Printable · GCSE Higher · ages 14-16

Ratio, proportion and rates of change worksheet — GCSE Higher

Fifteen questions across the ratio, proportion and rates of change statements at Higher tier. Choose the non-calculator filter to rehearse Paper 1, which counts for a third of the marks.

Non-calculator

VersionsA only A + B A + B + Csame questions, different order

AnswersQuestions only With answer key Key only

CalculatorMixed Non-calculator (Paper 1)Calculator (Papers 2 and 3)

New sheet

Ratio, proportion and rates of change worksheet — GCSE Higher

Maths · GCSE Higher · Ratio, proportion and rates of change · Non-calculator · 15 questions

MathsUKwww.geekhero.co.uk

1.The price of a jacket increases by 50% and then decreases by 50%. Describe the overall change from the original price.
(a)no change
(b)an increase of 25%
(c)a decrease of 25%
(d)a decrease of 50%
2.Two mathematically similar jugs have heights 8 cm and 12 cm. The smaller jug holds 200 ml when it is full. Work out how much the larger jug holds when it is full.
(a)675 ml
(b)300 ml
(c)450 ml
(d)900 ml
3.In a school choir the ratio of boys to girls is 3:4. When 6 more boys join the choir, the ratio of boys to girls becomes 1:1. Work out how many girls are in the choir.
(a)18
(b)24
(c)42
(d)30
4.x × y is used to test whether two quantities are in inverse proportion. For the pairs x = 4, y = 15 and x = 6, y = 10, which statement is correct?
(a)They are not in inverse proportion, because y ÷ x is different for each pair (3.75 and 1.67).
(b)They are in inverse proportion, because x × y = 60 for both pairs.
(c)They are in inverse proportion, because x × y = 40 for both pairs.
(d)They are not in inverse proportion, because x + y is different for each pair (19 and 16).
5.A concert hall has 54 seats in total, of which 24 are reserved and the rest are free. Write the number of free seats as a fraction of the number of reserved seats. Give your answer in its simplest form.
(a)4/5
(b)5/6
(c)5/9
(d)5/4
6.A box holds 60 crayons. 25 of the crayons are broken and the rest are unbroken. Write the number of unbroken crayons as a fraction of the number of broken crayons. Give your answer in its simplest form.
(a)5/7
(b)2/5
(c)7/12
(d)7/5
7.The tangent to a curve at the point where x = 4 has equation y = 3x − 2. Work out the instantaneous rate of change of y with respect to x at x = 4.
y = 3x − 2
(a)−2
(b)4
(c)3
(d)10
8.A charity shop and a school share collection-box money in the ratio 5 : 8. The charity shop receives £47.50. Work out how much the school receives.
(a)£29.69
(b)£76.00
(c)£57.00
(d)£123.50
9.Water flows into a tank at a constant rate. After 8 minutes the tank holds 200 litres. Write the ratio of time in minutes to volume in litres, in its simplest form.
(a)25:1
(b)1:25
(c)25:8
(d)8:25
10.Aisha invests £3200 in Account A, which pays 5% compound interest each year. She also invests £3200 in Account B, which pays 3% simple interest each year. Work out how much more Account A is worth than Account B after 2 years.
(a)£3528
(b)£3392
(c)£136
(d)£128
11.Write 45 minutes : 2 hours as a ratio in its simplest form.
(a)9:24
(b)8:3
(c)45:2
(d)3:8
12.A tangent to the graph of population against time at the point where t = 4 passes through (2, 180) and (6, 260). Work out the instantaneous rate of change of the population at t = 4, in people per year.
(a)20 people/year
(b)84 people/year
(c)80 people/year
(d)−20 people/year
13.Write the ratio 2 : 1/4 as a ratio of whole numbers in its simplest form.
(a)8:1
(b)8:4
(c)1:8
(d)2:4
14.A map's scale is given as '1 cm represents 2 km'. Write this scale in the form 1 : n.
(a)1:2
(b)1:200000
(c)1:2000
(d)1:20000
15.y is directly proportional to x. When x = 7, the value of y is 21. Work out the value of x when y = 12.
(a)4
(b)36
(c)84
(d)9

Build your own mix at the worksheet builder.