Higher June 2023 Paper 1R Q20
20 Curve C has equation \(\;y = \mathrm{f}(x)\)
The graph of curve C has one maximum point.
The coordinates of this maximum point are \((3, 5)\)
(a) Write down the coordinates of the maximum point on the curve with equation
(i) \(y = 2\mathrm{f}(x)\) (1)
(ii) \(y = \mathrm{f}(x) - 7\) (1)
(iii) \(y = \mathrm{f}(-x)\) (1)
Curve L has equation \(\;y = x^2 + 7x + 20\)
Curve L is transformed to curve S under the translation \(\begin{pmatrix} 2 \\ 0 \end{pmatrix}\)
(b) Find an equation for S
Give your answer in the form \(y = ax^2 + bx + c\) (4)
Give your answer in the form \(y = ax^2 + bx + c\) (4)
| Scheme | Marks |
|---|---|
| (i) (3, 10) | B1 |
| (ii) (3, \(-2\)) | B1 |
| (iii) (\(-3\), 5) | B1 |
| (3) |
| Scheme | Marks |
|---|---|
\((x \pm 2)\) or \((x + 3.5 \pm 2)\)....... or \(\left(x + \dfrac{7}{2} \pm 2\right)\ldots\) | M1 |
| \((x - 2)^2 + 7(x - 2) + 20\) or \((x + 3.5 - 2)^2 - 3.5^2 + 20\) or \((x + 1.5)^2 + 7.75\) | M1 |
| \(x^2 - 4x + 4 + 7x - 14 + 20\) or \(x^2 + 3x + 2.25 - 12.25 + 20\) or \(x^2 + 3x + 2.25 + 7.75\) | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: \(x^2 + 3x + 10\) | A1 |
| (4) | |
| (7 marks) |
Notes
M1: for sight or use of \((x \pm 2)\) or \((x + 1.5)\) or \((x + 5.5)\)
M1: for correct substitution or correct use of \((x - 2)\) for \(x\) into L
M1: dep on M2
for expanding brackets correctly