Higher June 2018 Paper 1R Q21
21
(a) Show that \(x(x - 1)(x + 1) = x^3 - x\) (1)
(b) Prove that the difference between a whole number and the cube of this number is always a multiple of 6 (3)
| Scheme | Marks |
|---|---|
| \(x(x^2 - 1)\) or \((x^2 - x)(x + 1)\) Answer: \(x^3 - x\) | B1 |
| (1) |
Notes
B1: for correct expansion of a pair of brackets and then \(x^3 - x\) written down
| Scheme | Marks |
|---|---|
| (One of the numbers) is even or multiple of 2 or 2 is a factor | M1 |
| (One of the numbers) is a multiple of 3 or 3 is a factor | M1 |
| Hence a multiple of 6 Answer: Proof | A1 |
| (3) | |
| (4 marks) |