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.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
2.Solve 2x + 1 = 9
(a)x = 8
(b)x = 16
(c)x = 4
(d)x = 5
3.A sofa costs £800. Its price is increased by 25%. Work out the new price of the sofa.
(a)£1,000
(b)£600
(c)£825
(d)£200
4.Expand 4(2x − 3).
(a)2x + 1
(b)8x + 12
(c)8x − 12
(d)8x − 3
5.Expand 2(x − 13)
(a)2x + 26
(b)2x − 11
(c)2x − 13
(d)2x − 26
6.Priya says that x = 6 is the solution of the equation 4x + 8 = 24. Priya is wrong. Work out the correct value of x.
(a)12
(b)4
(c)8
(d)16
7.Three angles lie on a straight line. They measure 38°, 95° and x°. Work out the value of x.
(a)133
(b)47
(c)227
(d)142
8.In triangle ABC the angle at A is 90° and BC = 10 cm. For the angle at B, sin B = 3/5. Work out the length of AC.
(a)3 cm
(b)6 cm
(c)8 cm
(d)30 cm
9.A straight line has gradient −3 and passes through the point (0, 1). Work out the value of y when x = 2.
(a)7
(b)−5
(c)5
(d)−7
10.To solve 6x − 4 = 2x + 20, Yusuf's first step is to subtract 2x from both sides. Work out what equation this gives.
(a)4x = 20
(b)4x − 4 = 20
(c)4x − 4 = 2x + 20
(d)8x − 4 = 20
11.Grace's mean mark in her maths tests rises from 70 to 84. Work out the percentage increase in her mean mark.
(a)20%
(b)120%
(c)17%
(d)14%
12.A recipe for pastry uses flour and butter in the ratio 3:2. A baker has 180 g of butter and wants to make pastry using all of it. Work out the total mass of pastry the baker can make.
(a)300 g
(b)540 g
(c)450 g
(d)270 g
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.Solve 4x + 3 = 19
(a)3.75
(b)5.5
(c)4
(d)4.75
15.2.4 kg of cheese costs £36. Work out the cost of 1.5 kg of the same cheese.
(a)£15
(b)£57.60
(c)£22.50
(d)£54
16.Solve 3x + 14 = 8x − 6
(a)x = 15
(b)x = 2.5
(c)x = 4
(d)x = −1.6
17.A jug holds 3 litres of a drink that is 60% fruit juice. 1 litre of water is added to the jug. Work out the percentage of the new mixture that is fruit juice.
(a)60%
(b)75%
(c)45%
(d)15%
18.Amelia's mean mark over four tests is 29. Her first three marks are 31, 26 and 26. Work out her fourth mark.
(a)116
(b)4
(c)33
(d)29
19.A ribbon of length 90 cm is cut into two pieces in the ratio 4:5. Work out the length of the shorter piece.
(a)50 cm
(b)10 cm
(c)40 cm
(d)45 cm
20.A straight line passes through the points (−1, 2) and (3, 14). Work out the equation of the line.
(a)y = 6x − 4
(b)y = x/3 + 13
(c)y = 3x + 5
(d)y = 3x + 23

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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