| 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 \(n{\text{th}}\) strike of the hammer, is \({d_n}\).
The distances \({d_1},{\text{ }}{d_2},{\text{ }}{d_3}{\text{ }} \ldots ,{\text{ }}{d_n}\) form a geometric sequence.
The distance that the post is driven into the ground by the first strike of the hammer, \({d_1}\), is 64 cm.
The distance that the post is driven into the ground by the second strike of the hammer, \({d_2}\), is 48 cm.
Find the value of the common ratio for this sequence.
Find the distance that the post is driven into the ground by the eighth strike of the hammer.
Find the total depth that the post has been driven into the ground after 10 strikes of the hammer.
Markscheme
\(48 = 64r\) (M1)
Note: Award (M1) for correct substitution into geometric sequence formula.
\( = 0.75\left( {\frac{3}{4},{\text{ }}\frac{{48}}{{64}}} \right)\) (A1) (C2)
[2 marks]
\(64 \times {(0.75)^7}\) (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.
\( = 8.54{\text{ }}({\text{cm}}){\text{ }}(8.54296 \ldots {\text{ cm}})\) (A1)(ft) (C2)
[2 marks]
\({\text{depth}} = \frac{{64\left( {1 - {{(0.75)}^{10}}} \right)}}{{1 - 0.75}}\) (M1)
Note: Award (M1) for correct substitution into geometric series formula. Follow through from part (a), only if answer is positive.
\( = 242({\text{cm}}){\text{ }}(241.583 \ldots )\) (A1)(ft) (C2)
[2 marks]
