cameroon gce A level June 2024 pure mathematics with mechanics 2

cameroon gce A level June 2024 pure mathematics with mechanics 2

cameroon gce A level June 2024 pure mathematics with mechanics 2

(i ) Express
(2x – l)(3x + 1)
(ii) If the roots of the quadratic equation x2 + (/c + l)x + Ic = 0 are a and /?,
find the values of the real constant k for which a = 2/?. (5 marks)
2. The polynomial f(x), where f(x) = ax3 – 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. The 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 33.11
By drawing a suitable linear graph, verify that these values of x and y satisfy approximately a
relationship of 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 \ 2
2
(ii) Obtain the first four terms of the binomial expansion of (l X )
values of x for which the expansion is valid.
Hence, deduce the first four terms of the binomial expansion of (2 – 3x)-2 .
and find the set of
(7 marks)
5. (i) The parametric equations of a curve are given by
x = 1 + t, y = 2 +-, t ^ 0 is a parameter.
Show that an equation of the normal to the curve at the point where t = 2 is
8x – 2y – 19 = 0.
Find the value of t at the point where this normal meets the curve again. (6 marks)
(ii) A new primary school intends to recruit a head teacher and 7 other teachers.
There are 3 male and 2 iemale applicants foi the position ot head teacher
, 4 male and 6 female
other applications for the teaching positions.
Find the number of different ways of selecting the staff of 8 if gender equity must be respected.
(7 marks)