Download and practise with this A-Level Pure Mathematics 2002 question paper. Useful for revision, practice, and exam preparation in Zimbabwe.
A free account is needed to download. Sign in or create one
This is the A-Level Pure Mathematics question paper for Paper 1 from 2002. Use it for exam practice under timed conditions.
TRIAL AND FINAL EXAMINATION, 2002 MATHEMATICS
PURE MATHEMATICS
PAPER 1
Q1. Find the ascending powers of x , the first four terms of the expansion
\[
(1-3 x)^{2}
\]
Hence obtain the coefficient of $x^{2}$ in the expansion of $(2 x-1-\underline{7})\left(1-3 x^{2}\right)$
\[
9 x
\]
2. If the line $3 x-5 y=8$ meets the curve $\underline{3}-\underline{1}=4$ at A and B, find the
\[
x \quad y
\]
coordinates of the midpoint of AB . Hence find the equation of the perpendicular bisector of AB . (5)
3. A circular disc of radius 30 cm rests on two supports each 20 cm tall. Calculate:
i. Angle $A O B$ in radians
(2)
ii. the length of the arc $A C B$
(2)
iii. the fraction of the area of the disc that lies above the level of line $A B$. (3)
4. Relative to a fixed origin O , the points $\mathrm{A}, \mathrm{B}, \mathrm{C}$ and D have position vectors given respectively by
\[
a=2 i+3 j-k, \quad b=5 j-2 j+3 k, \quad c=4 i+j-2 k \quad d=i+t j+3 k
\]