Higher November 2021 Paper 2 Q21

EdexcelHigherCurrent spec6 marksCompleting the Square Graphical Transformations

21 The curve C has equation \(y = \mathrm{f}(x)\) where \(\mathrm{f}(x) = 9 - 3(x + 2)^2\)
The point \(A\) is the maximum point on C.

(a) Write down the coordinates of \(A\). (1)

The curve C is transformed to the curve S by a translation of \(\begin{pmatrix} 4 \\ 0 \end{pmatrix}\)

(b) Find an equation for the curve S. (1)

The curve C is transformed to the curve T.
The curve T has equation \(y = 3(x + 2)^2 - 9\)

The graph of \(y = a\cos(x - b)° + c\) for \(-180 \leqslant x \leqslant 360\) is drawn on the grid below.

Graph of a cosine curve for x from −180 to 360 with maximum value 5 at x = −90 and x = 270, minimum value −1 at x = 90, crossing the y-axis at 2

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

Scheme	Marks
(−2, 9)	B1
	(1)

Scheme	Marks
\((y =)\ 9 - 3(x - 4 + 2)^2\)	B1
	(1)

Scheme	Marks
Reflection in the line \(y = 0\) or \(x\)-axis	B1
	(1)

Mark scheme (d)

Scheme	Marks
(3, −90, 2) (−3, 90, 2) (3, 270, 2) (−3, 450, 2) etc Answer: eg \(a = 3\) \(b = -90\) \(c = 2\)	B3
	(3)
	(6 marks)

Notes

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