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.Two ordinary fair dice are rolled. Work out the probability that the difference between the two scores is 1.
- 2.In triangle ABC, angle A is 2x°, angle B is 3x° and angle C is 4x°. Work out the size of angle B.
- 3.Write 3/4 as a percentage.
- 4.The number of members of a running club increases from 45 to 54. Work out the percentage increase.
- 5.A café sold 10 sandwiches on each of four days: 10, 10, 10, 10. Work out the range of the numbers sold.
- 6.Write 0.25 as a percentage.
- 7.The rent on a flat increases by 10% one year and by a further 10% the following year. Work out the overall percentage increase over the two years.
- 8.Three angles lie on a straight line. They measure 38°, 95° and x°. Work out the value of x.
- 9.In a test, Amelia answered 18 of the 24 questions correctly. Work out the percentage of the questions she answered correctly.
- 10.A sum of £150 is divided between Ben and Chloe in the ratio 2:3. Work out Chloe's share.
- 11.Solve x/4 + 1 = 3
- 12.£120 is shared between three cousins in the ratio 3:4:5. Work out the largest share.
- 13.Two ordinary fair dice are rolled and the two scores are added together. Work out the probability that the total is a prime number.
- 14.A regular polygon has 12 sides. Work out the size of one exterior angle of the polygon.
- 15.40% of a number is 12 more than 25% of the same number. Work out the number.
- 16.A chocolate bar is a prism. Its cross-section is a triangle with a base of 6 cm and a perpendicular height of 5 cm, and the bar is 12 cm long. Work out the volume of the bar.
- 17.The masses of eight school bags, in kilograms, are 3, 4, 4, 5, 6, 7, 8 and 11. Work out the median mass.
- 18.Solve 6x + 4 = 28
- 19.Order these three values from smallest to largest: 3/8, 0.43, 41%.
- 20.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.
- 21.To solve 5x − 4 = 2x + 8, Chloe's working is shown. Line 1: 5x − 4 = 2x + 8. Line 2: 3x − 4 = 8. Line 3: 3x = 4. Line 4: x = 4/3. Chloe has made a mistake in her working. Which line contains the mistake?
- 22.A straight transversal crosses a pair of parallel lines. At one crossing point, the angle between the transversal and a parallel line is 118°. Work out the size of the co-interior (allied) angle at the other crossing point.
- 23.A jug of squash is made by mixing water and syrup in the ratio 6:1. Nia wants to make 8.4 litres of squash. Work out how much syrup she needs, in litres.
- 24.A rectangular tile measures 4.5 cm by 6 cm. Work out the area of the tile.
- 25.The ratio of Josh's savings to Mia's savings is 4:7. Mia has £39 more than Josh. Work out Josh's savings.
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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