Examples, ours
One example from each option, written by us
A mechanics, a discrete and a pure example in the style of 7367, plus a practice set. None is an AQA question.
Our mechanics example, dimensional analysis (MA). A pendulum's period T is thought to depend on its length l and on g, as T = k la gb with k dimensionless. Dimensions: T is [T], l is [L], g is [L T−2]. Matching powers of L: 0 = a + b. Matching powers of T: 1 = −2b. So b = −½ and a = ½, giving T = k√(l/g). The method predicts the form but never the value of k, a limitation worth stating.
Our mechanics example, circular motion (MD). A 0.5 kg mass moves in a horizontal circle of radius 0.75 m on a smooth table, at 3 m s−1, held by a string to the centre. The tension supplies the central force: T = mv2/r = 0.5 × 9 ÷ 0.75 = 6 N.
Our discrete example, game theory (DF). In a two-person zero-sum game, player A's pay-offs are: row 1 gives 3 or −1; row 2 gives 2 or 1, against B's columns 1 and 2.
Play-safe strategies
Row minima are −1 and 1, so A's play-safe choice is row 2, guaranteeing 1. Column maxima are 3 and 1, so B's play-safe choice is column 2, conceding at most 1.
Stable solution
The largest row minimum equals the smallest column maximum, both 1, so there is a saddle point at row 2, column 2. The value of the game is 1, and neither player gains by changing alone.
Our pure example, matrices (C). For the 3 × 3 matrix with rows (1, 2, 0), (0, 1, 3), (2, 0, 1), expanding along the first row gives det = 1(1 − 0) − 2(0 − 6) + 0 = 13. The matrix is non-singular, so it has an inverse and the linear system it represents has a unique solution. AQA's required calculator can confirm the determinant; the expansion shows the method.
Six practice questions we wrote for 7367 students (answers checked in Python)| No. | Question (ours) | Where it fits | Answer |
|---|
| 1 | Express 1 + i√3 in modulus-argument form and find (1 + i√3)6. | 1 or 2 | 2(cos π/3 + i sin π/3); 64 |
| 2 | Show that arsinh(3/4) = ln 2. | 1 or 2 | ln(3/4 + √(9/16 + 1)) = ln 2 |
| 3 | Use the standard formula to find the sum of r2 for r = 1 to 12. | 1 or 2 | 650 |
| 4 | A 2 kg block slides from rest down a smooth slope through a vertical drop of 5 m. Find its speed, g = 9.8. | 3, mechanics | 9.90 m s−1 |
| 5 | X ~ Po(4). Find P(X ≤ 1). | 3, statistics | 0.0916 |
| 6 | T has an exponential distribution with rate 0.2. Find P(T > 10). | 3, statistics | e−2, about 0.135 |
Written by us on 31 October 2026; no AQA question is reproduced. AQA publishes specimen papers, past papers and examiners' reports on its 7367 resources.
