O-LevelMathematicsTrigonometry4024/21 · Oct/Nov 2020 · Q310 Marks

In triangle PQR, PR = 7.5 cm and QR = 6 cm. Using a ruler and compasses only, construct triangle PQR. Line PQ has been drawn for you.

(a)(i)In triangle PQR, PR = 7.5 cm and QR = 6 cm. Using a ruler and compasses only, construct triangle PQR. Line PQ has been drawn for you.[2]
(a)(ii)By taking suitable measurements from your triangle, calculate the area of triangle PQR.[2]
(b)(i)The diagram shows two triangles. AB = 9.7 cm, BC = 6.4 cm, CD = 3.8 cm and AC = 5.3 cm. ADC = 63°. Calculate DÂC.[3]
(b)(ii)Calculate ABC.[3]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.

[2] Correct triangle with intersecting arcs B1 for acceptable vertex R indicated with no/incorrect arcs After 0 scored, SC1 for triangle with P = 6 cm and QR = 7.5 cm with intersecting arcs
[2] 20.8 to 21.6 M1 for 1/2 ×8×their height oe or 1/2 ×8×7.5×sin their 45 or 1/2 ×8×6×sin their 63 or 1/2 ×6×7.5×sin their 72
[3] 39.7 or 39.70... M2 for [sin =] 3.8xsin 63 / 5.3 or M1 for sin[...] = 3.8 / 5.3 sin 63 oe
[3] 30.5 or 30.51 to 30.52 M2 for [cos =] 6.4^2 + 9.7^2 - 5.3^2 / (2x6.4x9.7) or M1 for 5.3^2 = 6.4^2 + 9.7^2 -2x6.4x9.7xcos[...]

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