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Candidate surname Other names

Pearson Edexcel Centre Number Candidate Number

International
Advanced Level

Wednesday 10 June 2020

Afternoon (Time: 2 hours 30 minutes) Paper Reference WMA02/01

Mathematics
International Advanced Level
Core Mathematics C34

You must have: Total Marks

Mathematical Formulae and Statistical Tables (Blue), 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.

• Fill
If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
in the boxes at the top of this page with your name, centre number and

• clearly
candidate number.
Answer all questions and ensure that your answers to parts of questions are

• – there may
labelled.
Answer the questions in the spaces provided

• without working may

be more space than you need.
You should show sufficient working to make your methods clear. Answers

• stated.
not gain full credit.
Inexact answers should be given to three significant figures unless otherwise

Information
•• AThere
booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
are 14 questions in this question paper. The total mark for this paper

• The
is 125.
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.

•• Check
Try to answer every question.
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

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1. The curve C has equation

16 2
y= x>
3(5 x − 2)3 5
dy
(a) Find, in simplest form,
dx
(2)

4
The point P with x coordinate lies on C.
5

(b) Find the equation of the tangent to C at P writing your answer in the form y = mx + c,
where m and c are constants to be found.
(4)
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2. The growth of pond weed on the surface of a pond is being investigated.

The surface area of the pond covered by the weed, A m2, is modelled by the equation

1200e0.04t
A= t ∈ , t  0
4e0.04t + 1

where t is the number of weeks after the start of the investigation.

Using the model,

(a) calculate the surface area of the pond covered by the weed at the start of the
investigation,
(1)

(b) calculate the value of t when A = 260, giving your answer to 2 decimal places.

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

(4)

The pond weed continues to grow until it completely covers the surface of the pond.

Using the model,

(c) deduce the maximum possible surface area of the pond.

(1)
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Question 2 continued
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(Total 6 marks)

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4.
y

O P x

Figure 1

Figure 1 shows a sketch of the curve with equation

y = x ln x – 6 x , x > 0

The curve crosses the x-axis at the point P and has a minimum turning point at Q.

(a) Show that the x coordinate of P lies in the interval [8, 8.5].
(2)

(b) Show that the x coordinate of Q is a solution of the equation

3
−1
x
x=e
(4)

Using the iterative formula

3
−1
xn
xn + 1 = e with x1 = 2.5

(c) find the value of x2 and the value of x3 to 3 decimal places.

(2)
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Question 4 continued
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5. The functions f and g are defined by

3
f(x) = –1 x ∈ , x ≠ 0
x
g(x) = e4x x∈

(a) Find f(x + 2) – 2f(x)

Write your answer as a single fraction in simplest form.

(3)

(b) Find f –1(7)

(2)

(c) Find the exact solution to the equation

fg(x) = 8
(3)
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7. (a) Use the identity for tan(A + B) to show that

3 tan A − tan 3 A
tan 3A ≡
1 − 3 tan 2 A
(4)

π π
(b) Hence solve, for – <x<
6 6

tan 3x = 4 tan x

Give each answer to 3 significant figures where appropriate.

(4)
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11.
y

O x

Figure 5

Figure 5 shows a sketch of part of the graph with equation y = f(x), where

f(x) = ½ x – 2a½ – 3b, x∈

and where a and b are positive constants.

All answers to parts (a), (b), (c) and (d) should be expressed in terms of a and/or b.

(a) Find the values of x such that f(x) = 0

(2)

The point P, as shown in Figure 5, is the vertex of the graph.

(b) State the coordinates of the point P.

(1)

(c) State the coordinates of the image of P under the transformation represented by the
graph with equation

(i) y = 2½ f(x)½

(ii) y = 3f(2x)
(2)

(d) Solve the equation

½ x – 2a½ – 3b = 2x + a
(3)
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12. (i) Find

∫
4
dy
(5 y − 7) 4
(2)

(ii) Find, in simplest form,

∫ (1 − 4 tan 3x) dx2

(4)

(iii) Using the substitution u = 1 + 2 cos θ, or otherwise, find

π
2sin 2θ
∫ 1 + 2cos θ dθ
2

giving your answer in the form ln(Ae2), where A is a constant to be found.

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

(6)
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