June 2024 Paper 2 Q13
13 Expand and simplify fully \(\quad (3x - 1)(4 - x)(2x + 5)\) [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1: expands \((3x - 1)(4 - x)\) first | ||
| Exactly 4 terms with at least 3 correct from \((+)12x \quad -3x^2 \quad -4 \quad (+)x\) | M1 | oe eg \(13x - 3x^2 - 4\) terms may be seen in a grid implied by \(13x - 3x^2 + k\) or \(13x + px^2 - 4\) where \(k\) and \(p\) are non-zero constants |
| Full expansion of their 3 or 4 term quadratic with \((2x + 5)\) with correct multiplication of their 3 or 4 terms by \(2x\) or by \((+)5\) | M1 | eg \(24x^2 - 6x^3 - 8x + 2x^2 + 60x - 15x^2 - 20 + 5x\) or \(26x^2 - 6x^3 - 8x + 65x - 15x^2 - 20\) terms may be seen in a grid |
| \(-6x^3 + 11x^2 + 57x - 20\) | A1 | terms in any order |
| Alternative method 2: expands \((4 - x)(2x + 5)\) first | ||
| Exactly 4 terms with at least 3 correct from \((+)8x \quad (+)20 \quad -2x^2 \quad -5x\) | M1 | oe eg \(3x + 20 - 2x^2\) terms may be seen in a grid implied by \(3x + 20 + kx^2\) or \(3x + p - 2x^2\) where \(k\) and \(p\) are non-zero constants |
| Full expansion of their 3 or 4 term quadratic with \((3x - 1)\) with correct multiplication of their 3 or 4 terms by \(3x\) or by \(-1\) (corrected from the printed mark scheme: printed as \((3x + 1)\)) | M1 | eg \(24x^2 + 60x - 6x^3 - 15x^2 - 8x - 20 + 2x^2 + 5x\) or \(9x^2 + 60x - 6x^3 - 3x - 20 + 2x^2\) terms may be seen in a grid |
| \(-6x^3 + 11x^2 + 57x - 20\) | A1 | terms in any order |
| Alternative method 3: expands \((3x - 1)(2x + 5)\) first | ||
| Exactly 4 terms with at least 3 correct from \((+)6x^2 \quad (+)15x \quad -2x \quad -5\) | M1 | oe eg \(6x^2 + 13x - 5\) terms may be seen in a grid implied by \(6x^2 + 13x + k\) or \(px^2 + 13x - 5\) where \(k\) and \(p\) are non-zero constants |
| Full expansion of their 3 or 4 term quadratic with \((4 - x)\) with correct multiplication of their 3 or 4 terms by 4 or by \(-x\) | M1 | eg \(24x^2 + 60x - 8x - 20 - 6x^3 - 15x^2 + 2x^2 + 5x\) or \(24x^2 + 52x - 20 - 6x^3 - 13x^2 + 5x\) terms may be seen in a grid |
| \(-6x^3 + 11x^2 + 57x - 20\) | A1 | terms in any order |
Additional guidance
| M1 may be awarded for correct work with no answer or incorrect answer, even if this is seen amongst multiple attempts | |
| Condone one transcription error for A1 after fully correct answer seen | |
| Alt 1 \(\ 12x + 3x^2 - 5 + x \quad\) only 2 terms correct \((12x + 3x^2 - 5 + x)(2x + 5)\) \(= 24x^2 + 6x^3 - 10x + 2x^2 + 17x + 15x^2 + 25 + 5x^2\) 8 terms (full expansion) with correct multiplication of their 4 terms by \(2x\) | M0 M1 |
| Alt 2 \(\ 3x + 20 + 2x^2 \quad\) implied 4 terms with 3 correct \((3x - 1)(3x + 20 + 2x^2)\) \(= 6x^2 + 60x + 5x^3 - 3x - 20 - 2x^2\) 6 terms (full expansion) with correct multiplication of their 3 terms by \(-1\) | M1 M1 |
| If the 1st M1 is scored with a 4-term expansion but this is then incorrectly simplified to 3 terms, the 2nd M1 can still be scored using their 3 terms | |
| Accept eg \(+ -3x^2\) as a correct term for M marks but not for A1 | |
| M2A1 response followed by further work eg1 \(-6x^3 + 11x^2 + 57x - 20\) in working with answer \(x(-6x^2 + 11x + 57) - 20\) eg2 \(-6x^3 + 11x^2 + 57x - 20\) in working with answer \(-(6x^3 - 11x^2 - 57x + 20)\) | M2A0 M2A0 |
| One single expansion is full marks or zero |