O-LevelMathematicsTrigonometry4024/21 · May/June 2023 · Q713 Marks

ABC is a triangle with AC = 8.3 cm and BÂC = 105°. Construct triangle ABC. Line AB has been drawn for you.

(a)(i)ABC is a triangle with AC = 8.3 cm and BÂC = 105°. Construct triangle ABC. Line AB has been drawn for you.[2]
(a)(ii)By taking suitable measurements from your triangle, calculate the perimeter of triangle ABC.[2]
(b)(i)The diagram shows quadrilateral PQRS. SQ = 15 cm, S^PQ = 67° and P^QS = 74°. [Figure 7.1] Calculate PS.[3]
(b)(ii)(a)P^SR = 96° and the area of triangle QRS is 63 cm². Show that SR = 10.0 cm, correct to 1 decimal place.[3]
(b)(ii)(b)Calculate QR.[3]

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Mark scheme

Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.

[2] (a)(i) Correct triangle B1 for either AC = 8.3 or ∠BAC = 105°
[2] (a)(ii) 30.8 to 31.2 FT (17.1 to 17.5) + their BC B1FT for their BC measured
[3] (b)(i) 15.7 or 15.66... M2 for [PS =] (15 sin 74)/(sin 67) or M1 for (PS/sin 74) = (15/sin 67) oe
[1] (b)(ii)(a) ∠ QSR = 57 B1
[1] (b)(ii)(a) (1/2) × 15 × SR × sin(their 57) = 63 oe M1
[1] (b)(ii)(a) 10.01 to 10.02 A1
[3] (b)(ii)(b) 12.7 or 12.71 to 12.72... M2 for √(15² +10²-2×15×10cos(their57)) oe OR M1 for 15² + 10² – 2 × 15 × 10 cos(their 57) A1 for 162 or 161.6 to 161.7

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