1.
Share £96 in the ratio 3 : 5. [2]
JD SCIENCE
Ratio, proportion and rates of change
Answer all questions. Show working. Answers are in a separate file on the Worksheets page — do not look at them until you have finished.
2.
A recipe for 8 people uses 200 g of flour. How much flour is needed for 12 people? [2]
3.
It takes 6 workers 8 hours to decorate a room. How long would 4 workers take, at the same rate? [3]
4.
A car travels 120 miles at 48 mph. How long does the journey take? [2]
5.
Convert 48 mph to km/h. Use 1 mile = 1.6 km. [2]
6.
A map has scale 1 : 25000. Two towns are 4.8 cm apart on the map. Work out the real distance in km. [3]
7.
£1 = $1.25. Convert £60 to dollars. [2]
8.
A recipe is in the ratio flour : sugar : butter = 5 : 2 : 3. Amira uses 200 g of flour. How much sugar is used? [2]
9.
The ratio of boys to girls in a class is 3 : 5. There are 20 girls. How many boys are there? [2]
10.
The ratio of red to blue counters is 2 : 7. There are 20 red counters. How many blue counters? [2]
11.
y is directly proportional to x. y = 12 when x = 4. Find y when x = 10. [3]
12.
y is inversely proportional to x. y = 8 when x = 5. Find y when x = 2. [3]
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]
14.
Increase £80 by 15%. [2]
15.
Decrease £80 by 15%. [2]
16.
A population of 2000 grows by 4% each year. Estimate the population after 3 years. [3]
17.
Density = mass ÷ volume. A block of mass 240 g has volume 30 cm³. Find the density. [2]
18.
Pressure = force ÷ area. A force of 120 N acts on an area of 0.4 m². Find the pressure. [2]
19.
A speed camera records 90 km in 1 hour 15 minutes. Work out the average speed in km/h. [3]
20.
Convert 2 hours 24 minutes to hours as a decimal, then find the distance at 50 mph. [3]
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]
22.
A metal bar is 1.2 m long. It is cut in the ratio 5 : 7. Find the two lengths. [3]
23.
Best buy: 4 cans for £2.40 or 6 cans for £3.30. Which is better value? [3]
24.
A currency conversion charges 3% commission. Amira changes £400. How much is left to convert? [2]
25.
Scale 1 : 50 000. A road is 3 km long. How long is it on the map in cm? [3]
26.
A graph shows a straight line through (0, 0) and (4, 10).
(a) Explain why this could be direct proportion. [1]
(b) Find the constant of proportionality. [2]
27.
Mix orange paint in the ratio red : yellow = 2 : 5. How much yellow is needed with 300 ml of red? [2]
28.
A cyclist rides 18 km in 40 minutes. Work out the speed in km/h. [2]
29.
Write the formula triangle for speed, distance and time, and state two rearranged formulae. [3]
30.
y ∝ x² and y = 12 when x = 2. Find y when x = 5. [3]
31.
On AQA 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]