### cameroon gce advance level June 2015 math with mechanics paper 2

cameroon gce advance level June 2015 math with mechanics paper 2

(i) Given that ( x + 1) is a factor of f(x), where f( x ) = x3 + 6×2 + llx + 6, factorise f(x) completely.

(4 marks)

( ii) Let X be a real constant. Show that the roots of the quadratic equation

3x 2 + (-4 — 2X)x + 2 X = 0

are always real . (5 marks)

(i) Given that y = ln(4 -F x 2),

find

i

Amt

•

cly

(a) (2 marks)

(a) the equations of the tangent and normal to the curve y = ln(4 + x 2 ) at the point where x = 1.

(4 marks)

(ii) Solve the differential equation -(I tjA- = xy — x, given that y = 2 when x = 0, expressing^ in terms ofx

(4 marks)

cix’

3. (i) Draw the truth table for each of the propositions p => q and ~ p V q and show that they arc identical.

(6 marks)

(ii) Given that sin !(x) = a and cos !(x) = /? show that sin(a + /?) =!. (4 marks)