WMA11 Pure Mathematics 1 (P1): January 2026 Paper 01A

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

Find the set of values of x for which

(a)4(x – 5) < 2x – 9[2]

(b)x (2x – 5)  63[3]

(c)4(x – 5) < 2x – 9 and x (2x – 5)  63[1]

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

(i)Using the laws of indices, solve the equation

[3]

(ii)Solve the equation

writing the answer in the form a b where a and b are integers.[4]

(a)Find f ′(x), writing the answer in simplest form.[5]

(b)Hence find an equation of the tangent to the curve y = f (x) at the point (4, 25).

Write the answer in the form y = mx + c, where m and c are constants to be found.[3]

The line l₁, shown in Figure 1, has equation 2y = 3x + 8 The line l₁ intersects the y-axis at the point P and passes through the point Q with x coordinate 6

(a)Find

(i)the coordinates of P,

(ii)the coordinates of Q.[2]

The line l₂ is perpendicular to l₁ and passes through the point Q.

(b)Find an equation for l₂, writing the answer in the form ax + by + c = 0, where a, b and c are integers.[4]

The line l₂ cuts the x-axis at the point R.

(c)Find the area of quadrilateral OPQR, making the method clear.[3]

Figure 2 shows a sketch of part of the curve with equation y = f (x).

The curve crosses the y-axis at the point (0, 8).

The line with equation y = 10 is the only asymptote to the curve.

The curve has a single turning point, a minimum point at (2, 5), as shown in Figure 2.

(a)State the coordinates of the minimum point of the curve with equation y  f  1 4 x 

[1]

(b)State the equation of the asymptote to the curve with equation y = f (x) – 3[1]

The curve with equation y = f (x) meets the line with equation y = k, where k is a constant, at two distinct points.

(c)State the set of possible values for k.[2]

(d)Sketch the curve with equation y = –f (x). On your sketch, show clearly the coordinates of the turning point, the coordinates of the intersection with the y-axis and the equation of the asymptote.[3]

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

Figure 3 shows the design for a shop sign ABCDA.

The sign consists of a triangle AOD joined to a sector of a circle DOBCD with radius 1.8 m and centre O.

The points A, B and O lie on a straight line.

Given that AD = 3.9 m and angle BOD is 0.84 radians,

(a)calculate the size of angle DAO, giving the answer in radians to 3 decimal places.[2]

(b)Find, in m, the length of AO giving the answer to 2 decimal places.[3]

(c)Find, in m , the area of the shop sign, giving the answer to one decimal place.[3]

(d)Find, in m, the perimeter of the shop sign, giving the answer to one decimal place.[3]

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

Given that the point P (9, 20) lies on C,

(a)find f (x), simplifying the answer,[5]

(b)find an equation of the normal to C at the point P, giving the answer in the form ax + by + c = 0 where a, b and c are integers.[4]

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

Find the range of values of k for which the quadratic equation

has no real roots.[6]

Given that k is a constant, 0 < k < 1, state the number of solutions of the equation

(a)sin x = k in the interval 0 < x  π

(b)tan x = k in the interval 0 < x  π

(c)cos 2x = k in the interval 0 < x  100π

(d)sin x = k + 1 in the interval –100π < x  100π[4]

Figure 4 shows a sketch of the curve C₁ with equation y = f (x) where f (x) is a cubic function in x.

The curve

• cuts the x and y axes at (–1, 0) and (0, 12) respectively

• has a minimum turning point at (4, 0)

as shown in Figure 4.

(a)Find f (x)[4]

The curve C₂ has equation y = g (x) where g (x) = 6(x + 1)(x – 2)

(b)Find the exact x coordinates of the points of intersection of curves C₁ and C₂

[4]

Centre Number Candidate Number

Pearson Edexcel International Advanced Level

Thursday 8 January 2026

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. 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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