Pearson Edexcel International Advanced Level Mathematics International Advanced Subsidiary/ Advanced Level Further Pure Mathematics
F1 QP January 2024 Please check the examination details below before entering your candidate information
Candidate surname Other names
Centre Number Candidate Number
Pearson Edexcel International Advanced Level
Friday 12 January 2024
Morning (Time: 1 hour 30 minutes)
Paper
reference WFM01/01
⯌ ⯌
Mathematics
International Advanced Subsidiary/ Advanced Level
Further Pure Mathematics F1
You must have: Total Marks
Mathematical Formulae and Statistical Tables (Yellow), calculator
Candidates may use any calculator allowed by Pearson regulations. Calculators must not have the
facility for symbolic algebra manipulation, differentiation andintegration, 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 marks for each question are shown in brackets
– use this as a guide as to how much time to 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.
If you change your mind about an answer, cross it out and put your new answer and any
working underneath.
Turn over
P74309A
©2024 Pearson Education Ltd.
S:1/1/1/
, 1.
k
2k 1 where k is a constant
M
DO NOT WRITE IN THIS AREA
k 7 k 4
(a) Show that M is non-singular for all real values of k.
(3)
(b) Determine M–1 in terms of k.
(2)
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 5 marks)
Turn over
3
, 2.
f (z) = 2z3 + pz2 + qz – 41
DO NOT WRITE IN THIS AREA
where p and q are integers.
The complex number 5 – 4i is a root of the equation f (z) = 0
(a) Write down another complex root of this equation.
(1)
(b) Solve the equation f (z) = 0 completely.
(4)
(c) Determine the value of p and the value of q.
(2)
When plotted on an Argand diagram, the points representing the roots of the equation
f (z) = 0 form the vertices of a triangle.
(d) Determine the area of this triangle.
(2)
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
4
🞍🞍🞍🞍
F1 QP January 2024 Please check the examination details below before entering your candidate information
Candidate surname Other names
Centre Number Candidate Number
Pearson Edexcel International Advanced Level
Friday 12 January 2024
Morning (Time: 1 hour 30 minutes)
Paper
reference WFM01/01
⯌ ⯌
Mathematics
International Advanced Subsidiary/ Advanced Level
Further Pure Mathematics F1
You must have: Total Marks
Mathematical Formulae and Statistical Tables (Yellow), calculator
Candidates may use any calculator allowed by Pearson regulations. Calculators must not have the
facility for symbolic algebra manipulation, differentiation andintegration, 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 marks for each question are shown in brackets
– use this as a guide as to how much time to 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.
If you change your mind about an answer, cross it out and put your new answer and any
working underneath.
Turn over
P74309A
©2024 Pearson Education Ltd.
S:1/1/1/
, 1.
k
2k 1 where k is a constant
M
DO NOT WRITE IN THIS AREA
k 7 k 4
(a) Show that M is non-singular for all real values of k.
(3)
(b) Determine M–1 in terms of k.
(2)
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 5 marks)
Turn over
3
, 2.
f (z) = 2z3 + pz2 + qz – 41
DO NOT WRITE IN THIS AREA
where p and q are integers.
The complex number 5 – 4i is a root of the equation f (z) = 0
(a) Write down another complex root of this equation.
(1)
(b) Solve the equation f (z) = 0 completely.
(4)
(c) Determine the value of p and the value of q.
(2)
When plotted on an Argand diagram, the points representing the roots of the equation
f (z) = 0 form the vertices of a triangle.
(d) Determine the area of this triangle.
(2)
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
4
🞍🞍🞍🞍
