O-LevelMathematicsMensuration4024/21 · May/June 2023 · Q119 Marks

The diagram shows an open container on a horizontal surface. The container is a prism with trapezium ABCD as its cross-section. AB = 28 cm, DC = 24 cm, AD = 16cm and BF = 29 cm. Angle ADC and angle DAB are right angles. [Figure 11.1]

(a)Calculate angle DCB.[3]
(b)Khalil pours water into the empty container at a rate of 4000 cm³/minute for 2 minutes. He says that the container is now more than two thirds full. Is he correct? Show your working.[3]
(c)Calculate angle DFH.[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.

[3] (a) 104[.0...] M2 for 90 + tan⁻¹((28-24)/16) oe or 180 – tan⁻¹(16/(28-24)) oe or M1 for tan[...] = (28-24)/16 oe or tan[...] = 16/(28-24) oe
[2] (b) (1/2) × 16 × (24 + 28) × h = 4000 × 2 M2 M1 for (1/2) × 16 × (24 + 28) × h or (1/2) × 16 × (24 + 28) × (2/3) × 29 A1
[1] (b) No and 19.2[3...] and 19.3[3...] 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
[3] (c) 42[.0] or 41.96... M2 for tan [...] = 29/√(28² +16²) oe or M1 for 28² +16² oe or tan [...] = 29/their HF

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