### cameroon gce advance level June 2015 math with mechanics paper 1

cameroon gce advance level June 2015 math with mechanics paper 1

A function/(x)is continuous in the

interval [a,b ] and differentiable on the

interval (a, b). The mean value theorem

states that there exists a valuec, where

a < c < b, such that lim x -> 0 X

A 0

B – 1

C co

D 1

12. Using the substitutions u = 1 + x 2 A f ( b ) + /(a)

/'(c) =

f 2x( l + x 2 )3dx =

Jo

a — b

B m – /(a)

/'(c) =

b — a

/'(a) ~ f’ (b) ‘

b – a

f’ ( b) – /'(a)

A 15 C

4 /'(C) =

B 7

D

4 /'(C)

C 1 a – b

D 17

* .

4

The tangent of the acute angle between the

lines y = 4x — 3 and y = x — 2 .is

17.

13.

2x + 1

dx

2x

3

A 1 A

x +-lnx + K

Ls

1

1+-x~,x + K

x + 2 In 2x + K

55

B B

3

c 2 ••.

C

5

D x + 2 In x + K 5

D

3

Using De Moiver’s theorem, the complex

number

(cos 9 + i sin 0)sis equal to

14.

The general solution of the differential

equation 3—dx = x 2 + x

18.

t

1 /x2 1

1( x2 1

y =

3 T + xJ + C

A (cos 05 + tsin 65 ) A

+ c

B 5(sin 0 + i sin 0)

C (cos 50 + i sin 50) B

o\

D COS 6s + Lsms ) 1(1 XN

=

3 \x

_

C 2j + c

15. Given that u and vare coplanar vectors,

whereu = 2i — j + 6k andv = —3i + 5j + k,

u x v =

1 ( 1 x\

y =

D 3 [ x + 2 ) +