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
MathsUKwww.geekhero.co.uk
- 1.A train leaves Leeds at 08:47 and arrives in London at 11:05. Work out how long the journey takes.
- 2.A tank holds 3.2 m³ of water. Work out this volume in litres.
- 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.A cheese counter sells cheddar at £8.40 per kilogram. Work out the cost of a 350 g piece of cheddar.
- 5.Loose sweets are sold at £1.20 per 100 g. Work out the cost of 350 g of sweets.
- 6.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.
- 7.A parallelogram has a base of 9 cm and a perpendicular height of 4 cm. Work out its area.
- 8.A footpath is 3750 m long. Work out this distance in kilometres.
- 9.A tap fills a tank at a rate of 18 litres per minute. The tank holds 0.45 m³. Work out how long the tap takes to fill the tank.
- 10.A kitchen scale is marked in equal divisions of 20 g. The pointer rests three divisions past the 400 g mark. Work out the reading on the scale.
- 11.A parallelogram has an area of 54 cm² and a base of 9 cm. Work out its perpendicular height.
- 12.A shop sells rice in packs of 250 g. Aisha buys 4 packs. Work out the total mass of rice she buys, in kilograms.
- 13.A footpath sign shows a distance of 0.45 km to the next village. Work out this distance in metres.
- 14.A trapezium has parallel sides of length 6 cm and 10 cm, and a perpendicular height of 4 cm. Work out its area.
- 15.A bus journey takes 2.5 hours. Work out how many minutes this is.
Answer key
- (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.
- (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.
- (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.
- (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.
- (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.
- (c) 36 cm² — The area of a parallelogram is base × height = 9 × 4 = 36 cm². 26 cm² is 2 × (9 + 4), the perimeter you would get by treating the perpendicular height as though it were a side length — and a perimeter is a length, not an area. 18 cm² uses the triangle formula, half of base × height, by mistake. 72 cm² doubles the correct area.
- (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.
- (b) 25 minutes — Method: a rate in litres per minute can only be used on a volume measured in litres, so convert the tank first and then divide. Working: 1 m³ = 1000 litres, so the tank holds 0.45 × 1000 = 450 litres, and the time is 450 ÷ 18 = 25. Answer: 25 minutes. Using 1 m³ = 100 litres gives 45 ÷ 18 = 2.5 minutes. Using 1 m³ = 1 000 000 litres, which is the factor that turns cubic metres into cubic centimetres, gives 450 000 ÷ 18 = 25 000 minutes. Multiplying by the rate instead of dividing by it gives 450 × 18 = 8100.
- (c) 460 g — Each division is 20 g, so three divisions past the mark is 3 × 20 = 60 g. Adding this to the 400 g mark gives 400 + 60 = 460 g. Treating each division as worth 1 g instead of 20 g gives 400 + 3 = 403 g. Working out the extra amount correctly but forgetting to add the 400 g mark gives just 60 g. Treating each division as worth 10 g instead of 20 g gives 400 + 30 = 430 g.
- (c) 6 cm — For a parallelogram, area = base × height, so height = area ÷ base = 54 ÷ 9 = 6 cm. 12 cm comes from using the triangle's reverse formula, height = 2 × area ÷ base, which does not apply to a parallelogram. 45 cm comes from subtracting the base from the area, 54 − 9, instead of dividing. 486 cm comes from multiplying the area by the base, 54 × 9, instead of dividing.
- (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) 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.
- (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) 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.
Build your own mix at the worksheet builder.