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.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
2.Solve (2x + 1)/3 = 5
(a)7
(b)14
(c)8
(d)2
3.In triangle ABC the base BC is 10 cm long and the sloping side AB is 13 cm long. The perpendicular height from A down to BC is 12 cm. Work out the area of triangle ABC.
(a)65 cm²
(b)60 cm²
(c)120 cm²
(d)78 cm²
4.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
5.In a science lesson Priya has 10 litres of a solution that is 30% salt. She adds water to make a solution that is 20% salt. Work out how many litres of water she adds.
(a)15 litres
(b)5 litres
(c)3 litres
(d)2 litres
6.To solve 6x − 4 = 2x + 20, Yusuf's first step is to subtract 2x from both sides. Work out what equation this gives.
(a)4x = 20
(b)4x − 4 = 20
(c)4x − 4 = 2x + 20
(d)8x − 4 = 20
7.A trapezium has an area of 45 cm², a perpendicular height of 5 cm, and one parallel side of length 10 cm. Work out the length of the other parallel side.
(a)18 cm
(b)28 cm
(c)8 cm
(d)4 cm
8.A netball team scored 50, 83 and 68 points in three matches. Work out the mean number of points scored.
(a)68
(b)33
(c)67
(d)100.5
9.Noah says that y = 3 is the solution of the equation y + 10 = 12. Noah is wrong. Work out the correct value of y.
(a)y = 22
(b)y = −2
(c)y = 2
(d)y = 12
10.Solve 3x − 5 = 4.
(a)9
(b)−1/3
(c)6
(d)3
11.A triangular prism has a cross-section that is a triangle with a base of 3.5 cm and a perpendicular height of 4 cm. The prism is 10 cm long. Work out the volume of the prism.
(a)7 cm³
(b)70 cm³
(c)35 cm³
(d)140 cm³
12.A ramp's sloped surface crosses two horizontal parallel rails. At the top rail, the angle between the ramp and the rail on the right of the ramp is (3x + 10)°. At the bottom rail, the angle between the ramp and the rail on the left of the ramp is (5x − 30)°. Work out the value of x.
(a)−10
(b)47.5
(c)25
(d)20
13.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
14.Solve 5x + 2 = 17.
(a)3
(b)3.8
(c)15
(d)1.4
15.Solve 6x − 5 = 3x + 13.
(a)18
(b)2
(c)2.67
(d)6
16.A rectangular bookmark measures 2 cm by 25 cm. Work out the area of the bookmark.
(a)54 cm
(b)50 cm²
(c)25 cm²
(d)27 cm
17.A plumber charges a £35 call-out fee plus £20 for each hour worked, h. On a certain job the total charge was £115. Work out how many hours the plumber worked.
(a)4
(b)7.5
(c)5.75
(d)2.71
18.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
19.Solve 5(x + 3) = 40
(a)x = 8
(b)x = 11
(c)x = 7.4
(d)x = 5
20.At an animal shelter, the ratio of cats to dogs is 2:5. There are 18 more dogs than cats. Work out the number of cats.
(a)6
(b)12
(c)9
(d)30
21.A regular polygon has an interior angle of 156°. Work out the number of sides of the polygon.
(a)17
(b)24
(c)15
(d)7.5
22.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
23.At a point on a straight line, two angles are formed. One of them is 63°. Work out the size of the other angle.
(a)297
(b)117
(c)27
(d)63
24.The mean of three numbers is 50. A fourth number, 100, is added to the set. Work out the mean of the four numbers.
(a)62.5
(b)75
(c)37.5
(d)50
25.Grace asked 12 children how many brothers and sisters they have. Her results, in order, were 0, 0, 1, 1, 1, 1, 2, 2, 3, 3, 4, 6. Work out the median number of brothers and sisters.
(a)1.5
(b)1
(c)6
(d)2

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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