4024/21 May/Jun 2023, Question 11: Choosing the Right Trigonometric Ratio
Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 9 marks
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The question, in short
For a prism-shaped open container with trapezium cross-section, find an angle, check a fill claim, and find another angle using given dimensions.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Part (a) · 3 marks
Calculate angle DCB using the trapezium dimensions AB = 28, DC = 24 and AD = 16.
- 1Drop a perpendicular from C to AB: horizontal gap = 28 − 24 = 4, height = 16
- 2tan⁻¹(16/4) = 75.96…°
- 3Angle DCB = 180 − 75.96… = 104.0…°
Answer104.0…
Part (b) · 3 marks
Decide whether 4000 cm³/min for 2 minutes fills more than two thirds of the container; show working.
- 1Area of ABCD = 1/2 × 16 × (24 + 28) = 416 cm²
- 2Volume = 416 × 29 = 12 064 cm³
- 32/3 of 12 064 = 8042.66… cm³
- 4Water = 4000 × 2 = 8000 cm³
- 58000 < 8042.66…, so No, he is not correct
AnswerNo and 19.23… and 19.33… OR No and 19.23/29 or 8000/12064 = 0.663… and 0.666 to 0.667 OR No and 8040 or 8042 to 8043 and 8000
Part (c) · 3 marks
Calculate angle DFH using the prism dimensions, including BF = 29.
- 1HF = DB = √(28² + 16²) = √1040 = 32.24…
- 2Triangle DHF has a right angle at H and DH = 29
- 3tan(DFH) = 29/√1040
- 4Angle DFH = 41.96… ≈ 42.0°
Answer42.0 or 41.96…
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