O-LevelMathematicsTrigonometry4024/22 · May/June 2022 · Q911 Marks

[Figure showing a vertical pole PQ, a rope PR=20m, RQ=11m, RQP=90°] PQ is a vertical pole. A rope is attached from the top of the pole, P, to a point on the ground, R. PR = 20 m, RQ = 11 m and RQP = 90°.

(a)Show that PQ = 16.70 m, correct to 2 decimal places.[2]
(b)[Figure showing a vertical pole PQ, rope PR=20m, RQ=11m, RS=30m, PQS=90° and PSQ=36°] A second rope is attached from P to a point S. PQS = 90° and RS = 30 m. The angle of elevation of P from S is 36°. Calculate RQS.[5]
(c)[Figure showing a vertical pole PQ=16.70m, rope PT, TPQ=40°, PQT=97°] A third rope is attached from P to a point T. TPQ = 40° and PQT = 97°. Calculate PT.[4]

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Mark scheme

Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.

[2] M1 for 20² – 11² or √(20² – 11²) or PQ² + 11² = 20² → PQ² = 279 A1 for 16.703...
[5] M2 for [QS =] 16.70/tan 36 oe or M1 for tan 36 = 16.70/QS oe AND M2 for cos[...] = (11² + (their23)² – 30²) / (2 × 11 × their23) oe or M1 for 30² = 11² + (their23)² - 2 × 11 × their23 × cos[...] oe
[4] B1 for [PTQ=] 43° M2 for (16.7[0]sin 97) / sin(their43) oe or M1 for sin 97 / PT = sin(their43) / 16.7[0] oe

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