Mental Arithmetic: Practice Set 5
Mental Arithmetic: Practice Set 5 is a fifth timed set of 13+ Common Entrance mental arithmetic questions, building on Sets 1 to 4 with further quick-fire practice at calculation, fractions, percentages, ratio and simple algebra under time pressure.
Before you start
Make sure you're comfortable with these topics first:
Method
- Practise collecting like terms and expanding simple brackets mentally, since Set 5 often asks for a quick algebraic simplification.
- Recall square numbers up to 15^2 and common cube numbers, since these appear often without a written method expected.
- Use factor pairs to simplify a fraction or ratio quickly, spotting the highest common factor of the two numbers involved.
- For percentage change questions, decide whether the amount is increasing or decreasing before choosing whether to add or subtract from 100%.
- Read a question fully before starting to calculate, since one extra word (such as 'remaining' or 'difference') can change which operation is needed.
- Keep a running total in your head for multi-step problems by updating one number at a time rather than trying to remember several separate results.
Worked example
Expand and simplify 3(x + 4) - 2x.
- Expand the bracket: 3(x + 4) = 3x + 12.
- Combine this with the remaining term: 3x + 12 - 2x.
- Collect the like terms: 3x - 2x = x, so the expression simplifies to x + 12.
Practice questions
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Q1Work out 13^2.Show answer
Answer: 169
Q2Find the highest common factor of 24 and 36.Show answer
Answer: 12
Q3A coat costs 80 pounds. Its price increases by 25%. Work out the new price.Show answer
Answer: 100 pounds (25% of 80 = 20, 80 + 20 = 100)
Q4Simplify 4(2x - 3) + 5.Show answer
Answer: 8x - 7
Q5Work out 7 x 8 + 6 x 3.Show answer
Answer: 74 (56 + 18 = 74)
Q6Write 0.35 as a fraction in its simplest form.Show answer
Answer: 7/20
Exam-style questions
Written in the style of a 13+ Common Entrance exam paper, with a full mark scheme.
Simplify fully 5x + 2y - x + 6y.
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Nothing ticked yet - 2 available
A phone was originally priced at 240 pounds. It is reduced by 15% in a sale. Work out the sale price.
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Nothing ticked yet - 3 available
A number is squared, then 7 is subtracted, giving 42. Work out the two possible values of the original number.
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Nothing ticked yet - 4 available
Free printable worksheet
Want more practice on paper? Download the mental arithmetic: practice set 5 worksheet pack - 13 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.
This topic is chapter 5 of 13+ Maths Workbook, the whole course as one free printable PDF.
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