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Date November 2018 Marks available 1 Reference code 18N.1.AHL.TZ0.H_3
Level Additional Higher Level Paper Paper 1 Time zone Time zone 0
Command term Write down Question number H_3 Adapted from N/A

Question

Consider the function  g ( x ) = 4 cos x + 1 a x π 2 where  a < π 2 .

For  a = π 2 , sketch the graph of  y = g ( x ) . Indicate clearly the maximum and minimum values of the function.

[3]
a.

Write down the least value of a such that g has an inverse.

[1]
b.

For the value of a found in part (b), write down the domain of g 1 .

[1]
c.i.

For the value of a found in part (b), find an expression for g 1 ( x ) .

[2]
c.ii.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

concave down and symmetrical over correct domain       A1

indication of maximum and minimum values of the function (correct range)       A1A1

 

[3 marks]

a.

a = 0      A1

Note: Award A1 for a = 0 only if consistent with their graph.

 

[1 mark]

b.

1 x 5      A1

Note: Allow FT from their graph.

 

[1 mark]

c.i.

y = 4 cos x + 1

x = 4 cos y + 1

x 1 4 = cos y       (M1)

y = arccos ( x 1 4 )

g 1 ( x ) = arccos ( x 1 4 )       A1

 

[2 marks]

c.ii.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.i.
[N/A]
c.ii.

Syllabus sections

Topic 2—Functions » SL 2.2—Functions, notation domain, range and inverse as reflection
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