AQA AS Level Mathematics 2025 Paper 1
Question Paper [VERIFIED]
AQA AS LEVEL MATHEMATICS
PAPER 1 — PURE MATHEMATICS
Professional 2025-Style Practice Examination
Time allowed: 1 hour 30 minutes
Total marks: 80
Instructions
• Answer all questions.
• Give exact answers unless otherwise stated.
• You may use a calculator.
• Show sufficient working to make your method clear.
• Give non-exact numerical answers to an appropriate degree of accuracy.
• You may use the AQA Formulae for A-level Mathematics booklet.
QUESTION 1 — ALGEBRA AND INDICES [5 MARKS]
The expression
[
\frac{3x^2-12}{x^2-4}
]
is defined for values of (x) for which the denominator is non-zero.
(a) Factorise the numerator and denominator. [2]
(b) Hence simplify the expression fully. [1]
(c) State the values of (x) that must be excluded from the simplified expression. [2]
, QUESTION 2 — QUADRATIC FUNCTIONS [6 MARKS]
The function (f) is defined by
[
f(x)=2x^2-8x+3.
]
(a) Express (f(x)) in the form
[
2(x-a)^2+b.
]
[3]
(b) State the coordinates of the minimum point of the graph of (y=f(x)). [1]
(c) Solve
[
2x^2-8x+3=0.
]
Give your answers in exact form. [2]
QUESTION 3 — COORDINATE GEOMETRY [7
MARKS]
The points (A(2,5)) and (B(8,-1)) lie on a straight line.
(a) Find the gradient of (AB). [2]
(b) Find the equation of the line (AB) in the form
[
y=mx+c.
]
[2]
Question Paper [VERIFIED]
AQA AS LEVEL MATHEMATICS
PAPER 1 — PURE MATHEMATICS
Professional 2025-Style Practice Examination
Time allowed: 1 hour 30 minutes
Total marks: 80
Instructions
• Answer all questions.
• Give exact answers unless otherwise stated.
• You may use a calculator.
• Show sufficient working to make your method clear.
• Give non-exact numerical answers to an appropriate degree of accuracy.
• You may use the AQA Formulae for A-level Mathematics booklet.
QUESTION 1 — ALGEBRA AND INDICES [5 MARKS]
The expression
[
\frac{3x^2-12}{x^2-4}
]
is defined for values of (x) for which the denominator is non-zero.
(a) Factorise the numerator and denominator. [2]
(b) Hence simplify the expression fully. [1]
(c) State the values of (x) that must be excluded from the simplified expression. [2]
, QUESTION 2 — QUADRATIC FUNCTIONS [6 MARKS]
The function (f) is defined by
[
f(x)=2x^2-8x+3.
]
(a) Express (f(x)) in the form
[
2(x-a)^2+b.
]
[3]
(b) State the coordinates of the minimum point of the graph of (y=f(x)). [1]
(c) Solve
[
2x^2-8x+3=0.
]
Give your answers in exact form. [2]
QUESTION 3 — COORDINATE GEOMETRY [7
MARKS]
The points (A(2,5)) and (B(8,-1)) lie on a straight line.
(a) Find the gradient of (AB). [2]
(b) Find the equation of the line (AB) in the form
[
y=mx+c.
]
[2]
