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Centre Number Candidate Number

Write your name here

Surname Other names

Total Marks

Paper Reference

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Pearson EdexcelInternationalAdvanced Level

Candidates may use any calculator allowed by the regulations of theJoint Council for Qualifications. Calculators must not have the facilityfor symbolic algebra manipulation, differentiation and integration, orhave retrievable mathematical formulae stored in them.

Instructions

Use blackink 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 boxesat the top of this page with your name,centre number and candidate number.

Answer allquestions and ensure that your answers to parts of questions areclearly 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. Answerswithout 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 eachquestion 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.

*P46958A0144*P46958A2016 Pearson Education Ltd.

1/1/1/1/

You must have:Mathematical Formulae and Statistical Tables (Blue)

WMA02/01Tuesday 19 January 2016 Morning

Time: 2 hours 30 minutes

Core Mathematics C34Advanced

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1. f (x) = (3 2x)4, x3

2

Find the binomial expansion of f(x), in ascending powers of x, up to and including the

term inx2, giving each coefficient as a simplified fraction.

(4)

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(Total 4 marks)

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2. (a) Show that

cot2x cosecx 11 = 0

may be expressed in the form cosec2x cosecx+ k= 0, where kis a constant.

(1)

(b) Hence solve for 0 x360

cot2x cosecx 11 = 0

Give each solution in degrees to one decimal place.

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

(5)

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(Total 6 marks)

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3. A curve C has equation

3x+ 6y=3

2xy2

Find the exact value ofd

d

y

xat the point on C with coordinates (2, 3). Give your answer in

the forma b+ ln

8, where aand bare integers.

(7)

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(Total 7 marks)

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4.

Figure 1

The curve C with equation y =2

4 3( )+ x, x

4

3is shown in Figure 1

The region bounded by the curve, the x-axis and the lines x= 1 and x= 23

, is shown

shaded in Figure 1

This region is rotated through 360 degrees about thex-axis.

(a) Use calculus to find the exact value of the volume of the solid generated.

(5)

A

B

Figure 2

Figure 2 shows a candle with axis of symmetry ABwhereAB= 15 cm. A is a point at

the centre of the top surface of the candle and Bis a point at the centre of the base of the

candle. The candle is geometrically similar to the solid generated in part (a).

(b) Find the volume of this candle.

(2)

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5.

f(x) = x3+ 4x2 6

(a) Show that the equation f (x) = 0 has a root betweenx= 1 andx= 2

(2)

(b) Show that the equation f (x) = 0 can be rewritten as

xx

=

6

4

(2)

(c) Starting withx1= 1.5 use the iterationx

n+1=

6

4

xnto calculate the values ofx

2,

x3andx

4giving all your answers to 4 decimal places.

(3)

(d) Using a suitable interval, show that 1.572 is a root of f (x) = 0 correct to 3 decimal

places.

(2)

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(Total 9 marks)

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6. A hot piece of metal is dropped into a cool liquid. As the metal cools, its temperature

Tdegrees Celsius, tminutes after it enters the liquid, is modelled by

T= 300e0.04t+ 20, t0

(a) Find the temperature of the piece of metal as it enters the liquid.

(1)

(b) Find the value of tfor which T= 180, giving your answer to 3 significant figures.

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

(4)

(c) Show, by differentiation, that the rate, in degrees Celsius per minute, at which the

temperature of the metal is changing, is given by the expression

20

25

T

(3)

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(Total 8 marks)

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7.

Figure 3

Figure 3 shows part of the curve Cwith equation

y=3 1

1

2

2

ln( )

( )

x

x

++

, x

(a) Findd

d

y

x (2)

(b) Using your answer to (a), find the exact coordinates of the stationary point on the

curve Cfor whichx0. Write each coordinate in its simplest form.(5)

The finite regionR, shown shaded in Figure 3, is bounded by the curve C, thex-axis and

the linex= 3

(c) Complete the table below with the value ofycorresponding tox= 1

x 0 1 2 3

y 0 3

5ln5

3

10ln10

(1)

(d) Use the trapezium rule with all the y values in the completed table to find an

approximate value for the area ofR, giving your answer to 4 significant figures.

(3)

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(Total 11 marks)

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8. f () = 9cos2+ sin2

(a) Show that f() = a + bcos2, where aand bare integers which should be found.

(3)

(b) Using your answer to part (a) and integration by parts, find the exact value of

2

0

2f ()d(6)

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(Total 9 marks)

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9. (a) Express3 4

3 2

2

2

x

x x

( )

in partial fractions.

(4)

(b) Given thatx2

3

, find the general solution of the differential equation

x2(3x 2)d

d

y

x=y(3x2 4)

Give your answer in the formy= f (x).

(6)

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Question 9 continued

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(Total 10 marks)

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10. (a) Express 3sin2x+ 5cos2x in the formRsin(2x+ ), whereR0 and 0 2

Give the exact value ofR and give thevalue of to 3 significant figures.

(3)

(b) Solve, for 0 x,

3sin2x+ 5cos2x= 4

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

(5)

g(x) = 4(3sin2x+ 5cos2x)2+ 3

(c) Using your answer to part (a) and showing your working,

(i) find the greatest value of g(x),

(ii) find the least value of g(x).

(4)

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Question 10 continued

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