Printable · GCSE Foundation · ages 14-16
Standard units of measure worksheet — GCSE Foundation
Fifteen questions on "standard units of measure" — DfE statement G14. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.
Standard units of measure worksheet — GCSE Foundation
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- 1.A footpath is 3750 m long. Work out this distance in kilometres.
- 2.A footpath sign shows a distance of 0.45 km to the next village. Work out this distance in metres.
- 3.A triangular flag has a base of 40 cm and a perpendicular height of 25 cm. Work out its area.
- 4.A shop sells rice in packs of 250 g. Aisha buys 4 packs. Work out the total mass of rice she buys, in kilograms.
- 5.A tank holds 3.2 m³ of water. Work out this volume in litres.
- 6.A train leaves Leeds at 08:47 and arrives in London at 11:05. Work out how long the journey takes.
- 7.Loose sweets are sold at £1.20 per 100 g. Work out the cost of 350 g of sweets.
- 8.A triangular sail for a small boat has a base of 2.4 m and a height of 1.75 m. Sailcloth costs £12.50 per m². Work out the total cost of the sailcloth needed for the sail.
- 9.A recipe uses 1.25 kg of flour. Work out how many grams of flour this is.
- 10.A bus journey takes 2.5 hours. Work out how many minutes this is.
- 11.A triangle has a base of 8 cm and a perpendicular height of 5 cm. Work out its area.
- 12.A cheese counter sells cheddar at £8.40 per kilogram. Work out the cost of a 350 g piece of cheddar.
- 13.A cake recipe takes 135 minutes from start to finish. Write this time as hours and minutes.
- 14.A flower bed in the shape of a parallelogram has a base of 3.5 m and a perpendicular height of 2 m. Compost costs £4.80 per m². Work out the total cost of covering the flower bed with compost.
- 15.A plumber charges a £45 call-out fee, plus £28 for each hour worked. She works on a job for 3 hours 30 minutes, and her hours are billed by rounding up to the next whole hour. Work out the total amount she charges.
Answer key
- (a) 3.75 km — To convert metres to kilometres, divide by 1000: 3750 ÷ 1000 = 3.75 km. Dividing by 100 instead of 1000 gives 37.5 km. Dividing by 10 instead of 1000 gives 375 km. Dividing by 10 000 instead of 1000 gives 0.375 km.
- (c) 450 m — To convert km to m, multiply by 1000: 0.45 × 1000 = 450 m. Multiplying by 100 instead of 1000 gives 45 m. Multiplying by 10 000 instead of 1000 gives 4500 m. Not converting at all, just relabelling the number, gives 0.45 m.
- (c) 500 cm² — The area of a triangle is half of base × height. First, base × height = 40 × 25 = 1,000. Half of 1,000 is 500 cm². 1,000 cm² forgets to halve and just gives base × height. 65 cm² adds the base and height together instead of multiplying them. 2,000 cm² doubles base × height instead of halving it.
- (d) 1 kg — First find the total mass in grams: 4 × 250 = 1000 g. Then convert to kilograms by dividing by 1000: 1000 ÷ 1000 = 1 kg. Finding the correct total in grams but forgetting to divide by 1000 gives 1000 kg. Adding the number of packs to the pack mass instead of multiplying, 4 + 250 = 254 g, gives 0.254 kg. Dividing the pack mass by the number of packs instead of multiplying, 250 ÷ 4 = 62.5 g, gives 0.0625 kg.
- (c) 3200 — Method: to change cubic metres to litres, multiply by 1000. Working: 3.2 × 1000 = 3200. Answer: 3200 litres. A candidate who multiplies by 100 instead of 1000 gets 320. A candidate who multiplies by 10000 instead of 1000 gets 32000. A candidate who does not convert at all gives 3.2.
- (d) 2 h 18 min — Method: count on from the departure time in whole steps, rather than subtracting the two clock readings as if they were ordinary decimals. Working: from 08:47 to 09:00 is 13 minutes; from 09:00 to 11:00 is 2 hours; from 11:00 to 11:05 is a further 5 minutes. 13 + 5 = 18, so the journey lasts 2 hours and 18 minutes. Answer: 2 h 18 min. Subtracting as decimals gives 11.05 − 8.47 = 2.58 and the false reading 2 h 58 min, because an hour holds 60 minutes and not 100. Taking the minutes the wrong way round, 47 take away 5, gives 2 h 42 min. Counting the hours as 11 − 8 = 3 and then attaching the 18 minutes gives 3 h 18 min.
