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Date November 2016 Marks available 2 Reference code 16N.1.sl.TZ0.10
Level SL only Paper 1 Time zone TZ0
Command term Find Question number 10 Adapted from N/A

Question

A hydraulic hammer drives a metal post vertically into the ground by striking the top of the post. The distance that the post is driven into the ground, by the nth strike of the hammer, is dn.

The distances d1, d2, d3 , dn form a geometric sequence.

The distance that the post is driven into the ground by the first strike of the hammer, d1, is 64 cm.

The distance that the post is driven into the ground by the second strike of the hammer, d2, is 48 cm.

Find the value of the common ratio for this sequence.

[2]
a.

Find the distance that the post is driven into the ground by the eighth strike of the hammer.

[2]
b.

Find the total depth that the post has been driven into the ground after 10 strikes of the hammer.

[2]
c.

Markscheme

48=64r    (M1)

 

Note:     Award (M1) for correct substitution into geometric sequence formula.

 

=0.75(34, 4864)    (A1)     (C2)

[2 marks]

a.

64×(0.75)7    (M1)

 

Note:     Award (M1) for correct substitution into geometric sequence formula or list of eight values using their r. Follow through from part (a), only if answer is positive.

 

=8.54 (cm) (8.54296 cm)     (A1)(ft)     (C2)

 

[2 marks]

b.

depth=64(1(0.75)10)10.75    (M1)

 

Note:     Award (M1) for correct substitution into geometric series formula. Follow through from part (a), only if answer is positive.

 

=242(cm) (241.583)    (A1)(ft)     (C2)

[2 marks]

c.

Examiners report

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

Syllabus sections

Topic 1 - Number and algebra » 1.8
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