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 angles of a triangle are in the ratio 2:3:4. Work out the size of the smallest angle.
(a)80°
(b)60°
(c)40°
(d)20°
2.Simplify the ratio 45 : 30 : 75 to its simplest form.
(a)2 : 3 : 5
(b)15 : 10 : 25
(c)9 : 6 : 15
(d)3 : 2 : 5
3.Work out 2 × (−3 + 7)
(a)1
(b)6
(c)−20
(d)8
4.A sponsored walk is 36 km long. Aisha has completed 8/12 of the walk. Work out how far she has walked.
(a)288 km
(b)4.5 km
(c)12 km
(d)24 km
5.Three business partners share a profit of £48,000 in the ratio 3:5:4. Work out how much the partner with 5 parts receives.
(a)£20,000
(b)£12,000
(c)£4,000
(d)£16,000
6.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.
(a)4
(b)24
(c)96
(d)20
7.A sum of £150 is divided between Ben and Chloe in the ratio 2:3. Work out Chloe's share.
(a)£60
(b)£75
(c)£90
(d)£30
8.A jug holds 3 1/3 litres of juice. Each glass holds 2/3 of a litre. Work out how many glasses can be filled from the jug.
(a)5
(b)20/9
(c)5/3
(d)2
9.Freya buys three items whose prices are in the ratio 2:3:5. Altogether she pays £400. Work out the price of the most expensive item.
(a)£120
(b)£80
(c)£40
(d)£200
10.2/3 of an amount of money is £30. Work out the amount.
(a)£15
(b)£45
(c)£20
(d)£90
11.Work out 3/8 of 96.
(a)72
(b)12
(c)32
(d)36
12.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
13.Work out −7 − (−3).
(a)4
(b)−4
(c)10
(d)−10
14.A country's population is 8,340,000, and it is estimated that 1,950,000 of them live in the capital city. By rounding each number to 1 significant figure, work out an estimate for the number of people who do not live in the capital city.
(a)6,300,000
(b)8,000,000
(c)6,390,000
(d)6,000,000
15.Which statement about the number 51 is correct?
(a)51 is prime, because it is not divisible by 2, 3 or 5.
(b)51 is not prime, because it is divisible by 2.
(c)51 is prime, because it is an odd number.
(d)51 is not prime, because 51 = 3 × 17.
16.Is 120 divisible by 5? Give a reason for your answer.
(a)Yes, because 120 ends in 0
(b)No, because 1 + 2 + 0 = 3 is not a multiple of 5
(c)Yes, because 120 is even
(d)No, because 5 does not divide into 12
17.Work out −4.5 + 2.8.
(a)1.7
(b)−7.3
(c)−2.3
(d)−1.7
18.Work out an estimate for 89 + 52, by rounding each number to the nearest 10.
(a)141
(b)130
(c)150
(d)140
19.Write 1/5 as a percentage.
(a)20%
(b)5%
(c)50%
(d)25%
20.Work out 100 − 4 × 5²
(a)0
(b)2400
(c)60
(d)−300

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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