Write down the missing number in each metric conversion fact.
(a)1 km = _____ m(1)
(b)1 kg = _____ g(1)
(c)1 litre = _____ ml(1)
(d)1 m = _____ cm(1)
(Total for Question 1 is 4 marks)
2
Convert each measurement to the unit shown.
(a)Convert 3.5 m to cm.(1)
(b)Convert 4200 g to kg.(1)
(c)Convert 1.2 litres to ml.(1)
(Total for Question 2 is 3 marks)
3
Aisha has four lengths of ribbon: 850 mm, 0.7 m, 76 cm and 0.008 km. Write the four lengths in order of size, starting with the smallest.
(Total for Question 3 is 3 marks)
4
Convert between units of time.
(a)Convert 2.25 hours into hours and minutes.(2)
(b)Convert 100 minutes into hours and minutes.(2)
(Total for Question 4 is 4 marks)
5
A coach timetable shows a coach leaving Sheffield at 08:55 and arriving in Leeds at 11:20 (both times shown using the 24-hour clock).
(a)Write 19:45 using the 12-hour clock.(1)
(b)Work out how long the coach journey from Sheffield to Leeds takes. Give your answer in hours and minutes.(2)
(Total for Question 5 is 3 marks)
6
The exchange rate is 1 pound sterling (GBP) = 1.16 euros (EUR).
(a)Nadia changes 250 pounds sterling into euros. Work out how many euros she receives.(2)
(b)On the way home Nadia changes 87 euros back into pounds sterling, using the same exchange rate. Work out how many pounds sterling she receives.(2)
(Total for Question 6 is 4 marks)
7
You are given that 5 miles is approximately 8 km, and 1 kg is approximately 2.2 pounds (lb).
(a)A road sign shows a distance of 40 miles. Change this to kilometres.(2)
(b)A parcel weighs 9 kg. Change this to pounds (lb).(2)
(Total for Question 7 is 4 marks)
8
Priya is weighing out sugar for a cake.
(a)Write down the mass of sugar shown on the scale, in grams.(1)
(b)A recipe needs 0.8 kg of sugar. Does Priya have enough sugar to make the recipe? You must show working to support your answer.(2)
(Total for Question 8 is 3 marks)
9
Two tins of the same paint are sold in a DIY shop. Tin A contains 2.5 litres and costs 18 pounds sterling. Tin B contains 750 ml and costs 5.85 pounds sterling.
(a)Work out the price per litre for Tin A.(1)
(b)Work out the price per litre for Tin B.(2)
(c)Which tin is the better value for money? Give a reason for your answer.(1)
(Total for Question 9 is 4 marks)
10
The graph converts between pounds sterling (GBP) and Singapore dollars (SGD).
(a)Use the graph to change 40 pounds sterling into Singapore dollars.(1)
(b)Use the graph to change 108 Singapore dollars into pounds sterling.(2)
(Total for Question 10 is 3 marks)
11
A car travels at a constant speed of 72 km/h.
(a)Show that this speed is equal to 20 m/s.(2)
(b)A cyclist travels at 8 m/s. Work out this speed in km/h.(2)
(Total for Question 11 is 4 marks)
12
Convert the following areas.
(a)Convert 3.2 m2 to cm2.(2)
(b)Convert 45000 cm2 to m2.(2)
(Total for Question 12 is 4 marks)
13
A fish tank in the shape of a cuboid has length 60 cm, width 30 cm and height 40 cm.
Diagram NOT accurately drawn
(a)Work out the volume of the tank in cm3.(2)
(b)Given that 1000 cm3 = 1 litre, work out the maximum volume of water the tank can hold. Give your answer in litres.(2)
(Total for Question 13 is 4 marks)
14
The density of aluminium is 2.7 g/cm3. Work out the density of aluminium in kg/m3.
(Total for Question 14 is 3 marks)
15
A recipe for flapjacks that serves 6 people uses 750 g of oats.
(a)Write 750 g in kilograms.(1)
(b)Bilal wants to make enough flapjacks to serve 15 people, using the recipe in the same proportions. Work out how many kilograms of oats he needs.(3)
(Total for Question 15 is 4 marks)
16
The diagram shows part of a ruler.
(a)Write down the length shown by the arrow. Give your answer in centimetres.(1)
(b)Give your answer to part (a) in millimetres.(1)
(Total for Question 16 is 2 marks)
17
A film lasts 1 hour 48 minutes and starts at 14:35.
(a)Write the length of the film in minutes only.(1)
(b)Work out the time the film finishes. Give your answer using the 24-hour clock.(2)
(Total for Question 17 is 3 marks)
18
Deepak buys three pieces of fencing wire with lengths 2.4 m, 85 cm and 630 mm. He joins them together to make one length of wire. Work out the total length of the wire. Give your answer in metres.
(Total for Question 18 is 3 marks)
19
Freya drives a distance of 175 miles. You are given that 5 miles is approximately 8 km. The journey takes 2 hours 30 minutes.
(a)Work out the distance in kilometres.(2)
(b)Work out Freya's average speed for the journey in km/h.(3)
(Total for Question 19 is 5 marks)
20
A car's fuel consumption is quoted as 40 miles per gallon (mpg). You are given that 1 gallon is approximately 4.5 litres, and 5 miles is approximately 8 km.
