20 questions with no calculator: the four operations, fractions, percentages, order of operations, factors and estimation.

✏️ Paper 1 non-calculator warm-up — Foundation

Maths · GCSE Foundation · 20 questions · ~25 min

MathsUKwww.geekhero.co.uk

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.The rent on a flat increases by 10% one year and by a further 10% the following year. Work out the overall percentage increase over the two years.
(a)121%
(b)11%
(c)21%
(d)20%
2.Light travels at 2.998 × 10⁸ metres per second. A distant object in space is 3.1 × 10¹⁵ metres from Earth. Work out an estimate for the number of seconds light takes to travel from the object to Earth, by rounding each number to 1 significant figure.
(a)9 × 10²³ seconds
(b)3 × 10⁷ seconds
(c)1 × 10⁻⁷ seconds
(d)1 × 10⁷ seconds
3.Work out the highest common factor of 20 and 32.
(a)8
(b)4
(c)2
(d)160
4.Work out an estimate for 2.9² + 3.1², by rounding each number to the nearest whole number.
(a)18
(b)36
(c)6
(d)12
5.A jumper costs £45 at Shop A, where it is reduced by 20%. The same jumper costs £34 at Shop B, where a further 10% reduction is then applied. Work out the difference between the two reduced prices.
(a)£11.00
(b)£66.60
(c)£1.60
(d)£5.40
6.Hannah works out 3.1 × 19.6 on her calculator and writes down 6.076. Work out an estimate for 3.1 × 19.6, by rounding each number to 1 significant figure.
(a)6
(b)62
(c)600
(d)60
7.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.
(a)£65
(b)£67.50
(c)£60
(d)£70
8.Write down the decimal that is equal to 3/5.
(a)1.67
(b)0.6
(c)0.35
(d)0.53
9.Write the fraction 9/25 as a decimal.
(a)0.9
(b)2.8
(c)0.36
(d)0.925
10.Work out (−2/5) × (−10/3). Give your answer as a fraction in its simplest form.
(a)−56/15
(b)3/25
(c)−4/3
(d)4/3
11.At an animal shelter, the ratio of cats to dogs is 2:5. There are 18 more dogs than cats. Work out the number of cats.
(a)6
(b)12
(c)9
(d)30
12.Work out an estimate for 312 × 19, by rounding each number to 1 significant figure.
(a)6200
(b)5928
(c)6000
(d)600
13.Write 0.35 as a fraction in its lowest terms.
(a)7/25
(b)35/10
(c)3/10
(d)7/20
14.Write 0.36 as a fraction in its simplest form.
(a)36/10
(b)9/25
(c)9/50
(d)3/10
15.Write down the reciprocal of 0.2
(a)−0.2
(b)0.8
(c)5
(d)0.5
16.Work out 3/8 of 96.
(a)72
(b)12
(c)32
(d)36
17.Grace works out 7 × 99 by writing 99 as 100 − 1. Use her method to work out 7 × 99.
(a)707
(b)700
(c)693
(d)699
18.A bag contains red counters and blue counters in the ratio 5:3. There are 56 counters in the bag altogether. Work out how many counters are blue.
(a)35
(b)7
(c)28
(d)21
19.A jacket normally costs £65. In a sale it is reduced by 20%, and the shop then takes a further £5 off at the till. Work out the final price.
(a)£48.00
(b)£52.00
(c)£47.00
(d)£40.00
20.The number 72 can be written as 2³ × 3², and the number 108 can be written as 2² × 3³. Work out the highest common factor of 72 and 108.
(a)36
(b)6
(c)108
(d)216

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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