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 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
2.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.
3.A fair coin is flipped and a fair three-sided spinner, labelled X, Y and Z, is spun. Every outcome is listed as a pair, such as (H, X). Work out the probability that the outcome is a head and Z.
(a)1/2
(b)1/6
(c)1/3
(d)1/5
4.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°
5.Two ordinary fair dice are rolled. Work out the probability that the difference between the two scores is 1.
(a)1/4
(b)1/6
(c)5/36
(d)5/18
6.Solve 6x + 4 = 28
(a)x = 4
(b)x = 144
(c)x = 24
(d)x = 18
7.Two fair four-sided dice, numbered 1 to 4, are rolled and the two scores are added together. Work out the probability that the total is 5.
(a)1/16
(b)1/4
(c)1/8
(d)3/16
8.A charity fun run raises money through entry fees and donations. Entry fees raise £1,260, which is 60% of the total amount raised. Work out how much money was raised through donations.
(a)£504
(b)£1,890
(c)£840
(d)£2,100
9.Solve 4(x − 3) = 2x + 6.
(a)4.5
(b)−3
(c)3
(d)9
10.At a school fête, a stall invites visitors to spin a fair spinner with 8 equal sections numbered 1 to 8, and separately toss a fair coin. A visitor wins a small prize only if the spinner lands on a multiple of 3 and the coin lands on heads. Work out the probability that a visitor wins a prize, giving your answer as a fraction in its simplest form.
(a)1/2
(b)1/16
(c)1/4
(d)1/8
11.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
12.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
13.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
14.2.4 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
15.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
16.Spinner P and Spinner Q are each fair and have 5 equal sections, numbered 1 to 5. Both spinners are spun once, and every outcome is listed as an ordered pair, Spinner P then Spinner Q, such as (2, 4). Work out how many of the outcomes have the score on Spinner P less than the score on Spinner Q.
(a)4
(b)10
(c)15
(d)20
17.Spinner E has 4 equal sections, numbered 1 to 4. Spinner F has 6 equal sections, numbered 1 to 6. Both spinners are spun once. Work out the probability of getting at least one 3.
(a)3/8
(b)1/4
(c)5/12
(d)5/8
18.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
19.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
20.Solve 3(2x − 1) = 27
(a)4
(b)5
(c)4.5
(d)4 2/3
21.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
22.A parallelogram has a base of 4 cm and a perpendicular height of 17 cm. Work out the area of the parallelogram.
(a)42 cm
(b)21 cm
(c)34 cm²
(d)68 cm²
23.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
24.Solve (2x + 1)/3 = 5
(a)7
(b)14
(c)8
(d)2
25.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

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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