### cameroon gce A level June 2023 pure maths with statistics 2

cameroon gce A level June 2023 pure maths with statistics 2

1 . ( i) A polynomial P is defined on the set IK of real numbers by

P(x) = 4×3 + 4x 2 – llx- 6. {‘ s’ *

Given that (2x – 3) is a factor of P( x )’.

(a) factorise P( x ) completely.

(b) solve the inequality P(x) < 0.

(5, 3 marks)

2. (i) Solve for x, the equation log 2(x — 3) + log2x — 2. i (3 marks)

(ii) Express f(0), where

in the form reos(0 f—(0A)),=where ^ cosr0>+0^and sin0A, an acute angle.

• 2

Hence find the maximum value of the expression (7 marks)

3. (i) A function f is defined on IK by

K

(a) State the domain of f.

Show that f is

(b) injective,

(c) monotone decreasing.

> .

, ‘ O s’ > i t ;.i i 1 t i .

< t ! ; (1, 3, 3 marks) •• • t t 3x^ i (ii) Find the range of real values of the function y = —4x —1, x e IK , x =£ -4 . (3 marks) . e* ri;’-VJ ,-}/ v ‘4 * Ve.{> i * – « j *. ) j”

4. The table below shows corresponding values of x and y which approximately satisfy a relation of the form

y = a x 2 + b x ,

x 2.0 2.5 3.0 3.5 4.0 4.5 5.0

y 28.0 31.3 33.0 33.3 32.0 29.3 25.0

By drawing a suitable linear graph, determine, correct to one decimal place, the values of the constsnts a and b.

( 9 marks)

5 + i

5. (i) Given the complex number Z =

2 + 3i

(a) express Z in the form x + yi where x and y are real constants.

((cb)) show By equating that z =the V2form (cosin^ (a) to that in (b) show that cos- = —

t s

(ii) The line y = 3- 2x is a tangent to a circle whose centre is at the point (3, 2).

Find the equation of this circle.

(3, 4, 2 marks)

( 3 marks)