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.A company's profit this year is 130% of last year's profit. Last year's profit was £40,000. Work out this year's profit.
- 2.Two straight lines cross at a point. Which statement about a pair of vertically opposite angles is always true?
- 3.Solve 4(x − 3) = 2x + 6.
- 4.A straight line crosses two parallel lines. An angle of 65° is formed at one crossing. At the other crossing, the angle that lies between the two parallel lines on the opposite side of the crossing line is also 65°. Write down the angle fact that explains why these two angles are equal.
- 5.A cylinder has a radius of 3 cm and a height of 10 cm. Using π = 3.14, work out the volume of the cylinder. Give your answer to the nearest whole number of cubic centimetres.
- 6.A square tile has sides of length 6 cm. Work out the area of the tile.
- 7.A trapezium has parallel sides of 5 cm and 11 cm, and a perpendicular height of 4 cm. Work out the area of the trapezium.
- 8.Three angles lie on a straight line. They measure 38°, 95° and x°. Work out the value of x.
- 9.To solve 6x − 4 = 2x + 20, Yusuf's first step is to subtract 2x from both sides. Work out what equation this gives.
- 10.Two ordinary fair dice are rolled. Work out the probability that the difference between the two scores is 1.
- 11.A cylinder has a radius of 3 cm and a height of 10 cm. Using π = 3.14, work out the volume of the cylinder.
- 12.Noah says that y = 3 is the solution of the equation y + 10 = 12. Noah is wrong. Work out the correct value of y.
- 13.A shop sold seven pairs of shoes in these sizes: 4, 4, 5, 6, 6, 6, 9. Write down the modal size.
- 14.Solve 3(2x − 1) = 27
- 15.Which of these describes an obtuse angle?
- 16.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.
- 17.The midday temperature in Leeds was recorded on each day of one week: 22 °C, 24 °C, 23 °C, 25 °C, 26 °C, 21 °C, 24 °C. Work out the mean midday temperature, giving your answer to 2 decimal places.
- 18.Two classes sat the same test. The 30 pupils in Class A had a mean mark of 72. The 20 pupils in Class B had a mean mark of 82. Work out the mean mark of all 50 pupils.
- 19.Solve x − 4 = −9
- 20.Solve x/4 + 1 = 3
- 21.Four books have 120, 200, 160 and 80 pages. Work out the mean number of pages.
- 22.A solid cube has a volume of 8 cm³. Work out the length of one edge of the cube.
- 23.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.
- 24.Work out the median of these six numbers: 13, 21, 22, 36, 37, 47
- 25.In a board game Mia moves forward by the total of two ordinary fair dice. Work out the probability that her total is 7. Give your answer as a fraction in its simplest form.
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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