25 questions on the topics that decide a grade 4: percentages, ratio, area and perimeter, linear equations, averages and probability.

🎯 Grade 4 pass booster

Maths · GCSE Foundation · 25 questions · ~40 min

MathsUKwww.geekhero.co.uk

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 transversal crosses a pair of parallel lines. At one line, the angle is (5x + 4)°. The corresponding angle at the other line is (3x + 24)°. Work out the value of x.
(a)19
(b)10
(c)20
(d)14
2.The numbers 2, 4, 6, 8, 10 and 12 have a mean of 7 and a median of 7. The value 100 is now added to the list. Which measure is changed more by adding 100, and why?
(a)The median, because the median always jumps when the count of values changes from even to odd.
(b)The mean, because adding 100 to the list raises the mean by 100, from 7 up to 107.
(c)The mean, because every value counts towards it, so 100 pulls it from 7 up to about 20.3.
(d)The median, because 100 becomes the largest value, so the middle value moves from 7 to 12.
3.A conservatory has a roof panel shaped like a regular octagon. Work out the interior angle of the octagon, then use it to work out the size of the reflex angle at the same vertex, on the outside of the roof panel.
(a)225
(b)45
(c)315
(d)135
4.Solve 4(x − 3) = 2x + 6.
(a)4.5
(b)−3
(c)3
(d)9
5.A netball team scored 50, 83 and 68 points in three matches. Work out the mean number of points scored.
(a)68
(b)33
(c)67
(d)100.5
6.The perimeter of a square is 20 cm. Work out the area of the square.
(a)5 cm
(b)25 cm²
(c)100 cm²
(d)400 cm²
7.Solve 4x + 3 = 19
(a)3.75
(b)5.5
(c)4
(d)4.75
8.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.
(a)The means are equal, and Class B's marks are the more consistent because its range is smaller.
(b)Class A's mean mark is higher, and Class A's marks are also the more consistent.
(c)The means are equal, and Class A's marks are the more consistent because its range is larger.
(d)Class B's mean mark is higher, and its smaller range makes its marks the more consistent.
9.A rectangular bookmark measures 2 cm by 25 cm. Work out the area of the bookmark.
(a)54 cm
(b)50 cm²
(c)25 cm²
(d)27 cm
10.Solve 5x − 9 = 16
(a)1.4
(b)5
(c)25
(d)3.2
11.Solve (3x + 2)/5 = (x + 4)/3
(a)x = 3.5
(b)x = 4.5
(c)x = 10
(d)x = 1
12.Solve 3x − 1 = 8
(a)x = 9
(b)x = 6
(c)x = 27
(d)x = 3
13.Order these three values from smallest to largest: 3/8, 0.43, 41%.
(a)3/8, 41%, 0.43
(b)0.43, 41%, 3/8
(c)3/8, 0.43, 41%
(d)41%, 0.43, 3/8
14.Two fair four-sided dice, numbered 1 to 4, are rolled and the two scores are added together. Work out the probability that the total is 5.
(a)1/16
(b)1/4
(c)1/8
(d)3/16
15.In a test, Amelia answered 18 of the 24 questions correctly. Work out the percentage of the questions she answered correctly.
(a)75%
(b)133%
(c)25%
(d)18%
16.In a recipe the mass of chocolate to the mass of milk is in the ratio 1:4. Amelia uses 200 g of milk. Work out the mass of chocolate she needs.
(a)800 g
(b)250 g
(c)40 g
(d)50 g
17.The price of a jacket increases by 50% and then decreases by 50%. Describe the overall change from the original price.
(a)no change
(b)an increase of 25%
(c)a decrease of 25%
(d)a decrease of 50%
18.Spinner A is numbered 1 to 3 and Spinner B is numbered 1 to 5. Both spinners are spun once, and every outcome is listed as a pair, one number from each spinner. Work out how many equally likely outcomes there are in total.
(a)3
(b)25
(c)8
(d)15
19.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.
(a)15 litres
(b)5 litres
(c)3 litres
(d)2 litres
20.Grace rolls two ordinary fair dice at the same time and works out the total of the two scores. Work out the probability that the total is greater than 10.
(a)33/36
(b)4/36
(c)2/36
(d)3/36
21.A garden water trough is a prism whose cross-section is a right-angled triangle with base 40 cm and height 30 cm. The trough is 120 cm long. Work out the volume of water needed to fill the trough completely.
(a)36 000 cm³
(b)72 000 cm³
(c)144 000 cm³
(d)720 cm³
22.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.
(a)£12,000
(b)£52,000
(c)£5,200
(d)£40,130
23.Two ordinary fair dice are rolled and the two scores are multiplied together. Work out the probability that the product is odd.
(a)3/4
(b)1/2
(c)1/12
(d)1/4
24.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.
(a)125 g
(b)75 g
(c)25 g
(d)175 g
25.A box holds 80 chocolates. 75% of them are milk chocolates. Work out how many milk chocolates are in the box.
(a)55
(b)75
(c)20
(d)60

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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