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Date May 2017 Marks available 3 Reference code 17M.1.SL.TZ1.T_5
Level Standard Level Paper Paper 1 (with calculator from previous syllabus) Time zone Time zone 1
Command term Find Question number T_5 Adapted from N/A

Question

The company Snakezen’s Ladders makes ladders of different lengths. All the ladders that the company makes have the same design such that:

the first rung is 30 cm from the base of the ladder,

the second rung is 57 cm from the base of the ladder,

the distance between the first and second rung is equal to the distance between all adjacent rungs on the ladder.

The ladder in the diagram was made by this company and has eleven equally spaced rungs.

M17/5/MATSD/SP1/ENG/TZ1/05

Find the distance from the base of this ladder to the top rung.

[3]
a.

The company also makes a ladder that is 1050 cm long.

Find the maximum number of rungs in this 1050 cm long ladder.

[3]
b.

Markscheme

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

30 + ( 11 1 ) × 27     (M1)(A1)

 

Note:     Award (M1) for substituted arithmetic sequence formula, (A1) for correct substitutions.

 

= 300  (cm)     (A1)     (C3)

 

Note:     Units are not required.

 

[3 marks]

a.

1050 30 + ( n 1 ) × 27     (M1)(A1)(ft)

 

Note:     Award (M1) for substituted arithmetic sequence formula 1050 , accept an equation, (A1) for correct substitutions.

 

n = 38     (A1)(ft)     (C3)

 

Note:     Follow through from their 27 in part (a). The answer must be an integer and rounded down.

 

[3 marks]

b.

Examiners report

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

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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