Higher November 2020 Paper 1 Q29
29 The graph of \(\quad y = x^3 + 6 \quad\) is translated 4 units to the right.
The translated graph has equation \(\quad y = \mathrm{f}(x)\)
Work out \(\mathrm{f}(x)\).
Give your answer in the form \(\quad x^3 + ax^2 + bx + c \quad\) where \(a\), \(b\) and \(c\) are integers. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| \((x - 4)^3\) | B1 | \((x + 4)^3\) is B0 |
| \(x^2 - 4x - 4x + 16\) with 3 terms correct or \(x^2 - 8x + k\) where \(k\) is a non-zero constant | M1 | ft \((x + 4)^3\) only |
| \(x^3 - 4x^2 - 4x^2 + 16x - 4x^2 + 16x + 16x - 64\ (+ 6)\) or \(x^3 - 8x^2 + 16x - 4x^2 + 32x - 64\ (+ 6)\) or \(x^3 - 12x^2 + 48x - 64\ (+ 6)\) | M1dep | oe full expansion of their 4 terms by \((x - 4)\) with at least 4 terms correct or full expansion of their 3 terms by \((x - 4)\) with at least 3 terms correct ft \((x + 4)^3\) only |
| \(x^3 - 12x^2 + 48x - 58\) | A1 |
Additional guidance
| Using \((x + 4)^3\) can score a maximum of B0M1M1A0 \(x^2 + 4x + 4x + 16\) with 3 terms correct or \(x^2 + 8x + k\) where \(k\) is a non-zero constant \(x^3 + 4x^2 + 4x^2 + 16x + 4x^2 + 16x + 16x + 64\ (+ 6)\) or \(x^3 + 8x^2 + 16x + 4x^2 + 32x + 64\ (+ 6)\) or \(x^3 + 12x^2 + 48x + 64\) or \(x^3 + 12x^2 + 48x + 70\) | B0M1 B0M1M1A0 |