June 2023 Paper 2 Q11
11 Expand and simplify fully \(\quad (2x^3 - 9)(3x^2 + 4) + x(x - 4)^2\) [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| 3 correct from \(6x^5 + 8x^3 - 27x^2 - 36\) | M1 | expansion of \((2x^3 - 9)(3x^2 + 4)\) may be seen in a grid |
| \(6x^5 + 8x^3 - 27x^2 - 36\) | M1dep | may be seen in a grid |
| \(x^3 - 4x^2 - 4x^2 + 16x\) or \(x^3 - 8x^2 + 16x\) | M1 | expansion of \(x(x - 4)^2\) may be seen in a grid |
| \(6x^5 + 9x^3 - 35x^2 + 16x - 36\) | A1 |
Additional guidance
| A correct term includes the sign (in a grid allow eg \(8x^3\) for \(+8x^3\)) | |
| Terms may be in any order throughout | |
| Terms must be fully processed eg do not allow \(2x^3 \times 3x^2\) for \(6x^5\) | |
| Allow eg \(+ -27x^2\) for \(-27x^2\) for M marks | |
| \(6x^5 + 8x^3 - 27x^2 - 36\) scores the 1st M1 and 2nd M1 even if incorrectly simplified (or differentiated) eg \(6x^5 + 8x^3 - 27x^2 - 36 = 6x^5 - 19x^2 - 36\) | M1M1 |
| \(x^3 - 4x^2 - 4x^2 + 16x\) (or \(x^3 - 8x^2 + 16x\)) scores the 3rd M1 even if incorrectly simplified (or differentiated) eg \(x^3 - 4x^2 - 4x^2 + 16x = x^3 - 16x^2 + 16x\) | 3rd M1 |
| Correct answer then incorrect further work eg differentiation | M3A0 |
| \(6x^5 + 9x^3 - 35x^2 + 16x - 36 = x(6x^4 + 9x^2 - 35x + 16) - 36\) | M3A0 |