7/21/2019 Edexcel C4 - June 2014 Model Answers by FAHIM

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Sttr

c,k

utr-

1. A

curve

C

has the

equation

x3

+2xy-x-y3

-20:o

(a)

Find

9Z

in terms of

x

andy.

dx

(b)

Find an equation

of the

tangent

to

C atthe

point

(3,

_,2),

giving

y

form ax

+

by

+

c:0,

where

a,

b

a,.d

c

are

integers.

g.

1*t*'#*zg-\-jf*=o

7/21/2019 Edexcel C4 - June 2014 Model Answers by FAHIM

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2.

Given

that

the binomial

expansion

of

(1

+

kx)-|,

I

k'

l

'

1,

i'

l-6x+Axz-t...

(a)

find

the

value

of

the constant

k,

(b)

find

the

value

of

the constant

A,

givingyour

answer

in

its

simples

MtPuS'

2

7/21/2019 Edexcel C4 - June 2014 Model Answers by FAHIM

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3.

Figure

1

Figurel

showsasketchofparlofthecurvewithequation

y-

10-

7/21/2019 Edexcel C4 - June 2014 Model Answers by FAHIM

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(A=\

,t3

:("4 tr=

Ay-

-__

_,_,--,------- t_

b

t12

t

l

7/21/2019 Edexcel C4 - June 2014 Model Answers by FAHIM

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4.

Figure

2

A

vase

with

a

circular

cross-section

is

shown

in Figure

2.

Water

is

flow

7/21/2019 Edexcel C4 - June 2014 Model Answers by FAHIM

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5.

Figure

3

Figure

3 shows

a sketch

of

the

curve

C

with

parametric

equations

7/21/2019 Edexcel C4 - June 2014 Model Answers by FAHIM

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-6 -;

tt

S r n

1k-

-:)--e-S-

t:* rrtt--

q-.f-Tz--

-

?

tu-

=3tl=Jl ef

7/21/2019 Edexcel C4 - June 2014 Model Answers by FAHIM

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6.

(i)

Find

(ii)

Find

tr"o.

a*

1

2

,(iii)

Given

that

y

:

.2

u,

x

:

0,

soive

the

differential

equation

dv

d,

:

t'cosec'lY

cosec)"

7/21/2019 Edexcel C4 - June 2014 Model Answers by FAHIM

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7.

Figure

4

shows a

sketch

of parl of

the

curve

C

with

parametric

equation

Figure

4

7/21/2019 Edexcel C4 - June 2014 Model Answers by FAHIM

10/13

IFo

+

a*:@

e

t{

"_II l"_ _b'( Elgl

7/21/2019 Edexcel C4 - June 2014 Model Answers by FAHIM

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/-r\

8.

Relative

to a

flxed origin

O,

the

point Ahas

positio,

,..,".

I

;

I

IrJ

/-r\

and

the point B

has

position

u..ro,

|

,

I

[-J

The

line

/,

passes through

the

points

A ar:d

B.

(a)

Find

the

vector

Ai.

(b)

Hence

flnd

a vector

equation

for the

line

/,

ro)

The

point

P

has

position vector

2

I

7/21/2019 Edexcel C4 - June 2014 Model Answers by FAHIM

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7/21/2019 Edexcel C4 - June 2014 Model Answers by FAHIM

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-

fuJ0-:

:.

h