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Candidate surname Other names

Pearson Edexcel Centre Number Candidate Number

International
Advanced Level

Wednesday 3 June 2020

Afternoon (Time: 1 hour 30 minutes) Paper Reference WMA13/01

Mathematics
International Advanced Level
Pure Mathematics P3

You must have: Total Marks

Mathematical Formulae and Statistical Tables (Lilac), 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).
• candidate
Fill in the boxes at the top of this page with your name, centre number and
number.
• clearly labelled.
Answer all questions and ensure that your answers to parts of questions are

• 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
stated.
answers should be given to three significant figures unless otherwise

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
•• Try
Read each question carefully before you start to answer it.
to answer every question.
•• If you change
Check your answers if you have time at the end.
your mind about an answer, cross it out and put your new answer
and any working underneath.
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1. Solve, for 0  x < 360°, the equation

2 cos 2 x = 7 cos x

giving your solutions to one decimal place.

(Solutions based entirely on graphical or numerical methods are not acceptable.)

(5)
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2. A scientist monitored the growth of bacteria on a dish over a 30‑day period.

The area, N mm2, of the dish covered by bacteria, t days after monitoring began, is
modelled by the equation

log10 N = 0.0646 t + 1.478 0  t  30

(a) Show that this equation may be written in the form

t
N = ab

where a and b are constants to be found. Give the value of a to the nearest integer
and give the value of b to 3 significant figures.
(4)

(b) Use the model to find the area of the dish covered by bacteria 30 days after monitoring
began. Give your answer, in mm2, to 2 significant figures.
(2)
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3. y

O x

Figure 1

Figure 1 shows a sketch of a curve with equation y = f (x) where

2x + 3 1
f (x) = x>
4x − 1 4

(a) Find, in simplest form, f ʹ(x).

(4)

(b) Hence find the range of f.

(3)
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4.
y

y = f (x)

O x

Figure 2

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

f (x) = 21 − 2 | 2 − x | x0

(a) Find f f (6)

(2)

(b) Solve the equation f (x) = 5x

(2)

Given that the equation f (x) = k , where k is a constant, has exactly two roots,

(c) state the set of possible values of k.

(2)

The graph with equation y = f (x) is transformed onto the graph with equation y = a f (x − b)

The vertex of the graph with equation y = a f (x − b) is (6, 3).

Given that a and b are constants,

(d) find the value of a and the value of b.

(2)
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Question 4 continued
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