cameroon gce advanced level June 2022 pure maths with statistics 2

cameroon gce advanced level June 2022 pure maths with statistics 2

cameroon gce advanced level June 2022 pure maths with statistics 2

( i) Given that the roots of the equation 3×2 — 4x + 2 = 0 are a and /?,
(a) show that (« + ( P +f) = 3.
(ii)(The b) find polynomial an equation P( xwith ) is such integral thatcoefficients P(x) = nx,3whose 4- fax2roots – 2xare -^6.and
Given that /’(x) leaves a remainder 10 when divided by x — 2 and that 2x — 3 is a factor of P(x ),
1 .
^ .*
(3, 3 marks)
find the values of the constants a and fa. (4, 2 marks)
2. (i) A function f:E — {—1} •
(a) Show that f is surjective.
(b) Find the composite function (f° f)(x), stating its domain.
(c) Determine whether f ° f(x) is an even or odd function.
I . . . .
‘
. .
* 1 — x
(ii) Expand T as a series in ascending power of x as far as term in x2.
(1 + 2x)3
E — {1}, is defined by
(3, 3, 2 marks)
(4 marks)
3. The position vectors of the points A, B and C arc a, b and c respectively, where
a = i + 5j — 3k , b = -3i — j + 7k and c = i + j.
Given that M is the midpoint of AB,
find
(a) an equation of the line AB, in the form r = a + tb,
(b) the position vector of M,
(c) the Cartesian equation of the plane ABC,
(d) the value of the constant a for which the line r = j + 2k + A(2i + aj + k) is parallel
to the plane ABC. (2, 2, 5, 5 marks)
cost) sin 0
4. ‘ Given that f(0) =
1-tanO l-cotO *
(a) prove that f(0) = cos 9 + sin 9.
(b) express f(0) in the form /?sin(0 + A),where R > 0 and X an acute angle.
(c) find the general solutions of the equation f(0) = 1.
•
(3, 3, 3 marks)
5. (i) The sum of the sixth and the eighth terms of an arithmetic progression is 40.
The seventh term of this progression is 4 times the second term.
Find,
(a) the first term and the common difference,
(b) the least number of terms required for the sum of the progression to exceed 1000. (3, 3 marks)
(ii) If
d y .
(c) y ~ (sinx)( Inx), find —
(d ) x = 1 + t 3 and y = t + t 4, find^ in terms of of the parameter t. (2, 2 marks)