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.£120 is shared between three cousins in the ratio 3:4:5. Work out the largest share.
- 2.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.
- 3.A rectangular tile measures 4.5 cm by 6 cm. Work out the area of the tile.
- 4.A parallelogram has a base of 9 cm and a perpendicular height of 6 cm. Work out the area of the parallelogram.
- 5.A red fair dice and a blue fair dice are rolled together. Every outcome is listed as an ordered pair, red score then blue score. Work out the probability that the red score is less than the blue score.
- 6.Amelia's mean mark over four tests is 29. Her first three marks are 31, 26 and 26. Work out her fourth mark.
- 7.Three angles lie on a straight line. They measure 38°, 95° and x°. Work out the value of x.
- 8.The equation 3(2x − 1) = 4x + 9 is rearranged by expanding the brackets. Which of these is the correctly expanded equation?
- 9.Jack rolls two ordinary fair dice and adds the two scores together. Work out the probability that the total is 6.
- 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.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.
- 12.A square tile has sides of length 6 cm. Work out the area of the tile.
- 13.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.
- 14.Solve 3x − 1 = 8
- 15.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.
- 16.A sofa costs £800. Its price is increased by 25%. Work out the new price of the sofa.
- 17.Kwame flips a fair coin three times and writes down what it lands on each time. Work out the probability that it lands on heads all three times.
- 18.Seven pupils were asked how many books they had read last month. Their answers were 3, 5, 5, 7, 8, 5, 3. Write down the mode.
- 19.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.
- 20.A rectangular bookmark measures 2 cm by 25 cm. Work out the area of the bookmark.
- 21.To solve 6x − 4 = 2x + 20, Yusuf's first step is to subtract 2x from both sides. Work out what equation this gives.
- 22.Solve 6x + 4 = 28
- 23.Two ordinary fair dice are rolled. Work out the probability that both dice show the same score.
- 24.The price of a jacket increases by 50% and then decreases by 50%. Describe the overall change from the original price.
- 25.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.
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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