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O-LevelMathematicsMensuration4024/22 · Oct/Nov 2024 · Q310 Marks

[Figure showing a cuboid tank with length 1.2, width 0.6, and height h. Labelled 'NOT TO SCALE'.] The diagram shows a tank. The tank is a cuboid with length 1.2 m, width 0.6 m and height h m. The volume of the tank is 1.8 m³.

  1. (a)(i)Calculate the value of h.[2]
  2. (a)(ii)Fuel is pumped into the empty tank at a rate of 0.2 m³ per minute. Calculate the time taken to fill the tank to 90% of its volume. Give your answer in minutes and seconds.[3]
  3. (b)[Figure showing a prism tank with an open top. The cross-section is trapezium ABCD. AB is parallel to CD. AD = 70, BC = 70, CD = 80, AB = 110. The base of the tank is a square. Labelled 'NOT TO SCALE'.] The diagram shows a tank with an open top. The tank is a prism with trapezium ABCD as its cross-section. AD = BC = 70 cm, CD = 80 cm and AB = 110 cm. The base of the tank is a square. Calculate the total surface area of the outside of the tank.[5]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2024). The mark or mark type is shown in brackets.

  1. [2] 2.5
  2. [M1] for 1.2 × 0.6 × h = 1.8 oe
  3. [3] 8 [minutes] 6 [seconds]
  4. [M2] for (1.8 × 90/100) / 0.2 oe
  5. [M1] for 1.8 / 0.2 or 1.8 × 90/100 isw
  6. [5] 30 600 or 30 590 to 30 591[. ...]
  7. [M2] for 70² + ((110-80)/2)²
  8. [M1] for 70² = ((110-80)/2)² + h²
  9. [M1dep] for 1/2 × (110 + 80) × their 68.37 oe
  10. [M1] for 80 × 80 oe and [2 ×] 80 × 70 oe

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About this question

Topic
Mensuration, O-Level Mathematics (syllabus 4024). Structured question, 10 marks.
Source
O-Level Mathematics, Oct/Nov 2024 Paper 2 Variant 2, question 3.

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