Geometry and measures, Year 8: more practice：全部卡片
整套按顺序列出——孩子看到之前，您可以先通读一遍。
- A translation moves every point 4 left and 1 up. Point B ends at (0, 6). Where was B before the translation?
(4, 5)
提示Reverse the movement: go back 4 right and 1 down.
为什么Before the move B was 4 to the right and 1 lower: (0 + 4, 6 − 1) = (4, 5). Check: 4 left and 1 up from (4, 5) lands on (0, 6).
- What is the area of a parallelogram with base 3.5 m and perpendicular height 4 m?
14 m²
提示Multiply the base by the perpendicular height.
为什么3.5 × 4 = 14, in square metres.
- A trapezium has parallel sides of 6 cm and 10 cm, and the distance between them is 4 cm. What is its area?
32 cm²
提示Find the mean of the parallel sides, then multiply by the height.
为什么Mean of the parallel sides is (6 + 10) ÷ 2 = 8, and 8 × 4 = 32 cm².
- A trapezium has area 45 cm² and parallel sides of 7 cm and 11 cm. What is the height between them?
5 cm
提示Write the area formula with h as the unknown, then solve.
为什么45 = ½ × (7 + 11) × h = 9h, so h = 5. Check: ½ × 18 × 5 = 45.
- A circle has radius 4 cm. Find its circumference to 1 decimal place, using the π button.
25.1 cm
提示Circumference is π times the diameter, and the diameter is twice the radius.
为什么d = 8 cm, so C = π × 8 = 25.13… ≈ 25.1 cm.
- Point (2, 1) is rotated 90° clockwise about the origin. Where does it land?
(1, −2)
提示Picture the point turning like a clock hand. It starts to the right of and above the origin and ends below.
为什么A 90° clockwise turn sends (x, y) to (y, −x). The point lands 1 right and 2 down, at (1, −2).
- A 2 cm by 5 cm rectangle is enlarged by scale factor 4. What is the perimeter of the image?
56 cm
提示Find the new side lengths first.
为什么The sides become 8 cm and 20 cm, so the perimeter is 2 × (8 + 20) = 56 cm. The original perimeter, 14 cm, is also multiplied by 4.
- A prism has a cross-section area of 12 cm² and is 9 cm long. What is its volume?
108 cm³
提示Volume of a prism = area of cross-section × length.
为什么12 × 9 = 108, and the units are cubic because three lengths are multiplied.
- A prism has volume 150 cm³ and length 6 cm. What is the area of its cross-section in cm²? (number only)
25
提示Work backwards: volume = cross-section area × length.
为什么150 ÷ 6 = 25. Check: 25 × 6 = 150.
- Find the total surface area of a cuboid that is 2 cm by 3 cm by 4 cm.
52 cm²
提示A cuboid has three pairs of identical faces.
为什么The faces are 2 × 3 = 6, 2 × 4 = 8 and 3 × 4 = 12. The total is 2 × (6 + 8 + 12) = 52 cm².
1★ KS3-MATH-GEO-0104
2★ KS3-MATH-GEO-0105
3★ KS3-MATH-GEO-0106
4★ KS3-MATH-GEO-0107
5★ KS3-MATH-GEO-0108
6★ KS3-MATH-GEO-0109
7★ KS3-MATH-GEO-0110
8★ KS3-MATH-GEO-0111
9★ KS3-MATH-GEO-0112
10★ KS3-MATH-GEO-0113