O-LevelMathematicsAlgebra and graphs4024/22 · May/June 2018 · Q912 Marks

On Monday, Ravi goes on a 20km run.

(a)(i)His average speed for the first 12km is x km/h. Write down an expression, in terms of x, for the time taken for the first 12km. Give your answer in minutes.[1]
(a)(ii)His average speed for the final 8 km of the run is 1.5km/h slower than for the first 12km. Write an expression, in terms of x, for the time taken for the final 8 km of the run. Give your answer in minutes.[1]
(a)(iii)Ravi takes 110 minutes to complete the full 20km. Form an equation in x and show that it simplifies to 22x² - 273x + 216 = 0 .[4]
(a)(iv)Solve the equation 22x² - 273x + 216 = 0 . Show your working and give each answer correct to 2 decimal places.[3]
(b)On Friday, Ravi ran the whole 20km at the same average speed that he ran the final 8km on Monday. Calculate the time Ravi took to run 20km on Friday. Give your answer in hours and minutes, correct to the nearest minute.[3]

Mark scheme

Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.

[1] 12×60 / x oe
[1] 8×60 / (x-1.5) oe
[4] M1 FT their (a)(i) and (a)(ii) if functions of x
M1 Dep on equation of form c/px + d/(qx+r) = e where p, q, r, c, d and e are numeric and non zero, AND either correctly uses a common denominator for their fractions or correctly removes their fractions
A1 Correct elimination of correct brackets
A1
[3] B2 B1 for (-273)^2 - 4×22×216 or for -(-273)±√their55521 / (2×22)
B1
11.56 and 0.85 cao
[3] M2 for 20 / (their11.56 – 1.5) [×60] oe or M1 for their 11.56 – 1.5 or for 20 / their x

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