A-LevelMathematicsSeries9709/12 · Oct/Nov 2019 · Q89 Marks
Find the distance she runs on the last day of the 21-day period.
- (a)(i)Find the distance she runs on the last day of the 21-day period.[1]
- (a)(ii)Find the total distance she runs in the 21-day period.[2]
- (b)(i)Find the value of x.[2]
- (b)(ii)Find the fourth term of the progression.[2]
- (b)(iii)Find the sum to infinity of the progression.[2]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.
- [B1] 21st term = 13 + 20 × 1.2 = 37 (km)
- [M1] S₂₁ = (21/2)(26 + 20 × 1.2) or (21/2)(13 + their 37) A correct sum formula used with correct values for a, d and n.
- [A1] 525 (km)
- [M1] (x-3)/x = (x-5)/(x-3) oe (or use of a, ar and ar²) Any valid method to obtain an equation in one variable.
- [A1] (a = or x =) 9
- [M1] r = (9-3)/9 or (9-5)/(9-3) or = 2/3. Fourth term = 9 × (2/3)³ Any valid method to find r and the fourth term with their a & r.
- [A1] 2⅔ or 2.67 OE, AWRT
- [M1] S∞ = 9/(1 - 2/3) Correct formula and using their ‘r' and 'a', with |r|<1, to obtain a numerical answer.
- [A1] 27 or 27.0 AWRT
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