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 cake recipe takes 135 minutes from start to finish. Write this time as hours and minutes.
- 2.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.
- 3.A bottle holds 2 litres of water. A glass holds 250 ml. Work out how many of these glasses can be filled from one full bottle.
- 4.Loose sweets are sold at £1.20 per 100 g. Work out the cost of 350 g of sweets.
- 5.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.
- 6.A water tank holds 2.5 m³. Work out this volume in cm³.
- 7.A recipe uses 0.75 kg of sugar. Work out how many grams of sugar this is.
- 8.A footpath sign shows a distance of 0.45 km to the next village. Work out this distance in metres.
- 9.A recipe uses 1.25 kg of flour. Work out how many grams of flour this is.
- 10.A trapezium has parallel sides of length 6 cm and 10 cm, and a perpendicular height of 4 cm. Work out its area.
- 11.A triangular flag has a base of 40 cm and a perpendicular height of 25 cm. Work out its area.
- 12.A train leaves Leeds at 08:47 and arrives in London at 11:05. Work out how long the journey takes.
- 13.Sam says: '3.2 litres is the same as 320 ml, because you multiply by 100.' Which statement about Sam's claim is correct?
- 14.A triangle has a base of 8 cm and a perpendicular height of 5 cm. Work out its area.
- 15.A tank holds 3.2 m³ of water. Work out this volume in litres.
Answer key
- (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) £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.
- (a) 8 — Method: two capacities can only be divided once they are written in the same unit. Working: there are 1000 ml in 1 litre, so the bottle holds 2 × 1000 = 2000 ml. Then 2000 ÷ 250 = 8. Answer: 8 glasses. Using 1 litre = 10 000 ml gives 20 000 ÷ 250 = 80. Dividing the two numbers as they stand, 250 ÷ 2 = 125, ignores the units altogether. Converting the glass into litres with the wrong factor, as though 250 ml were 2.5 litres, gives 2 ÷ 2.5 = 0.8.
- (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.
- (b) 2 500 000 cm³ — Method: a volume conversion uses the length factor three times, once for each dimension. Working: 1 m = 100 cm, so a cube of side 1 m is a cube of side 100 cm, and 100 × 100 × 100 = 1 000 000, giving 1 m³ = 1 000 000 cm³. Then 2.5 × 1 000 000 = 2 500 000. Answer: 2 500 000 cm³. Using the plain length factor 100 gives 250 cm³. Using 1000, which is the factor that turns cubic metres into litres, gives 2500 cm³. Using 10 000, which is the factor that belongs to square metres and square centimetres, gives 25 000 cm³.
- (a) 750 — Method: to change kilograms to grams, multiply by 1000. Working: 0.75 × 1000 = 750. Answer: 750 g. A candidate who multiplies by 100 instead of 1000 gets 75. A candidate who multiplies by 10000 instead of 1000 gets 7500. A candidate who divides by 1000 instead of multiplying gets 0.00075.
- (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.
- (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.
- (b) 32 cm² — The area of a trapezium is half of the sum of the parallel sides, multiplied by the height. Add the parallel sides: 6 + 10 = 16. Multiply by the height: 16 × 4 = 64. Half of 64 is 32 cm². 64 cm² forgets to halve and just gives (6+10)×4. 8 cm² averages the two parallel sides, (6+10)÷2 = 8, but forgets to multiply by the height. 20 cm² treats it as a triangle using only the longer parallel side as the base: half of 10 × 4.
- (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) 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.
- (b) Wrong: 1 litre = 1000 ml, so 3.2 l = 3200 ml. — 1 litre = 1000 ml, so 3.2 litres = 3.2 × 1000 = 3200 ml — Sam is wrong because he multiplied by 100 instead of 1000. Saying Sam is correct accepts the wrong multiplier. Saying Sam is wrong only because 3.2 should be rounded first misses the real error, which is the multiplier, not the starting number. Saying '1 litre is 100 ml' misstates the basic fact and blames the wrong part of Sam's working.
- (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.
- (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.
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