Find P(X > 54). → 0.1587
10. What happens to the demand curve for a normal good when consumer income rises? → Demand curve shifts right
11. For the arithmetic series 5 + 9 + 13 + ..., find the sum of the first 20 terms. → 840
12. What is the hybridisation of carbon in methane (CH₄)? → sp³
13. A ball is thrown horizontally from a height of 20m. Taking g = 10 m/s², how long does it take to reach the ground? → 2s
14. For the binomial distribution X ~ B(20, 0.3), what is the expected value E(X)? → 6
15. What is the current account of the Balance of Payments? → Records trade in goods and services, income flows, and current transfers
16. Two capacitors of 4μF and 6μF are connected in series. What is the combined capacitance? → 2.4μF
17. What does the Gini coefficient measure? → Income inequality within a population
18. The function f(x) = x³ - 3x² + 2. Find f'(x) and determine the nature of all stationary points. → f'(x) = 3x²-6x; maximum at x=0, minimum at x=2
19. What is the test for an aldehyde using Tollens' reagent? → A silver mirror forms on the test tube walls
20. In GP essay writing, what is the function of a 'counter-argument'? → To show awareness of opposing views, which when rebutted strengthens your overall argument
21. What is the test for a primary amine? → React with nitrous acid at 0-5°C, then couple with a phenol to form an azo dye
22. What is the work-energy theorem as applied in Singapore A-Level Physics? → The net work done on a body equals the change in its kinetic energy
23. What is meant by 'terminal velocity'? → The constant velocity reached when drag force equals driving force (or weight)
24. Express 2sin(x) + 2cos(x) in the form R sin(x + α), where R > 0 and 0 < α < π/2. → 2√2 sin(x + π/4)
25. Evaluate lim(x→0) [sin(3x)/x]. → 3
26. What is the primary reason rivers deposit their load in the lower course? → Decreased velocity and energy
27. Which species is the oxidising agent in: MnO₄⁻ + 8H⁺ + 5Fe²⁺ → Mn²⁺ + 4H₂O + 5Fe³⁺? → MnO₄⁻
28. What is the order of reaction if doubling the concentration of A doubles the rate? → First order
29. Find the stationary points of y = x³ - 3x. → (1,-2) and (-1,2)
30. Solve for x: log₂(x) + log₂(x-6) = 4. → x = 8