Chapter 8 Practice Paper: Trigonometric Ratios — mark scheme (print)

QuizQuipPractice Series

QQ/S2MATH/CH8

Secondary 2 · Lower Secondary Mathematics (G2 / G3)

Mark scheme

Trigonometric Ratios

Chapter 8 Practice Paper · Maximum mark: 30

Notes for markers

Award one mark for each point marked [1], up to the marks shown for the part.
Accept answers worded differently that show the same understanding.
Units are required where the answer line shows one. ecf: allow an error carried forward.

Section A: Multiple-choice questions[10 marks]

Question	Answer
1	AThe hypotenuse faces the right angle and is the longest side.	1
2	CTOA: tangent is opposite over adjacent.	1
3	BA famous value: half a unit rise on a unit slope.	1
4	Dsin θ = 5/10 = 0.5, and sin 30° = 0.5.	1
5	Atan 45° = 1, so opposite equals adjacent.	1
6	Cadj = 20 × cos 25° ≈ 18.1.	1
7	BOpposite with hypotenuse means sine, inverted.	1
8	Dtan θ = 3/4 = 0.75, so θ ≈ 36.9°.	1
9	CHeight = 12 × sin 65° ≈ 10.9 m.	1
10	Acos 0° = 1 and cos 90° = 0, falling between them.	1

Section B: Structured questions[20 marks]

Question	Answer and marking points	Marks
1(a)	8/17 [1]	1
1(b)	15/17 [1]	1
1(c)	8/15 [1]	1
1(d)	8² + 15² = 64 + 225 = 289 = 17². Squares 64 and 225 added [1] 289 = 17² confirmed [1]	2
	Total for Question 1	5
2(a)	Sine (sin 32° = opposite ÷ hypotenuse) Sine chosen [1]	1
2(b)	opp = 14 × sin 32° ≈ 7.42. 14 × sin 32° used [1] ≈ 7.42 [1]	2
2(c)	adj = 14 × cos 32° ≈ 11.87. 14 × cos 32° used [1] ≈ 11.87 [1]	2
	Total for Question 2	5
3(a)	40/75 (= 8/15) [1]	1
3(b)	θ = tan⁻¹(40/75) ≈ 28.1°. tan⁻¹ applied [1] ≈ 28.1° [1]	2
3(c)	Length = √(40² + 75²) = √(1600 + 5625) = √7225 = 85 m. 1600 + 5625 formed [1] √7225 = 85 m [1]	2
	Total for Question 3	5
4(a)	Height = 7.5 × sin 72° ≈ 7.13 m. 7.5 × sin 72° used [1] ≈ 7.13 m [1]	2
4(b)	7.5 × cos 72° ≈ 2.32 m [1]	1
4(c)	No: the ladder reaches about 7.13 m, which is below 7.2 m. Compares 7.13 with 7.2 [1] Conclusion: does not reach [1]	2
	Total for Question 4	5

— End of mark scheme —