Please check the examination details below before entering your candidate information
Candidate surname Other names
Centre Number Candidate Number
Pearson Edexcel International Advanced Level
Thursday 16 January 2025
Morning (Time: 1 hour 30 minutes) Paper
reference WMA13/01
Mathematics
International Advanced Level
Pure Mathematics P3
You must have: Total Marks
Mathematical Formulae and Statistical Tables (Yellow), calculator
Candidates may use any calculator permitted by Pearson regulations.
Calculators must not have the facility for symbolic algebra manipulation,
differentiation and integration, or have retrievable mathematical formulae
stored in them.
Instructions
•• Use black ink or ball-point pen.
• Fill
If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
in the boxes at the top of this page with your name,
• clearly
centre number and candidate number.
Answer all questions and ensure that your answers to parts of questions are
• Answer
labelled.
the questions in the spaces provided
• You
– there may be more space than you need.
should show sufficient working to make your methods clear. Answers without
•Information
working may not gain full credit.
Inexact answers should be given to three significant figures unless otherwise stated.
•• AThere
booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
•
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.
•• Check
Try to answer every question.
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
P76195A
©2025 Pearson Education Ltd.
H:1/1/1/1/
*P76195A0132*
, π
1. f (x) = 2sec x + 6x – 3 0 < x <
2
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
The equation f (x) = 0 has a single root α
(a) Show that 0.1 < α < 0.2
(2)
(b) Show that α is a solution of
1 1
x= –
2 3cos x
(1)
The iterative formula
1 1
xn + 1 = –
2 3cos xn
is used to find α
(c) Starting with x1 = 0.15 and using the iterative formula,
(i) find, to 4 decimal places, the value of x2
(ii) find, to 4 decimal places, the value of α
(3)
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2
*P76195A0232*
, Question 1 continued
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(Total for Question 1 is 6 marks)
3
*P76195A0332* Turn over
, 2. The weed on the surface of a pond is being monitored.
The surface area of the pond covered by the weed, A m2, is modelled by the equation
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
log10 A = 1 + 0.03t
where t is the number of weeks after monitoring began.
Use the equation of the model to answer parts (a) and (b).
(a) Find the surface area of the pond initially covered by the weed.
(1)
After T weeks, 25 m2 of the pond is covered by the weed.
(b) Find the value of T, giving your answer to 2 decimal places.
(2)
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4
*P76195A0432*
Candidate surname Other names
Centre Number Candidate Number
Pearson Edexcel International Advanced Level
Thursday 16 January 2025
Morning (Time: 1 hour 30 minutes) Paper
reference WMA13/01
Mathematics
International Advanced Level
Pure Mathematics P3
You must have: Total Marks
Mathematical Formulae and Statistical Tables (Yellow), calculator
Candidates may use any calculator permitted by Pearson regulations.
Calculators must not have the facility for symbolic algebra manipulation,
differentiation and integration, or have retrievable mathematical formulae
stored in them.
Instructions
•• Use black ink or ball-point pen.
• Fill
If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
in the boxes at the top of this page with your name,
• clearly
centre number and candidate number.
Answer all questions and ensure that your answers to parts of questions are
• Answer
labelled.
the questions in the spaces provided
• You
– there may be more space than you need.
should show sufficient working to make your methods clear. Answers without
•Information
working may not gain full credit.
Inexact answers should be given to three significant figures unless otherwise stated.
•• AThere
booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
•
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.
•• Check
Try to answer every question.
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
P76195A
©2025 Pearson Education Ltd.
H:1/1/1/1/
*P76195A0132*
, π
1. f (x) = 2sec x + 6x – 3 0 < x <
2
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
The equation f (x) = 0 has a single root α
(a) Show that 0.1 < α < 0.2
(2)
(b) Show that α is a solution of
1 1
x= –
2 3cos x
(1)
The iterative formula
1 1
xn + 1 = –
2 3cos xn
is used to find α
(c) Starting with x1 = 0.15 and using the iterative formula,
(i) find, to 4 decimal places, the value of x2
(ii) find, to 4 decimal places, the value of α
(3)
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2
*P76195A0232*
, Question 1 continued
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(Total for Question 1 is 6 marks)
3
*P76195A0332* Turn over
, 2. The weed on the surface of a pond is being monitored.
The surface area of the pond covered by the weed, A m2, is modelled by the equation
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
log10 A = 1 + 0.03t
where t is the number of weeks after monitoring began.
Use the equation of the model to answer parts (a) and (b).
(a) Find the surface area of the pond initially covered by the weed.
(1)
After T weeks, 25 m2 of the pond is covered by the weed.
(b) Find the value of T, giving your answer to 2 decimal places.
(2)
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4
*P76195A0432*
