Higher June 2018 Paper 1 Q18

EdexcelHigherCurrent spec5 marksGraphical Transformations

Sketch of a U-shaped curve y = f(x) with its minimum point marked at (-2, -1), crossing the x-axis twice to the left of the y-axis

The diagram shows the curve with equation \(y = \mathrm{f}(x)\)
The coordinates of the minimum point of the curve are (−2, −1)

(a) Write down the coordinates of the minimum point of the curve with equation

(i) \(y = \mathrm{f}(x - 5)\)

(ii) \(y = \dfrac{1}{2}\mathrm{f}(x)\) (2)

The graph of \(y = a\sin(x - b)^\circ + c\) for \(-90 \leqslant x \leqslant 450\) is drawn on the grid below.

Grid with x from -90 to 450 and y from -1 to 3: a sine-shaped curve with minimum points at (0, -1) and (360, -1), a maximum at (180, 3), and passing through (-90, 1), (90, 1), (270, 1) and (450, 1)

(b) Find the value of \(a\), the value of \(b\) and the value of \(c\). (3)

Scheme	Marks
(i) (3, −1)	B1
(ii) (−2, −0.5) oe	B1
	(2)

Mark scheme (b)

Scheme	Marks
e.g. 2, 90, 1	B3
	(3)
	(5 marks)

Notes

B3: for all 3 correct values
e.g. 2, 90, 1 or −2, 270, 1
If not B3 then B2 for any 2 correct values
NB. 2 values from 2, 90, 1 OR 2 values from −2, 270, 1
NB: accept a value of (90 + 360n) in place of 90 or (270 + 360n) in place of 270 where n is an integer (could be negative)
If not B2 then B1 for any 1 correct value or the graph of \(y = \sin x^\circ\) for \(0 \leqslant x \leqslant 360\)