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.Priya invests £750 in a savings account that pays simple interest. After 3 years, the account contains £840. Work out the annual rate of simple interest.
(a)12%
(b)4%
(c)112%
(d)0.04%
2.Work out 25% of 200.
(a)50
(b)100
(c)25
(d)800
3.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
4.The midday temperature in Leeds was recorded on each day of one week: 22 °C, 24 °C, 23 °C, 25 °C, 26 °C, 21 °C, 24 °C. Work out the mean midday temperature, giving your answer to 2 decimal places.
(a)24 °C
(b)5 °C
(c)27.5 °C
(d)23.57 °C
5.Solve the inequality x − 10 < −3.
(a)x < 13
(b)x > 7
(c)x < −13
(d)x < 7
6.Three business partners share a profit of £48,000 in the ratio 3:5:4. Work out how much the partner with 5 parts receives.
(a)£20,000
(b)£12,000
(c)£4,000
(d)£16,000
7.An amount of money is shared in the ratio 1:2:3. The largest share is £90 more than the smallest share. Work out the total amount that was shared.
(a)£180
(b)£540
(c)£135
(d)£270
8.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
9.The masses of eight school bags, in kilograms, are 3, 4, 4, 5, 6, 7, 8 and 11. Work out the median mass.
(a)5 kg
(b)5.5 kg
(c)8 kg
(d)4 kg
10.Factorise fully 56x − 24
(a)8(7x − 16)
(b)8(56x − 3)
(c)8(7x + 3)
(d)8(7x − 3)
11.A candle is 30 cm tall and burns down at a steady rate of 1 cm per hour. Write down the function for the height of the candle y, in centimetres, after x hours.
(a)y = −30x + 1
(b)y = x + 30
(c)y = −x + 30
(d)y = 30x − 1
12.Solve the inequality 3x + 6 ≤ 0.
(a)x ≤ 2
(b)x ≤ −2
(c)x ≥ −2
(d)x ≤ −18
13.2.4 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
14.Solve 3x − 5 = 4.
(a)9
(b)−1/3
(c)6
(d)3
15.Solve the inequality 3x − 1 ≤ 11.
(a)x ≥ 4
(b)x ≤ 4
(c)x ≤ 12
(d)x ≤ 10/3
16.A straight line has equation y = 4x + 3. A second line is parallel to the first line and passes through the point (0, −5). Work out the equation of the second line.
y = 4x + 3
(a)y = 3x − 5
(b)y = 4x + 5
(c)y = 4x − 5
(d)y = −4x − 5
17.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
18.A café sold 10 sandwiches on each of four days: 10, 10, 10, 10. Work out the range of the numbers sold.
(a)20
(b)40
(c)10
(d)0
19.A support strut for a shed roof is in the shape of a right-angled triangle. The two shorter sides of the strut are 5 m and 9 m. Work out the length of the sloping strut (the hypotenuse). Give your answer correct to 1 decimal place.
(a)106 m
(b)10.2 m
(c)14 m
(d)10.3 m
20.A car park charges a £4 fixed fee plus £3 for each hour. Kofi has exactly £25 to spend on parking. Using the inequality 4 + 3h ≤ 25, work out the greatest number of whole hours, h, he can park for.
(a)7
(b)8
(c)6
(d)9

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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