Graphical Transformations

Topic

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Higher June 2025 Paper 2R Q25

EdexcelCurrent spec3 marksGraphical Transformations

25 The graph of \(y = a\sin(x + b)^\circ + c\) for \(0 \leqslant x \leqslant 360\) is drawn on the grid below.

Graph of a sine curve for x from 0 to 360 with y from -4 to 5, maximum 4 at x = 45 and minimum -2 at x = 225, crossing the y-axis at 3

Find a suitable value for \(a\), for \(b\) and for \(c\)

(3)

Mark scheme

Scheme	Marks
\(a = 3\) \(b = 45\) \(c = 1\) OR \(a = -3\) \(b = 225\) \(c = 1\)	B1 B1 B1
	(3)
	(3 marks)

Notes

B1 B1 B1: B1 for \(a = 3\) or \(a = -3\)

B1 for \(a \gt 0\) and \(b = 45\) or for \(a \lt 0\) and \(b = 225\)
if no answer for \(a\) is seen allow this mark for \(b = 45\)

B1 for \(c = 1\)

Allow correct alternative angles for the value of \(b\), eg 45 or –315, 225 or –135

Higher June 2025 Paper 1R Q21

EdexcelCurrent spec3 marksGraphical Transformations

21 The curve with equation \(y = \mathrm{f}(x)\) has one turning point.
The coordinates of this turning point are \((-6, 9)\)

(a) Write down the coordinates of the turning point on the curve with equation \(y = \mathrm{f}(3x)\) (1)

The curve C with equation \(y = \mathrm{g}(x)\) is transformed to give the curve S with equation \(y = \mathrm{g}(x + a) + b\)

The point \((4, -5)\) on C is mapped to the point \((1, -16)\) on S

(b) Write down the value of \(a\) and the value of \(b\) (2)

Scheme	Marks
\((-2, 9)\)	B1
	(1)

Scheme	Marks
\(a = 3\)	B1
\(b = -11\)	B1
	(2)
	(3 marks)

Higher June 2025 Paper 1 Q19

EdexcelCurrent spec2 marksGraphical Transformations

19 The equation of a curve is \(y = \mathrm{f}(x)\)

There is only one minimum point on the curve.
The coordinates of this minimum point are \((8, -12)\)

Write down the coordinates of the minimum point on the curve with equation

(i) \(y = \mathrm{f}(x) + 3\) (1)

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

Scheme	Marks
8, \(-9\)	B1
	(1)

Scheme	Marks
4, \(-12\)	B1
	(1)
	(2 marks)

Higher November 2024 Paper 2 Q19

EdexcelCurrent spec3 marksGraphical Transformations

19 A curve has equation \(y = \mathrm{f}(x)\)
There is only one minimum point on the curve.
The coordinates of this minimum point are (5, 4)

Write down the coordinates of the minimum point on the curve with equation

(i) \(y = \mathrm{f}(x + 5)\) (1)

(ii) \(y = 3\mathrm{f}(x)\) (1)

(iii) \(y = \mathrm{f}(x) - 7\) (1)