Maths: Full Practice Paper (Core, Non-Calculator)
The Core Non-Calculator paper is one of the two Common Entrance Maths papers every 13+ candidate sits, alongside the Core Calculator paper (Additional Mathematics is a further paper set only for candidates entered for it by their school).
Before you start
Make sure you're comfortable with these topics first:
Method
- Work through the paper in order but do not get stuck: if a question resists after a minute or so, note your best attempt, move on, and come back if time allows, since every early mark is worth the same as a late one.
- Since there is no calculator, rely on efficient written methods (column addition, subtraction, short and long multiplication and division) and know times tables to 12 x 12 without hesitation, so basic steps do not eat into your time.
- For fractions, percentages and ratio without a calculator, use non-calculator-friendly routes: percentages built from 10%, 5% and 1%; fractions of an amount by dividing by the denominator then multiplying by the numerator; ratio by finding the value of one share first.
- Show every step of your working in the space provided, even when an answer is obvious, since method marks are awarded independently of the final answer mark.
- Estimate before and after a calculation, by rounding each number to 1 significant figure, to check the final answer is a sensible size.
- Budget your time roughly in proportion to the marks on offer, so the longest, highest-mark question near the end gets proper time rather than being rushed.
- In the last few minutes, check every answer box has something written in it, and re-read each question to confirm the answer matches exactly what was asked, including any units or rounding instruction.
Worked example
A school tuck shop buys 60 chocolate bars for 45 pounds in total. It sells every bar for 95p. Work out the total profit the tuck shop makes once all 60 bars are sold.
- Find the total revenue from selling all the bars: 60 x 95p = 5700p, which is 57 pounds.
- Recall the total cost, which is already given as 45 pounds.
- Subtract the cost from the revenue to find the profit: 57 - 45 = 12.
- So the tuck shop makes 12 pounds profit.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1A cinema charges 6.50 pounds for an adult ticket and 4.20 pounds for a child ticket. A family buys tickets for 2 adults and 3 children. Work out the total cost, without using a calculator.Show answer
Answer: 25.60 pounds (2 x 6.50 = 13.00, 3 x 4.20 = 12.60, total = 25.60)
Q2Find 2/5 of 65.Show answer
Answer: 26
Q3Without a calculator, work out 15% of 180.Show answer
Answer: 27 (10% = 18, 5% = 9, 15% = 18 + 9 = 27)
Q4A charity bake sale raises 200 pounds, split between three charities in the ratio 3 : 2 : 5. Work out the amount the largest share receives.Show answer
Answer: 100 pounds (one part = 200 / 10 = 20, largest share = 5 x 20 = 100)
Q5Simplify 5x + 3y - 2x + 7y.Show answer
Answer: 3x + 10y
Q6A rectangle has length 9 cm and width 6 cm. Work out its area and its perimeter.Show answer
Answer: Area = 54 cm^2, perimeter = 30 cm
Q7The probability that a spinner lands on red is 0.35. Work out the probability that it does not land on red.Show answer
Answer: 0.65
Exam-style questions
Written in the style of a 13+ Common Entrance exam paper, with a full mark scheme.
Without a calculator, work out 7^2 - 3^3.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 2 available
A bakery makes 240 cupcakes. 5/6 of the cupcakes are sold in the morning. Of the cupcakes not sold in the morning, half are sold in the afternoon and the rest are given to a local charity. Work out how many cupcakes are given to the charity.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 3 available
A market stall sells apples in bundles of 3 for 60p, or individually at 25p each. Selin buys 12 apples as four bundles of 3. Work out how much she pays, then work out how much she would have paid buying all 12 apples individually, and state how much she saves by buying in bundles.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 4 available
Free printable worksheet
Want more practice on paper? Download the maths: full practice paper (core, non-calculator) 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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