20 questions on the grade 4-5 content both tiers share — a fair test of whether a Higher entry is the right call.

⚖️ Foundation to Higher crossover check

Maths · GCSE Foundation · 20 questions · ~35 min

MathsUKwww.geekhero.co.uk

The tier decision is made by the school, but it is made on evidence, and this sheet is designed to produce some. Every question on it sits in the crossover band — the grade 4 to 5 content that appears on both the Foundation and the Higher papers: multiplying out and factorising, solving linear equations and inequalities, straight-line graphs and gradients, ratio and proportion, Pythagoras' theorem, angle reasoning, and averages from a frequency table. A student who works through this comfortably has the foundation a Higher entry needs. A student who is guessing on half of it will almost certainly come away with a better grade from a Foundation paper they can attempt in full. Useful for a parents' evening conversation, and for a department deciding entries.

1.A right-angled triangle has angles of 90°, 40° and x°. Work out the value of x.
(a)45
(b)130
(c)90
(d)50
2.The top of a clock tower is 25 m above level ground. Oliver stands on the ground 25 m from the foot of the tower. Work out the angle of elevation of the top of the tower from the point where Oliver stands.
(a)50°
(b)1°
(c)45°
(d)90°
3.Write 1/5 as a percentage.
(a)20%
(b)5%
(c)50%
(d)25%
4.A water butt holds 200 litres and is being drained at a steady 8 litres per minute. Write down the function for the amount of water y, in litres, left after x minutes.
(a)y = 200x − 8
(b)y = −8x − 200
(c)y = 200 − 8x
(d)y = 8x + 200
5.Factorise fully 56x − 24
(a)8(7x − 16)
(b)8(56x − 3)
(c)8(7x + 3)
(d)8(7x − 3)
6.In a right-angled triangle one of the other two angles is 45°, and the side opposite that 45° angle is 7 cm. Work out the length of the hypotenuse. Give your answer to 1 decimal place.
(a)7.0 cm
(b)14.0 cm
(c)9.9 cm
(d)5.0 cm
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.
(a)121%
(b)11%
(c)21%
(d)20%
8.A regular polygon has 12 sides. Work out the size of one exterior angle of the polygon.
(a)30°
(b)150°
(c)15°
(d)36°
9.Two of the angles in a triangle are 50° and 70°. Work out the size of the third angle.
(a)60°
(b)240°
(c)110°
(d)120°
10.The price of a share falls by 10% on Monday and then rises by 10% on Tuesday. Work out the overall percentage change from Monday's starting price.
(a)0%
(b)−1%
(c)−2%
(d)+1%
11.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.
(a)3800 marks
(b)78 marks
(c)76 marks
(d)77 marks
12.In a right-angled triangle, the two shorter sides are a and b, and the hypotenuse is c. Write down the correct statement of Pythagoras' theorem.
(a)a² − b² = c²
(b)a² + b² = c
(c)a + b = c
(d)a² + b² = c²
13.Four books have 120, 200, 160 and 80 pages. Work out the mean number of pages.
(a)120
(b)560
(c)140
(d)280
14.Solve 5x − 9 = 16
(a)1.4
(b)5
(c)25
(d)3.2
15.Five pupils spent these numbers of minutes on their homework: 50, 65, 55, 90, 60. Work out the median time.
(a)64 minutes
(b)40 minutes
(c)60 minutes
(d)70 minutes
16.A shop sold seven pairs of shoes in these sizes: 4, 4, 5, 6, 6, 6, 9. Write down the modal size.
(a)3
(b)9
(c)4
(d)6
17.At an animal shelter, the ratio of cats to dogs is 2:5. There are 18 more dogs than cats. Work out the number of cats.
(a)6
(b)12
(c)9
(d)30
18.Solve the inequality 3x + 6 ≤ 0.
(a)x ≤ 2
(b)x ≤ −2
(c)x ≥ −2
(d)x ≤ −18
19.The mean of the numbers x, 20 and 30 is equal to the mean of the numbers 15 and 25. Work out the value of x.
(a)20
(b)−10
(c)10
(d)70
20.The ratio of Josh's savings to Mia's savings is 4:7. Mia has £39 more than Josh. Work out Josh's savings.
(a)£39
(b)£52
(c)£91
(d)£13

What is on this worksheet?

The sheet holds 20 questions drawn from the MathsUK bank — the content areas covered: Algebra, Ratio, proportion and rates of change, Geometry and measures, Statistics (statements A4, A17, A22, A9, R5, R9, G20, G3, S4). It is pitched at GCSE Foundation and takes about 35 minutes to work through in full. It works as a class handout, a homework, or a warm-up before a test.

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 20 questions before checking — about 35 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 20 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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