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.Two angles are supplementary. One of them is twice the size of the other. Work out the size of the smaller angle.
(a)30
(b)120
(c)90
(d)60
2.Four angles meet at a point. Three of them measure 82°, 105° and 96°. Work out the size of the fourth angle.
(a)159
(b)283
(c)182
(d)77
3.The mean of 5 numbers is 8. Work out the total of the 5 numbers.
(a)40
(b)1.6
(c)13
(d)8
4.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
5.The masses of eight school bags, in kilograms, are 3, 4, 4, 5, 6, 7, 8 and 11. Work out the median mass.
(a)5 kg
(b)5.5 kg
(c)8 kg
(d)4 kg
6.A square tile has sides of length 6 cm. Work out the area of the tile.
(a)18 cm²
(b)12 cm
(c)36 cm²
(d)24 cm
7.Jack rolls two ordinary fair dice and adds the two scores together. Work out the probability that the total is 6.
(a)5/36
(b)5/12
(c)4/36
(d)1/11
8.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°
9.In a spelling test the 20 pupils in Group A had a mean mark of 80, and the 30 pupils in Group B had a mean mark of 70. Work out the mean mark of all 50 pupils.
(a)75 marks
(b)74 marks
(c)76 marks
(d)150 marks
10.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
11.A raised garden bed is a prism whose cross-section is a triangle with a base of 1.2 m and a perpendicular height of 0.8 m. The bed is 3 m long. Work out the volume of soil needed to fill it, in m³.
(a)3.6 m³
(b)2.88 m³
(c)1.44 m³
(d)0.48 m³
12.Order these three values from smallest to largest: 3/8, 0.43, 41%.
(a)3/8, 41%, 0.43
(b)0.43, 41%, 3/8
(c)3/8, 0.43, 41%
(d)41%, 0.43, 3/8
13.Seven pupils were asked how many books they had read last month. Their answers were 3, 5, 5, 7, 8, 5, 3. Write down the mode.
(a)7
(b)8
(c)5
(d)3
14.After a 20% discount, a jacket costs £48. Work out the original price of the jacket.
(a)£40
(b)£60
(c)£57.60
(d)£38.40
15.Solve 6x − 5 = 3x + 13.
(a)18
(b)2
(c)2.67
(d)6
16.Angle ABC is 130°. The line BF divides angle ABC into two equal parts. Work out the size of angle FBC.
(a)65°
(b)32.5°
(c)50°
(d)130°
17.Divide 84 in the ratio 3:4. Work out the smaller share.
(a)42
(b)48
(c)36
(d)28
18.In triangle ABC, angle A is 2x°, angle B is 3x° and angle C is 4x°. Work out the size of angle B.
(a)60°
(b)20°
(c)120°
(d)80°
19.A straight line crosses a pair of parallel lines. One of the co-interior (allied) angles is 118°. Work out the size of the other co-interior angle.
(a)242
(b)62
(c)118
(d)28
20.A raffle has two independent draws. In the first, a winning ticket is picked at random from 5 red tickets and 3 blue tickets. In the second, a winning number is picked using a fair spinner with 4 equal sections, numbered 1 to 4. Work out the probability that the first winning ticket is blue and the second winning number is greater than 2.
(a)5/16
(b)1/2
(c)3/8
(d)3/16
21.Priya says that x = 6 is the solution of the equation 4x + 8 = 24. Priya is wrong. Work out the correct value of x.
(a)12
(b)4
(c)8
(d)16
22.Work out 25% of 200.
(a)50
(b)100
(c)25
(d)800
23.A wooden cube has edges of length 4 cm. Work out the total surface area of the cube.
(a)96 cm²
(b)24 cm²
(c)16 cm²
(d)64 cm³
24.A parallelogram has a base of 9 cm and a perpendicular height of 6 cm. Work out the area of the parallelogram.
(a)30 cm²
(b)54 cm²
(c)15 cm²
(d)27 cm²
25.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%

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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