13+ Common Entrance · Topic guide

Maths: Full Practice Paper (Core, Calculator, Set 7)

This full-length, ISEB-style 13+ Common Entrance Core Maths paper allows a calculator and is the seventh complete set of Core-specification questions on the site, covering number and calculation, fractions, decimals and percentages, ratio and proportion, algebra, geometry and measures, and statistics and probability, so that calculator technique and exam timing can be practised right up to the level of the real Common Entrance paper.

Year 7-8 (13+)MathsISEB

Before you start

Make sure you're comfortable with these topics first:

Method

  1. Look through the whole paper first and identify any question types you find harder, so you can allow yourself extra time for them later.
  2. For any question giving a real-life context, such as money, distance or time, decide what units your final answer should be in before you calculate.
  3. Use full calculator accuracy throughout a multi-step calculation and only round the very last answer, to avoid small rounding errors building up.
  4. Where a question could be solved by more than one method, such as using a formula or building a table of values, choose whichever method you find quickest and most reliable.
  5. For probability questions, check that any list of outcomes or fractions you use adds up to the total or to 1, as a way of spotting a missing case.
  6. Leave time at the end to check that answers are given to the accuracy requested and that every part of a question has been completed.

Worked example

A bag contains 5 red counters, 7 blue counters and 8 green counters. A counter is picked at random and not replaced, then a second counter is picked at random. Work out the probability that both counters picked are red.

  1. Find the total number of counters in the bag: 5 + 7 + 8 = 20.
  2. Find the probability the first counter picked is red: 5/20.
  3. After removing one red counter, find the new number of red counters and the new total: 4 red counters out of 19 remaining.
  4. Multiply the two probabilities together, since both events must happen: 5/20 x 4/19 = 20/380.
  5. Simplify the answer to its lowest terms: 20/380 = 1/19.

Practice questions

Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.

Q1A bag has 4 yellow and 6 purple counters. Find the probability of picking a purple counter.Show answer

Answer: 6/10 = 3/5

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Q2Work out 12.6 divided by 0.3.Show answer

Answer: 42

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Q3A car depreciates by 15% each year. It is worth 20,000 pounds now. Work out its value after 1 year.Show answer

Answer: 17,000 pounds (20000 x 0.85 = 17000)

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Q4Work out 2^5 - 3^3.Show answer

Answer: 5 (32 - 27 = 5)

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Q5A train travels 245 km in 3.5 hours. Work out its average speed.Show answer

Answer: 70 km/h (245 / 3.5 = 70)

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Q6Find the mean of 14, 18, 22, 16 and 20.Show answer

Answer: 18 (sum = 90, and 90 / 5 = 18)

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Exam-style questions

Written in the style of a 13+ Common Entrance exam paper, with a full mark scheme.

Q1[4 marks]

A spinner has 8 equal sections numbered 1 to 8. (a) Work out the probability of spinning a number greater than 5. (b) The spinner is spun twice. Work out the probability of spinning a number greater than 5 both times.

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Q2[4 marks]

A shop buys phone cases for 3.50 pounds each and sells them for 8.75 pounds each. (a) Work out the profit made on selling one phone case. (b) Work out the percentage profit, based on the buying price.

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Free printable worksheet

Want more practice on paper? Download the maths: full practice paper (core, calculator, set 7) 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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