CEM Style Numerical Reasoning Paper 1
CEM-style numerical reasoning papers, a format popularised by Durham University's Centre for Evaluation and Monitoring and still used as a practice style even where a different provider now sets the actual test, present a block of data such as a table, graph or short paragraph of figures and ask several questions off that same data set in a row, in standard written-answer format. They test extracting the right numbers from the data before calculating, often placing maths questions inside a wider mixed section alongside verbal or non-verbal items.
Before you start
Make sure you're comfortable with these topics first:
Method
- Read the data source, whether a table, graph or paragraph, fully before attempting the first question that uses it, and note what each row, column or axis represents.
- For each question, identify exactly which figures from the data are needed, since CEM-style data sets usually contain more numbers than any single question requires.
- Write your working in the space provided even though the format is standard rather than multiple choice, since a small slip is easier to spot in written-out steps.
- Expect the difficulty to increase through the section; do not assume later questions on the same data are as quick as the first.
- Because maths items can be mixed in with other question types in the same timed section, reset your focus fully for each new question rather than assuming the next one is also numerical.
- Keep track of time across the whole mixed section, not just the numerical questions, since there is usually no separate time allowance for the maths portion.
- If a question depends on an earlier answer you are unsure of, recompute it quickly from the original data rather than carrying an error forward.
Worked example
A school trip data table shows: Coach hire 340 pounds, Museum entry 6.50 pounds per pupil, Lunch 3.20 pounds per pupil. 28 pupils are going on the trip. (a) Calculate the total cost of museum entry and lunch for all 28 pupils. (b) Calculate the total cost of the whole trip, including coach hire.
- (a) Find the combined cost per pupil: museum entry 6.50 + lunch 3.20 = 9.70 per pupil.
- Multiply by the number of pupils: 9.70 x 28.
- 9.70 x 28 = 9.70 x 30 - 9.70 x 2 = 291.00 - 19.40 = 271.60, so museum entry and lunch together cost 271.60.
- (b) Add the coach hire: 271.60 + 340 = 611.60.
- The whole trip costs 611.60 (611.60 pounds).
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1A cinema sells popcorn at 3.40 pounds and a drink at 2.10 pounds. What is the cost of one popcorn and one drink together?Show answer
Answer: 5.50 pounds.
Q2A data table lists three towns' populations: Ashby 12,400, Byton 9,800, Carwell 15,650. What is the combined population of Byton and Carwell?Show answer
Answer: 25,450 (9,800 + 15,650).
Q3A graph shows a plant grows 4cm in week 1, 7cm in week 2 and 5cm in week 3. What is the total growth over the three weeks?Show answer
Answer: 16cm.
Q4A price list shows a return train ticket costs 14.80 pounds, and a single ticket costs 8.50 pounds. How much cheaper is the return ticket than buying two single tickets?Show answer
Answer: 2.20 pounds (2 x 8.50 = 17.00; 17.00 - 14.80 = 2.20).
Q5A factory makes 480 toys on Monday and 25% more on Tuesday. How many toys does it make on Tuesday?Show answer
Answer: 600 (25% of 480 = 120; 480 + 120 = 600).
Q6A survey of 60 pupils found 24 chose football and 18 chose swimming as their favourite sport, and the rest chose athletics. How many chose athletics?Show answer
Answer: 18 (60 - 24 - 18 = 18).
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A weather data table records the maximum temperature in a city over four days: Monday 18C, Tuesday 21C, Wednesday 15C, Thursday 20C. (a) Calculate the range of the temperatures. (b) Calculate the mean maximum temperature over the four days.
Show mark scheme
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A charity fundraising data sheet shows entry tickets raised 2,340 pounds from 180 people, and a raffle raised a further 615 pounds. (a) Calculate the average amount raised per person from ticket sales alone. (b) Calculate the total amount raised by the whole event.
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Nothing ticked yet - 3 available
Free printable worksheet
Want more practice on paper? Download the cem style numerical reasoning paper 1 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.
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