Advanced Level Core Mathematics C34 - Edexcel

Centre Number Candidate Number

Write your name hereSurname Other names

Total Marks

Paper Reference

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Pearson Edexcel InternationalAdvanced Level

Candidates may use any calculator allowed by the regulations of the Joint Council for Qualifications. 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).

Coloured pencils and highlighter pens must not be used. 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. When a calculator is used, the answer should be given to an appropriate

degree of accuracy.

Information The total mark for this paper is 125. 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.

*P44966A0144*P44966A©2014 Pearson Education Ltd.

5/5/5/5/

You must have:

Mathematical Formulae and Statistical Tables (Blue)

WMA02/01Monday 27 January 2014 – MorningTime: 2 hours 30 minutes

Core Mathematics C34Advanced

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*P44966A0244*

1. f ( ) ,x xx

=+

232 x

Find the set of values of x x) 0

You must show your working.

Solutions based entirely on graphical or numerical methods are not acceptable.)(6)

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Question 1 continued

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___________________________________________________________________________ Q1

(Total 6 marks)

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2. Solve, for 0 x 270°, the equation

tan tantan tan2 50

1 2 502x

x+

−=°

°

Give your answers in degrees to 2 decimal places.(6)

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___________________________________________________________________________ Q2

(Total 6 marks)

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3. Given that

4x3 + 2x2 + 17x + 8 Ax + B x2 + 4) + Cx + D

A, B, C and D.(4)

∫1

4 3 2

24 2 17 8

4x x x

xx+ + +

+d

giving your answer in the form p + ln q, where p and q are integers.(6)

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___________________________________________________________________________ Q3

(Total 10 marks)

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4.

Figure 1 Figure 2

Figure 1 shows a sketch of part of the graph y x), where

x) = 2|3 – x| + 5, x 0

Figure 2 shows a sketch of part of the graph y x), where

g( ) ,x xx

= ++

92 3

x 0

(2)

(2)

–1 x) and state its domain.(4)

x) = k, where k is a constant, has exactly two roots,

k.(3)

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O x

y x)

y

O x

y x)

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___________________________________________________________________________ Q4

(Total 11 marks)

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*P44966A01444*

5.

ddx

x x( ) ln2 2 2=

(3)

The curve C has the equation

2x + 3y2 + 3x2y + 12 = 4 × 2x

The point P C.

C at P. (6)

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___________________________________________________________________________ Q5

(Total 9 marks)

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*P44966A01844*

6. Given that the binomial expansion, in ascending powers of x, of

69

32√ √( )

,+

<Ax

xA

is B x Cx− + +23

2 4

A, B and C.(7)

x6

(2)

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___________________________________________________________________________ Q6

(Total 9 marks)

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*P44966A02044*

7.

Figure 3

Figure 3 shows a sketch of part of the curve with equation y = x), where

x) = 2x x) ln x, x 0

The curve has a minimum turning point at A.

x)(3)

x coordinate of A is the solution of the equation

xxx=

− ++e1

1 2

(3)

x xn

xxn

n+

−+

+= =1

11 2

0 0 46e , .

to find the values of x1, x2 and x3 to 4 decimal places.(3)

A to 2 decimal places.(2)

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___________________________________________________________________________ Q7

(Total 11 marks)

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*P44966A02444*

8.

2cosec 2A – cot A A, A 2nπ

, n (4)

02πθ� �

– cot 2 =

tan cot 5θ θ+ =

Give your answers to 3 significant figures.(6)

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___________________________________________________________________________ Q8

(Total 10 marks)

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*P44966A02844*

9. u = 4 – x to find

d4xx− √∫

(6)

A team of scientists is studying a species of slow growing tree.

The rate of change in height of a tree in this species is modelled by the differential equation

d 4d 20h ht

− √=

where h is the height in metres and t is the time measured in years after the tree is planted.

h for which the height of a tree in this species is increasing.(2)

would take to reach a height of 10 metres. Write your answer to 3 significant figures. (7)

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___________________________________________________________________________ Q9

(Total 15 marks)

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*P44966A03244*

10. With respect to a fixed origin O, the lines l1 and l2 are given by the equations

l1 : r i + 5j + 5k) + i + j – k)

l2 : r j + 12k) + i – j + 5k)

where and are scalar parameters.

l1 and l2 meet and find the position vector of their point of intersection.(6)

l1 and l2 are perpendicular to each other.(2)

The point A, with position vector 5i + 7j + 3k, lies on l1

The point B is the image of A after reflection in the line l2

B.(3)

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(Total 11 marks)

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*P44966A03644*

11. The curve C has parametric equations

x = 10 cos 2t, y = 6 sin t, 2 2π πt− � �

The point A C.

t at the point A.(1)

C at A is

3y = 10x – 41(6)

The normal to C at A cuts C again at the point B.

B.(8)

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___________________________________________________________________________ Q11

(Total 15 marks)

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*P44966A04044*

12.

Figure 4

Figure 4 shows a sketch of part of the curve with equation

(sin cos ), 04πy x x x x= + � �

The finite region R, shown shaded in Figure 4, is bounded by the curve, the x-axis and the

line 4πx = . This shaded region is rotated through 2 radians about the x-axis to form a

solid of revolution, with volume V.

4 2

0(1 sin 2 )d

π

V πx x x= +∫(3)

V.

You must show your working.

Solutions based entirely on graphical or numerical methods are not acceptable.)(9)

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y

O x

R

x = 4π

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TOTAL FOR PAPER: 125 MARKS

END

Q12

(Total 12 marks)

Date post:	30-Jan-2022
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Advanced Level Core Mathematics C34 - Edexcel

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