OCR GCSE EXAM MATHS 12.2 COMPOUND UNIT AND UNIT OF MEASUREMENTS LATEST QUESTIONS AND CORRECT SOLUTIONS

Exercise 1 1 Convert these areas. a 15m2 to cm2 b 8.8km2 to m2 c 3600mm2 to cm2 d cm2 to m2 2 Convert these volumes. a 6.2m3 to cm3 b cm3 to m3 c 750cm3 to mm3 d 0.6km3 to m3 12.2 Compound units of measurement ©Cambridge University Press and OCR 2020 2 3 Jack runs 42km in 3 hours and 15 minutes. What is his average speed in km/h? Speed = Common units are m/s, km/h or mph (miles per hour). Remember: m/s is read as metres per second, km/h as kilometres per hour, etc. Density = Common units are g/cm3 or kg/m3 . Pressure = Common units are N/m2 or N/mm2 . (You may need to rearrange the formulae above to work out different things.) WORKED EXAMPLE An athlete runs at an average speed of 10.26m/s. Is this faster or slower than an average speed of 40 kilometres per hour? Solution Convert 10.26m/s to kilometres per hour. 10.26 × 60 = 615.6m/min You travel 60 times further in 1 minute than you travel in 1 second. 615.6 × 60 = 36936m/h You travel 60 times further in 1 hour than you travel in 1 minute. 36936 ÷ 1000 = 36.936km/h To change from metres to kilometres you divide by 1000. So, 10.26m/s is equal to 36.936km/h. 36.936km/h is less than 40km/h. The athlete’s speed is slower than 40 kilometres per hour. 12.2 Compound units of measurement ©Cambridge University Press and OCR 2020 3 4 A car travels at 16m/s. Is this faster or slower than a speed of 60km/h? 5 A car travels 520km at an average speed of 95km/h. How long does this journey take? 6 Usain Bolt won the 100m at the Olympic Games in 2016 with a time of 9.81 seconds. What was his average speed in m/s? 7 A 10km run starts at 10:48 exactly. The average speed of the winner is 16.2 km/h. At what time does the winner cross the line? Give your answer to the nearest minute. 8 A cuboid with side lengths 15cm, 20cm and 30cm has a mass of 0.734kg. Calculate its density in g/cm3 . 9 A piece of copper has mass 0.375kg and its density is 8.96g/cm3 . Calculate its volume in cm3 . 10 Grass is to be grown on an area of 235m2 . 50g of grass seed is needed per m2 . Grass seed is sold in tubs containing 1kg of seed. a How many kilograms of seed are needed? b How many tubs should I buy? 11 An engine has a capacity of 2295cm3 . Convert this into litres. Give your answer to the nearest 0.1 litre. 12 A painter earns £18.80 per hour. One week he worked for 40 hours. How much did he earn that week? 13 I earn £500 for working 20 hours. What is my rate of pay in £/hour? 14 Petrol costs £55 for 40 litres. What is the cost in £/litre?