Download and practise with this ZIMSEC A-Level Mathematics Paper 1 November 2016 question paper. Useful for exam revision, past paper practice, and preparation in Zimbabwe.
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This is the ZIMSEC A-Level Mathematics question paper for Paper 1 from November 2016. Use it for exam practice under timed conditions. The paper code is 9164/1.
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1 The complex number $\frac{1}{-2+1}$ is denoted by $u$.
Find the
(ii) modulus of $u$.
(ii) argument of $u$
2 Find the series expansion of $(9+2 x)^{\frac{-3}{2}}$ up to and including the term in $x^{2}$, simplifying the coefficients
[4]
3 The equation of a circle is $x^{2}+y^{2}=4$ and the equation of its tangent is $y=2 m x+c$.
Show that $16 m^{2}-c^{2}+4=0$.
\[
y^{2}=a^{2}-(x+3)^{2}
\]
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4 (i) Given that $f(x)=2-|x+3|$, sketch the graph of $y=|f(x)|$.
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(ii) Hence from (i) solve the inequality $|f(x)|>1$.
[2]
5 The variable quantities $x$ and $y$ are related by the rule $y=\frac{P}{\sqrt{x}}$, where $P$ is a constant. Five pairs of values of $x$ and $y$ measured experimentally are shown in the table.
\multicolumn{6}{c}{0,22}
$\boldsymbol{x}$ | 20 | 30 | 45 | 50 | 75
$\boldsymbol{y}$ | 0.9 | 1.1 | 1.35 | 1.40 | 1.52
(i) Plot the graph of $y$ against $\frac{1}{\sqrt{x}}$.
(ii) Use the graph to find the value of $P$.
\[
y=\frac{p}{\sqrt{a}}
\]
6
The diagram shows the position of an aeroplane $P$ flying in a straight line at a constant height of 5500 metres. The angle of elevation of the plane from the observer O is $\theta^{\circ}$ when the observer is $x \mathrm{~m}$ from a point Q , on level ground, which is vertically below $P$. The speed of the aeroplane is $550000 \mathrm{~m} / \mathrm{hr}$.
Find the rate of change of angle $\theta$ when $\theta$ is $25^{\circ}$.
[5]
9164/1 N2016