Download and practise with this Tertiary Pure Mathematics Nov/Dec 2002 question paper. Useful for revision, practice, and exam preparation in Zimbabwe.
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This is the Pure Mathematics question paper for Paper 1 from Nov/Dec 2002. Use it for exam practice under timed conditions.
FIRST YEAR P1 - PURE MATHEMATICS NOV/DEC EXAMINATIONS 2002
1. The curve $x y=8$ and the line $2 x-3 y+8=0$ intersect at two points $A$ and $B$. Find the coordinates of $A$ and $B$.
2i). Given that $x^{2}-3 x+5=(x-p)^{2}+q$ for all real values of $x$. Calculate the vales of $p$ and $q$. Hence sketch the curve $y=x^{2}-3 x+5$
ii). Find the value (s) of p for which $x^{2}-p x+p+3=0$ has real and distinct roots. (5)
3. In the diagram, O is the centre of a circle of radius 8 cm and $\triangle \mathrm{PQR}$ is an isosceles triangle. If $\mathrm{QPR}=\theta$ radians and $\mathrm{QR}=7 \mathrm{~cm}$, calculate
i). the value of $\theta$
ii). the area of the minor segment QSR
4 i.
\[
\frac{\operatorname{Sin} A}{1+\operatorname{Cos} A}=\frac{1-\operatorname{Cos} A}{\operatorname{Sin} A}
\]
iii). Solve for x
\[
4 \tan 2 x=9,-180 \leq x \leq 180
\]
5. The function of where $f(x)=a-b \operatorname{Cos} x$
$X$ is defined for the domains $\quad 0 \leq x \leq 2 \Pi$
Given that $\mathrm{f} \frac{(3 \Pi)}{2}=2, \mathrm{f}(\Pi)=5$