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.Solve (3x + 2)/5 = (x + 4)/3
(a)x = 3.5
(b)x = 4.5
(c)x = 10
(d)x = 1
2.Amelia is buying books. Each book costs £5 and she has at most £30 to spend. Write down an inequality for x, the number of books she can buy.
(a)5x ≥ 30
(b)x + 5 ≤ 30
(c)5x < 30
(d)5x ≤ 30
3.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.
(a)£2,400
(b)£2,000
(c)£3,200
(d)£6,000
4.£120 is shared between three cousins in the ratio 3:4:5. Work out the largest share.
(a)£10
(b)£50
(c)£30
(d)£40
5.Work out the equation of the straight line through the points (−2, 1) and (0, 7).
(a)y = −3x + 7
(b)y = 3x + 1
(c)y = 3x + 7
(d)y = (1/3)x + 7
6.Solve 3x + 14 = 8x − 6
(a)x = 15
(b)x = 2.5
(c)x = 4
(d)x = −1.6
7.Solve (2x + 1)/3 = 5
(a)7
(b)14
(c)8
(d)2
8.Work out 50% of 60.
(a)6
(b)3000
(c)120
(d)30
9.The solution set of x ≥ −1 is drawn on a number line. Which description of that number line is correct?
(a)An open circle at −1 with the arrow pointing right
(b)An open circle at −1 with the arrow pointing left
(c)A solid circle at −1 with the arrow pointing right
(d)A solid circle at −1 with the arrow pointing left
10.Harry will spend at most £150 on a party. The cake costs £60 and each helium balloon costs £3. Solve an inequality to find all the possible numbers of balloons, x, that he can buy.
(a)x ≥ 30
(b)x ≤ 50
(c)x ≤ 90
(d)x ≤ 30
11.The price of a cycling helmet rises from £80 to £116. Work out the percentage increase.
(a)45%
(b)145%
(c)36%
(d)31%
12.Expand and simplify (x − 3)²
(a)x² + 6x + 9
(b)x² − 9
(c)x² − 3x + 9
(d)x² − 6x + 9
13.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.
14.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
15.Solve the inequality 5x − 3 > 2x + 9.
(a)x > 4
(b)x > 2
(c)x < 4
(d)x > 36
16.A jug of squash is made by mixing water and syrup in the ratio 6:1. Nia wants to make 8.4 litres of squash. Work out how much syrup she needs, in litres.
(a)0.84
(b)1.4
(c)1.2
(d)7.2
17.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°
18.A flagpole is 12 m tall. Freya stands 9 m from the base of the flagpole on level ground. Work out the angle of elevation of the top of the flagpole from where Freya stands. Give your answer correct to 1 decimal place.
(a)41.4°
(b)53.1°
(c)48.6°
(d)36.9°
19.40% of a number is 12 more than 25% of the same number. Work out the number.
(a)48
(b)80
(c)15
(d)30
20.Simplify 2b − 1 + 2b − 4 + 2b
(a)6b − 5
(b)6b − 3
(c)6b + 5
(d)8b − 5

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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