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Date November 2016 Marks available 2 Reference code 16N.2.AHL.TZ0.H_5
Level Additional Higher Level Paper Paper 2 Time zone Time zone 0
Command term State Question number H_5 Adapted from N/A

Question

Consider the function f defined by f ( x ) = 3 x arccos ( x ) where 1 x 1 .

Sketch the graph of f indicating clearly any intercepts with the axes and the coordinates of any local maximum or minimum points.

[3]
a.

State the range of f .

[2]
b.

Solve the inequality | 3 x arccos ( x ) | > 1 .

[4]
c.

Markscheme

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

N16/5/MATHL/HP2/ENG/TZ0/05.a/M

correct shape passing through the origin and correct domain     A1

 

Note: Endpoint coordinates are not required. The domain can be indicated by 1 and 1 marked on the axis.

( 0.652 ,   1.68 )    A1

two correct intercepts (coordinates not required)     A1

 

Note: A graph passing through the origin is sufficient for ( 0 ,   0 ) .

 

[3 marks]

a.

[ 9.42 ,   1.68 ]   ( or  3 π ,   1.68 ] )    A1A1

 

Note: Award A1A0 for open or semi-open intervals with correct endpoints. Award A1A0 for closed intervals with one correct endpoint.

 

[2 marks]

b.

attempting to solve either | 3 x arccos ( x ) | > 1 (or equivalent) or | 3 x arccos ( x ) | = 1 (or equivalent) (eg. graphically)     (M1)

N16/5/MATHL/HP2/ENG/TZ0/05.c/M

x = 0.189 ,   0.254 ,   0.937    (A1)

1 x < 0.189  or  0.254 < x < 0.937    A1A1

 

Note: Award A0 for x < 0.189 .

 

[4 marks]

c.

Examiners report

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

Syllabus sections

Topic 2—Functions » SL 2.2—Functions, notation domain, range and inverse as reflection
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Topic 2—Functions
Topic 3— Geometry and trigonometry

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