Edexcel GCSE Maths · R1–R16

Ratio, proportion and rates of change

50 maths questions with worked answers with answers for R1–R16 Ratio, proportion and rates of change in Edexcel GCSE Maths (spec 1MA1). Practise with flashcards, a topic quiz, a random quiz across the course, 5 crosswords, or read every question and answer below.

All 50 questions and answers

Question 1 · Units · R1
Change 2.5 hours to minutes.
Answer:
1 hour = 60 minutes.
2.5 × 60 = 150 minutes.
Question 2 · Scale · R1
A map has scale 1 : 50 000. Two towns are 6 cm apart on the map. Find the real distance in km.
Answer:
6 × 50 000 = 300 000 cm.
300 000 cm = 3 km.
Question 3 · Scale · R2
A model car is built to a scale of 1 : 24. The model is 18 cm long. How long is the real car?
Answer:
18 × 24.
432 cm = 4.32 m.
Question 4 · Scale drawings · R2
On a plan, 1 cm represents 2 m. A room is 4.5 m long. How long is it on the plan?
Answer:
4.5 ÷ 2.
2.25 cm.
Question 5 · Fractions · R3
Write 45 minutes as a fraction of 2 hours.
Answer:
2 hours = 120 minutes.
45120 = 38.
Question 6 · Ratio · R3
Write 35p : £2 as a ratio in its simplest form.
Answer:
Use the same units: 35 : 200.
Divide by 5: 7 : 40.
Question 7 · Simplifying ratios · R4
Simplify 24 : 36.
Answer:
HCF is 12.
2 : 3.
Question 8 · Simplifying ratios · R4
Simplify 1.5 : 4.5.
Answer:
Multiply by 2: 3 : 9.
1 : 3.
Question 9 · Ratio form · R4
Write 5 : 8 in the form 1 : n.
Answer:
Divide both parts by 5.
1 : 1.6.
Question 10 · Simplifying ratios · R4
Simplify 12 : 18 : 30.
Answer:
HCF is 6.
2 : 3 : 5.
Question 11 · Sharing · R5
Share £72 in the ratio 5 : 3.
Answer:
8 parts, so 1 part = £9.
£45 and £27.
Question 12 · Sharing · R5
Share 150 g in the ratio 1 : 2 : 3.
Answer:
6 parts, so 1 part = 25 g.
25 g, 50 g and 75 g.
Question 13 · Ratio problems · R5
Boys and girls are in the ratio 4 : 5. There are 35 girls. How many boys are there?
Answer:
5 parts = 35, so 1 part = 7.
4 × 7 = 28 boys.
Question 14 · Ratio problems · R5
Red and blue beads are in the ratio 3 : 7. There are 28 more blue than red. How many beads are there?
Answer:
The difference is 4 parts = 28, so 1 part = 7.
10 parts = 70 beads.
Question 15 · Ratio and fractions · R6
A drink is juice : water = 1 : 4. What fraction is juice?
Answer:
5 parts in total.
15.
Question 16 · Ratio and fractions · R6
37 of a class walk to school and the rest do not. Write the ratio walk : not walk.
Answer:
47 do not walk.
3 : 4.
Question 17 · Ratio and equations · R7
The ratio x : y is 2 : 5 and x + y = 63. Find x.
Answer:
7 parts = 63, so 1 part = 9.
x = 18.
Question 18 · Ratio and equations · R7
a : b = 3 : 4 and b = 20. Find a.
Answer:
4 parts = 20, so 1 part = 5.
a = 15.
Question 19 · Ratio and multiplication · R8
Write the ratio 3 : 8 as a multiplicative relationship.
Answer:
The second is 83 times the first.
b = 83a.
Question 20 · Percentages · R9
Write £18 as a percentage of £240.
Answer:
18240 × 100.
7.5%.
Question 21 · Percentages · R9
A school has 1200 pupils; 45% are boys. How many girls are there?
Answer:
55% are girls.
0.55 × 1200 = 660.
Question 22 · Direct proportion · R10
5 pens cost £3.40. Find the cost of 8 pens.
Answer:
1 pen costs 3.40 ÷ 5 = 68p.
8 × 0.68 = £5.44.
Question 23 · Inverse proportion · R10
4 workers take 9 days to build a wall. How long would 6 workers take?
Answer:
Total work = 4 × 9 = 36 worker-days.
36 ÷ 6 = 6 days.
Question 24 · Recipes · R10
A recipe for 4 people uses 300 g of rice. How much rice is needed for 10 people?
Answer:
For 1 person: 75 g.
10 × 75 = 750 g.
Question 25 · Best buy · R10
Which is better value: 500 g for £1.20 or 750 g for £1.70?
Answer:
Per 100 g: 24p and 22.7p.
750 g for £1.70 is better value.
Question 26 · Currency · R10
£1 = €1.15. Change £240 to euros.
Answer:
Multiply by 1.15.
240 × 1.15 = €276.
Question 27 · Currency · R10
£1 = $1.25. Change $85 to pounds.
Answer:
Divide by 1.25.
85 ÷ 1.25 = £68.
Question 28 · Compound measures · R11
A car uses 6 litres of petrol per 100 km. How much does it use on a 350 km journey?
