Printable · GCSE Foundation · ages 14-16
Standard and compound units worksheet — GCSE Foundation
Fifteen questions on "standard and compound units" — DfE statement N13. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.
Standard and compound units worksheet — GCSE Foundation
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- 1.A rectangular tile measures 45 cm by 0.6 m. Work out its area, in square centimetres.
- 2.A tap fills a 20 litre bucket in 2 minutes 30 seconds. Work out the rate of flow, in litres per minute.
- 3.A plumber charges a call-out fee of £45 and then £28 for each hour she works. She is at a house from 09:15 until 12:45. Work out the total charge.
- 4.A bus leaves the station at 09:47 and arrives at its destination at 11:23. Work out the journey time.
- 5.Which of these units would be most appropriate to use when stating the mass of a small car?
- 6.The density of a type of plastic is 0.9 g/cm³. Work out this density in kg/m³.
- 7.A market trader buys 8 melons at £1.35 each. He sells all of them for a total of £15.60. Work out his profit.
- 8.Josh buys 7 pencils at 85p each. He pays with a £10 note. Work out his change.
- 9.A metal cube has a mass of 540 g and a volume of 60 cm³. Work out its density in g/cm³.
- 10.A flight departs at 21:35 and lands at 06:10 the following morning. Work out the total flight time.
- 11.A jug holds 1.25 litres of water. Ella pours in another 400 ml. Work out the total volume, in litres.
- 12.A plane flies 2340 km at an average speed of 780 km/h. It departs at 08:20. Work out the arrival time, using the 24-hour clock.
- 13.A jar of jam costs £2.35. Tom buys 3 jars. He says the total cost is more than £7. Work out the exact total cost, and state whether Tom's claim is correct.
- 14.A lorry travels 105 miles in 1 hour 45 minutes. Work out its average speed in miles per hour.
- 15.A car is hired from 10:00 on Monday until 16:00 on Thursday. Work out the total length of the hire, in hours.
Answer key
- (c) 2700 cm² — Convert both lengths to the same unit before multiplying: 0.6 m = 60 cm. The area is 45 × 60 = 2700 cm². Multiplying without converting 0.6 m to centimetres at all, treating it as 0.6 cm, gives 45 × 0.6 = 27 cm². Converting 0.6 m to centimetres by multiplying by 10 instead of 100 gives 6 cm, and 45 × 6 = 270 cm². Converting 0.6 m to centimetres by multiplying by 1000 instead of 100 gives 600 cm, and 45 × 600 = 27000 cm².
- (a) 8 litres per minute — Method: write the time as a decimal number of minutes, then divide the volume by the time. Working: 30 seconds = 30/60 minute = 0.5 minute, so 2 minutes 30 seconds = 2.5 minutes. Rate = 20 ÷ 2.5 = 8 litres per minute. Answer: 8 litres per minute. (10 litres per minute comes from ignoring the extra 30 seconds and dividing by 2 minutes only. 8.7 litres per minute comes from misreading 2 minutes 30 seconds as 2.3 minutes instead of 2.5 minutes. 0.125 litres per minute comes from dividing the time by the volume instead of the volume by the time.)
- (d) £143 — From 09:15 to 12:45 is 3 hours 30 minutes, which is 3.5 hours. The charge for the time is 3.5 × £28 = £98, and the call-out fee is added on once: £98 + £45 = £143. £98 leaves out the call-out fee altogether, £129 charges for 3 hours instead of 3.5 hours, and £255.50 adds the fee to the hourly rate before multiplying, which charges the £45 for every hour.
- (d) 1 hour 36 minutes — From 09:47 to 10:47 is exactly 1 hour, and from 10:47 to 11:23 is a further 36 minutes, so the journey takes 1 hour 36 minutes in total. Subtracting the hours and minutes separately without carrying across the hour boundary — hours 11 − 9 = 2, minutes 47 − 23 = 24, taking the smaller minute figure from the larger regardless of which time each came from — gives 2 hours 24 minutes. Carrying the hour correctly but then subtracting the minutes the wrong way round, 47 − 23 = 24 instead of 60 − 47 + 23 = 36, gives 1 hour 24 minutes. Counting an extra hour by treating 09:47 as if it were 08:47 gives 2 hours 36 minutes.
- (a) Kilograms — A small car has a mass of roughly 1000–1500 kilograms, so kilograms gives a sensible number to work with — neither too small nor too large. Grams would give an enormous number, over a million, since grams suit much lighter objects. Litres measures capacity, not mass, so it is the wrong type of unit for a car's mass entirely. Metres measures length, not mass, so it is also the wrong type of unit.
- (a) 900 kg/m³ — Both parts of the compound unit change. There are 100 cm in a metre, so 1 m³ = 100³ = 1 000 000 cm³, and there are 1000 g in a kilogram. So 1 g/cm³ = 1 000 000 ÷ 1000 = 1000 kg/m³, and the plastic is 0.9 × 1000 = 900 kg/m³. 900 000 kg/m³ converts the volume but leaves the mass in grams, 0.0009 kg/m³ converts the mass but leaves the volume in cm³, and 0.09 kg/m³ uses the 100 cm in a metre without cubing it.
