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Date May Specimen paper Marks available 1 Reference code SPM.1.AHL.TZ0.14
Level Additional Higher Level Paper Paper 1 Time zone Time zone 0
Command term Write down Question number 14 Adapted from N/A

Question

The graph of y = x 3 is transformed onto the graph of y = 33 0.08 x 3 by a translation of a units vertically and a stretch parallel to the x -axis of scale factor b .

Write down the value of a .

[1]
a.i.

Find the value of b .

[2]
a.ii.

The outer dome of a large cathedral has the shape of a hemisphere of diameter 32 m, supported by vertical walls of height 17 m. It is also supported by an inner dome which can be modelled by rotating the curve y = 33 0.08 x 3 through 360° about the y -axis between y = 0 and y = 33, as indicated in the diagram.

Find the volume of the space between the two domes.

[5]
b.

Markscheme

a = 33    A1

[1 mark]

a.i.

1 0.08 3 = 2.32      M1A1

[2 marks]

a.ii.

volume within outer dome

2 3 π + 16 3 + π × 16 2 × 17 = 22 250.85       M1A1

volume within inner dome

π 0 33 ( 33 y 0.08 ) 2 3 d y = 3446.92        M1A1

volume between = 22 250.85 − 3446.92 = 18 803.93 m3       A1

[5 marks]

b.

Examiners report

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

Syllabus sections

Topic 2—Functions » AHL 2.8—Transformations of graphs, composite transformations
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Topic 5—Calculus » AHL 5.12—Areas under a curve onto x or y axis. Volumes of revolution about x and y
Topic 2—Functions
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