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.Isla and her brother share £60 in the ratio 1:2. Work out Isla's share.
(a)£40
(b)£20
(c)£120
(d)£30
2.In triangle ABC the angle at A and the angle at C are equal. The side AB is extended beyond B, and the exterior angle formed at B measures 98°. Work out the size of the angle at A.
(a)49°
(b)41°
(c)82°
(d)98°
3.A charity collects donations from adults and children in the ratio 5:2. Altogether, £238 is collected. Work out how much more the adults donate than the children.
(a)£102
(b)£68
(c)£136
(d)£170
4.Write 1/5 as a percentage.
(a)20%
(b)5%
(c)50%
(d)25%
5.Two classes sat the same maths test, both marked out of 100. Class A had a mean mark of 70 and a range of 30 marks. Class B had a mean mark of 70 and a range of 10 marks. Compare the marks of the two classes.
(a)The means are equal, and Class B's marks are the more consistent because its range is smaller.
(b)Class A's mean mark is higher, and Class A's marks are also the more consistent.
(c)The means are equal, and Class A's marks are the more consistent because its range is larger.
(d)Class B's mean mark is higher, and its smaller range makes its marks the more consistent.
6.The angles of a triangle are in the ratio 2:3:4. Work out the size of the smallest angle.
(a)80°
(b)60°
(c)40°
(d)20°
7.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
8.Which of these describes an obtuse angle?
(a)An angle between 180° and 360°
(b)An angle between 90° and 180°
(c)An angle of exactly 90°
(d)An angle between 0° and 90°
9.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
10.A roof truss has two horizontal parallel rafters, one above the other. A straight strut crosses both rafters. Where the strut crosses the lower rafter, the angle above the rafter and to the left of the strut is 65°. Work out the size of the angle above the upper rafter and to the right of the strut, where the strut crosses it.
(a)65
(b)25
(c)115
(d)245
11.Solve 6x − 5 = 3x + 13.
(a)18
(b)2
(c)2.67
(d)6
12.Solve 3(2x − 1) = 27
(a)4
(b)5
(c)4.5
(d)4 2/3
13.Solve 7x − 5 = 3x + 11
(a)−4
(b)1.5
(c)0.6
(d)4
14.Expand 7(a + 8)
(a)a + 56
(b)7a + 15
(c)7a + 8
(d)7a + 56
15.A straight line crosses two parallel lines. One of the angles formed is (2x + 10)°, and the angle alternate to it is 74°. Work out the value of x.
(a)−32
(b)48
(c)32
(d)37
16.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%
17.Expand and simplify 4(2x − 1) − 3(x + 2) − 5x
(a)−10
(b)5x − 10
(c)2
(d)−7
18.Solve 2x − 2 = 2
(a)x = 2
(b)x = 8
(c)x = 0
(d)x = 4
19.A rectangular garden gate is 3 m wide and 4 m high. A straight brace runs from one corner of the gate to the opposite corner. Work out the length of the brace.
(a)7 m
(b)5 m
(c)12 m
(d)25 m
20.A straight line has equation y = 5x. Work out the value of y when x = 3.
y = 5x
(a)8
(b)3
(c)−15
(d)15

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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