O-LevelMathematicsTrigonometry4024/21 · Oct/Nov 2021 · Q410 Marks

4 (a) [Figure diagram of villages P, Q, R with bearings] The diagram shows the positions of three villages, P, Q and R. R is due west of P and Q is on a bearing of 140° from P. PR = 3.8 km and QR = 7.5 km. (i) Calculate angle PRQ. Angle PRQ = (ii) Work out the bearing of R from Q. (b) The distance by road from village P to village T is 16.5 km. Kwesi leaves village P at 1030 and drives to village T at an average speed of 45 km/h. He stops in village T for 15 minutes. He then drives back to village P and arrives there at 1135. Calculate Kwesi's average speed, in km/h, for the journey back from village T to village P. km/h

(a)(i)Calculate angle PRQ.[4]
(a)(ii)Work out the bearing of R from Q.[2]
(b)The distance by road from village P to village T is 16.5 km. Kwesi leaves village P at 1030 and drives to village T at an average speed of 45 km/h. He stops in village T for 15 minutes. He then drives back to village P and arrives there at 1135. Calculate Kwesi's average speed, in km/h, for the journey back from village T to village P.[4]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.

[4] (a)(i) 27.1 to 27.2
[4] B1 for ∠RPQ = 130° soi
[4] M2 for sin[ ]= 3.8sin (their130) / 7.5 oe or M1 for 7.5 / sin(their130) = 3.8 / sin[ ] oe
[2] (a)(ii) 297.1 to 297.2
[2] FT 270+ their 27.2, where 0 < their 27.2 < 90 or for 320 – their ∠PQR where 0 < their ∠PQR < 90
[2] M1 for 180+90 + their 27.2 oe or for 360 - (40 + 180 - 130 – their 27.2) or for 360-40 – their ∠PQR
[4] (b) 35.3 to 35.4
[4] M1 for 16.5 / 45
[4] M1 for [time =] 65 – 15 – their 22 oe
[4] M1 for 16.5 / their 28 [×60]

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