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.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.
- 2.A rectangular tile measures 4.5 cm by 6 cm. Work out the area of the tile.
- 3.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.
- 4.A straight line crosses two parallel lines. One of the angles formed is (2x + 10)°, and the angle alternate to it is 74°. Work out the value of x.
- 5.A sum of £150 is divided between Ben and Chloe in the ratio 2:3. Work out Chloe's share.
- 6.The interior angles of a pentagon are 100°, 110°, 120°, x° and x°. Work out the size of each of the two angles marked x°.
- 7.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.
- 8.The masses of eight school bags, in kilograms, are 3, 4, 4, 5, 6, 7, 8 and 11. Work out the median mass.
- 9.A sofa costs £800. Its price is increased by 25%. Work out the new price of the sofa.
- 10.A raised garden bed is a prism whose cross-section is a triangle with a base of 1.2 m and a perpendicular height of 0.8 m. The bed is 3 m long. Work out the volume of soil needed to fill it, in m³.
- 11.A regular polygon has 12 sides. Work out the size of one exterior angle of the polygon.
- 12.Solve 7x − 5 = 3x + 11
- 13.£120 is shared between three cousins in the ratio 3:4:5. Work out the largest share.
- 14.Freya buys three items whose prices are in the ratio 2:3:5. Altogether she pays £400. Work out the price of the most expensive item.
- 15.Spinner A has 4 equal sections, numbered 1, 2, 3 and 4. Spinner B has 3 equal sections, coloured red, red and blue. Both spinners are spun once. Work out the probability of getting an even number on Spinner A and red on Spinner B.
- 16.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.
- 17.A fair four-sided dice, numbered 1 to 4, is rolled twice. Every outcome is listed as an ordered pair, first roll then second roll, such as (2, 3). Work out how many different outcomes are in the list.
- 18.A parallelogram has an area of 136 cm² and a base of 17 cm. Work out the perpendicular height of the parallelogram.
- 19.Two angles are supplementary. One of them is twice the size of the other. Work out the size of the smaller angle.
- 20.Jamal invests £600 in a savings account paying 3% simple interest per year. Work out the total amount in the account after 4 years.
- 21.Two ordinary fair dice are rolled. Work out the probability that both dice show the same score.
- 22.The price of a share falls by 10% on Monday and then rises by 10% on Tuesday. Work out the overall percentage change from Monday's starting price.
- 23.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.
- 24.At a point on a straight line, two angles are formed. One of them is 63°. Work out the size of the other angle.
- 25.An angle measures 108°. Write down the name given to an angle of this size.
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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