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) 2.00 kg — Convert the tin's mass to kilograms first: 650 g = 0.65 kg. Adding this to the bag's mass gives 0.65 + 1.35 = 2.00 kg. Converting 650 g to kilograms by dividing by 100 instead of 1000 gives 6.5 kg, and adding this to 1.35 kg gives 7.85 kg. Adding the two masses without converting grams to kilograms at all — treating 650 as if it were already measured in kilograms — gives 651.35 kg. Subtracting the tin's mass from the bag's mass instead of adding the two together, 1.35 − 0.65, gives 0.70 kg.
- (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) 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.
- (c) 3.05 kg — There are 1000 g in 1 kg, so 450 g = 450 ÷ 1000 = 0.45 kg. The total mass is 0.45 + 2.6 = 3.05 kg. 7.1 kg divides the grams by 100 instead of 1000, 2.645 kg divides them by 10 000, and 452.6 kg adds the two numbers without converting the grams at all.
- (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.
- (d) 15:20 — Method: add all three journey segments to the departure time, converting the total number of minutes into hours and minutes. Working: 55 + 20 + 40 = 115 minutes = 1 hour 55 minutes. 13:25 + 1 hour 55 minutes = 15:20. Answer: 15:20. (15:00 comes from leaving out the 20 minute break and adding only 55 + 40 = 95 minutes. 14:25 comes from leaving out the 55 minute first leg and adding only 20 + 40 = 60 minutes. 14:40 comes from leaving out the 40 minute second leg and adding only 55 + 20 = 75 minutes.)
- (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.
- (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.
- (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.
- (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) 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.)
- (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) 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.
- (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.
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