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.

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Ratio, proportion and rates of change worksheet — GCSE Higher

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

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1.y is inversely proportional to x². When x = 2, y = 8. Construct the equation connecting x and y, then work out the value of y when x = 4.
(a)2
(b)512
(c)4
(d)8
2.A science technician mixes 400 g of a salt solution of concentration 5% with 100 g of a salt solution of concentration 25%. Work out the concentration of the mixture.
(a)21%
(b)0.9%
(c)9%
(d)15%
3.A concrete mix is made from gravel and cement in the ratio 5 : 1 by mass. The mass of cement is c kg and the total mass of the mix is m kg. Write down a formula for m in terms of c.
(a)m = c + 5
(b)m = c/6
(c)m = 6c
(d)m = 5c
4.In a choir of 30 singers, 40% are altos and the rest are sopranos. Write the number of sopranos as a fraction of the number of altos. Give your answer in its simplest form.
(a)7/3
(b)3/5
(c)2/3
(d)3/2
5.A rope of length A is 1.5 times as long as a rope of length B. Write the ratio A : B in its simplest form.
(a)2 : 3
(b)3 : 5
(c)3 : 2
(d)1.5 : 1
6.A shop's daily profit, in pounds, is plotted against the price charged for an item, in pounds. A tangent to the profit graph at a price of £15 passes through the points (12, 540) and (18, 480). Work out the instantaneous rate of change of profit with respect to price at £15, and state whether profit is increasing or decreasing there.
(a)Profit is increasing by £6 per £1 rise in price.
(b)Profit is increasing by £10 per £1 rise in price.
(c)Profit is decreasing by £60 per £1 rise in price.
(d)Profit is decreasing by £10 per £1 rise in price.
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.Cheng is paid an hourly rate that is proportional to the number of hours she works. She earns £52.50 for 7 hours. Work out how much she earns for 11 hours, assuming the same rate.
(a)£99
(b)£56.50
(c)£30
(d)£82.50
9.The price of a share falls by 10% on Monday and then rises by 10% on Tuesday. Work out the overall percentage change from Monday's starting price.
(a)0%
(b)−1%
(c)−2%
(d)+1%
10.The number of tickets a group can afford is inversely proportional to the price per ticket. At £4 per ticket, the group can afford 12 tickets. Work out how many tickets the group can afford at £6 per ticket.
(a)6
(b)18
(c)12
(d)8
11.A shop's takings were £4500 in May. In June the takings fell by £900. Write the June takings as a fraction of the May takings, in its simplest form.
(a)4/5
(b)1/5
(c)5/4
(d)4/9
12.A shop's profit, P pounds, is in direct proportion to the number of items sold, n. When 15 items are sold, the profit is £45. Write down the ratio n : P in its simplest form for this shop.
(a)1 : 45
(b)3 : 1
(c)1 : 3
(d)15 : 3
13.The number of members of a running club increases from 45 to 54. Work out the percentage increase.
(a)9%
(b)120%
(c)20%
(d)16.7%
14.Two numbers a and b are in the ratio a : b = 3 : 4. Given that a = 15, work out the value of b.
(a)60
(b)16
(c)11.25
(d)20
15.The total cost, in pounds, of manufacturing a batch of components is plotted against the number of components produced. A tangent to this graph at a particular point has gradient 3.60. What does the value 3.60 represent?
(a)3.60% of the cost per component
(b)£3.60 total cost
(c)3.60 components per pound
(d)£3.60 per component

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