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.A cycle route is 350 m long. A footpath runs alongside it for 3/7 of that length. Work out the length of the footpath.
(a)200 m
(b)1050 m
(c)150 m
(d)50 m
2.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
3.Write 0.36 as a fraction in its simplest form.
(a)36/10
(b)9/25
(c)9/50
(d)3/10
4.Work out (−3) × 4 + 2 × (−5)
(a)−22
(b)50
(c)−2
(d)22
5.A bag contains 7 red counters and 15 blue counters. Write down the ratio of red counters to blue counters in its simplest form.
(a)7:5
(b)15:7
(c)1:2
(d)7:15
6.A roll of ribbon is 8.4 m long. Ribbon is cut into pieces that are each 0.6 m long. Work out how many complete pieces can be cut from the roll.
(a)14
(b)12
(c)140
(d)1
7.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
8.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
9.A sofa costs £800. Its price is increased by 25%. Work out the new price of the sofa.
(a)£1,000
(b)£600
(c)£825
(d)£200
10.Write the ratio 2 : 1/4 as a ratio of whole numbers in its simplest form.
(a)8:1
(b)8:4
(c)1:8
(d)2:4
11.A number, n, is a multiple of both 6 and 9. Work out the smallest possible value of n that is greater than 20.
(a)36
(b)18
(c)54
(d)27
12.The highest common factor of two numbers is 4 and their lowest common multiple is 60. One of the numbers is 20. Work out the other number.
(a)12
(b)240
(c)16
(d)15
13.Work out 2/5 of 45.
(a)36
(b)27
(c)18
(d)9
14.Write 2 m : 150 cm : 50 cm as a ratio of whole numbers in its simplest form.
(a)4:3:1
(b)4:3:2
(c)2:150:50
(d)3:4:1
15.Write 0.25 as a percentage.
(a)2.5%
(b)0.25%
(c)250%
(d)25%
16.Work out the difference between 45% of 70 and 35% of 80.
(a)11.5
(b)3.5
(c)59.5
(d)10
17.The same jumper is sold at two shops. Shop A charges £40 and Shop B charges £50. Write down the price at Shop A as a percentage of the price at Shop B.
(a)90%
(b)80%
(c)20%
(d)125%
18.Amelia estimates 48 × 21 by working out 50 × 20 = 1,000. Work out whether her estimate is an under-estimate or an over-estimate, and by how much.
(a)An over-estimate, by 19
(b)Neither — the estimate is exactly right
(c)An under-estimate, by 8
(d)An over-estimate, by 8
19.Write the ratio 8 : 15 in the form 1 : n.
(a)1.875 : 1
(b)1 : 1.875
(c)8 : 1.875
(d)1 : 0.53
20.Write 0.325 as a fraction in its simplest form.
(a)13/40
(b)3/8
(c)8/25
(d)13/4

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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