WMA13 Pure Mathematics 3 (P3): Oct/Nov 2025 Paper 01A

Find

(i)(a)(2x + 3)¹² dx ∫[2]

5x

(b)dx ² 4x  1[2]

(ii)Given that

find the exact value of constant a.

(Solutions relying on calculator technology are not acceptable.)[4]

Given that dydx = 0 when x = α

(a)show that

[6]

The iterative formula

can be used to find an approximation for α.

(b)Taking x₁= 0.7, find the values of x₂ and x₃, giving each answer to 4 decimal places.[2]

(c)By choosing a suitable interval and a suitable function that should be stated, show that α = 0.7283 to 4 decimal places.[2]

(a)Given that

find the values of the constants A and B.[4]

(b)Hence, or otherwise, find the equation of the tangent to the curve with equation y = g (x) at the point where x = 4. Give your answer in the form y = mx + c, where m and c are constants to be determined.

(Solutions relying on calculator technology are not acceptable.)[5]

A curve has equation

(a)dydx = k cot x, where k is a constant to be found.[4]

Hence find the exact coordinates of the point on the curve where

dy

(b)= 2 3

[4]

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

(a)Prove that

[4]

(b)Hence solve, for 0  θ  2

(i)2 cosec 4θ – cot 2θ = 3

(ii)tan θ + cot θ = 5

Give your answers to 3 significant figures.[5]

y y

Figure 1 shows a sketch of part of the graph y = f (x), where

Figure 2 shows a sketch of part of the graph y = g (x), where

(a)Find the value of fg (1)[2]

(b)State the range of g[2]

(c)Find g[3]

Given that the equation f (x) = k, where k is a constant, has exactly two roots,

(d)state the range of possible values of k.[3]

P

A colony of bees is being studied. The number of bees in the colony is modelled by the equation

where P is the number of bees, measured in thousands, t years after the study started. A sketch of the graph of P against t is shown in Figure 3

(a)Calculate the number of bees in the colony at the start of the study.[2]

(b)Find dPdt[3]

The population of bees initially decreases, reaching a minimum value after T years, as shown in Figure 3

(c)Using your answer to part (b), calculate the value of T to 2 decimal places.

[4]

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

(a)Express 10 cos θ –3 sin θ in the form R cos(θ + α), where R > 0 and 0 < α < 90°

Give the exact value of R and the value of α to 2 decimal places.[3]

Alana models the height above the ground of a passenger on a Ferris wheel by the equation

where the height of the passenger above the

ground is H metres at time t minutes after the wheel starts turning.

Use part (a) and the equation of the model to answer parts (b), (c) and (d).

(b)Calculate

(i)the maximum value of H

(ii)the value of t when this maximum first occurs.

Give each answer to 2 decimal places.[3]

(c)Calculate the value of t when the passenger is 18 m above the ground for the first time.

Give your answer to 2 decimal places.[4]

(d)Determine the time taken for the Ferris wheel to complete two revolutions.[2]

Centre Number Candidate Number

Pearson Edexcel International Advanced Level

Tuesday 21 October 2025

Afternoon (Time: 1 hour 30 minutes)

International Advanced Level Pure Mathematics P3 Answer Book

You must have: Question paper (sent separately),_TotalMarks 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. • 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 8 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.

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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