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.Write 1/5 as a percentage.
(a)20%
(b)5%
(c)50%
(d)25%
2.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
3.Grace asked 12 children how many brothers and sisters they have. Her results, in order, were 0, 0, 1, 1, 1, 1, 2, 2, 3, 3, 4, 6. Work out the median number of brothers and sisters.
(a)1.5
(b)1
(c)6
(d)2
4.Simplify 5x + 3y − 2x + y.
(a)3x + 2y
(b)7x + 4y
(c)3x + 4y
(d)6xy
5.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
6.The price of a cycling helmet rises from £80 to £116. Work out the percentage increase.
(a)45%
(b)145%
(c)36%
(d)31%
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.Factorise x² − 3x − 10.
(a)(x − 10)(x + 1)
(b)(x − 5)(x + 2)
(c)(x + 5)(x − 2)
(d)(x − 5)(x − 2)
9.Simplify 2a + 3b − a + 2b − b
(a)a + 4b
(b)a + 6b
(c)5ab
(d)3a + 4b
10.Solve (3x + 2)/5 = (x + 4)/3
(a)x = 3.5
(b)x = 4.5
(c)x = 10
(d)x = 1
11.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
12.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
13.A regular polygon has an interior angle of 156°. Work out the number of sides of the polygon.
(a)17
(b)24
(c)15
(d)7.5
14.A necklace is made using gold beads and silver beads in the ratio 7:3. There are 40 more gold beads than silver beads. Work out the total number of beads in the necklace.
(a)100
(b)40
(c)70
(d)30
15.Three friends share a raffle prize of £360 in the ratio 2:3:4. Work out the share of the friend whose part of the ratio is 3.
(a)£160
(b)£40
(c)£80
(d)£120
16.Harry counted the coins he found on each of six days: 5, 7, 8, 9, 11, 30. Write down the outlier.
(a)30
(b)8.5
(c)11
(d)5
17.Simplify 5a/6 − a/3
(a)7a/6
(b)2a/3
(c)4a/3
(d)a/2
18.Work out the median of these six numbers: 13, 21, 22, 36, 37, 47
(a)22
(b)36
(c)34
(d)29
19.In a right-angled triangle, the side opposite angle θ is 6 cm and the hypotenuse is 10 cm. Work out the size of angle θ. Give your answer correct to 1 decimal place.
(a)31.0°
(b)36.8°
(c)53.1°
(d)36.9°
20.At a youth club the ratio of juniors to seniors is 3:5. There are 40 members altogether. Work out how many seniors there are.
(a)24
(b)15
(c)5
(d)25

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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