WMA12 Pure Mathematics 2 (P2): January 2026 Paper 01A

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

An arithmetic series has first term a and common difference d.

Given that the sum of the first 9 terms is 54

(a)show that

[2]

Given also that the 8th term is half the 7th term,

(b)find the values of a and d.[4]

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

A sequence is defined by

Find the exact values of

(a)u₂, u₃ and u₄[3]

(b)u₆₁[1]

(c)u _i

[2]

Figure 1 shows a sketch of part of the curve with equation y  x  2 x  –2

The finite region R, shown shaded in Figure 1, is bounded by the curve, the x-axis and the line with equation x = 6

The table below shows corresponding values of x and y for y  x  2

(a)Use the trapezium rule, with all of the values of y in the completed table, to find an approximate value for the area of R, giving your answer to 3 decimal places.[3]

Use your answer to part (a) to find the approximate value of

(b)(2x  4x  8) dx ₂[3]

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

Given that (x – 2) is a factor of f (x),

(a)use the factor theorem to show that 2a + b = –7[2]

Given also that when f (x) is divided by (x + 1) the remainder is –36

(b)find the value of a and the value of b.[4]

(c)Hence find the quotient and remainder when f (x) is divided by (x – 5)[3]

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

Given that k is a constant and

find the exact value of k.[5]

Figure 2 shows a circle C with centre Z

Points X and Y lie on C and have coordinates (0, 3) and (6, 11) respectively.

Given that M is the midpoint of XY

(a)Find an equation for the straight line which passes through Z and M, giving your answer in the form ax + by + d = 0 where a, b and d are integers.[4]

Given that the y coordinate of Z is 10

(b)Find the x coordinate of Z[2]

(c)Hence find an equation of C[3]

The point W lies on C such that angle WXY = 90°

(d)Find the coordinates of W[2]

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

Figure 3 shows the plan view of a garden. The shape of this garden consists of a rectangle joined to a semicircle.

The rectangle has length x metres and width y metres.

The area of the garden is 100 m².

(a)Show that the perimeter, P metres, of the garden is given by

[4]

(b)Use calculus to find the exact value of x for which the perimeter of the garden is a minimum.[3]

(c)Justify, by further use of calculus, that the value of x found in part (b) gives a minimum value for P.[2]

(d)Find the minimum perimeter of the garden, giving your answer in metres to one decimal place.[2]

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

Given the first three terms of a geometric sequence are

where θ is a constant

(a)show that

[3]

Given that θ is acute,

(b)use trigonometric identities to find the exact value of the second term in the sequence.[3]

(c)find the value of the 11th term in the sequence.[3]

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

Given that a and b are positive constants, solve the simultaneous equations

Show each step of your working, giving exact values for a and b.[4]

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

The binomial expansion, in ascending powers of x, of (1 + kx) is

where k and p are non-zero constants and n is an integer greater than 1.

(a)Use this information to set up and solve two simultaneous equations to find the value of k and the value of n.[6]

(b)Hence find the value of p.[2]

Centre Number Candidate Number

Pearson Edexcel International Advanced Level

Tuesday 13 January 2026

Morning (Time: 1 hour 30 minutes)

International Advanced Subsidiary/Advanced Level Pure Mathematics P2 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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