Answer:
350 ÷ 100 = 3.5.
3.5 × 6 = 21 litres.
Question 29 · Unit pricing · R11
A 12-pack of cans costs £5.40. Find the price per can.
Answer:
5.40 ÷ 12.
45p.
Question 30 · Similar shapes · R12
Two similar rectangles have widths 4 cm and 10 cm. The smaller has length 6 cm. Find the larger length.
Answer:
Scale factor = 104 = 2.5.
6 × 2.5 = 15 cm.
Question 31 · Similar shapes · R12 · Higher only
Two similar shapes have length scale factor 3. What is the area scale factor?
Answer:
Area scale factor = (length scale factor)².
3² = 9.
Question 32 · Similar shapes · R12 · Higher only
Two similar solids have volumes 8 cm³ and 125 cm³. Find the length scale factor.
Answer:
Length scale factor = ∛(volume scale factor) = ∛1258.
52 = 2.5.
Question 33 · Similar shapes · R12 · Higher only
Two similar jugs have heights 10 cm and 15 cm. The smaller holds 400 ml. How much does the larger hold?
Answer:
Length scale factor 1.5, so volume scale factor 1.5³ = 3.375.
400 × 3.375 = 1350 ml.
Question 34 · Proportion graphs · R13
What does the graph of y = kx look like if y is directly proportional to x?
Answer:
It is a straight line.
It passes through the origin.
Question 35 · Direct proportion · R13
y is directly proportional to x. When x = 4, y = 14. Find y when x = 10.
Answer:
y = kx, so k = 14 ÷ 4 = 3.5.
y = 3.5 × 10 = 35.
Question 36 · Inverse proportion · R13 · Higher only
y is inversely proportional to x. When x = 3, y = 8. Find y when x = 6.
Answer:
y = kx, so k = 24.
y = 246 = 4.
Question 37 · Proportion · R13 · Higher only
y is directly proportional to x². When x = 2, y = 20. Find y when x = 5.
Answer:
y = kx², so 20 = 4k and k = 5.
y = 5 × 25 = 125.
Question 38 · Proportion · R13 · Higher only
y is inversely proportional to x². When x = 2, y = 9. Find y when x = 3.
Answer:
y = kx², so k = 36.
y = 369 = 4.
Question 39 · Proportion · R13 · Higher only
T is directly proportional to √L. When L = 16, T = 2. Find T when L = 25.
Answer:
T = k√L, so 2 = 4k and k = 0.5.
T = 0.5 × 5 = 2.5.
Question 40 · Gradient · R14
The gradient of a distance–time graph is 15. What does this mean?
Answer:
Gradient = distance ÷ time.
A speed of 15 (e.g. 15 m/s).
Question 41 · Rates of change · R14 · Higher only
What does the gradient of a tangent to a curve show?
Answer:
The rate of change at that instant.
For example, the speed at a moment on a distance–time curve.
Question 42 · Rates of change · R15 · Higher only
A water level rises from 12 cm to 30 cm in 6 minutes. Find the average rate of change.
Answer:
Change = 18 cm.
18 ÷ 6 = 3 cm per minute.
Question 43 · Compound interest · R16
£5000 is invested at 2% compound interest per year. Find its value after 3 years.
Answer:
5000 × 1.02³ = 5000 × 1.061208.
£5306.04.
Question 44 · Growth and decay · R16 · Higher only
A culture of 200 bacteria doubles every hour. How many are there after 5 hours?
Answer:
200 × 2⁵.
200 × 32 = 6400.
Question 45 · Growth and decay · R16 · Higher only
A car loses 20% of its value each year. After 2 years it is worth £9600. What did it cost new?
Answer:
9600 ÷ 0.8².
9600 ÷ 0.64 = £15 000.
Question 46 · Iterative processes · R16 · Higher only
A population is modelled by Pₙ₊₁ = 1.1Pₙ with P₀ = 1000. Find P₂.
Answer:
P₁ = 1100.
P₂ = 1.1 × 1100 = 1210.
Question 47 · Compound measures · R16
A machine fills 240 bottles in 8 minutes. How many bottles does it fill in an hour?
Answer:
240 ÷ 8 = 30 per minute.
30 × 60 = 1800.
Question 48 · Inverse proportion · R10
A journey takes 3 hours at 40 mph. How long would it take at 60 mph?
Answer:
Distance = 120 miles.
120 ÷ 60 = 2 hours.
Question 49 · Ratio form · R4
Write 6 : 15 in the form n : 1.
Answer:
Divide both parts by 15.
0.4 : 1.
Question 50 · Ratio problems · R5
Ali and Ben share money in the ratio 2 : 3. Ben gets £18. How much does Ali get?
Answer:
3 parts = £18, so 1 part = £6.
Ali gets £12.

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Ratio, proportion and rates of change

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