Maths: Full Practice Paper (Core, Calculator)
The Core Calculator paper is the second of the two Common Entrance Maths papers every 13+ candidate sits, pairing with the Core Non-Calculator paper (CE.M13) to cover the full Core syllabus.
Before you start
Make sure you're comfortable with these topics first:
Method
- Set up each calculation on paper before touching the calculator, writing the numbers and operation you intend to use, so the method is visible even if a button is pressed wrong.
- Use the calculator's memory or brackets for multi-step calculations, rather than rounding an intermediate answer and typing it back in, since early rounding is a common source of an inaccurate final answer.
- Check every calculator answer is a sensible size for the question, by estimating first, since a slipped decimal point or a wrong button is easy to miss otherwise.
- Read rounding instructions carefully (decimal places, significant figures, nearest penny or whole number) and apply them only to the final answer, not to values used in an earlier step.
- For questions built on a table, graph or list of data, extract the exact numbers needed before calculating, since a slow, careful read of the data is safer than working from memory of it.
- Include correct units in every answer (pounds, cm, cm^2, cm^3), since these questions often mix money, length, area and volume across the same paper.
- As with the non-calculator paper, budget time by mark value, and leave enough time at the end to check that multi-part answers all address what each part actually asked.
Worked example
Amrit invests 850 pounds in a savings account that pays 3% simple interest per year. Work out the total amount in the account after 4 years.
- Find one year's interest: 3% of 850 = 850 x 0.03 = 25.50 pounds.
- Since it is simple interest, the same interest is added every year, so multiply by 4: 25.50 x 4 = 102 pounds.
- Add the total interest to the original amount: 850 + 102 = 952.
- So the account holds 952 pounds after 4 years.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1A cylindrical water butt has a radius of 35 cm and a height of 120 cm. Work out its volume, giving your answer in cm^3 to 3 significant figures. (Use pi = 3.14159.)Show answer
Answer: 462000 cm^3 (volume = pi x 35^2 x 120 = 461813.7, which rounds to 462000 to 3 s.f.)
Q2A car valued at 12,000 pounds depreciates by 15% in its first year. Work out its value at the end of the first year.Show answer
Answer: 10,200 pounds (12000 x 0.85 = 10200)
Q3Find the midpoint of the line segment joining A(-3, 5) and B(7, -1).Show answer
Answer: (2, 2)
Q4The nth term of a sequence is 5n - 2. Work out the 15th term.Show answer
Answer: 73 (5 x 15 - 2 = 73)
Q5A survey asked 20 people how many pets they own: 5 people own 0 pets, 8 own 1 pet, 4 own 2 pets, and 3 own 3 pets. Work out the mean number of pets owned.Show answer
Answer: 1.25 (total pets = 0 + 8 + 8 + 9 = 25, mean = 25 / 20 = 1.25)
Q6A bag contains 12 red counters, 15 blue counters and 9 green counters only. A counter is picked at random. Work out the probability that it is blue, giving your answer as a decimal to 3 significant figures.Show answer
Answer: 0.417 (15 / 36 = 5/12 = 0.41666..., rounds to 0.417)
Q7A phone contract costs 18.50 pounds per month for 24 months, plus an upfront cost of 49 pounds. Work out the total cost of the contract.Show answer
Answer: 493 pounds (18.50 x 24 = 444, plus 49 = 493)
Exam-style questions
Written in the style of a 13+ Common Entrance exam paper, with a full mark scheme.
Convert 4.5 x 10^6 into an ordinary number.
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Nothing ticked yet - 2 available
A laptop has a normal price of 640 pounds. In a sale, the price is reduced by 20%. Chinedu has a discount voucher that then takes off a further 5% of the new sale price. Work out the final price Chinedu pays.
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The table shows the times, in minutes, taken by 30 runners to complete a fun run: 6 runners took between 20 and 30 minutes, 12 runners took between 30 and 40 minutes, 9 runners took between 40 and 50 minutes, and 3 runners took between 50 and 60 minutes. Work out an estimate for the mean time taken.
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Tick each line you got. Your score builds from the marks on the scheme.
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Free printable worksheet
Want more practice on paper? Download the maths: full practice paper (core, calculator) worksheet pack - 9 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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