2025 Pearson Edexcel A Level Further Mathematics Question Paper Option 1 June + Mark scheme

surname names


Number Number




Paper


Further Mathematics
🟐 🟐


Advanced
PAPER 1: Core Pure Mathematics 1




Candidates may use any calculator permitted by Pearson regulations. Calculators
must not have the facility for symbolic algebraic manipulation, differentiation and
integration, or have retrievable mathematical formulae stored in them.
Instructions
••Use black ink or ball-point pen.

•
If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
Fill in the boxes at the top of this page with your name,

•
centre number and candidate number.
Answer all questions and ensure that your answers to parts of questions are clearly

•
labelled.
Answer the questions in the spaces provided

•
– there may be more space than you need.
You should show sufficient working to make your methods clear. Answers without

•
working may not gain full credit.
Inexact answers should be given to three significant figures unless otherwise stated.

Information
••
A booklet ‘Mathematical Formulae and Statistical Tables’ is provided.

•
There are 10 questions in this question paper. The total mark for this paper is 75.
The
– usemarks
this asfor each as
a guide question
to how are
muchshown
timeintobrackets
spend on each question.
Advice
•
Read each question carefully before you start to answer it.
••
Try to answer every question.
Check your answers if you have time at the end.



2025 Pearson Edexcel A Level Further Mathematics Question Paper Option 1 June+ Mark
scheme

,1.

3 6 0





DO NOT WRITE IN THIS AREA
M = a 3 1  where a is a constant


2 a a


(a) Determine the values of a for which the matrix M is singular.
(3)
Given that matrix M is non-singular and that

• det(M) = −108
• a0

(b) determine the matrix M −1
(3)




DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA




2
■■■■

, DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA




■■■■
Question 1 continued




(Total for Question 1 is 6 marks)

3
Turn over

, 2. In this question you must show all stages of your working.

Solutions relying entirely on calculator technology are not acceptable.




DO NOT WRITE IN THIS AREA
Determine the exact values of x for which
sinh 2x = 3sinh x
(5)




DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA




4
■■■■