Measures and Units
Measures and units questions cover converting between metric units of length, mass and capacity, and applying these to real-life quantities such as speed, distance, time and flow rate. In 11+ maths papers they often combine unit conversion with a calculation, such as working out a cost per kilogram or the time taken for a journey at a given speed.
Before you start
Make sure you're comfortable with these topics first:
Method
- Learn the standard metric conversions: 1 km = 1000 m, 1 m = 100 cm = 1000 mm, 1 kg = 1000 g, 1 litre = 1000 ml, and use these to move between units.
- Before calculating, convert all quantities in a problem to the same unit.
- For speed, distance and time problems, use the relationship distance = speed x time, so speed = distance / time and time = distance / speed.
- For rate problems, such as cost per item or flow per minute, divide the total by the number of units to find the rate, then use the rate to answer the question.
- Show your working in clear stages, especially when a question combines two different types of unit, such as time and distance, or mass and money.
- Give your final answer with the correct unit, rounding sensibly only when the question asks for it.
Worked example
A cyclist travels 42 km at an average speed of 24 km/h. Calculate how long the journey takes, giving your answer in hours and minutes.
- Use time = distance / speed: time = 42 / 24 hours.
- 42 / 24 = 1.75 hours.
- Convert the decimal part of the hour into minutes: 0.75 x 60 = 45 minutes.
- The journey takes 1 hour 45 minutes.
Practice questions
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Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A recipe for 6 people uses 480 g of flour. Calculate how many grams of flour are needed for 15 people, assuming the amount is directly proportional to the number of people.
A rectangular lawn measures 8 m by 5 m. A path of uniform width 1 m is built all the way around the outside of the lawn. Calculate the area of the path only.
A cuboid water tank has length 50 cm, width 30 cm and height 24 cm. (a) Calculate the volume of the tank in cm^3. (b) Water is poured into the tank until it is 2/3 full. Calculate the volume of water in the tank. (c) Given that 1000 cm^3 = 1 litre, calculate how many litres of water this is.
Free printable worksheet
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