Maths: Full Practice Paper (Core, Non-Calculator, Set 4)
This is a full-length, ISEB-style 13+ Common Entrance Core Maths paper taken without a calculator, drawing on every strand of the Core specification, number and calculation, fractions, decimals and percentages, ratio and proportion, algebra, geometry and measures, and statistics and probability, so that reliable written and mental methods are practised together under timed, exam-like conditions.
Before you start
Make sure you're comfortable with these topics first:
Method
- Skim the whole paper before starting so you know how many questions there are and roughly how long you have for each one, then attempt the shortest, most familiar questions first to bank marks early.
- For every calculation, pick a written method you can carry out reliably without a calculator, such as column addition and subtraction, long multiplication, or short or long division.
- Convert between fractions, decimals and percentages using standard equivalences you have memorised, for example 1/4 = 0.25 = 25%, rather than starting a division from scratch.
- Write down every stage of your working, even for questions that feel easy, since Common Entrance mark schemes award marks for a correct method even where the final answer contains a slip.
- Round the numbers in a question to estimate the answer before you calculate exactly, then compare your exact answer with the estimate to catch mistakes.
- In the last few minutes, re-read each question to check you have answered what was actually asked, and re-do at least one long calculation by a different method to confirm it.
Worked example
A school hall has 320 seats. 3/8 of the seats are reserved for parents, and then 15% of the seats that remain are reserved for staff. The rest of the seats are for pupils. Work out how many seats are for pupils.
- Find the number of seats reserved for parents: 3/8 of 320 = (320 / 8) x 3 = 40 x 3 = 120.
- Find how many seats remain after the parents' seats are removed: 320 - 120 = 200.
- Find 15% of the 200 remaining seats: 10% of 200 = 20 and 5% of 200 = 10, so 15% = 20 + 10 = 30.
- Subtract the staff seats from the 200 remaining seats: 200 - 30 = 170.
- State the final answer: 170 seats are for pupils.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1Work out 3/4 of 148.Show answer
Answer: 111 (148 / 4 = 37, and 37 x 3 = 111)
Q2Write 0.35 as a fraction in its simplest form.Show answer
Answer: 7/20 (0.35 = 35/100, and dividing the top and bottom by 5 gives 7/20)
Q3A jacket costs 64 pounds. It is reduced by 15% in a sale. Work out the sale price.Show answer
Answer: 54.40 pounds (10% of 64 = 6.4, 5% of 64 = 3.2, so 15% = 9.6, and 64 - 9.6 = 54.40)
Q4Work out 207 divided by 9, showing your written method.Show answer
Answer: 23
Q5Write the ratio 18:24 in its simplest form.Show answer
Answer: 3:4 (dividing both parts by 6)
Q6A recipe needs 250 g of flour to make 8 muffins. Work out how much flour is needed to make 20 muffins at the same recipe strength.Show answer
Answer: 625 g (250 / 8 = 31.25 g per muffin, and 31.25 x 20 = 625 g)
Exam-style questions
Written in the style of a 13+ Common Entrance exam paper, with a full mark scheme.
A garden centre sells young trees at 18 pounds each. (a) Hana buys 7 trees and pays cash, which earns her a discount of 1/9 of the total cost. Work out how much Hana pays. (b) Priya buys some trees at the full price of 18 pounds each and spends exactly 234 pounds. Work out how many trees Priya buys.
Show mark scheme
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(a) A number, n, is multiplied by 4 and then 7 is subtracted, giving a result of 41. Form an equation in n and solve it. (b) A different number, m, satisfies 3m + 5 = 2m - 4. Find the value of m.
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Free printable worksheet
Want more practice on paper? Download the maths: full practice paper (core, non-calculator, set 4) 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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