13+ Common Entrance · Topic guide

Maths: Full Practice Paper (Core, Non-Calculator, Set 6)

This full-length, ISEB-style 13+ Common Entrance Core Maths paper is taken without a calculator and gives a sixth complete set of Core-specification questions, spanning number and calculation, fractions, decimals and percentages, ratio and proportion, algebra, geometry and measures, and statistics and probability, so pupils can keep practising exam timing and written methods on unfamiliar questions.

Year 7-8 (13+)MathsISEB

Before you start

Make sure you're comfortable with these topics first:

Method

  1. Work through the paper in the order the questions are set unless one looks especially long, in which case flag it and return to it once you have picked up the more accessible marks.
  2. For non-calculator arithmetic, break a calculation into simpler parts, for example working out 15% by finding 10% and 5% separately and adding them together.
  3. Underline or note the key numbers and the operation each part of a question needs before you begin calculating, especially in worded, multi-step problems.
  4. For geometry questions, sketch and label a diagram if one is not given, marking on any lengths, angles or areas you already know.
  5. Keep exact values, such as fractions or simplified ratios, rather than converting to a decimal too early, since this reduces the risk of a rounding error carrying through several steps.
  6. At the end, check that every part of a multi-part question has been answered and that units have been given where the question asks for them.

Worked example

A rectangular lawn measures 9 m by 6 m. A path 1.5 m wide is built along one of the longer sides, inside the lawn. Work out the area of the lawn that is left after the path is built.

  1. Sketch the lawn as a 9 m by 6 m rectangle and mark the 1.5 m wide path running along one of the 9 m sides.
  2. Work out the area of the whole lawn: 9 x 6 = 54 m^2.
  3. Work out the area of the path, which is 9 m long and 1.5 m wide: 9 x 1.5 = 13.5 m^2.
  4. Subtract the area of the path from the area of the whole lawn: 54 - 13.5 = 40.5 m^2.
  5. State the final answer: the remaining lawn has an area of 40.5 m^2.

Practice questions

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

Q1Work out 2/5 of 65.Show answer

Answer: 26 (65 / 5 = 13, and 13 x 2 = 26)

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Q2Write 0.6 as a fraction in its simplest form.Show answer

Answer: 3/5

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Q3A pair of trainers costs 45 pounds. The price increases by 20%. Work out the new price.Show answer

Answer: 54 pounds (10% of 45 = 4.5, 20% = 9, and 45 + 9 = 54)

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Q4Work out 312 divided by 8, using a written method.Show answer

Answer: 39

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Q5Simplify the ratio 45:60.Show answer

Answer: 3:4 (dividing both parts by 15)

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Q6Find the area of a triangle with base 12 cm and height 7 cm.Show answer

Answer: 42 cm^2 (area = 1/2 x 12 x 7 = 42)

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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 box contains red, blue and green counters in the ratio 2:3:5. There are 40 counters in total. (a) Work out the number of blue counters. (b) One green counter is removed from the box. Work out the new probability of picking a red counter at random from the box.

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Q2[5 marks]

(a) Solve the equation 7 - 2x = 3x - 8. (b) A number is increased by 30% and the result is 91. Work out the original number.

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Free printable worksheet

Want more practice on paper? Download the maths: full practice paper (core, non-calculator, set 6) worksheet pack - 11 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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