CEM Style Numerical Reasoning Paper 3
CEM-style numerical reasoning Paper 3 continues the written-answer, non-calculator format of Papers 1 and 2, but leans towards data sets involving ratio, proportion and scaling, such as recipe quantities, mixing amounts, or exchange rates, where the questions ask pupils to scale a given data set up or down rather than simply reading it off directly.
Before you start
Make sure you're comfortable with these topics first:
Method
- Identify the given ratio, rate or proportion in the data source before attempting the first question, since every question that follows will scale from it.
- Find the value of one unit or one part of the ratio first, since almost every scaling question is solved more easily once you know what one part is worth.
- Check whether a question is scaling up (multiplying) or scaling down (dividing) before calculating, since CEM-style wrong options often show the opposite operation.
- Where a question changes the context slightly, such as asking for a different quantity than the ones given in the data, adapt your method rather than assuming the same numbers apply.
- Write out each step of your scaling calculation, since it is easy to lose track of which number represents which part of the ratio.
- Keep track of the time allowed for the whole mixed timed section, since numerical reasoning is usually just one part of it.
Worked example
A recipe for 6 people uses 450g of pasta. (a) Find how much pasta is needed for 1 person. (b) Find how much pasta is needed for 10 people.
- Find the amount needed for 1 person by dividing by the number of people: 450 / 6.
- 450 / 6 = 75, so 75g of pasta is needed per person.
- Multiply this by 10 to find the amount for 10 people: 75 x 10.
- 75 x 10 = 750, so 750g of pasta is needed for 10 people.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1A recipe for 4 people uses 200g of rice. How much rice is needed for 9 people?Show answer
Answer: 450g (200 / 4 = 50g per person; 50 x 9 = 450).
Q2A map has a scale where 2cm represents 5km. How many km does 8cm represent?Show answer
Answer: 20km (8 / 2 = 4; 4 x 5 = 20).
Q3Paint is mixed in the ratio blue:white = 3:5. If 12 litres of blue is used, how much white is needed?Show answer
Answer: 20 litres (12 / 3 = 4; 4 x 5 = 20).
Q4An exchange rate shows 10 pounds is equal to 12 US dollars. How many dollars is 25 pounds equal to?Show answer
Answer: 30 dollars (10 pounds = 1.2 dollars per pound; 1.2 x 25 = 30).
Q5A model car is built at a scale of 1:20. If the real car is 4m long, how long is the model, in cm?Show answer
Answer: 20cm (4m = 400cm; 400 / 20 = 20).
Q6A fruit squash is mixed in the ratio squash:water = 1:4. How much water is needed for 50ml of squash?Show answer
Answer: 200ml (50 x 4).
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A cake recipe for 8 people uses 320g of flour, 200g of sugar and 4 eggs. A baker wants to make enough for 20 people. (a) Find the amount of flour needed. (b) Find the amount of sugar needed. (c) Find the number of eggs needed, given that eggs can only be used as whole eggs.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 4 available
An exchange rate data sheet shows 50 pounds is equal to 57.50 euros. (a) Find the value of 1 pound in euros. (b) Using this rate, find how many euros 120 pounds is equal to. (c) A traveller has 92 euros. Using the same rate, find how many pounds this is equal to.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 4 available
Free printable worksheet
Want more practice on paper? Download the cem style numerical reasoning paper 3 worksheet pack - 6 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
Next topics
Not quite what you needed?
Tell us what is missing on cem style numerical reasoning paper 3, or which topic to write up next. Every request is read, and we reply to every one.
Build a full practice pack.
This topic is one of hundreds in the library - pick the ones a student needs and generate a printable PDF in minutes.