Ratio and proportion, 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。
- Red and white paint are mixed in the ratio 3 : 2. How many litres of red paint are needed to make 20 litres of the mixture? (number only)
12
提示Find the total number of parts, then the size of one part.
为什么3 + 2 = 5 parts, so one part is 20 ÷ 5 = 4 litres, and red is 3 × 4 = 12 litres.
- On a map, 1 cm represents 2 km. Write the scale as a ratio 1 : n.
1 : 200 000
提示Change the kilometres into centimetres first.
为什么2 km = 2000 m = 200 000 cm, so 1 cm on the map stands for 200 000 cm, giving 1 : 200 000. A ratio scale needs both sides in the same unit.
- Pack A has 6 pens for £2.40. Pack B has 10 pens for £3.50. Which pack is the better buy?
Pack B
提示Work out the price of a single pen in each set.
为什么Pack A is £2.40 ÷ 6 = 40p a pen. Pack B is £3.50 ÷ 10 = 35p a pen. Pack B is cheaper per pen, so it is better value.
- A 250 g jar of jam costs £1.80. How many pence does 100 g cost? (number only)
72
提示Find the price of 1 g, or of 50 g, and then scale up.
为什么£1.80 is 180p. 180 ÷ 250 = 0.72p per gram, so 100 g costs 72p.
- A cyclist rides 45 km at a steady 15 km/h. How many hours does the ride take? (number only)
3
提示Rearrange speed = distance ÷ time to find time.
为什么time = distance ÷ speed = 45 ÷ 15 = 3 hours.
- A stone has a mass of 270 g and a density of 2.7 g/cm³. What is its volume?
100 cm³
提示Density is mass ÷ volume, so volume is mass ÷ density.
为什么270 ÷ 2.7 = 100, so the stone's volume is 100 cm³.
- The price of a coat falls from £80 to £68. What is the percentage decrease?
15%
提示Compare the change with the original price, not the new one.
为什么The fall is £80 − £68 = £12, and 12/80 × 100 = 15%.
- Two people share money in the ratio 4 : 7, and the larger share is £21 more than the smaller. How much is the larger share?
£49
提示The difference between the shares covers a known number of parts.
为什么The difference is 7 − 4 = 3 parts, which is £21, so one part is £7. The larger share is 7 × £7 = £49.
- A toy costs $26. The exchange rate is £1 = $1.30. What does the toy cost in pounds?
£20
提示Dollars to pounds means going from the bigger number to the smaller one.
为什么26 ÷ 1.30 = 20, so the toy costs £20. Each £1 buys $1.30, so you divide the dollars by 1.30.
- The cost of apples is directly proportional to their mass, and 5 kg cost £8. What is the gradient of the straight-line graph of cost against mass?
£1.60 per kg
提示The gradient of such a graph is the cost of one unit of mass.
为什么The line passes through the origin, so gradient = 8 ÷ 5 = 1.6, which is £1.60 for each kilogram.
1★ KS3-MATH-RAT-0082
2★ KS3-MATH-RAT-0083
3★ KS3-MATH-RAT-0084
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5★ KS3-MATH-RAT-0086
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8★ KS3-MATH-RAT-0089
9★ KS3-MATH-RAT-0090
10★ KS3-MATH-RAT-0091