- (a) £4.80 — The total cost of the melons is 8 × £1.35 = £10.80. Profit is the selling total minus the cost, so £15.60 − £10.80 = £4.80. Subtracting the price of just one melon from the selling total instead of the total cost of all eight, £15.60 − £1.35, gives £14.25. Miscalculating the cost of the melons as 8 × £1.30 = £10.40, dropping the 5p from each price, gives a profit of £15.60 − £10.40 = £5.20. Adding the selling total and the cost together instead of subtracting them, £15.60 + £10.80, gives £26.40.
- (c) £4.05 — The total cost is 7 × 85p = £5.95. Josh's change is £10.00 − £5.95 = £4.05. Taking off the pounds and then only the 5p digit, £10.00 − £5.00 = £5.00 followed by £5.00 − £0.05, ignoring the 90p altogether, gives £4.95. Rounding the cost up to £6.00 and never accounting for the extra 5p at all gives £4.00. Multiplying 7 × 85 incorrectly as 605 (a slip in 7 × 5) gives a total cost of £6.05, and correctly subtracting that from £10.00 gives £3.95.
- (b) 9 g/cm³ — Method: density = mass ÷ volume. Working: 540 ÷ 60 = 9. Answer: 9 g/cm³. (0.11 g/cm³ comes from dividing the volume by the mass instead of the mass by the volume. 480 g/cm³ comes from subtracting the volume from the mass instead of dividing. 32400 g/cm³ comes from multiplying the mass by the volume instead of dividing.)
- (c) 8 hours 35 minutes — From 21:35 to midnight is 2 hours 25 minutes, and from midnight to 06:10 is a further 6 hours 10 minutes, giving a total of 8 hours 35 minutes. Misreading the departure time as 22:35 instead of 21:35 loses an hour from the calculation and gives 7 hours 35 minutes. Misreading the departure time as 20:35 instead of 21:35 gains an hour and gives 9 hours 35 minutes. Subtracting the times as if both fell on the same day, without crossing midnight, gives 15 hours 25 minutes.
- (d) 1.65 litres — Method: convert both volumes to the same unit, then add. Working: 400 ml = 400 ÷ 1000 = 0.4 litres. Total = 1.25 + 0.4 = 1.65 litres. Answer: 1.65 litres. (401.25 litres comes from adding 1.25 and 400 directly without converting millilitres to litres first. 0.85 litres comes from subtracting 0.4 from 1.25 instead of adding. 5.25 litres comes from dividing 400 by 100 instead of by 1000 — using the centimetre-to-metre factor — which turns 400 ml into 4 litres before adding.)
- (a) 11:20 — Method: find the flight time using time = distance ÷ speed, then add this to the departure time. Working: 2340 ÷ 780 = 3 hours; 08:20 + 3 hours = 11:20. Answer: 11:20. 08:40 comes from dividing speed by distance instead of distance by speed, giving a flight time of 1/3 hour (20 minutes) rather than 3 hours. 11:00 comes from adding the 3-hour flight time to the hour of the departure time only, 8 + 3 = 11, and losing the 20 minutes. 03:00 comes from finding the flight time correctly but giving it as a clock time on its own, forgetting to add it to the departure time.
- (c) £7.05 — Tom is correct — Method: multiply the cost of one jar by the number of jars, then compare the total to £7. Working: 3 × £2.35 = £7.05, and since £7.05 is more than £7, Tom's claim is correct. Answer: £7.05 — Tom is correct. "£7.05 — Tom is incorrect" comes from reaching the right total but reading the 05 after the point as making the amount less than £7. "£6.95 — Tom is incorrect" comes from working out 3 × 35p as 3 × 30p + 5p = 95p, multiplying only the tens digit, and adding it to 3 × £2 = £6. "£7.20 — Tom is correct" comes from rounding £2.35 up to £2.40 before multiplying: 3 × £2.40 = £7.20.
- (d) 60 mph — Average speed = distance ÷ time, with the time measured in hours. 45 minutes is 45/60 of an hour, which is 0.75 of an hour, so the journey takes 1.75 hours. Speed = 105 ÷ 1.75 = 60 mph. 52.5 mph rounds the time up to 2 hours, 72.4 mph writes 1 hour 45 minutes as 1.45 hours, and 183.75 mph multiplies the distance by the time instead of dividing.
- (b) 78 hours — From 10:00 on Monday to 10:00 on Thursday is exactly 3 complete days, which is 3 × 24 = 72 hours. From 10:00 to 16:00 on the Thursday is a further 6 hours, giving a total of 72 + 6 = 78 hours. Counting Monday to Thursday as 4 full calendar days instead of 3 complete 24-hour periods gives 4 × 24 = 96 hours. Undercounting the number of complete days as 2 instead of 3 gives 2 × 24 + 6 = 54 hours. Subtracting the extra 6 hours instead of adding them to the 3 complete days gives 72 − 6 = 66 hours.
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