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 fair coin is flipped and a fair three-sided spinner, labelled X, Y and Z, is spun. Every outcome is listed as a pair, such as (H, X). Work out the probability that the outcome is a head and Z.
- 2.There are 400 students at a school. 25% of them have a brother, 40% have a sister and 15% have both a brother and a sister. Work out how many of the students have neither a brother nor a sister.
- 3.A shop sold seven pairs of shoes in these sizes: 4, 4, 5, 6, 6, 6, 9. Write down the modal size.
- 4.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.
- 5.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.
- 6.Five pupils spent these numbers of minutes on their homework: 50, 65, 55, 90, 60. Work out the median time.
- 7.A raffle has two independent draws. In the first, a winning ticket is picked at random from 5 red tickets and 3 blue tickets. In the second, a winning number is picked using a fair spinner with 4 equal sections, numbered 1 to 4. Work out the probability that the first winning ticket is blue and the second winning number is greater than 2.
- 8.£120 is shared between three cousins in the ratio 3:4:5. Work out the largest share.
- 9.Bag A contains 3 red balls and 2 blue balls. Bag B contains 1 red ball and 3 blue balls. One ball is taken at random from each bag. Work out the probability that both balls are red.
- 10.Two straight lines cross at a point. Which statement about a pair of vertically opposite angles is always true?
- 11.Work out the median of these five numbers: 2, 4, 7, 12, 26
- 12.Amelia's mean mark over four tests is 29. Her first three marks are 31, 26 and 26. Work out her fourth mark.
- 13.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.
- 14.Priya invests £750 in a savings account that pays simple interest. After 3 years, the account contains £840. Work out the annual rate of simple interest.
- 15.Work out the difference between 45% of 70 and 35% of 80.
- 16.A small pack contains 5 cards, numbered 1 to 5. One card is drawn at random from the pack, and a fair coin is flipped. Every outcome is listed as a pair, such as (3, H). Work out how many equally likely outcomes there are in total.
- 17.Noah says that y = 3 is the solution of the equation y + 10 = 12. Noah is wrong. Work out the correct value of y.
- 18.Solve 4x − (2x − 6) = 18
- 19.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.
- 20.The number of members of a running club increases from 45 to 54. Work out the percentage increase.
- 21.Solve 2(x + 3) = 10
- 22.The equation 3(2x − 1) = 4x + 9 is rearranged by expanding the brackets. Which of these is the correctly expanded equation?
- 23.Two angles are complementary. One of them is 35°. Work out the size of the other angle.
- 24.In a science lesson Priya has 10 litres of a solution that is 30% salt. She adds water to make a solution that is 20% salt. Work out how many litres of water she adds.
- 25.Solve 2x − 2 = 2
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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