Paper 3

Question 1

find gdashedx

Answer 1

e^3xsec2x(3+2tan2x)

Question 2

derivative of sec2x

Answer 2

2sec2xtan2x

Question 3

x-coordinate of stationary point C

Answer 3

-0.49

Question 4

x cannot be

Answer 4

e^2

Question 5

explanation for > 0

Answer 5

• multiply numerator and denominator by x
• squared numbers have to be greater than 0
• x has to be greater than 0
• dividing one by a number greater than zero will always result in a number greater zero

Question 6

A co-ordinate

Answer 6

(-4,0)

Question 7

At B, t=

Answer 7

-2

Question 8

At intersection, t =

Answer 8

20/7

Question 9

At intersection, x =

Answer 9

-40/49

Question 10

A =

Answer 10

1

Question 11

B =

Answer 11

6

Question 12

C =

Answer 12

-15

Question 13

integral of x + 6 + (-15)/(x+2)

Answer 13

1/2x^2 + 6x - 15ln(x+2) + 15ln(2)

Question 14

final answer for ln(2) integral

Answer 14

54 - 30ln(2)

Question 15

integral of lnx/x^2

Answer 15

(-lnx -1)/x + c

Question 16

Area under the curve

Answer 16

1 + 2ln2

Question 17

final substitution

Answer 17

• use root (2x-1)

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