25 questions on the topics that decide a grade 4: percentages, ratio, area and perimeter, linear equations, averages and probability.

🎯 Grade 4 pass booster

Maths · GCSE Foundation · 25 questions · ~40 min

MathsUKwww.geekhero.co.uk

A grade 4 is the standard pass that colleges, apprenticeships and employers ask for, and most students who miss it do not miss it on the hard questions — they miss it by dropping marks across the accessible ones. This sheet gathers twenty-five of those: percentage of an amount and percentage change, sharing in a ratio, area and perimeter of rectangles, triangles and compound shapes, solving a linear equation, reading the mean, median, mode and range from a list or a table, and simple probability. Nothing here is a stretch topic, and all of it is worth marks on every paper, on both tiers. Work through it, mark it honestly, and treat anything you got wrong as a priority over anything further up the specification — a secured mark is worth more than an attempted one.

1.In a school choir the ratio of boys to girls is 3:4. When 6 more boys join the choir, the ratio of boys to girls becomes 1:1. Work out how many girls are in the choir.
(a)18
(b)24
(c)42
(d)30
2.Two classes sat the same maths test, both marked out of 100. Class A had a mean mark of 70 and a range of 30 marks. Class B had a mean mark of 70 and a range of 10 marks. Compare the marks of the two classes.
(a)The means are equal, and Class B's marks are the more consistent because its range is smaller.
(b)Class A's mean mark is higher, and Class A's marks are also the more consistent.
(c)The means are equal, and Class A's marks are the more consistent because its range is larger.
(d)Class B's mean mark is higher, and its smaller range makes its marks the more consistent.
3.Solve 4x + 3 = 19
(a)3.75
(b)5.5
(c)4
(d)4.75
4.Work out the median of these five numbers: 2, 4, 7, 12, 26
(a)24
(b)14
(c)7
(d)10.2
5.Oliver flips three fair coins at the same time. Work out the probability that exactly two of the three coins land on heads.
(a)4/8
(b)6/8
(c)3/8
(d)2/8
6.Kwame flips a fair coin three times and writes down what it lands on each time. Work out the probability that it lands on heads all three times.
(a)1/6
(b)1/2
(c)1/4
(d)1/8
7.There are 400 students at a school. 25% of them have a brother, 40% have a sister and 15% have both a brother and a sister. Work out how many of the students have neither a brother nor a sister.
(a)140 students
(b)300 students
(c)200 students
(d)260 students
8.At a youth club the ratio of juniors to seniors is 3:5. There are 40 members altogether. Work out how many seniors there are.
(a)24
(b)15
(c)5
(d)25
9.Solve (3x + 2)/5 = (x + 4)/3
(a)x = 3.5
(b)x = 4.5
(c)x = 10
(d)x = 1
10.Three numbers are in the ratio 1:2:3. The three numbers add up to 72. Work out the largest of the three numbers.
(a)36
(b)12
(c)216
(d)24
11.A solid cube has a volume of 8 cm³. Work out the length of one edge of the cube.
(a)4 cm
(b)2 cm
(c)2.83 cm
(d)8 cm
12.A company's profit this year is 130% of last year's profit. Last year's profit was £40,000. Work out this year's profit.
(a)£12,000
(b)£52,000
(c)£5,200
(d)£40,130
13.A rectangular garden has its length and width in the ratio 5:3. Given that the perimeter of the garden is 64 m, work out the width of the garden.
(a)8 m
(b)24 m
(c)12 m
(d)20 m
14.The ratio of Josh's savings to Mia's savings is 4:7. Mia has £39 more than Josh. Work out Josh's savings.
(a)£39
(b)£52
(c)£91
(d)£13
15.Three friends share a raffle prize of £360 in the ratio 2:3:4. Work out the share of the friend whose part of the ratio is 3.
(a)£160
(b)£40
(c)£80
(d)£120
16.Solve 6x − 5 = 3x + 13.
(a)18
(b)2
(c)2.67
(d)6
17.A regular polygon has an exterior angle of 45°. Work out the number of sides of the polygon.
(a)4
(b)45
(c)8
(d)315
18.A padlock code is formed by arranging three different digits chosen from 2, 3, 4 and 5, with no digit repeated. Work out how many different three-digit codes can be made.
(a)64
(b)12
(c)6
(d)24
19.Work out the difference between 45% of 70 and 35% of 80.
(a)11.5
(b)3.5
(c)59.5
(d)10
20.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%
21.A rectangular photograph has an area of 96 cm². One of its sides is 8 cm long. Work out the length of the other side.
(a)40 cm
(b)12 cm
(c)88 cm
(d)768 cm
22.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
23.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%
24.The numbers 2, 4, 6, 8, 10 and 12 have a mean of 7 and a median of 7. The value 100 is now added to the list. Which measure is changed more by adding 100, and why?
(a)The median, because the median always jumps when the count of values changes from even to odd.
(b)The mean, because adding 100 to the list raises the mean by 100, from 7 up to 107.
(c)The mean, because every value counts towards it, so 100 pulls it from 7 up to about 20.3.
(d)The median, because 100 becomes the largest value, so the middle value moves from 7 to 12.
25.The mean of the four numbers 10, 15, 20 and x is 18. Work out the value of x.
(a)27
(b)72
(c)45
(d)18

What is on this worksheet?

The sheet holds 25 questions drawn from the MathsUK bank — the content areas covered: Ratio, proportion and rates of change, Geometry and measures, Algebra, Statistics, Probability (statements R5, R9, G16, G3, A17, S4, P7). It is pitched at GCSE Foundation and takes about 40 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 25 questions before checking — about 40 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 25 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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