Mathematics · May / June 2025 · Paper 21 · Question 18
0580
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The question as text
One day, Anya runs 12 km at a speed of x km/h. The next day she walks 10 km at a speed of ( ) x 4 Ä km/h.
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18(a)[1]
12 x [1]
18(b)[1]
10 − x 4 [1]
18(c)[4]
their 10 – their 12 = 1 oe − x 4 x 10x – 12x + 48 = x2 – 4x Leading to 0 = x2 – 2x – 48 [8]
M1 M2 Correctly multiplying their brackets and clearing algebraic fractions ) 12 e.g. ( − + = x 4 1 10 x 48 − + − = leading to 12 x 4 10 and then x − + 2 − = 12 x 48 x 4 x 10 x
or M1 for correctly clearing, or correctly collecting into a single fraction, two fractions both with different algebraic denominators e.g. 10x – 12(x – 4) = x(x – 4) or − ( − ) 10 x 12 x 4 [= 1] ( ) − x x 4 A1 With no errors or omissions seen, dep on M3
18(d)[3]
(x + 6)(x – 8) –6, 8 [4]
M2 M1 for x(x – 8) + 6(x – 8) or x(x + 6) – 8(x + 6) or (x + a)(x + b) where ab = –48 or a + b = –2 B1
18(e)[1]
1.5 or 1 1 2 [1]
FT 12 their 8
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