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 + 14 = 8x − 6
(a)x = 15
(b)x = 2.5
(c)x = 4
(d)x = −1.6
2.Work out the equation of the straight line that passes through (−2, 3) and (4, −9).
(a)y = −2x − 1
(b)y = −2x + 1
(c)y = −(1/2)x + 2
(d)y = 2x + 7
3.The price of a games console is reduced by 10%. In a later sale the reduced price is reduced by 10% again. Work out the overall percentage decrease.
(a)21%
(b)81%
(c)20%
(d)19%
4.40% of a number is 12 more than 25% of the same number. Work out the number.
(a)48
(b)80
(c)15
(d)30
5.Two angles are supplementary. One of them is twice the size of the other. Work out the size of the smaller angle.
(a)30
(b)120
(c)90
(d)60
6.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
7.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
8.After a 20% discount, a jacket costs £48. Work out the original price of the jacket.
(a)£40
(b)£60
(c)£57.60
(d)£38.40
9.The number of members of a running club increases from 45 to 54. Work out the percentage increase.
(a)9%
(b)120%
(c)20%
(d)16.7%
10.A right-angled triangle has a hypotenuse of 8 cm, and one of its shorter sides is 4 cm. Work out the size of the angle between that 4 cm side and the hypotenuse.
(a)90°
(b)45°
(c)30°
(d)60°
11.The marks scored by four pupils in a quiz were 8, 8, 8, 8. Work out the mean, the median and the mode of these marks.
(a)mean = 2, median = 8, mode = 8
(b)mean = 8, median = 8, mode = 4
(c)mean = 8, median = 8, mode = 8
(d)mean = 32, median = 8, mode = 8
12.Solve the inequality 3x + 6 ≤ 0.
(a)x ≤ 2
(b)x ≤ −2
(c)x ≥ −2
(d)x ≤ −18
13.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
14.Jamal invests £600 in a savings account paying 3% simple interest per year. Work out the total amount in the account after 4 years.
(a)£675.31
(b)£72
(c)£672
(d)£618
15.A plumber charges a call-out fee plus an hourly rate. The total cost, y in pounds, of a job lasting x hours is given by y = 45x + 60. Work out the total cost of a job that lasts 3 hours.
y = 45x + 60
(a)£315
(b)£108
(c)£135
(d)£195
16.A rectangular garden has length (x + 7) m and width (x − 7) m. Work out an expression for the area of the garden, giving your answer in its simplest form.
(a)2x
(b)x² + 49
(c)x² − 14x − 49
(d)x² − 49
17.Solve x/4 + 1 = 3
(a)x = 16
(b)x = 8
(c)x = 0.5
(d)x = 2
18.In a test, Amelia answered 18 of the 24 questions correctly. Work out the percentage of the questions she answered correctly.
(a)75%
(b)133%
(c)25%
(d)18%
19.A car is bought for £17,500. Its value decreases by 12% in the first year, and by a further 10% of its reduced value in the second year. Work out the value of the car at the end of the second year, giving your answer to the nearest pound.
(a)£15,400
(b)£13,860
(c)£13,650
(d)£15,750
20.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

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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