20 questions with no calculator: the four operations, fractions, percentages, order of operations, factors and estimation.
✏️ Paper 1 non-calculator warm-up — Foundation
Paper 1 is worth exactly as much as each calculator paper, and it is the one most Foundation students practise least. This sheet is a warm-up for it: twenty questions drawn from the number and ratio statements that turn up on the non-calculator paper year after year — column arithmetic with decimals and negatives, adding and subtracting fractions, percentages of amounts, priority of operations, factors and multiples, and estimating by rounding to one significant figure. Do it with a pen and nothing else. Twenty-five minutes is about right, but do not stop early if you need longer; the point is to find out which of these have quietly gone rusty, not to score well. Mark it, then go back to the topic page for whichever one cost you the most.
- 1.There are 400 students at a school. 25% of them have a brother, 40% have a sister and 15% have both a brother and a sister. Work out how many of the students have neither a brother nor a sister.
- 2.A cinema has 250 seats. 12% of the seats are reserved. Work out how many of the seats are reserved.
- 3.The number of members of a running club increases from 45 to 54. Work out the percentage increase.
- 4.A recipe for pastry uses flour and butter in the ratio 3:2. A baker has 180 g of butter and wants to make pastry using all of it. Work out the total mass of pastry the baker can make.
- 5.Write the ratio 5 : 8 in the form 1 : n.
- 6.Work out 2 × 3 × 5 + 1 and decide whether the result is a prime number.
- 7.A sponsored walk raised £350 for charity. 20% of the money raised is spent on equipment. Work out how much is spent on equipment.
- 8.Simplify the ratio 45 : 30 : 75 to its simplest form.
- 9.A gardener has 42 tulip bulbs and 56 daffodil bulbs. She plants them in rows, with every row containing the same number of tulip bulbs and the same number of daffodil bulbs, and no bulbs left over. Work out the greatest number of rows she can plant.
- 10.Write the ratio 8 : 15 in the form 1 : n.
- 11.Two investors put money into a business in the ratio 3:5. The first investor puts in £1,200. Work out the total amount invested by both investors.
- 12.Write the ratio 3/4 : 1/2 as a ratio of whole numbers in its simplest form.
- 13.Two lighthouses flash at the start of the same minute. The first lighthouse flashes every 8 minutes and the second flashes every 12 minutes. Work out how many minutes it will be until they next flash together.
- 14.Write 0.25 as a percentage.
- 15.Work out an estimate for 6.4 × 3.9, by rounding each number to the nearest whole number.
- 16.Work out an estimate for 2.9² + 3.1², by rounding each number to the nearest whole number.
- 17.Work out an estimate for 6.8 × 41, by rounding each number to 1 significant figure.
- 18.A necklace is made using gold beads and silver beads in the ratio 7:3. There are 40 more gold beads than silver beads. Work out the total number of beads in the necklace.
- 19.Divide 84 in the ratio 3:4. Work out the smaller share.
- 20.Write 0.875 as a fraction in its simplest form.
What is on this worksheet?
The sheet holds 20 questions drawn from the MathsUK bank — the content areas covered: Number, Ratio, proportion and rates of change (statements N2, N3, N4, N10, N12, N14, R4, R5, R9). It is pitched at GCSE Foundation and takes about 25 minutes to work through in full. It is built for independent practice, with full answers at the end for self-marking.
How to use the sheet well
- Print it or open it on screen — both work. Printing is A4; the screen view fits phones and tablets.
- Do all 20 questions before checking — about 25 minutes is the guide, but there is no time pressure.
- Check the answers — press “Show answers” or print the answer page separately.
- Redo the questions you got wrong — twice as effective as doing 20 fresh ones.
- “New questions” — builds a fresh sheet on the same statements, so you can practise again without repeats.
Why this sheet helps
MathsUK worksheets use questions graded by difficulty and a fair spread of correct-answer positions (the answer is not always (a)) — so the student really has to think about each question rather than guess a pattern. Every question is tagged to a DfE content statement and checked before it enters the bank. The answers come with a step-by-step explanation, not just a value — so a wrong answer becomes a lesson.
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