Higher June 2019 Paper 1 Q22
22 The graph of \(y = \sin x^\circ\) for \(0 \leqslant x \leqslant 360\) is drawn on the grid.
(a) On the grid, draw the graph of \(y = 2\sin(x + 30)^\circ\) for \(0 \leqslant x \leqslant 360\) (2)
(b)
(i) Write \(x^2 - 6x + 10\) in the form \((x - a)^2 + b\) where \(a\) and \(b\) are integers. (2)
(ii) Hence, describe fully the single transformation that maps the curve with equation \(y = x^2\) onto the curve with equation \(y = x^2 - 6x + 10\) (2)
| Scheme | Marks |
|---|---|
 Answer: correct graph (see end of mark scheme) [must go through (60, 2), (150, 0), (240, −2), (330, 0)] and not through (0, 0) | B2 |
| (2) |
Notes
B2: if not B2 then award B1 for a graph of the correct shape going through 2 or 3 of the given points or for a clear stretch of SF2 (ie a maximum point on graph at (\(x_1\), 2) and a minimum point at (\(x_2\), −2))
or a clear translation of \(\begin{pmatrix}-30\\0\end{pmatrix}\) (ie a point on graph at (150, \(y\)) and a point at (330, \(y\)))
| Scheme | Marks |
|---|---|
| (i) Answer: \((x - 3)^2 + 1\) | B2 |
| (ii) Answer: translation of \(\begin{pmatrix}3\\1\end{pmatrix}\) | B1 |
| B1 | |
| (4) | |
| (6 marks) |
Notes
B2: (B1 for \(\left(x - \dfrac{6}{2}\right)^2 + n\) (where \(n \ne 1\)) or for \((x - m)^2 + 1\) (where \(m \ne 3\)) or for
\(x^2 - ax - ax + a^2 + b\) with \(2a = 6\) or \(a^2 + b = 10\))
B1: for translation
B1: For \(\begin{pmatrix}3\\1\end{pmatrix}\) ft from (b)(i)
must be column vector