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 straight transversal crosses a pair of parallel lines. At one crossing point, the angle between the transversal and a parallel line is 118°. Work out the size of the co-interior (allied) angle at the other crossing point.
(a)59°
(b)118°
(c)62°
(d)236°
2.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
3.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
4.Two of the angles in a triangle are 50° and 70°. Work out the size of the third angle.
(a)60°
(b)240°
(c)110°
(d)120°
5.The number of members of a running club increases from 45 to 54. Work out the percentage increase.
(a)9%
(b)120%
(c)20%
(d)16.7%
6.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
7.2.4 kg of cheese costs £36. Work out the cost of 1.5 kg of the same cheese.
(a)£15
(b)£57.60
(c)£22.50
(d)£54
8.A fruit punch is made from orange juice, pineapple juice and lemonade in the ratio 5:3:2. A jug holds 3.5 litres of punch in total. Work out the volume of pineapple juice needed.
(a)1.75 litres
(b)0.35 litres
(c)1.05 litres
(d)0.7 litres
9.Two straight lines cross at a point. Which statement about a pair of vertically opposite angles is always true?
(a)They are always equal to 90° each
(b)They always add up to 360°
(c)They always add up to 180°
(d)They are always equal to each other
10.Solve 2x + 1 = 9
(a)x = 8
(b)x = 16
(c)x = 4
(d)x = 5
11.A parallelogram has an area of 84 cm² and a base of 12 cm. Work out the perpendicular height of the parallelogram.
(a)0.14 cm
(b)1008 cm
(c)3.5 cm
(d)7 cm
12.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
13.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
14.Write 0.25 as a percentage.
(a)2.5%
(b)0.25%
(c)250%
(d)25%
15.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
16.Solve 2x − 2 = 2
(a)x = 2
(b)x = 8
(c)x = 0
(d)x = 4
17.A charity collects donations from adults and children in the ratio 5:2. Altogether, £238 is collected. Work out how much more the adults donate than the children.
(a)£102
(b)£68
(c)£136
(d)£170
18.A cylinder has a radius of 3 cm and a height of 10 cm. Using π = 3.14, work out the volume of the cylinder. Give your answer to the nearest whole number of cubic centimetres.
(a)188 cm³
(b)1130 cm³
(c)94 cm³
(d)283 cm³
19.Three angles lie on a straight line. They measure 38°, 95° and x°. Work out the value of x.
(a)133
(b)47
(c)227
(d)142
20.Work out the difference between 45% of 70 and 35% of 80.
(a)11.5
(b)3.5
(c)59.5
(d)10
21.Solve 5x − 9 = 16
(a)1.4
(b)5
(c)25
(d)3.2
22.A small pack contains 5 cards, numbered 1 to 5. One card is drawn at random from the pack, and a fair coin is flipped. Every outcome is listed as a pair, such as (3, H). Work out how many equally likely outcomes there are in total.
(a)5
(b)20
(c)10
(d)7
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.A garden water trough is a prism whose cross-section is a right-angled triangle with base 40 cm and height 30 cm. The trough is 120 cm long. Work out the volume of water needed to fill the trough completely.
(a)36 000 cm³
(b)72 000 cm³
(c)144 000 cm³
(d)720 cm³
25.Solve (2x + 1)/3 = 5
(a)7
(b)14
(c)8
(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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