7/29/2019 Mathcad - CAPE - 2001 - Math Unit 2 - Paper 02

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CAPE - 2001Pure Mathematics - Unit 2

Paper 02

Section A (Module 1)

1 a( ) The parametric equations of a curve are given by

x t3

et

tt

y t et.tt

i( ) Show thatdy

dx

t 1

t2

t 3( )

dy

dx

t

t t

[4 marks]

ii( ) Hence state the values of t for which the derivative of the curve is not defined

[3 marks]

iii( ) Determine the equation of the tangent at the stationary point on the curve

[3 marks]

b( ) Using the derivatives of sin x and cos x with respect to x show that the derivative oftan x with respect to x is

sec2

x [5 marks]

c( ) A curve has equation y tan x

6

. x where 0 x 1)

S4

1 R4

1.

R 1

41

beginning of fifth month: Amount 1000 R4 PR R

41.

R 1

41PR

d( ) 0 1000 Rn PR R

n1.

R 1R

nnPR R

n1. 1000 R

nR 1( )R

nn

P1000 R

nR 1( )

R Rn

1.

Rnn

P1000 R

n 1R 1( )

Rn

1

Rn 1n

10