Download and practise with this ZIMSEC O-Level Mathematics Paper 2 June 1996 question paper. Useful for exam revision, past paper practice, and preparation in Zimbabwe.
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This is the ZIMSEC O-Level Mathematics question paper for Paper 2 from June 1996. Use it for exam practice under timed conditions. Time allowed: 2 hours 30 minutes.
Ordinary Level
MATHENATICS
5 JUNE 1996
PAPER 2
2 hours 30 minutes
Answer all questions in Section A and any three questions from Section B.
Section A [64 marks]
Answer all the questions in this section.
1 (a) Given that $a=2$ and $b=-3$, calculate
(i) $\quad a^{2}-b^{2}$,
(ii) $(a-b)^{2}$,
(iii) $\frac{1}{a b}$.
[3]
(b) Solve the equation
\[
\frac{2}{x-1}+1=\frac{2}{3}
\]
[3]
(c) The values of $x$ and $y$ are such that
\[
\begin{array}{l}
x+3 y=3
x-3 y=5
\end{array}
\]
(i) Factorise
\[
x^{2}-9 y^{2}
\]
and hence, without solving the above equations, write down the numerical value of $x^{2}-9 y^{2}$.
(ii) Solve the simultaneous equations
\[
\begin{array}{l}
x+3 y=3
x-3 y=5
\end{array}
\]
[4]
2 (a) A tourist in Zimbabwe cashed an $£ 80$ cheque at the official exchange rate of $Z $ 12,85$ for $£ 1$ sterling.
(i) Calculate how many Zimbabwean dollars he received for $£ 80$.
(ii) He then bought a camera for $Z $ 578,25$. Calculate the equivalent cost, in $£$ sterling, of the camera.
[3]
(b) It is given that $c$ is an integer and that
$\mathscr{E}=\{c: 1 \leqslant c<10\}$,
$P=\{c: c$ is even $\}$,
$Q=\{c: c$ is a perfect cube $\}$.
(i) List the elements of
(a) $Q$,
(b) $P \cap Q$,
(c) $(P \cup Q)^{\prime}$.
(ii) Write down the value of $\mathrm{n}(P \cup Q)$.
[6]