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.Which of these equations is equivalent to 5x − 2 = 3x + 8?
(a)8x = 6
(b)2x = 6
(c)2x = −10
(d)2x = 10
2.Solve 6x + 4 = 28
(a)x = 4
(b)x = 144
(c)x = 24
(d)x = 18
3.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°
4.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
5.Solve x/4 + 1 = 3
(a)x = 16
(b)x = 8
(c)x = 0.5
(d)x = 2
6.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
7.Solve 2x + 7 = x + 13
(a)x = 2
(b)x = 20
(c)x = −6
(d)x = 6
8.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
9.Four books have 120, 200, 160 and 80 pages. Work out the mean number of pages.
(a)120
(b)560
(c)140
(d)280
10.Two ordinary fair dice are rolled and the two scores are added together. Work out the probability that the total is a prime number.
(a)13/36
(b)19/36
(c)7/18
(d)5/12
11.Harry counted the coins he found on each of six days: 5, 7, 8, 9, 11, 30. Write down the outlier.
(a)30
(b)8.5
(c)11
(d)5
12.A garden flower bed is in the shape of a trapezium. Its two parallel edges are 3.5 m and 6.5 m long, and the perpendicular distance between them is 4 m. Bedding plants cost £2.50 per square metre to cover the bed. Work out the total cost of the bedding plants.
(a)£100
(b)£65
(c)£35
(d)£50
13.Two ordinary fair dice are rolled and the two scores are multiplied together. Work out the probability that the product is odd.
(a)3/4
(b)1/2
(c)1/12
(d)1/4
14.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
15.A charity shop and a school share collection-box money in the ratio 5 : 8. The charity shop receives £47.50. Work out how much the school receives.
(a)£29.69
(b)£76.00
(c)£57.00
(d)£123.50
16.Which of these describes an obtuse angle?
(a)An angle between 180° and 360°
(b)An angle between 90° and 180°
(c)An angle of exactly 90°
(d)An angle between 0° and 90°
17.A textbook is reduced from £60 to £45. Work out the percentage reduction.
(a)33%
(b)15%
(c)75%
(d)25%
18.£120 is shared between three cousins in the ratio 3:4:5. Work out the largest share.
(a)£10
(b)£50
(c)£30
(d)£40
19.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
20.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
21.A sum of £150 is divided between Ben and Chloe in the ratio 2:3. Work out Chloe's share.
(a)£60
(b)£75
(c)£90
(d)£30
22.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.
23.Noah wrote down the numbers 9, 3, 7, 1, 5 and said, “The median is 7, because 7 is in the middle of my list.” Is Noah right? Give a reason for your answer.
(a)Yes — the mean of the five numbers is 7, so the median is 7 as well.
(b)No — in order the numbers are 1, 3, 5, 7, 9, so the median is 5.
(c)No — in order the numbers are 1, 3, 5, 7, 9, so the median is 3.
(d)Yes — 7 is the third of the five numbers he wrote, so it is the median.
24.Work out the difference between 45% of 70 and 35% of 80.
(a)11.5
(b)3.5
(c)59.5
(d)10
25.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°

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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