### cameroon gce A level June 2024 pure mathematics with statistics 2

cameroon gce A level June 2024 pure mathematics with statistics 2

I. ((ii i)) If Express the roots (2of x -the l )(quadratic 3x + 1) , xequation e H&, x ^x 2 +^(/r^+inlpartial )x + kfractions = 0 arc.a and /?,

find the values of the real constant k for which a = 2(3. (5 marks)

2. The polynomial f(x), where f(x) = ax 3 – x 2 + bx + 6 has a factor (x + 2).

f(x) leaves a remainder 10 when divided by (x + 1).

Find

(a) the values of the constants a and b,

(b) the values of x for which f(x) = 0. (8 marks)

3. 1he table below shows approximate values of a variable y corresponding to certain values of another

variable x.

80

x 10 20 35 50 60

79.43

y 3.47 5.50 10.47 20.89 33.1I

By drawing a suitable linear graph, verify that these values of x and y satisfy approximately a relationship ol the

form y = abx.

Using your graph, find approximate values of the constants a and b, giving the answers correct to 2 decimal

places. (10 marks)

4. (i) The first and last terms of an arithmetic progression are 7 and 43 respectively.

The sum of the terms of the progression is 250.

Find the number of terms and the common difference of the progression. (3 marks)

3 X “2

(ii) Obtain the first four terms of the binomial expansion of (l -xj and find the set of values of x for

which the expansion is valid.

Hence, state the first four terms of the binomial expansion of (2 — 3x)-2 (7 marks)

5. (i) The parametric equations of a curve are given by

2 + -p, t ^ 0 is a parameter.

Show that an equation of the normal to the curve at the point where t – 2 is

8x – 2y — 1 9 = 0.

Find the value of t at the point where this normal meets the curve again

(ii) A new primary school intends to recruit a head teacher and 7 other teachers.

There are 3 male and 2 female applicants for the position of head teacher, 4 male and 6 female other

applicants for the teaching positions.

Find the number of different ways of selecting the staff of 8 if gender equity must be respected.

X F l + t, y =

(6 marks)

(7 marks)