June 2016 Paper 1 Q9
9 Expand and simplify \(\qquad (x - 5)^3\) [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(x^2 - 5x - 5x + 25 \quad\) or \(\quad x^2 - 10x + 25\) | M1 | allow one error |
| \(x^3 - 5x^2 - 5x^2 + 25x - 5x^2 + 25x + 25x - 125\) or \(x^3 - 10x^2 + 25x - 5x^2 + 50x - 125\) | M1dep | oe ft their \(x^2 - 5x - 5x + 25 \quad\) or \(\quad x^2 - 10x + 25\) and allow one error only if no errors made for the 1st M1 |
| \(x^3 - 15x^2 + 75x - 125\) | A1 | |
| Alternative method 2 | ||
| \(1x^3 + 3x^2(-5) + 3x(-5)^2 + 1(-5)^3\) | M1 | Using 1 3 3 1 ... coefficients from Pascal's triangle for the cubic expansion |
| \(x^3 - 15x^2 + 75x - 125\) | M1 | allow one error |
| \(x^3 - 15x^2 + 75x - 125\) | A1 | |
Additional guidance
Penalise further work
There must be three or four terms for the 1st M1 in alt 1
In alt 1 ... for M1 M1 they must make at most one error in the 1st two steps
In the 2nd step, \(-50x\) (instead of \(+50x\)) and \(-10x\) (instead of \(+50x\)) are examples of one error
In alt 2 ...
\(1x^3 + 3x^2(-5) + 3x(-5)^2 + 1(-5)^3 = x^3 - 15x^2 + 75x - 125\) written directly, with no intermediate steps needed or seen, automatically scores 3 marks