A-LevelMathematicsSeries9709/12 · Oct/Nov 2013 · Q78 Marks
An athlete runs the first mile of a marathon in 5 minutes. His speed reduces in such a way that each mile takes 12 seconds longer than the preceding mile. Given that the nth mile takes 9 minutes, find the value of n.
- (a)(i)An athlete runs the first mile of a marathon in 5 minutes. His speed reduces in such a way that each mile takes 12 seconds longer than the preceding mile. Given that the nth mile takes 9 minutes, find the value of n.[2]
- (a)(ii)Assuming that the length of the marathon is 26 miles, find the total time, in hours and minutes, to complete the marathon.[2]
- (b)The second and third terms of a geometric progression are 48 and 32 respectively. Find the sum to infinity of the progression.[4]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2013). The mark or mark type is shown in brackets.
- [1] a = 300, d = 12 Use of nth term. Ans 20 gets 0.
- [1] 540 = 300 + (n − 1)12 → n = 21 Ignore incorrect units
- [1] S₂₆ = ½(26)(600 + 25×12) = 11700 Correct use of s_n formula.
- [1] → 3 hours 15 minutes.
- [1] ar = 48 and ar² = 32 Needs ar and ar² + attempt at a and r.
- [1] → r = ⅔
- [1] → a = 72.
- [1] S_∞ = 72/(1−⅔) = 216. Correct S_∞ formula with |r| < 1
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