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AQA GCSE Higher June 2025 Paper 1 (non-calculator)
25 questions · 80 marks. Every question from the paper, recreated, with the official mark scheme, an annotated worked solution and a shadow question (the same skill with new numbers). Open the paper in the Ultimate Exam Question Finder to present it, print it or build a set.
Question 1 (3 marks)
Solve the simultaneous equations
2x + 5y = 18
2x + y = 6(3 marks)
Question 2 (2 marks)
1.07 < x/9 < 1.17 where x is an integer.
Work out the value of x.
(2 marks)
Question 3 (2 marks)
A metal solid has volume 11 cm³
The density of the metal is 8.5 g/cm³Work out the mass of the solid.
(2 marks)
Question 4 (2 marks)
Here are 11 numbers.
2 8 10 12 12 14 19 23 26 31 33
Work out the inter-quartile range.
(2 marks)
Question 5 (3 marks)
The table shows information about the marks of students in a test.
Mean mark Range of marks School A 61 14 School B 56 21 Tick one box for each statement.
True May be true Not true On average, School A had higher marks square square square There are more students in School B square square square School B had a greater spread of marks square square square (3 marks)
Question 6 (4 marks)
(a)
Work out 0.6 ÷ 100
Give your answer in standard form.
(2 marks)
(b)
Work out 40 × 30 × 10⁵
Give your answer in standard form.
(2 marks)
Question 7 (4 marks)
330 students from Year 10 and Year 11 take part in a competition.
• number of students in Year 10 : number of students in Year 11 = 1 : 2
• 125 students win a medal.
• 73 of the students who win a medal are in Year 11Complete the frequency tree.
Diagram: A frequency tree: 330 at the start, branching into Year 10 and Year 11, then each branching into Medal and No medal. The other six ovals are empty.
(4 marks)
Question 8 (3 marks)
Work out 4/15 + 1/5 ÷ 1/2
Give your answer as a fraction.
(3 marks)
Question 9 (1 mark)
y = 1/x
Which of these values of x gives the greatest value of y?
Circle your answer.9/20 2/5 –80 95 (1 mark)
Question 10 (4 marks)
Diagram: A rectangle. The top side is labelled (x + 2) cm and the left side is labelled (x – 5) cm.
The area of the rectangle is 120 cm²
Work out the value of x.
(4 marks)
Question 11 (3 marks)
Diagram: A grid with x from –5 to 5 and y from –1 to 6. Shape A is a 2 by 2 square with corners (–4, 3), (–2, 3), (–2, 5) and (–4, 5). Shape B is a 2 by 2 square with corners (2, 1), (4, 1), (4, 3) and (2, 3).
(a)
Write down the translation vector that maps shape A to shape B.
(1 mark)
(b)
Describe fully a rotation that maps A to B.
(2 marks)
Question 12 (3 marks)
Oscar and Nikita share some money in the ratio 8 : 5
Oscar has £27 more than Nikita.How much do they have altogether?
(3 marks)
Question 13 (2 marks)
c and d are consecutive cube numbers, where c < 4.5³ < d
Work out the value of d – c
(2 marks)
Question 14 (4 marks)
(a)
Complete the table of values for y = 2^x
x –1 0 1 2 3 y 1 4 (2 marks)
(b)
Draw the graph of y = 2^x for values of x from –1 to 3
Diagram: A grid of graph paper with x from –2 to 4 and y from –3 to 11, 5 small squares to each unit.
(2 marks)
Question 15 (4 marks)
A, C and D are points on a circle, diameter AC.
ABC is an isosceles triangle with AC = BC
BCD is a straight line.Diagram: A circle with diameter AC. D is on the circle, above the diameter. B is outside the circle, below and to the right of C. Lines join A to D, D through C to B, A to C and A to B. The angle at B between BA and BC is 20°. The angle at A between AC and AD is marked x.
Work out the size of angle x.
(4 marks)
Question 16 (3 marks)
A and B are two events.
Match each box on the left to the correct shaded area on the Venn diagrams.
One has been done for you.Diagram: On the left, 4 boxes, top to bottom: A ∩ B; A ∪ B; A’ ∪ B; A’ ∩ B’. On the right, 5 Venn diagrams, top to bottom, each a rectangle ξ with overlapping circles A and B. Shaded: 1st, A only, the overlap, B only; 2nd, the overlap; 3rd, outside both circles; 4th, the overlap, B only, outside both circles; 5th, A only, B only, outside both circles. A line joins box 1 to the 2nd diagram.
(3 marks)
Question 17 (4 marks)
A bus is due to arrive at a bus stop at 1 pm
The probability that the bus is on time is halved when it is raining.(a)
Complete the tree diagram.
Diagram: A probability tree diagram. Raining: Yes (1/6) or No (a blank). After each, Bus on time: Yes or No. After Yes: a blank and 9/13. After No: a blank and a blank.
(2 marks)
(b)
Work out the probability that at 1 pm it is raining and the bus is not on time.
(2 marks)
Question 18 (3 marks)
Show that (sin 30° × cos 45°)/(tan 60°) can be written in the form dfrac√ab
where a and b are integers.
(3 marks)
Question 19 (5 marks)
(a)
Work out the value of (9/16)^(-3/2)
(3 marks)
(b)
√125 = 5ⁿ
Work out the value of n.
(2 marks)
Question 20 (3 marks)
Express √44 + √99 + √275 in the form a√n where a and n are integers.
(3 marks)
Question 21 (2 marks)
The graph of y = f(x) for 0 ≤ x ≤ 3 is shown.
(a)
On the grid below, draw the graph of y = -f(x) for 0 ≤ x ≤ 3
The graph of y = f(x) is shown to help you.Diagram: A grid with x and y from –5 to 5, with the graph of y = f(x) dashed: from (0, 0) up to (1, 3), then down to (3, 0).
(1 mark)
(b)
On the grid below, draw the graph of y = f(x) + 1 for 0 ≤ x ≤ 3
The graph of y = f(x) is shown to help you.Diagram: A grid with x and y from –5 to 5, with the graph of y = f(x) dashed: from (0, 0) up to (1, 3), then down to (3, 0).
(1 mark)
Question 22 (3 marks)
Here is a sketch of straight line EG.
Diagram: A sketch of x and y axes. A straight line runs from E (–18, 9) down to the right to G (6, 3).
F is a point on EG such that EF = 1/3EG
Work out the coordinates of F.
(3 marks)
Question 23 (4 marks)
(a)
Write x² + 12x + 50 in the form (x + a)² + b where a and b are integers.
(2 marks)
(b)
A curve has the equation y = (x – 3)² – 8
Write down the coordinates of the turning point of the curve.
(2 marks)
Question 24 (4 marks)
Prove that (60x⁴ – 15x²)/(-2x – 1) × 1/(6x – 3) can never be positive.
(4 marks)
Question 25 (5 marks)
There are n counters in a box.
6 of the counters are black.Two counters are chosen at random without replacement.
The probability that both counters are black is 1/8
Use an algebraic method to work out the value of n.
(5 marks)
Questions © AQA, recreated by Mr Barton Maths for teaching. Each question is credited to its board, series, paper and number.