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)
