Download and practise with this Tarakino N.P. (Trockers) A-Level Pure Mathematics September 2020 question paper. Useful for school exam revision, classroom practice, homework support, and preparation in Zimbabwe.
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Answers: Lockdown Pure Maths Test 51 Answers Marking Scheme
This is the A-Level Pure Mathematics question paper from September 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 35
Tuesday 01 September 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. Find the equation of the plane which contains the lines $L_{1}: \boldsymbol{r}=\left(\begin{array}{c}-1 2 3\end{array}\right)+s\left(\begin{array}{c}1 -3 2\end{array}\right)$ and
\[
L_{2}: r=\left(\begin{array}{c}
2
0
-1
\end{array}\right)+s\left(\begin{array}{c}
-5
15
-10
\end{array}\right) .
\]
[4]
2.
The diagram shows the curve $y=\sqrt{1+4 x}$, which intersects the $x$-axis at $A$ and the $y$-axis at $B$. The normal to the curve at $B$ meets the $x$-axis at $C$. Find
(a) the equation of $B C$,
[4]
(b) the area of the shaded region.
[5]
3. For each of the following curves, find the gradients at the point where the curve crosses the $y$-axis.
(i) $y=\frac{1+x^{2}}{1+e^{2 x}}$.
[3]
(ii) $2 x^{3}+5 x y+y^{3}=8$.
[4]
Mathew 26:13 ~ Tarakino N.P. (Trockers)
A river cuts through a rock not because of its power, but its persistence.
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