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This is the ZIMSEC A-Level Mathematics study guide. It is a free study guide for revision. The paper code is 9202/1. Time allowed: 3 hours.
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ZIMBABWE SCHOOL EXAMINATIONS COUNCIL
General Certificate of Education Advanced Level
MATHEMATICS
9202/1
PAPER 1
Monday
4 NOVEMBER 2002
Allermonn
3 hours
Additional materials:
Answer paper
Graph paper
List of Formulate
TIME 3 hours
INSTRUCTIONS TO CANDIDATES
Write your name, Centre number and candidate number in the spaces provided on the answer paper/answer booklet.
There is no restriction on the number of questions which you may attempt.
If a numerical answer cannot be given exactly, and the accuracy required is not specitied in the question, then in the case of an angle it should be given to the nearest degree, and in other cases it should be given correct to 2 significant figures.
INFORMATION FOR CANDIDATES
The number of marks is given in brackets [] at the end of each question or part question.
The total number of marks for this paper is 120 .
Questions are printed in the order of their mark allocation and candidates are advised to attempt questions sequentially.
The use of an electronic calculator is expected, where appropriate.
You are reminded of the need for clear presentation in your answers.
This question paper consists of 7 printed pages and 1 blank page.
1 (a) Find the set of values of $k$, for which the equation $k x^{2}-3 x=k-3$ has real roots.
[2]
(b) Values of $x$ and $y$ are related by the equation $y=A x^{\mathrm{b}}$. State the type of graph you would plot and what shape would confirm the relationship.
[2]
12 Express $\frac{2}{3-\sqrt{7}}-\sqrt{63}$ in the form $a+b \sqrt{c}$.
where $a, b$ and $c$ are integers.
[3]
3 Estimate the value of -
\[
\int_{0}^{1} \cos \left(x^{2}\right) d x
\]
using the trapezium rule with 5 equal intervals, giving the answer correct to 3 significant figures.
[3]
4 The population of a country increases by $3 \%$ every year. Find the time, in years, it takes for the population to double.
15
[4]
The diagram above shows the graph of $y=e^{x}+1$. The region between the curve, the $x$-axis, the lines $x=-1$ and $x=1$ is rotated through 4 right angles about the $x$-axis. Find the volume of this solid giving the answer correct to 2 decimal places.
141
If 6 Sketch, on the same axes, the graphs of
\[
y=|3 x-6| \text { and } y=2 x+2 .
\]
[2]
Hence, or otherwise, solve the inequality
\[
2 x+2>|3 x-6| .
\]
[3]