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CAEC Mathematics Preparation Course：CAEC geometry and measurement

不限时专题测验：关于CAEC geometry and measurement的17道题，每道题作答后都有解释。每次题目和选项都会重新打乱。

  • 课程
  • 加拿大
  • 100道题
  • 核对于2026年10月13日
  • 事实核查：2026年10月13日
从课文开始CAEC Mathematics Preparation: Lessons：阅读时间约360分钟。测试中的每道题在课文中都有讲解。

专题测验5：CAEC geometry and measurement

  1. 第1题，共17题

    How many metres are in 2.4 km?
    显示答案

    答案: C. 2,400 m

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

  2. 第2题，共17题

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

    答案: A. 8

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

  3. 第3题，共17题

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

    答案: B. 41 m

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

  4. 第4题，共17题

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

    答案: D. 14.7 m²

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

  5. 第5题，共17题

    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?
    显示答案

    答案: C. 50 m

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

  6. 第6题，共17题

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

    答案: A. 139.7 cm

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

  7. 第7题，共17题

    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?
    显示答案

    答案: 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. 第8题，共17题

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

    答案: A. 12 m²

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

  9. 第9题，共17题

    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?
    显示答案

    答案: A. 21 m²

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

  10. 第10题，共17题

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

    答案: D. 28.3 m²

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

  11. 第11题，共17题

    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?
    显示答案

    答案: 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. 第12题，共17题

    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?
    显示答案

    答案: B. 37.5 cm

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

  13. 第13题，共17题

    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?
    显示答案

    答案: 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. 第14题，共17题

    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)
    显示答案

    答案: A. 240 L

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

  15. 第15题，共17题

    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)
    显示答案

    答案: C. 942 L

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

  16. 第16题，共17题

    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.)
    显示答案

    答案: B. 7 L

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

  17. 第17题，共17题

    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?
    显示答案

    答案: 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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