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.Freya types 4² + 3² into her calculator and writes down 49. Work out the correct value of 4² + 3².
- 2.Write the ratio 5 : 8 in the form 1 : n.
- 3.The number 36 can be written as 2² × 3², and the number 84 can be written as 2² × 3 × 7. Work out the highest common factor of 36 and 84.
- 4.A car is bought for £17,500. Its value decreases by 12% in the first year, and by a further 10% of its reduced value in the second year. Work out the value of the car at the end of the second year, giving your answer to the nearest pound.
- 5.A pair of trainers is priced at £80 online. The shop takes 25% off the price and then adds £10 for next-day delivery. Work out the total cost.
- 6.Work out 3/7 × 14/9. Give your answer as a fraction in its simplest form.
- 7.3/5 of the students in a year group walk to school. 90 students walk to school. Work out the total number of students in the year group.
- 8.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.
- 9.A shop assistant says that 7.2 × 3.9 = 56.16. Work out an estimate for 7.2 × 3.9, by rounding each number to the nearest whole number, to show that the assistant’s answer cannot be correct.
- 10.£120 is shared between three cousins in the ratio 3:4:5. Work out the largest share.
- 11.Work out an estimate for 588 ÷ 31, by rounding each number to 1 significant figure.
- 12.Amelia has 49 boxes of apples with 21 apples in each box. Work out an estimate for the total number of apples, by rounding each number to 1 significant figure.
- 13.Oliver drives 95 km at an average speed of 50 km/h. Work out an estimate for the time the journey takes, by rounding the distance to the nearest 100 km.
- 14.Work out an estimate for 8,900 ÷ 29, by rounding each number to 1 significant figure.
- 15.After a 20% discount, a jacket costs £48. Work out the original price of the jacket.
- 16.A recipe uses 0.625 kg of flour. Write this mass as a fraction of a kilogram, in its simplest form.
- 17.Write the ratio 2 : 1/4 as a ratio of whole numbers in its simplest form.
- 18.Work out 1/2 of 1/4 of 80.
- 19.Work out (2/3)² + (1/2)². Give your answer as a fraction.
- 20.Work out an estimate for 37 × 84, by rounding each number to 1 significant figure.
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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