WMA12 Pure Mathematics 2 (P2): Oct/Nov 2025 Paper 01A

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

A sequence u₁, u₂, u₃, is defined by

where k is a constant.

(a)Write down expressions for u₂ and u₃ in terms of k.[2]

Given that u₃= 6

(b)find the possible values of k.[3]

Find the first 3 terms in ascending powers of x of

giving each term in its simplest form.[4]

Figure 1 shows a sketch of part of the graph of y  x  2

The table below gives values of y rounded to 3 decimal places.

(a)Use the trapezium rule with all the values of y from the table to find an approximate value, to 2 decimal places, for

[3]

(b)Use your answer to part (a) to estimate a value for

[3]

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

Given that (x + 3) is a factor of f (x),

(a)(i)show that a possible value of k is 5

(ii)find the other possible value of k.[3]

Given that k = 5

(b)(i)write f (x) as the product of two algebraic factors

(ii)show that the equation f (x) = 0 has only one real solution.[6]

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

(i)Given that

log_a x + log_a 3 = log_a27 –1 where a is a positive constant

find, in its simplest form, an expression for x in terms of a.[4]

(ii)Solve the equation

showing each step of your working.[4]

A circle C has equation x²+ y²– 6x – 14y + k = 0 where k is constant.

(a)Find the coordinates of the centre of C.[2]

(b)Find the radius of C when k = –32[2]

(c)Find the range of values of k for which C lies completely within the first quadrant.[4]

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

(i)Solve, for 0  θ < 180°, the equation

giving your answers, in degrees, to one decimal place.[4]

(ii)Solve, for 0  x < 2π, the equation

giving your answers, in radians, to 3 decimal places.[5]

A curve has equation y = (x + 2) (4 – x)

The finite region R is bounded by the curve and the x-axis.

(a)Using algebraic integration and showing each step of your working, find the exact area of R.[5]

(b)Using the answer to part (a) and explaining your reasoning, find the area of the

finite region bounded by the curve with equation y  (3x  6)²  2  12 x  and

the x-axis.[2]

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

(i)A car has five gears. Given that

• the maximum speed of the car in first gear is 22 km h

• the maximum speed in each successive gear forms a geometric sequence

• the maximum speed of the car in fifth gear is 130 km h

find the maximum speed of the car in second gear, giving your answer, in km h , to one decimal place.[4]

(ii)The first two terms of an arithmetic sequence are 208 and 207.2

Given that Sn is the sum to n terms,

(a)find the maximum value of Sn[4]

(b)Hence or otherwise state the smallest value of N such that SN < 0[1]

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

Figure 2 shows the plan view of the design for a stage at a trade fair.

The shape of the stage ABCDEFA, consists of a rectangle ACDF joined to two congruent sectors of circles. ABC is a sector of a circle centre A and FDE is a sector of a circle centre F.

Given that AC = 2r metres, CD = r metres, angle DFE = θ radians and the area of the stage is 30 m ,

(a)show that the perimeter, P metres, of the stage, is given by

[4]

(b)Use calculus to find the minimum value for P, giving your answer in the form a b , where a and b are integers to be found.[4]

(c)Justify that the value of P found in part (b) is the minimum.[2]

Centre Number Candidate Number

Pearson Edexcel International Advanced Level

Wednesday 15 October 2025

Morning (Time: 1 hour 30 minutes)

International Advanced Subsidiary/Advanced Level Pure Mathematics P2 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 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. • 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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