CAEC Mathematics Preparation Course: CAEC geometry and measurement

1. Pergunta 1 de 17

   How many metres are in 2.4 km?

   • A24,000 m
   • B24 m
   • C2,400 m
   • D240 m
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   Resposta: C. 2,400 m

   1 km = 1,000 m, so 2.4 × 1,000 = 2,400 m.

2. Pergunta 2 de 17

   A bag holds 3.6 kg of rice. Each batch of a recipe uses 450 g. How many full batches can you make?

   • A8
   • B12
   • C0.8
   • D80
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   Resposta: A. 8

   Change to the same unit: 3.6 kg = 3,600 g. Then 3,600 ÷ 450 = 8 batches.

3. Pergunta 3 de 17

   A fence goes around a rectangular yard that is 12 m long and 8.5 m wide. How much fencing is needed?

   • A20.5 m
   • B41 m
   • C102 m
   • D32.5 m
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   Resposta: B. 41 m

   Perimeter of a rectangle = 2 × (length + width) = 2 × (12 + 8.5) = 41 m.

4. Pergunta 4 de 17

   A bedroom floor is 4.2 m long and 3.5 m wide. What is its area?

   • A147 m²
   • B15.4 m²
   • C7.7 m²
   • D14.7 m²
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   Resposta: D. 14.7 m²

   Area of a rectangle = length × width = 4.2 × 3.5 = 14.7 m².

5. Pergunta 5 de 17

   A rectangular lot is 30 m by 40 m. A path goes straight across it from one corner to the opposite corner. How long is the path?

   • A35 m
   • B1,200 m
   • C50 m
   • D70 m
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   Resposta: C. 50 m

   The path is the hypotenuse: c² = 30² + 40² = 900 + 1,600 = 2,500, so c = 50 m.

6. Pergunta 6 de 17

   1 inch = 2.54 cm. A TV screen measures 55 inches across. What is that in centimetres?

   • A139.7 cm
   • B1,397 cm
   • C57.54 cm
   • D21.65 cm
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   Resposta: A. 139.7 cm

   Inches to centimetres: multiply by 2.54. 55 × 2.54 = 139.7 cm.

7. Pergunta 7 de 17

   1 kg is about 2.2 lb. An airline allows checked bags up to 23 kg. Your bag weighs 48 lb. Is it within the limit?

   • AYes, it is about 21.8 kg
   • BNo, it is about 105.6 kg
   • CNo, it is about 50.2 kg
   • DNo, it is about 48 kg
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   Resposta: A. Yes, it is about 21.8 kg

   Pounds to kilograms: divide by 2.2. 48 ÷ 2.2 ≈ 21.8 kg, which is under 23 kg.

8. Pergunta 8 de 17

   A gable wall is a triangle with a base of 8 m and a height of 3 m. What is its area?

   • A12 m²
   • B11 m²
   • C24 m²
   • D5.5 m²
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   Resposta: A. 12 m²

   Area of a triangle = base × height ÷ 2 = 8 × 3 ÷ 2 = 12 m².

9. Pergunta 9 de 17

   An L-shaped room is a 6 m by 4 m rectangle with a 2 m by 1.5 m piece missing from one corner. What is the floor area?

   • A21 m²
   • B20.5 m²
   • C27 m²
   • D24 m²
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   Resposta: A. 21 m²

   Split or subtract: big rectangle 6 × 4 = 24 m², missing piece 2 × 1.5 = 3 m². 24 − 3 = 21 m².

10. Pergunta 10 de 17

    A round garden bed has a diameter of 6 m. What is its area, to one decimal place?

    • A9.4 m²
    • B18.8 m²
    • C113.1 m²
    • D28.3 m²
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    Resposta: D. 28.3 m²

    The radius is half the diameter: 3 m. Area = πr² = 3.14159 × 9 ≈ 28.3 m².

11. Pergunta 11 de 17

    A 5 m ladder leans against a wall. Its foot is 1.5 m from the wall. How high up the wall does it reach, to the nearest centimetre?

    • A4.77 m
    • B6.5 m
    • C5.22 m
    • D3.5 m
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    Resposta: A. 4.77 m

    The ladder is the hypotenuse: height² = 5² − 1.5² = 25 − 2.25 = 22.75, so height = √22.75 ≈ 4.77 m.

12. Pergunta 12 de 17

    A photo is 10 cm wide and 15 cm tall. It is enlarged to 25 cm wide, keeping the same shape. How tall is the enlargement?

    • A40 cm
    • B37.5 cm
    • C30 cm
    • D6 cm
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    Resposta: B. 37.5 cm

    Scale factor = 25 ÷ 10 = 2.5. New height = 15 × 2.5 = 37.5 cm.

13. Pergunta 13 de 17

    A 2 m post casts a 1.5 m shadow. At the same time, a tree casts a 9 m shadow. How tall is the tree?

    • A10.5 m
    • B12 m
    • C13.5 m
    • D6.75 m
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    Resposta: B. 12 m

    The triangles are similar. Height ÷ shadow is the same: 2 ÷ 1.5 = tree ÷ 9, so tree = 9 × 2 ÷ 1.5 = 12 m.

14. Pergunta 14 de 17

    A planter box is 1.2 m long, 0.5 m wide and 0.4 m deep. How many litres of soil fill it? (1 m³ = 1,000 L)

    • A240 L
    • B2.1 L
    • C24 L
    • D2,400 L
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    Resposta: A. 240 L

    Volume = 1.2 × 0.5 × 0.4 = 0.24 m³. 0.24 × 1,000 = 240 L.

15. Pergunta 15 de 17

    A water tank is a cylinder with a radius of 0.5 m and a height of 1.2 m. About how many litres does it hold? (1 m³ = 1,000 L)

    • A300 L
    • B3,770 L
    • C942 L
    • D1,885 L
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    Resposta: C. 942 L

    Volume of a cylinder = πr²h = 3.14159 × 0.25 × 1.2 ≈ 0.942 m³, which is about 942 L.

16. Pergunta 16 de 17

    You will paint the four walls of a room that is 4 m by 3 m with walls 2.5 m high. One litre of paint covers 10 m². How much paint do you need for two coats? (Ignore doors and windows.)

    • A9.4 L
    • B7 L
    • C6 L
    • D3.5 L
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    Resposta: B. 7 L

    Wall area = 2 × (4 + 3) × 2.5 = 35 m². Two coats = 70 m². 70 ÷ 10 = 7 L.

17. Pergunta 17 de 17

    A floor is 14.7 m². You add 10% extra for cutting waste. Each box of flooring covers 2.2 m². How many boxes must you buy?

    • A6 boxes
    • B36 boxes
    • C7 boxes
    • D8 boxes
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    Resposta: D. 8 boxes

    14.7 × 1.10 = 16.17 m². 16.17 ÷ 2.2 ≈ 7.35, and you cannot buy part of a box, so round up to 8 boxes.

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