Printable · GCSE Foundation · ages 14-16

Ratio, proportion and rates of change worksheet — GCSE Foundation

Fifteen questions across the ratio, proportion and rates of change statements at Foundation 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 Foundation

Maths · GCSE Foundation · Ratio, proportion and rates of change · 15 questions

MathsUKwww.geekhero.co.uk

1.Grace's mean mark in her maths tests rises from 70 to 84. Work out the percentage increase in her mean mark.
(a)20%
(b)120%
(c)17%
(d)14%
2.A 1.5 kg bag of pasta costs £2.85 and a 2.4 kg bag of the same pasta costs £4.32. Work out which bag gives better value for money.
(a)The 1.5 kg bag, since it costs £1.19 per kg compared with £2.88 per kg for the 2.4 kg bag.
(b)The 2.4 kg bag, since it costs £1.80 per kg compared with £1.90 per kg for the 1.5 kg bag.
(c)The 1.5 kg bag, since it costs £1.80 per kg compared with £1.90 per kg for the 2.4 kg bag.
(d)The 1.5 kg bag, since £2.85 is less than £4.32.
3.A coach travels 210 miles at an average speed of 70 mph. Work out how long the journey takes.
(a)14700 hours
(b)140 hours
(c)3 hours
(d)280 hours
4.The value of a motorbike falls by 12% each year. The motorbike is worth £3200 now. Write down the calculation that gives its value after 3 years.
(a)3200 × 0.64
(b)3200 × 0.12³
(c)3200 × 0.88 × 3
(d)3200 × 0.88³
5.y is directly proportional to x. When x = 5, y = 18. Work out the value of y when x = 15.
(a)60
(b)28
(c)54
(d)6
6.Work out the time taken to travel 120 km at an average speed of 60 km/h.
(a)180 minutes
(b)0.5 hours
(c)2 hours
(d)2 minutes
7.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
8.Two mathematically similar picture frames have perimeters 30 cm and 45 cm. The area of the smaller frame is 40 cm². Work out the area of the larger frame.
(a)2.25 cm²
(b)60 cm²
(c)90 cm²
(d)135 cm²
9.Two printers' running costs are shown on separate straight-line graphs of total cost against number of pages printed. Printer A's graph has gradient £0.04 per page. Printer B's graph has gradient £0.05 per page. Work out how much cheaper it is to print 200 pages on Printer A than on Printer B, based on these running costs alone.
(a)£18.00
(b)£0.01
(c)£8.00
(d)£2.00
10.In a bag, the ratio of green counters to yellow counters is 3 : 8. There are 24 yellow counters. A student says, 'There must be 9 green counters.' Is the student correct? Choose the correct verdict and reason.
(a)No, incorrect, because 24 + 3 = 27 green counters.
(b)No, incorrect, because 24 ÷ 3 × 8 = 64.
(c)Yes, correct, because 24 ÷ 8 × 3 = 9.
(d)No, incorrect, because 24 ÷ 8 = 3 green counters.
11.A hosepipe fills a paddling pool at a constant rate. The volume of water in the pool increases by 15 litres every 3 minutes. Write down the gradient of the graph of volume against time.
(a)45
(b)18
(c)0.2
(d)5
12.A cartographer is choosing a scale for a map to show a small park in as much detail as possible. Which of these scales would show the MOST detail — 1 : 500, 1 : 5000, or 1 : 50 000? Give the correct scale and reason.
(a)1 : 50 000 — covers the largest real area, most detail
(b)1 : 500 — smallest real distance per cm (5 m), most detail
(c)1 : 5000 — the middle value, most balanced
(d)1 : 500 — smallest ratio, covers largest real distance
13.A footpath is drawn 3 cm long on a map with a scale of 1 : 50 000. Work out the real length of the footpath, in metres.
(a)15000 m
(b)1500 m
(c)50000 m
(d)150 m
14.A smoothie recipe combines 350 cm³ of mango juice with 650 cm³ of orange juice. Work out the total volume of the smoothie in litres.
(a)0.35 litres
(b)1.00 litres
(c)0.65 litres
(d)1000.00 litres
15.£5000 is invested in an account paying 4% compound interest each year. Work out the total interest earned after 3 years.
(a)£600.00
(b)£408.00
(c)£624.32
(d)£5624.32

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