June 2022 Paper 2 Q19
19 Expand and simplify fully \(\qquad (3x + 4)(2x - 3)(5x - 2)\) [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 Expands \((3x + 4)(2x - 3)\) first | ||
| \(6x^2 - 9x + 8x - 12\) or \(6x^2 - x - 12\) | M1 | oe 4 terms with at least 3 correct implied by \(6x^2 - x + k\) or \(px^2 - x - 12\) where \(k\) and \(p\) are non-zero constants may be seen in a grid |
| \(30x^3 - 45x^2 + 40x^2 - 60x - 12x^2\) \(+ 18x - 16x + 24\) or \(30x^3 - 5x^2 - 60x - 12x^2 + 2x + 24\) | M1 | oe full expansion with correct multiplication of their 3 or 4 terms by \(5x\) or \(-2\) may be seen in a grid |
| \(30x^3 - 17x^2 - 58x + 24\) | A1 | terms in any order |
| Alternative method 2 Expands \((2x - 3)(5x - 2)\) first | ||
| \(10x^2 - 4x - 15x + 6\) or \(10x^2 - 19x + 6\) | M1 | oe 4 terms with at least 3 correct implied by \(10x^2 - 19x + k\) or \(px^2 - 19x + 6\) where \(k\) and \(p\) are non-zero constants may be seen in a grid |
| \(30x^3 - 12x^2 - 45x^2 + 18x + 40x^2\) \(- 16x - 60x + 24\) or \(30x^3 - 57x^2 + 18x + 40x^2 - 76x\) \(+ 24\) | M1 | oe full expansion with correct multiplication of their 3 or 4 terms by \(3x\) or 4 may be seen in a grid |
| \(30x^3 - 17x^2 - 58x + 24\) | A1 | terms in any order |
| Alternative method 3 Expands \((3x + 4)(5x - 2)\) first | ||
| \(15x^2 - 6x + 20x - 8\) or \(15x^2 + 14x - 8\) | M1 | oe 4 terms with at least 3 correct implied by \(15x^2 + 14x + k\) or \(px^2 + 14x - 8\) where \(k\) and \(p\) are non-zero constants may be seen in a grid |
| \(30x^3 - 12x^2 + 40x^2 - 16x - 45x^2\) \(+ 18x - 60x + 24\) or \(30x^3 + 28x^2 - 16x - 45x^2 - 42x\) \(+ 24\) | M1 | oe full expansion with correct multiplication of their 3 or 4 terms by \(2x\) or \(-3\) may be seen in a grid |
| \(30x^3 - 17x^2 - 58x + 24\) | A1 | terms in any order |
Additional guidance
| For terms seen in a grid accept \(8x\) for \(+8x\) etc | |
| 2nd M1 A full expansion will be 8 terms if 4 terms are used in first expansion A full expansion will be 6 terms if 3 terms are used in first expansion | |
| Alt 1 \(6x^2 + 9x - 8x - 12 \qquad\) only 2 terms correct \((6x^2 + 9x - 8x - 12)(5x - 2)\) \(= 30x^3 + 45x^2 - 40x^2 - 60x - 12x^2 + 18x - 16x + 24\) 8 terms with correct multiplication of their 4 terms by \(5x\) | M0 M1A0 |
| Alt 2 \(10x^2 - 19x - 5 \qquad\) implied 4 terms with 3 correct \((3x + 4)(10x^2 - 19x - 5) = 30x^3 - 54x^2 - 15x + 40x^2 - 76x - 20\) 6 terms with correct multiplication of their 3 terms by 4 | M1 M1A0 |
| 1st M1 with a 4-term expansion followed by incorrect simplification to 3 terms can still score the 2nd M1 using their 3 terms | |
| One single expansion is full marks or zero |