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 width, the length and the height of a box are in the ratio 3:4:5. The length of the box is 16 cm. Work out the height of the box.
(a)20 cm
(b)80 cm
(c)4 cm
(d)12 cm
2.At midday the temperature in the Lake District was 3 °C. By midnight it had fallen to −6 °C. Work out the fall in temperature.
(a)9 °C
(b)6 °C
(c)3 °C
(d)−9 °C
3.A minibus can carry 16 passengers. A school is taking 179 pupils on a trip. By rounding 179 to the nearest 10, work out an estimate for the number of minibuses needed, given that the school cannot hire part of a minibus.
(a)180
(b)12
(c)10
(d)11
4.A laptop costs £720. A carrying case for it costs 1/9 of the price of the laptop. Work out the cost of the carrying case.
(a)£72
(b)£640
(c)£80
(d)£6480
5.Work out (5 + 2) × 3²
(a)147
(b)63
(c)23
(d)441
6.A laptop priced at £520 is first increased by 15%, and then the new price is decreased by 20%. Work out the final price of the laptop.
(a)£598
(b)£494
(c)£478.40
(d)£416
7.A school orders 187 packed lunches for a trip. Each packed lunch costs £4.85. The school has £900 to spend. By rounding each number to 1 significant figure, work out an estimate for the total cost and decide whether £900 is enough.
(a)£935, so £900 is not enough
(b)£1,000, so £900 is not enough
(c)£800, so £900 is enough
(d)£950, so £900 is not enough
8.Priya adds 3.6 and 0.45 on paper and writes down 3.65 as her answer. Work out the correct value of 3.6 + 0.45.
(a)3.65
(b)4.05
(c)4.5
(d)0.81
9.Find the missing number: 17 × ▢ = 391
(a)23
(b)374
(c)17
(d)6647
10.Work out 3/7 × 14/9. Give your answer as a fraction in its simplest form.
(a)17/16
(b)2/21
(c)2/3
(d)27/98
11.A class has 28 pupils. 16 of the pupils are girls and the rest are boys. Write the ratio of girls to boys in its simplest form.
(a)4:7
(b)3:4
(c)8:6
(d)4:3
12.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
13.Work out 18 − 4 × 2
(a)12
(b)−10
(c)10
(d)28
14.Work out the highest common factor of 12 and 18.
(a)2
(b)6
(c)36
(d)3
15.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.
(a)100
(b)40
(c)70
(d)30
16.A rectangular patio measures 90 cm by 120 cm. Ben wants to cover it exactly with identical square tiles, as large as possible, with no tiles cut. Work out the side length of the largest square tile he can use.
(a)30 cm
(b)360 cm
(c)15 cm
(d)10 cm
17.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
18.A gardener mixes 300 ml of plant feed concentrate with 1.2 litres of water to make a spray. Write the ratio of concentrate to water in its simplest form.
(a)4 : 1
(b)3 : 12
(c)1 : 4
(d)1 : 1.2
19.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
20.Write down the reciprocal of 0.2
(a)−0.2
(b)0.8
(c)5
(d)0.5

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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