Download and practise with this Trockers A-Level Pure Mathematicsugust 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 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 19
Tuesday 11August 2020
35 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.
The diagram above shows the curve with equation $y=x^{3}+a x^{2}+b x+c$, where $a$, $b$ and $c$ are constants. The curve crosses the $x$-axis at the point $(-1,0)$ and touches the $x$-axis at the point $(3,0)$. Show that $a=-5$ and find the values of $b$ and $c$.
[6]
2. Find the values of $y$ such that $\log _{2}(11 y-3)-\log _{2} 3-2 \log _{2} y=1, \quad y>\frac{3}{11}$.
[6]
3. Express $\sqrt{22.5}$ in the form $k \sqrt{10}$.
[3]
4. Given that $k$ is a rational constant to be found, show that
\[
\sum_{r=1}^{n} \frac{r+3}{2}=k n(n+7)
\]
5. Describe fully the single transformation that maps the graph of $y=e^{x}$ onto the graph of $y=\left(\frac{1}{e}\right)^{x}$. Hence sketch the two graphs on a single diagram.
[3]
6. The circle $C$ has equation $x^{2}+y^{2}-10 x+4 y+20=0$.
Find the length of the tangent to $C$ from the point ( $-4 ; 4$ ).
[5]
7. The coefficient of $x^{2}$ in the expansion of $\left(1+\frac{x}{2}\right)^{n}$, where $n$ is a positive integer, is 7 .
(a) Find the value of $n$.
[4]
(b) Hence find the coefficient of $x^{4}$.
[3]
Galatians 6:9~Tarakino N.P. (Trockers)
Never stop doing your best just because someone doesn't give you credit.
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