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Date May 2021 Marks available 2 Reference code 21M.1.SL.TZ1.8
Level Standard Level Paper Paper 1 Time zone Time zone 1
Command term Calculate Question number 8 Adapted from N/A

Question

Charlie and Daniella each began a fitness programme. On day one, they both ran 500m. On each subsequent day, Charlie ran 100m more than the previous day whereas Daniella increased her distance by 2% of the distance ran on the previous day.

Calculate how far

Charlie ran on day 20 of his fitness programme.

[2]
a.i.

Daniella ran on day 20 of her fitness programme.

[3]
a.ii.

On day n of the fitness programmes Daniella runs more than Charlie for the first time.

Find the value of n.

[3]
b.

Markscheme

attempt to find u20 using an arithmetic sequence         (M1)

e.g.  u1=500 and d=100  OR  u20=500+1900  OR  500, 600, 700,

(Charlie ran) 2400m             A1


[2 marks]

a.i.

r= 1.02         (A1)

attempt to find u20 using a geometric sequence         (M1)

e.g.  u1=500 and a value for r  OR  500×r19  OR  500, 510, 520.2, 

(Daniella ran) 728m  728.405             A1


[3 marks]

a.ii.

500×1.02n-1>500+n-1×100         (M1)

attempt to solve inequality         (M1)

n>184.215

n=185             A1


[3 marks]

b.

Examiners report

[N/A]
a.i.
[N/A]
a.ii.
[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 » SL 1.3—Geometric sequences and series
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