(a)Work out the car's fuel consumption in kilometres per litre. Give your answer to 1 decimal place.(3)
(b)The car's fuel tank holds 50 litres. Estimate how far the car can travel on a full tank. Give your answer in kilometres.(2)
(Total for Question 20 is 5 marks)
Mark scheme · 3.10 Conversions and Units
Question 1
(a) B1 1000 cao
(a) Answer: 1000
(b) B1 1000 cao
(b) Answer: 1000
(c) B1 1000 cao
(c) Answer: 1000
(d) B1 100 cao
(d) Answer: 100
Question 2
(a) B1 350 cao
(a) Answer: 350 cm
(b) B1 4.2 cao
(b) Answer: 4.2 kg
(c) B1 1200 cao
(c) Answer: 1200 ml
Question 3
M1 converts at least three of the four lengths to a common unit
A1 all four lengths correctly converted to a common unit, oe (70 cm, 76 cm, 85 cm, 800 cm)
A1 correct final order cao
Answer: 0.7 m, 76 cm, 850 mm, 0.008 km
Question 4
(a) M1 0.25 x 60 (= 15)
(a) A1 2 hours 15 minutes oe cao
(a) Answer: 2 hours 15 minutes
(b) M1 100 / 60 or equivalent division
(b) A1 1 hour 40 minutes oe cao
(b) Answer: 1 hour 40 minutes
Question 5
(a) B1 7:45 pm cao (accept 7.45 pm)
(a) Answer: 7:45 pm
(b) M1 correct method, e.g. 08:55 to 09:00 is 5 minutes, then 09:00 to 11:20 is 2 hours 20 minutes
(b) A1 2 hours 25 minutes cao
(b) Answer: 2 hours 25 minutes
Question 6
(a) M1 250 x 1.16
(a) A1 290 (euros) cao
(a) Answer: 290 euros
(b) M1 87 / 1.16
(b) A1 75 (pounds) cao
(b) Answer: 75 pounds
Question 7
(a) M1 40 / 5 x 8, or equivalent scaling
(a) A1 64 (km) cao
(a) Answer: 64 km
(b) M1 9 x 2.2
(b) A1 19.8 (lb) awrt 19.8
(b) Answer: 19.8 lb
Question 8
(a) B1 650 cao
(a) Answer: 650 g
(b) M1 converts 0.8 kg to 800 g, or 650 g to 0.65 kg, for comparison
(b) A1 No, ft, with correct comparison stated (650 g is less than 800 g needed)
(b) Answer: No, she does not have enough (she has 650 g but needs 800 g).
Question 9
(a) B1 7.20 (pounds per litre) cao
(a) Answer: 7.20 pounds per litre
(b) M1 converts 750 ml to 0.75 litres, then 5.85 / 0.75
(b) A1 7.80 (pounds per litre) cao
(b) Answer: 7.80 pounds per litre
(c) C1 Tin A, ft, with correct reason (lower price per litre: 7.20 < 7.80)
(c) Answer: Tin A, because it costs less per litre (7.20 pounds compared with 7.80 pounds).
Question 10
(a) B1 72 (SGD), ft from graph, awrt 70-74
(a) Answer: 72 SGD
(b) M1 108 / 1.8, or correct reading from the graph
(b) A1 60 (GBP) ft, awrt 58-62
(b) Answer: 60 GBP
Question 11
(a) M1 72 x 1000 / 3600, or equivalent unit conversion method
(a) A1 20 (m/s) cso, answer given
(a) Answer: 20 m/s
(b) M1 8 x 3600 / 1000, or equivalent unit conversion method
(b) A1 28.8 (km/h) cao
(b) Answer: 28.8 km/h
Question 12
(a) M1 3.2 x 10000, using 1 m2 = 10000 cm2
(a) A1 32000 (cm2) cao
(a) Answer: 32000 cm2
(b) M1 45000 / 10000, using 1 m2 = 10000 cm2
(b) A1 4.5 (m2) cao
(b) Answer: 4.5 m2
Question 13
(a) M1 60 x 30 x 40
(a) A1 72000 (cm3) cao
(a) Answer: 72000 cm3
(b) M1 their (a) / 1000, dep on (a)
(b) A1 72 (litres) ft
(b) Answer: 72 litres
Question 14
M1 converts 2.7 g to kg, e.g. 2.7 / 1000 = 0.0027 kg (per cm3), or uses 1 g/cm3 = 1000 kg/m3
dM1 dep, converts the cm3 to m3 correctly, e.g. divides by (1/100)3 = 1000000, or completes 0.0027 x 1000000
A1 2700 (kg/m3) cao
Answer: 2700 kg/m3
Question 15
(a) B1 0.75 cao
(a) Answer: 0.75 kg
(b) M1 750 / 6 (= 125), finding the oats needed per person
(b) M1 their 125 x 15, dep
(b) A1 1.875 (kg) oe cao (accept 1875 g)
(b) Answer: 1.875 kg
Question 16
(a) B1 7.4 cao
(a) Answer: 7.4 cm
(b) B1 74 ft from (a)
(b) Answer: 74 mm
Question 17
(a) B1 108 cao
(a) Answer: 108 minutes
(b) M1 adds 1 hour 48 minutes to 14:35, e.g. via 15:35 then + 48 minutes
(b) A1 16:23 cao
(b) Answer: 16:23
Question 18
M1 converts all three lengths to metres: 2.4 m, 0.85 m, 0.63 m