Advanced level 2025 Adamawa regional mock pure maths statistics 2
Advanced level 2025 Adamawa regional mock pure maths statistics 2
1. (i) Find the set of values of x for which the roots of the quadratic equation
.v2 + (a– 3)x + 2a- 1 = 0 are real and distinct.
(ii) Given that 5* = 2y and that 2.v + 3y = 6, show that x = log log10 2 (7 marks)
2. (i) The first term of an arithmetic progression is 2a and the common difference is 3. If
the sum of the first 2n terms is equal to the sum of the first n terms of this progression,
express a in terms of n.
Obtain the value of a when n = 5 and hence find the sum of the first 10 terms of the
progression.
(ii) Find the position of the term in x”
18 in the expansion of(,x4+ .^30 (10 marks)
3. (i) Differentiate with respect to x
(‘(ab))‘ S(COS x^2+22()32 X – 2)
(ii) If f W = 2x 4 — 4x 3 – 3x 2 +l.find f’(x ) and hence determine the set of values of x
for which /(x) is increasing (5, 6 marks)
4. (i) Find the general solution of the equation c o s2 x = 2 sin x.
(ii) f W = 2cosx 4– 2 sinx.
(a) Express f ( x ) in the form rcos(x – a) where r > 0 and 0° < a < 90°
(b) Find, to the nearest tenth of a degree, the set of values of x which satisfy the
equation 2cosx + sinx = V3
| (c) Find the maximum value of 7+TSAx)– 5. Vector parametric equations of the lines and l2 are given by |
(4, 7 marks) |
| J i i r = 2 1 + J + A( i + j + 2k ), where t is a constant. Find |
l 2 : r = 2i+ 2j + t i c + p(i+ 2 j + k ) |
| (a)The value of t for which l x and l 2 intersect. (b) The position vector of the point of intersection of fx and l 2 . (c) The cosine of the acute angle between l x and l 2 . |
(4 marks) (2 marks) (3 marks) |
(d) The vector parametric equation of the plane containing and f 2. (2 marks)
2x–l
6. (i) The function f is defined by f {x ) =
(a) Express f (x ) in partial fractions.
Hence,
(b) Evaluate /Q2/(x) d x
(ii) ) Sketch the curve of y = x3 – 3x2 – 4x + 12, showing clearly the intercepts with
the coordinate axes and the behavior of the curve as it approaches its asymptotes.
(5 marks)
