AQA GCSE Mathematics Paper 1 (Higher), June 2025
Every question from AQA GCSE Mathematics Paper 1 (Higher), June 2025 (8300): 25 questions, 80 marks, each with its mark scheme and topic.
- Question 1 3 marks
Solve the pair of linear simultaneous equations 2x + 5y = 18 and 2x + y = 6.
Algebra · 3.2.3 Solving equations and inequalities
- Question 2 2 marks
Work out the integer value of x that satisfies the double inequality 1.07 < x/9 < 1.17.
Algebra · Number · 3.1.1 Structure and calculation · 3.2.3 Solving equations and inequalities
- Question 3 2 marks
Calculate the mass of a metal solid given its volume is 11 cm³ and its density is 8.5 g/cm³.
Ratio, proportion and rates of change · 3.3 Ratio, proportion and rates of change
- Question 4 2 marks
Work out the inter-quartile range of a given set of 11 ordered numbers.
Statistics · 3.6 Statistics
- Question 5 3 marks
Evaluate statements comparing two schools' test results based on their mean marks and ranges as True, May be true, or Not true.
Statistics · 3.6 Statistics
- Question 6 4 marks
Calculate division and multiplication calculations involving powers of 10 and give the answers in standard form.
Number · 3.1.1 Structure and calculation
- Question 7 4 marks
Complete a frequency tree showing the number of Year 10 and Year 11 students who did and did not win a medal.
Ratio, proportion and rates of change · Statistics · 3.3 Ratio, proportion and rates of change · 3.6 Statistics
- Question 8 3 marks
Calculate the value of 4/15 + 1/5 ÷ 1/2 and give the answer as a fraction.
Number · 3.1.1 Structure and calculation · 3.1.2 Fractions, decimals and percentages
- Question 9 1 mark
Identify which given value of x results in the greatest value of y for the reciprocal equation y = 1/x.
Number · Algebra · 3.1.1 Structure and calculation · 3.1.2 Fractions, decimals and percentages · 3.2.1 Notation, vocabulary and manipulation
- Question 10 4 marks
Form and solve a quadratic equation to find the value of x given a rectangle with sides (x - 5) cm and (x + 2) cm and an area of 120 cm².
Algebra · Geometry and measures · 3.2.1 Notation, vocabulary and manipulation · 3.2.3 Solving equations and inequalities · 3.4.2 Mensuration and calculation
- Question 11 3 marks
Find the translation vector mapping shape A to shape B, and fully describe a rotation mapping shape A to shape B.
Geometry and measures · 3.4.1 Properties and constructions · 3.4.3 Vectors
- Question 12 3 marks
Calculate the total amount of money shared between Oscar and Nikita in the ratio 8 : 5 given that Oscar receives £27 more than Nikita.
Ratio, proportion and rates of change · 3.3 Ratio, proportion and rates of change
- Question 13 2 marks
Find the difference between two consecutive cube numbers that lie on either side of 4.5 cubed.
Number · 3.1.1 Structure and calculation
- Question 14 4 marks
Complete a table of values and draw the graph of the exponential function y = 2^x for x from -1 to 3.
Algebra · Number · 3.1.1 Structure and calculation · 3.2.2 Graphs
- Question 15 4 marks
Work out the size of angle x given that A, C and D are points on a circle with diameter AC, ABC is an isosceles triangle with AC = BC, and BCD is a straight line.
Geometry and measures · 3.4.1 Properties and constructions
- Question 16 3 marks
Match set notation expressions involving events A and B to the corresponding shaded areas on Venn diagrams.
Probability · 3.5 Probability
- Question 17 4 marks
Complete a probability tree diagram involving conditional probabilities for a bus being on time depending on whether it is raining, and calculate the probability that it is raining and the bus is not on time.
Probability · Number · 3.5 Probability · 3.1.2 Fractions, decimals and percentages
- Question 18 3 marks
Show that (sin 30° × cos 45°) / tan 60° can be written in the form √a / b, where a and b are integers.
Geometry and measures · Number · 3.1.1 Structure and calculation · 3.4.2 Mensuration and calculation
- Question 19 5 marks
Work out the value of (9/16)^(-3/2) and find the value of n such that sqrt(125) = 5^n.
Number · 3.1.1 Structure and calculation
- Question 20 3 marks
Express the sum of square roots $\sqrt{44} + \sqrt{99} + \sqrt{275}$ in the simplified surd form $a\sqrt{n}$.
Number · 3.1.1 Structure and calculation
- Question 21 2 marks
Draw the transformed graphs of $y = -f(x)$ and $y = f(x) + 1$ on the provided coordinate grids given the graph of $y = f(x)$ for $0 \le x \le 3$.
Algebra · 3.2.2 Graphs
- Question 22 3 marks
Find the coordinates of point F on the line segment EG connecting E(-18, 9) and G(6, 3) such that EF is one third of EG.
Algebra · Geometry and measures · 3.2.2 Graphs · 3.4.1 Properties and constructions
- Question 23 4 marks
Complete the square for a quadratic expression and determine the turning point coordinates of a quadratic curve given in vertex form.
Algebra · 3.2.1 Notation, vocabulary and manipulation · 3.2.2 Graphs
- Question 24 4 marks
Prove algebraically that the product of algebraic fractions (60x^4 - 15x^2)/(-2x - 1) and 1/(6x - 3) can never be positive.
Algebra · 3.2.1 Notation, vocabulary and manipulation
- Question 25 5 marks
Use an algebraic method to find the total number of counters in a box given that 6 are black and the probability of picking two black counters without replacement is 1/8.
Algebra · Probability · 3.2.1 Notation, vocabulary and manipulation · 3.2.3 Solving equations and inequalities · 3.5 Probability