Higher November 2023 Paper 6 Q13

(a) The graph of \(y = 3^x\) is sketched below.

On the same axes, sketch the graph of \(y = 2^x\). [3]

(b) Charlie sketches this graph.

Charlie says

The equation of my graph is \(y = \sin x\).

(i) Explain how you know that Charlie is not correct. [1]

(ii) Write down a possible equation for Charlie’s graph. [1]

Answer	Marks	Part marks and guidance
	3	B1 for correct shape and same \(y\)-intercept B1 for sketch drawn below \(y = 3^x\) for positive \(x\)-values or has shallower gradient (by eye) B1 for sketch drawn above \(y = 3^x\) for negative \(x\)-values

Mark scheme (b)

Answer	Marks	Part marks and guidance
(i) eg. \(\sin x\) should initially increase/be positive [after \(x = 0\)]	1	Other acceptable answers include: [The sketch is a] reflection of \(y = \sin x\) [in the \(x\)-axis]; First turning point should be a maximum; \(\sin x\) has a maximum at 90 [and then a minimum at 270].
(ii) eg. \(y = -\sin x\)	1	Accept any other possibly correct equations such as: \(y = -k \sin x\) or \(y = \sin(-x)\) or \(y = k\cos(x + 90)\)