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 500 m500m. On each subsequent day, Charlie ran 100 m100m more than the previous day whereas Daniella increased her distance by 2%2% of the distance ran on the previous day.
Calculate how far
Charlie ran on day 2020 of his fitness programme.
Daniella ran on day 2020 of her fitness programme.
On day nn of the fitness programmes Daniella runs more than Charlie for the first time.
Find the value of nn.
Markscheme
attempt to find u20u20 using an arithmetic sequence (M1)
e.g. u1=500u1=500 and d=100d=100 OR u20=500+1900u20=500+1900 OR 500, 600, 700, …500, 600, 700,…
(Charlie ran) 2400 m2400m A1
[2 marks]
(r=) 1.02(r=) 1.02 (A1)
attempt to find u20u20 using a geometric sequence (M1)
e.g. u1=500u1=500 and a value for rr OR 500×r19500×r19 OR 500, 510, 520.2, …500, 510, 520.2, …
(Daniella ran) 728 m (728.405…)728m (728.405…) A1
[3 marks]
500×1.02n-1>500+(n-1)×100500×1.02n−1>500+(n−1)×100 (M1)
attempt to solve inequality (M1)
n>184.215…n>184.215…
n=185n=185 A1
[3 marks]