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AQA
A-level
MATHEMATICS
Paper 1
Wednesday 3 June 2025 Afternoon Time allowed: 2 hours
Materials You must have the AQA Formulae for A‑ level Mathematics booklet.
You should have a graphical or scientific calculator that meets the requirements of the specification.
Instructions Use black ink or black ball‑ point pen. Pencil should only be used
for drawing. Fill in the boxes at the top of this page. Answer all questions. For Examiner’s Use Question Mark 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 TOTAL
Do not write outside the box You must answer each question in the space provided for that question. If you need extra space for your answer(s), use the lined pages at the end of this book. Write the question number against your answer(s). Show all necessary working; otherwise marks for method may be lost. Do all rough work in this book. Cross through any work that you do not want to be marked.
Information The marks for questions are shown in brackets. The maximum mark for this paper is
Advice
Unless stated otherwise, you may quote formulae, without proof, from the booklet. You do not necessarily need to use all the space provided. (JUN207357101) PB/Jun20/E7 7357/ Answer all questions in the spaces provided. 1
The first three terms, in ascending powers of x, of the binomial expansion of (9 þ
2 x) are given by
x
x^2 (9 þ 2 x) a þ
where a is a constant.
Please write clearly in block capitals. Centre number Candidate number Surname ________________________________________________________________________ Forename(s) ________________________________________________________________________ Candidate signature ________________________________________________________________________ I declare this is my own work.
Do not write outside the box 2
A student is searching for a solution to the equation f (x) ¼ 0 He
correctly evaluates
f (1) ¼ 1 and f (1) ¼ 1
and concludes that there must be a root between 1 and 1 due to the change of sign.
Select the function f (x) for which the conclusion is incorrect.
Circle your answer. [1 mark] 1
f (x) ¼ f (x) ¼ x
x
f (x) ¼ x^3 2 x þ 1
f (x) ¼
x þ 2
The diagram shows a sector OAB of a circle with centre O and radius 2
The angle AOB is y radians and the perimeter of the sector is 6
Find the value of y
Circle your answer. [1 mark]
B
A
O
Do not write outside the box Turn over pffiffiffi 3 2 1 Turn over for the next question
(03)
Do not write outside the box Turn over (04)
Do not write outside the box
5 Prove that, for integer values of n such that 0 n < 4
2 nþ 2 > 3 n [2 marks]
Turn over for the next question
Do not write outside the box 6 (b) Explain why Floella and Georgia’s answers are equivalent. [2 marks]
(06) 7 Consecutive terms of a sequence are related by
unþ 1 ¼ 3 (un) 2
7 (a) In the case that^ u^ ¼^2
1
7 (a) (i) Find u
3 [2 marks]
7 (a) (ii)
Find u
50 [1 mark]
Do not write outside the box Turn over
7 (b) State a different value for u which gives the same value for u as found in
1 50 part (a)(ii). [1 mark]
Turn over for the next question (07)
Do not write outside the box Turn over 8 (b) Find the maximum number of consecutive days where the number of hours of darkness predicted by Mike’s model exceeds 14 [3 marks]
Question 8 continues on the next page
Do not write outside the box (09)
Do not write outside the box (10)
Do not write outside the box Turn over
Do not write outside the box Turn over 9 (a) (ii) Explain her mistake in Step 1. [1 mark]
(12)
Do not write outside the box
9 (b) 2 x^2 þ x
Write as partial fractions, with constant numerators. (x þ
1)(x þ 2)^2
[4 marks]
