PMT

Please check the examination details below before entering your candidate information
Candidate surname Other names

Centre Number Candidate Number

Pearson Edexcel International Advanced Level

Time 1 hour 30 minutes
Paper
reference WMA11/01
Mathematics
 

International Advanced Subsidiary/Advanced Level

Pure Mathematics P1

You must have: Total Marks

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.
• clearly
Answer all questions and ensure that your answers to parts of questions are
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
•• AThere
booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
are 9 questions in this question paper. The total mark for this paper is 75.
• – use this asfora guide
The marks each question are shown in brackets
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.
Turn over

*P72137A0128*
P72137A
©2022 Pearson Education Ltd.

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1. The curve C has equation

x3 17
y= − x2 + x>0
4 x
dy
(a) Find , giving your answer in simplest form.
dx
(3)

 13 
The point R  2,  lies on C.
 2

(b) Find the equation of the tangent to C at the point R. Write your answer in the form
ax + by + c = 0, where a, b and c are integers to be found.
(3)
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Question 1 continued
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(Total for Question 1 is 6 marks)

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2. Given that

(x – 5)(2x + 1)(x + 3) ≡ ax 3 + bx2 –32x – 15

where a and b are constants,

(a) find the value of a and the value of b.
(2)
(b) Hence find

( x − 5)(2 x + 1)( x + 3)
∫ 5 x
dx

writing each term in simplest form.

(5)
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Question 2 continued
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(Total for Question 2 is 7 marks)

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3. The share price of a company is monitored.

Exactly 3 years after monitoring began, the share price was £1.05
Exactly 5 years after monitoring began, the share price was £1.65
The share price, £V, of the company is modelled by the equation

V = pt + q

where t is the number of years after monitoring began and p and q are constants.
(a) Find the value of p and the value of q.
(3)
Exactly T years after monitoring began, the share price was £2.50
(b) Find the value of T, according to the model, giving your answer to
one decimal place.
(2)
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Question 3 continued
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(Total for Question 3 is 5 marks)

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4. In this question you must show detailed reasoning.

Solutions relying on calculator technology are not acceptable.

f(x) = x 2(2x + 1) – 15x

(a) Solve

f(x) = 0
(4)
(b) Hence solve

4 2 2
3
( 3
)
y 2y + 1 – 15y = 0 3
y>0

giving your answer in simplified surd form.

(2)
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Question 4 continued
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(Total for Question 4 is 6 marks)

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

Solutions relying entirely on calculator technology are not acceptable.

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

Given that
12 x
• f ′(x) = + –4
x 3
• the point P(9, 8) lies on C

(a) find, in simplest form, f(x)

(5)
The line l is the normal to C at P
(b) Find the coordinates of the point at which l crosses the y‑axis.
(4)
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Question 5 continued
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Question 5 continued
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Question 5 continued
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(Total for Question 5 is 9 marks)

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6. (a) Given that k is a positive constant such that 0 < k < 4 sketch, on separate axes, the
graphs of
(i) y = (2x – k)(x + 4)2
k
(ii) y =
x2
showing the coordinates of any points where the graphs cross or meet the coordinate
axes, leaving coordinates in terms of k, where appropriate.
(5)
(b) State, with a reason, the number of roots of the equation

k
(2x – k)(x + 4)2 =
x2
(1)

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Question 6 continued

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(Total for Question 6 is 6 marks)

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7.
y

(–4, 6) (–1, 6) (2, 6) (3, 6)

O x

y = f(x)

Figure 1

Figure 1 shows the curve with equation y = f(x).

The points P(–4, 6), Q(–1, 6), R(2, 6) and S(3, 6) lie on the curve.
(a) Using Figure 1, find the range of values of x for which

f(x) < 6
(3)
(b) State the largest solution of the equation

f(2x) = 6
(1)

(c) (i) Sketch the curve with equation y = f(–x).

On your sketch, state the coordinates of the points to which P, Q, R and S
are transformed.
(ii) Hence find the set of values of x for which

f(–x)  6 and x < 0

(4)
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Question 7 continued
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Question 7 continued
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Question 7 continued
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(Total for Question 7 is 8 marks)

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8.
Diagram NOT
to scale
X B 8m
3m π C
rad
6
O 2π
rad
3
3m

Figure 2

Figure 2 shows the plan view of a design for a pond.

The design consists of a sector AOBX of a circle centre O joined to a quadrilateral AOBC.
• BC = 8 m
• OA = OB = 3 m
2π
• angle AOB is radians
3
π
• angle BCA is radians
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(a) Calculate  (i) the exact area of the sector AOBX,

(ii) the exact perimeter of the sector AOBX.

(5)
(b) Calculate the exact area of the triangle AOB.
(2)
(c) Show that the length AB is 3 3 m.
(2)
(d) Find the total surface area of the pond. Give your answer in m2 correct to
2 significant figures.
(5)
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Question 8 continued
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Question 8 continued
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Question 8 continued
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(Total for Question 8 is 14 marks)

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9.
y

P
O x

Figure 3

Figure 3 shows a sketch of the curve C with equation

1 2
y= x – 10x + 22
2

1 2
(a) Write x – 10x + 22 in the form
2
2
a(x + b) + c

where a, b and c are constants to be found.

(3)
The point M is the minimum turning point of C, as shown in Figure 3.
(b) Deduce the coordinates of M
(2)
The line l is the normal to C at the point P, as shown in Figure 3.
1
Given that l has equation y = k – x, where k is a constant,
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(c) (i) find the coordinates of P
(ii) find the value of k
(6)

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Question 9 continued

P
O x

Figure 4

Figure 4 is a copy of Figure 3. The finite region R, shown shaded in Figure 4, is

bounded by l, C and the line through M parallel to the y‑axis.
(d) Identify the inequalities that define R.
(3)
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Question 9 continued
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Question 9 continued
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Question 9 continued
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(Total for Question 9 is 14 marks)

TOTAL FOR PAPER IS 75 MARKS

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