Higher January 2020 Paper 2 Q21
21 The diagram shows a sketch of part of the curve with equation \(\;y = \mathrm{f}(x)\)
There is one maximum point on this curve.
The coordinates of this maximum point are \((4, 6)\)
(a) Write down the coordinates of the maximum point on the curve with equation
(i) \(y = \mathrm{f}(x + 4)\)
(ii) \(y = \mathrm{f}(2x)\) (2)
(i) \(y = \mathrm{f}(x + 4)\)
(ii) \(y = \mathrm{f}(2x)\) (2)
The equation of a curve C is \(\;y = x^2 + 3x + 4\)
The curve C is transformed to curve S under the translation \(\begin{pmatrix} 4 \\ 6 \end{pmatrix}\)
(b) Find an equation of curve S.
You do not need to simplify the equation. (2)
You do not need to simplify the equation. (2)
| Scheme | Marks |
|---|---|
| (i) \((0, 6)\) | B1 |
| (ii) \((2, 6)\) | B1 |
| (2) |
Notes
(the printed mark scheme labels the second row “(iii)”; it is part (ii))
| Scheme | Marks |
|---|---|
eg \((x - 4)^2 + 3(x - 4) + 4\) oe or eg \(\left(x + \dfrac{3}{2} - 4\right)^2 - \dfrac{9}{4} + 4\) oe or eg \(x^2 + 3x + 10\) oe or eg \(\left(x + \dfrac{3}{2}\right)^2 - \dfrac{9}{4} + 4 + 6\) oe eg \(y - 6 = x^2 + 3x + 4\) | M1 |
\(y = (x - 4)^2 + 3(x - 4) + 10\) or \(y = \left(x + \dfrac{3}{2} - 4\right)^2 - \dfrac{9}{4} + 4 + 6\) | A1 |
| (2) | |
| (4 marks) |
Notes
M1: for applying one of the transformations to the equation
A1: oe eg \(y = \left(x - \dfrac{5}{2}\right)^2 + \dfrac{31}{4}\) or
\(y = x^2 - 5x + 14\) oe