- (a) £4.20 — 350 g is 3.5 lots of 100 g, since 350 ÷ 100 = 3.5, so the cost is 3.5 × £1.20 = £4.20. Multiplying the mass in grams directly by the price, without dividing by 100 first, gives £420.00. Working out 100 ÷ 350 instead of 350 ÷ 100 inverts the ratio and gives about £0.34. Rounding 350 g down to 300 g gives 3 × £1.20 = £3.60.
- (b) £26.25 — First multiply the base and height: 2.4 × 1.75 = 4.2. The area of the triangular sail is half of that: half of 4.2 is 2.1 m². Then multiply by the cost per m²: 2.1 × £12.50 = £26.25. £52.50 forgets to halve in the area formula, giving an area of 4.2 m² and doubling the true cost. £30.00 multiplies the base length by the cost per m² (2.4 × £12.50) without ever finding the area. £25.00 rounds the area to 2 m² before multiplying by the cost, losing accuracy.
- (d) 1250 g — There are 1000 g in a kilogram, so 1.25 kg = 1.25 × 1000 = 1250 g. Multiplying by 100 instead of 1000 gives 125 g. Converting only the whole 1 kg and forgetting the extra 0.25 kg gives 1000 g. Treating the 0.25 kg as 25 g instead of 250 g, a quarter of 1000, gives 1025 g.
- (c) 150 minutes — There are 60 minutes in an hour, so 2.5 hours is 2.5 × 60 = 150 minutes. Multiplying by 100 instead of 60, as if hours worked like a decimal metric unit, gives 250 minutes. Converting only the whole 2 hours and forgetting the extra 0.5 hours gives 120 minutes. Treating the 0.5 as 50 minutes, out of 100, instead of 30 minutes, out of 60, gives 170 minutes.
- (c) 20 cm² — The area of a triangle is half of base × height. First, base × height = 8 × 5 = 40. Half of 40 is 20 cm². 40 cm² forgets to halve and just gives base × height. 13 cm² adds the base and height together instead of multiplying them. 80 cm² doubles base × height instead of halving it.
- (b) £2.94 — Method: the price is quoted for each kilogram, so the mass has to be written in kilograms before it is multiplied by the price. Working: 1 kg = 1000 g, so 350 ÷ 1000 = 0.35 and the piece weighs 0.35 kg. The cost is then 8.40 × 0.35 = 2.94. Answer: £2.94. Treating 350 g as 3.5 kg, a division by 100 rather than by 1000, gives 8.40 × 3.5 = 29.40. Multiplying the price by the number of grams gives 8.40 × 350 = 2940. Dividing the price by the mass instead of multiplying gives 8.40 ÷ 0.35 = 24.
- (c) 2 hours 15 minutes — Divide the total minutes by 60: 135 ÷ 60 = 2 remainder 15, so that is 2 hours 15 minutes. Treating 100 minutes as one hour, a metric-style mistake, gives 135 − 100 = 35, so 1 hour 35 minutes. Subtracting 60 twice to reach the 15 minutes left over, but losing count and recording only one of the two hours removed, gives 1 hour 15 minutes. Writing 135 ÷ 60 = 2.25 and then reading the '25' as minutes, instead of converting the 0.25 of an hour into 15 minutes, gives 2 hours 25 minutes.
- (b) £33.60 — The area of the parallelogram flower bed is base × height = 3.5 × 2 = 7 m². The cost is 7 × £4.80 = £33.60. £16.80 comes from using the triangle formula instead of the parallelogram formula: 3.5 × 2 = 7, and half of 7 is 3.5 m², then 3.5 × £4.80 = £16.80. £26.40 comes from adding the base and height, 3.5+2 = 5.5, instead of multiplying them, then multiplying by £4.80. £7.00 correctly finds the area, 7 m², but forgets to multiply it by the cost per m².
- (b) £157 — Method: round the hours worked up to the next whole hour, multiply by the hourly rate, then add the call-out fee. Working: 3 hours 30 minutes rounds up to 4 hours; 28 × 4 = 112; 112 + 45 = 157. Answer: £157. A candidate who uses the unrounded time of 3.5 hours, working out 28 × 3.5 = 98 and adding 45, gets £143. A candidate who forgets the call-out fee, giving only 28 × 4, gets £112. A candidate who rounds down to 3 hours instead of up, working out 28 × 3 = 84 and adding 45, gets £129.
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