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Date	May 2018	Marks available	2	Reference code	18M.1.SL.TZ1.T_7
Level	Standard Level	Paper	Paper 1	Time zone	Time zone 1
Command term	Find	Question number	T_7	Adapted from	N/A

Question

Sergei is training to be a weightlifter. Each day he trains at the local gym by lifting a metal bar that has heavy weights attached. He carries out successive lifts. After each lift, the same amount of weight is added to the bar to increase the weight to be lifted.

The weights of each of Sergei’s lifts form an arithmetic sequence.

Sergei’s friend, Yuri, records the weight of each lift. Unfortunately, last Monday, Yuri misplaced all but two of the recordings of Sergei’s lifts.

On that day, Sergei lifted 21 kg on the third lift and 46 kg on the eighth lift.

For that day find how much weight was added after each lift.

[2]

a.i.

For that day find the weight of Sergei’s first lift.

[2]

a.ii.

On that day, Sergei made 12 successive lifts. Find the total combined weight of these lifts.

[2]

Markscheme

5d = 46 − 21 OR u₁ + 2d = 21 and u₁ + 7d = 46 (M1)

Note: Award (M1) for a correct equation in d or for two correct equations in u₁ and d.

(d =) 5 (kg) (A1) (C2)

[2 marks]

a.i.

u₁ + 2 × 5 = 21 (M1)

u₁ + 7 × 5 = 46 (M1)

Note: Award (M1) for substitution of their d into either of the two equations.

(u₁=) 11 (kg) (A1)(ft) (C2)

Note: Follow through from part (a)(i).

[2 marks]

a.ii.

$\frac{{12}}{2}\left( {2 \times 11 + \left( {12 - 1} \right) \times 5} \right)$ (M1)

Note: Award (M1) for correct substitution into arithmetic series formula.

= 462 (kg) (A1)(ft) (C2)

Note: Follow through from parts (a) and (b).

[2 marks]

Examiners report

[N/A]

a.i.

[N/A]

a.ii.

[N/A]

Syllabus sections

Topic 1—Number and algebra » SL 1.2—Arithmetic sequences and series

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Topic 1—Number and algebra

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