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.
Answer key: Standard and compound units worksheet — GCSE Foundation
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- (c) 20p — Turn each price into the same rate before comparing. The small bag is 400 g = 0.4 kg, so it costs £1.12 ÷ 0.4 = £2.80 per kg. The large bag costs £3.90 ÷ 1.5 = £2.60 per kg. The saving is £2.80 − £2.60 = £0.20, which is 20p per kg. 2p compares the prices per 100 g rather than per kilogram, £2.78 subtracts one bag price from the other without turning either into a rate, and £2.60 is the large bag's price per kilogram rather than the saving.
- (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.
- (c) £0.45 — Method: find the total cost, then subtract from £20. Working: 4 × £3.20 = £12.80. £12.80 + £6.75 = £19.55. Change = £20.00 − £19.55 = £0.45. Answer: £0.45. (£7.20 comes from forgetting to include the compost and subtracting only the plants' cost from £20. £1.45 comes from dropping the carry when adding the pence: 80p + 75p = £1.55, but only the 55p is written down, giving £18.55 instead of £19.55. £10.05 comes from buying only one plant instead of four, using £3.20 + £6.75.)
- (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.
- (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.)
- (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.
- (a) 28.8 km/h — A compound unit is converted one part at a time. There are 3600 seconds in an hour, so in one hour the cyclist travels 8 × 3600 = 28 800 metres. There are 1000 metres in a kilometre, so 28 800 m = 28 800 ÷ 1000 = 28.8 km/h. 28 800 km/h leaves the distance in metres, 0.48 km/h converts the seconds to minutes rather than to hours, and 2.22 km/h divides by 3.6 instead of multiplying.
- (c) 2000 mm — Put both lengths into the same unit first. There are 1000 mm in a metre, so the ribbon is 2.4 × 1000 = 2400 mm, and there are 10 mm in a centimetre, so the piece cut off is 40 × 10 = 400 mm. The length left is 2400 − 400 = 2000 mm. 2360 mm subtracts 40 mm instead of 400 mm, 200 mm works in centimetres and then labels the result as millimetres, and 2800 mm adds the piece that was cut off instead of subtracting it.
- (d) 1050 ml — Convert both amounts to millilitres: 1.8 litres = 1800 ml and 3/4 litre = 750 ml. Subtracting gives 1800 − 750 = 1050 ml. Confusing 3/4 with 75% and converting it as 75 ml instead of 750 ml gives 1800 − 75 = 1725 ml. Adding the amount poured out instead of subtracting it gives 1800 + 750 = 2550 ml. Misreading 1.8 litres as 0.8 litres, losing the whole litre, gives 800 − 750 = 50 ml.
- (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.)
- (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.
- (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.
- (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) £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.
- (a) 300 N/m² — Pressure is force ÷ area, and the unit N/m² says so: newtons divided by square metres. The calculation is 240 ÷ 0.8. Multiplying both numbers by 10 clears the decimal: 2400 ÷ 8 = 300 N/m². 192 N/m² multiplies the force by the area instead of dividing, 30 N/m² divides by 8 and so loses the decimal point, and 3000 N/m² multiplies only the force by 10 when clearing the decimal.
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