WMA11 Pure Mathematics 1 (P1): Oct/Nov 2025 Paper 01A

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

Figure 1 shows a sketch of a triangle LMN and a sketch of a triangle PQR.

Triangle LMN is an equilateral triangle with sides (x + 7) cm.

Triangle PQR is a right-angled isosceles triangle with PQ = PR = 2x cm and angle QPR = 90°

(a)Find, in its simplest form in terms of x, the length QR.[2]

Given that the perimeter of triangle LMN is equal to the perimeter of triangle PQR,

(b)find the value of x, writing your answer in the form a 2 + b , where a and b are integers.[5]

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

A curve has equation

(a)Find, in simplest form, dydx[3]

(b)Hence find the range of values for x such that

[4]

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

[5]

Figure 2 shows the points P, Q and R.

Points P and Q have coordinates (–1, 4) and (4, 7) respectively.

(a)Find an equation for the straight line passing through points P and Q.

Give your answer in the form ax + by + c = 0 where a, b and c are integers.[3]

The point R has coordinates ( p, –3), where p is a positive constant.

Given that angle QPR = 90°,

(b)find the value of p.

(Solutions relying on calculator technology are not acceptable.)[3]

Find

writing the answer in its simplest form.[5]

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

The equation

where k is a real constant, has no real roots.

Find the range of possible values for k.[7]

Figure 3 shows the design for a company logo.

The design consists of a triangle ABE joined to a sector BCDE of a circle with radius 6 cm and centre E. The line AE is perpendicular to the line DE and the length of AE is 9 cm.

The size of angle DEB is 3.5 radians, as shown in Figure 3.

(a)Find the length of the arc BCD.[2]

Find, to one decimal place,

(b)the perimeter of the logo,[3]

(c)the area of the logo.[4]

Figure 4 shows a sketch of the graph of y = g (x), –3  x  4 and part of the line l with

equation y = 12 x

The graph of y = g (x) consists of three line segments, from P (–3, 4) to Q (0, 4), from Q (0, 4) to R (2, 0) and from R (2, 0) to S (4, 10).

The line l intersects y = g (x) at the points A and B as shown in Figure 4.

(a)Use algebra to find the x coordinate of the point A and the x coordinate of the point B. Show each step of your working and give your answers as exact fractions.[6]

(b)Sketch the graph with equation

On your sketch show the coordinates of the points to which P, Q, R and S are transformed.[2]

The curve C has equation y = f (x), x > 0 where

Given that the point P (4, –8) lies on C,

(a)find the equation of the normal to C at P, giving your answer in the form y = mx + c, where m and c are constants.[4]

(b)Find f (x), giving each term in its simplest form.[5]

(a)On the axes in the answer book sketch and clearly label the graphs of

(i)y = x(a – x)

(ii)y = x (b – x)

where a and b are positive constants b > a

Show clearly the coordinates of all the points where the curves cross or meet the coordinate axes.[5]

(b)Show that the x-coordinates of the points of intersection of

are given by the solutions to the equation

[2]

The point A lies on both of the curves and the x and y coordinates of A are both positive.

(c)Find the exact coordinates of A, leaving the answer in the form p  q 3, r  s 3 ,

where p, q, r and s are integers.

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

Centre Number Candidate Number

Pearson Edexcel International Advanced Level

Thursday 9 October 2025

Morning (Time: 1 hour 30 minutes)

International Advanced Subsidiary/Advanced Level Pure Mathematics P1 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 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.

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 8

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Question 9

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Question 10

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