25 questions on the topics that decide a grade 4: percentages, ratio, area and perimeter, linear equations, averages and probability.
🎯 Grade 4 pass booster
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.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.
- 2.A metal alloy is made from copper and tin in the ratio 7:3. Work out the mass of tin in 250 g of the alloy.
- 3.Solve x − 4 = −9
- 4.A rectangular photograph has an area of 96 cm². One of its sides is 8 cm long. Work out the length of the other side.
- 5.Spinner A has 4 equal sections, numbered 1, 2, 3 and 4. Spinner B has 5 equal sections, numbered 1, 2, 3, 4 and 5. Both spinners are spun once, and the two numbers are multiplied together. Work out the probability that the product is 12.
- 6.Two angles are supplementary. One of them is twice the size of the other. Work out the size of the smaller angle.
- 7.A taxi company charges a £2.50 booking fee plus £1.80 per mile. A journey costs £15.10 in total. Work out the number of miles travelled.
- 8.A conservatory has a roof panel shaped like a regular octagon. Work out the interior angle of the octagon, then use it to work out the size of the reflex angle at the same vertex, on the outside of the roof panel.
- 9.After a 20% discount, a jacket costs £48. Work out the original price of the jacket.
- 10.A trapezium has parallel sides of 16 cm and 24 cm, and a perpendicular height of 7 cm. Work out the area of the trapezium.
- 11.A jug holds 3 litres of a drink that is 60% fruit juice. 1 litre of water is added to the jug. Work out the percentage of the new mixture that is fruit juice.
- 12.A wooden cube has edges of length 4 cm. Work out the total surface area of the cube.
- 13.£120 is shared between three cousins in the ratio 3:4:5. Work out the largest share.
- 14.Four books have 120, 200, 160 and 80 pages. Work out the mean number of pages.
- 15.Solve 6x + 4 = 28
- 16.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.
- 17.The price of a cycling helmet rises from £80 to £116. Work out the percentage increase.
- 18.Oliver flips three fair coins at the same time. Work out the probability that exactly two of the three coins land on heads.
- 19.Solve 2x + 1 = 9
- 20.Which of these describes an obtuse angle?
- 21.Two investors put money into a business in the ratio 3:5. The first investor puts in £1,200. Work out the total amount invested by both investors.
- 22.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.
- 23.In triangle ABC, angle A is 2x°, angle B is 3x° and angle C is 4x°. Work out the size of angle B.
- 24.A wooden block is a cuboid measuring 2 cm by 10 cm by 15 cm. Work out the volume of the block.
- 25.Freya is designing a triangular flower bed. Two of its corners have equal angles, and the angle at the third corner is 40°. Work out the size of one of the two equal corner angles.
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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