WMA13 Pure Mathematics 3 (P3): January 2026 Paper 01A

In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable.

The curve C has equation

The point P on C has x coordinate 4

Find an equation of the normal to C at the point P in the form ax + by + c = 0, where a, b and c are integers.[6]

Given that

(a)state the range of f,[2]

(b)find f[3]

(c)find fg (x).[1]

(d)Show that the equation fg (x) = gf (x) has no real solutions.[4]

In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable.

(i)(a)Divide (x – 3x + 6) by (x + 2)[2]

(b)Hence find  3x  6x  2 dx [3]

(ii)Using algebraic integration, find the exact value of

[5]

Given that

where A and B are integers to be found.[4]

In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.

(a)Show that

[3]

(b)Hence solve, for 0  x < 360°

Give each solution in degrees to one decimal place.[5]

In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.

The value of a particular car is modelled by the formula

where the value of the car is V pounds when the age of the car is t years.

A sketch of t against V is shown in Figure 1.

(a)State the range of V.[2]

According to this model,

(b)find the rate at which the value of the car is decreasing when t = 10 Give your answer in pounds per year.[3]

(c)Calculate the exact value of t when V = 15 000 giving the answer in its simplest form.[4]

In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.

(a)Express 5 cos θ  2sin θ in the form R cos (θ + α), where R > 0 and 0 < α < π2

State the value of R and give the value of α to 4 significant figures.[3]

(b)Solve, for –π < θ < π,

giving your answers to 3 significant figures.[4]

where A and B are constants.

Given that the range of f is

(c)find the value of B and the possible values of A.[4]

Given that a is a positive constant,

(a)on separate diagrams, sketch the graph with equation

Show on each sketch the coordinates, in terms of a, of each point at which the graph crosses or meets the axes.[4]

(b)Find, in terms of a, the values of x for which[4]

(a)Given that  π2 < g (x) < π2 , sketch the graph of y = g (x) where

[2]

(b)Find the exact value of x for which

[2]

The equation arctan x  4  12 x  0 has a positive root at x = α radians.

(c)Show that 5 < α < 6[2]

The iteration formula

can be used to find an approximation for α

(d)Taking x₀= 5, use this formula to find x₁ and α , giving each answer to 4 decimal places.[3]

Centre Number Candidate Number

Pearson Edexcel International Advanced Level

Monday 19 January 2026

Morning (Time: 1 hour 30 minutes)

International Advanced Level Pure Mathematics P3 Answer Book

You must have:_TotalMarks Question paper (sent separately). 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.

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.

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

There are 9 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.

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.

Question 1

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Question 2

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Question 3

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Question 4

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Question 5

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Question 6

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Question 7

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Question 8

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Question 9

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