Download and practise with this A-Level Pure Mathematicsugust 2020 question paper. Useful for revision, practice, and exam preparation in Zimbabwe.
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Answers: Lockdown Pure Maths Test 31 Answers Marking Scheme
This is the A-Level Pure Mathematics question paper from August 2020. Use it for exam practice under timed conditions, then check your work against the marking scheme. See the marking scheme.
Upper $6{ }^{\text {th }}$
LOCKDOWN PURE MATHS TEST 18
Monday 10 August 2020
20 MARKS ANSWER ALL QUESTIONS
***PRESENT YOUR WORK NEATLY***
NB: If a numerical answer cannot be given exactly, and the accuracy required is not specified 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 $\mathbf{2}$ significant figures.
1. An Hp laptop dealer values an Hp Pavilion laptop at $$ x$ on January $1^{\text {st }}$ 2016. The value, $$ m$, of the laptop $t$ years after this date may be modelled as a continuous variable. The rate of increase of $m$ may be assumed to be directly proportional to $m^{2}$.
a) Write down a differential equation satisfied by $m$.
[2]
b) Show that $\frac{1}{k}\left(\frac{m-x}{m x}\right)=t$, where $k$ is a constant.
[4]
c) The value of the laptop is $$ 800$ on January $1^{\text {st }} 2019$ and $$ 900$ on January $1{ }^{\text {st }}$ 2020 . Find the value of $x$.
[3]
2. A farmer wants to turn part of his garden into a circular field. In order to do this, he digs out a shallow circular hole of radius $r \mathrm{~m}$ and then divide it into two segments by means of a thin plank $A B$, as shown in the diagram. He plants maize in the minor segment and wheat in the major segment.
Let the centre of the field be denoted by $O$. Show that when $A \hat{O} B=2.6$ radians, the area of the field containing wheat is approximately twice the area containing maize.
[6]
3. Relative to the origin $O$, points $C$ and $D$ have position vectors $\left(\begin{array}{l}7 3 2\end{array}\right)$ and $\left(\begin{array}{c}10 a b\end{array}\right)$, respectively, where $a$ and $b$ are constants. The straight line through $C$ and $D$ has equation $\boldsymbol{r}=\left(\begin{array}{l}7 3 2\end{array}\right)+t\left(\begin{array}{l}1 3 0\end{array}\right)$. Find the values of $a$ and $b$.
[5]
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