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.Solve x/4 + 1 = 3
- 2.A textbook is reduced from £60 to £45. Work out the percentage reduction.
- 3.Work out the median of these five numbers: 2, 4, 7, 12, 26
- 4.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.
- 5.A cylinder has a volume of 942 cm³ and a height of 12 cm. Using π = 3.14, work out the radius of the cylinder.
- 6.The ratio of Josh's savings to Mia's savings is 4:7. Mia has £39 more than Josh. Work out Josh's savings.
- 7.A ribbon of length 90 cm is cut into two pieces in the ratio 4:5. Work out the length of the shorter piece.
- 8.Solve 2x − 2 = 2
- 9.Two angles are supplementary. One of them is twice the size of the other. Work out the size of the smaller angle.
- 10.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.
- 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.
- 12.A regular hexagon is divided into six identical triangles by joining its centre to each of the six vertices. Work out the size of the angle of one of these triangles at the centre of the hexagon.
- 13.Spinner C has 3 equal sections, numbered 2, 3 and 5. Spinner D has 6 equal sections, numbered 1 to 6. Both spinners are spun once, and the two numbers are multiplied together. Work out the probability that the product is a multiple of 5.
- 14.Four books have 120, 200, 160 and 80 pages. Work out the mean number of pages.
- 15.In triangle ABC the angle at A and the angle at C are equal. The side AB is extended beyond B, and the exterior angle formed at B measures 98°. Work out the size of the angle at A.
- 16.Solve 5(x + 3) = 40
- 17.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.
- 18.Three numbers are in the ratio 1:2:3. The three numbers add up to 72. Work out the largest of the three numbers.
- 19.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.
- 20.In a test, Amelia answered 18 of the 24 questions correctly. Work out the percentage of the questions she answered correctly.
- 21.Solve x − 4 = −9
- 22.A laptop priced at £520 is first increased by 15%, and then the new price is decreased by 20%. Work out the final price of the laptop.
- 23.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.
- 24.A car is bought for £17,500. Its value decreases by 12% in the first year, and by a further 10% of its reduced value in the second year. Work out the value of the car at the end of the second year, giving your answer to the nearest pound.
- 25.An amount of money is shared in the ratio 1:2:3. The largest share is £90 more than the smallest share. Work out the total amount that was shared.
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.
Similar worksheets worth a look
- ✏️ Paper 1 non-calculator warm-up — Foundation · 20 questions · ~25 min
- ⚖️ Foundation to Higher crossover check · 20 questions · ~35 min
- ⚗️ Ratio and proportion mastery — Higher · 24 questions · ~45 min
- 💷 Percentages and compound interest · 22 questions · ~40 min