1.
Share £120 in the ratio 3 : 5.
[2 marks]
- Total parts 8
- Final answer: £45.00 : £75.00
JD SCIENCE
Ratio, proportion and rates of change
Indicative marking points. Award marks for equivalent scientific or mathematical wording. Do not issue this sheet with the student worksheet.
2.
A recipe for 8 people uses 240 g of flour. How much flour is needed for 12 people?
[2 marks]
- Unitary method or × 1.5
- Final answer: 360 g
3.
It takes 6 workers 8 hours to decorate a room. How long would 4 workers take, at the same rate?
[3 marks]
- Inverse proportion: 6×8 = 4×t
- Final answer: 12 hours
4.
A car travels 140 miles at 56 mph. How long does the journey take?
[2 marks]
- t = d/s
- Final answer: 2.5 hours
5.
Convert 56 mph to km/h. Use 1 mile = 1.6 km.
[2 marks]
- Multiply by 1.6
- Final answer: 89.6 km/h
6.
A map has scale 1 : 35000. Two towns are 4.8 cm apart on the map. Work out the real distance in km.
[3 marks]
- Multiply by the scale, convert cm to km
- Final answer: 1.68 km
7.
£1 = $1.35. Convert £80 to dollars.
[2 marks]
- Multiply
- Final answer: $108.00
8.
A recipe is in the ratio flour : sugar : butter = 5 : 2 : 3. Grace uses 200 g of flour. How much sugar is used?
[2 marks]
- 200/5 = 40 g per part
- Final answer: 80 g
9.
The ratio of boys to girls in a class is 3 : 5. There are 20 girls. How many boys are there?
[2 marks]
- 20/5 × 3
- Final answer: 12
10.
The ratio of red to blue counters is 2 : 7. There are 20 red counters. How many blue counters?
[2 marks]
- 20/2 × 7
- Final answer: 70
11.
y is directly proportional to x. y = 12 when x = 4. Find y when x = 10.
[3 marks]
- y = 3x
- Final answer: 30
12.
y is inversely proportional to x. y = 8 when x = 5. Find y when x = 2.
[3 marks]
- y = 40/x
- Final answer: 20
13.
A tap fills a tank in 6 hours. A second tap fills it in 3 hours. How long if both taps are open?
[3 marks]
- 1/6 + 1/3 = 1/2
- Final answer: 2 hours
14.
Increase £100 by 15%.
[2 marks]
- × 1.15
- Final answer: £115.00
15.
Decrease £100 by 15%.
[2 marks]
- × 0.85
- Final answer: £85.00
16.
A population of 2200 grows by 4% each year. Estimate the population after 3 years.
[3 marks]
- Compound growth
- Final answer: 2475
17.
Density = mass ÷ volume. A block of mass 280 g has volume 30 cm³. Find the density.
[2 marks]
- D = m/v
- Final answer: 9.33 g/cm³
18.
Pressure = force ÷ area. A force of 160 N acts on an area of 0.4 m². Find the pressure.
[2 marks]
- P = F/A
- Final answer: 400.0 N/m²
19.
A speed camera records 90 km in 1 hour 15 minutes. Work out the average speed in km/h.
[3 marks]
- 90 ÷ 1.25
- Final answer: 72 km/h
20.
Convert 2 hours 24 minutes to hours as a decimal, then find the distance at 50 mph.
[3 marks]
- 2.4 hours × 50
- Final answer: 120 miles
21.
Which of these is inverse proportion: cost vs number of items at a fixed unit price, or time vs number of workers for a fixed job? Explain.
[3 marks]
- Time vs workers is inverse
- More workers, less time
22.
A metal bar is 1.2 m long. It is cut in the ratio 5 : 7. Find the two lengths.
[3 marks]
- 1.2 m = 120 cm, 12 parts
- Final answer: 50 cm and 70 cm
23.
Best buy: 4 cans for £2.40 or 6 cans for £3.30. Which is better value?
[3 marks]
- Unit cost
- Final answer: 6 for £3.30 (55p each vs 60p)
24.
A currency conversion charges 3% commission. Grace changes £500. How much is left to convert?
[2 marks]
- × 0.97
- Final answer: £485.00
25.
Scale 1 : 50 000. A road is 3 km long. How long is it on the map in cm?
[3 marks]
- 3 km = 300 000 cm; ÷ 50 000
- Final answer: 6 cm
26.
A graph shows a straight line through (0, 0) and (4, 10).
(a) [1 mark]
- Straight line through the origin
(b) [2 marks]
- k = 10/4 = 2.5
27.
Mix orange paint in the ratio red : yellow = 2 : 5. How much yellow is needed with 300 ml of red?
[2 marks]
- 300/2 × 5
- Final answer: 750 ml
28.
A cyclist rides 18 km in 40 minutes. Work out the speed in km/h.
[2 marks]
- 18 ÷ (2/3)
- Final answer: 27 km/h
29.
Write the formula triangle for speed, distance and time, and state two rearranged formulae.
[3 marks]
- s = d/t
- d = st
- t = d/s
30.
y ∝ x² and y = 12 when x = 2. Find y when x = 5.
[3 marks]
- y = 3x²
- Final answer: 75
31.
On OCR papers, ratio questions often hide a reverse-percentage step. A price is increased by 10% to £132. Show how to find the original price.
[3 marks]
- 132 ÷ 1.10 = £120