Download and practise with this 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 48
Monday 21 September 2020
25 MARKS ANSWER ALL QUESTIONS
***PRESENT YOUR WORK NEATI.Y***
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. Given that $x^{2}+x y+y^{2}=12$, find $\frac{d y}{d x}$.
[4]
2. Find the general solution of the differential equation $x y \frac{d y}{d x}+2-y^{2}=0$.
Deduce that the particular solution for which $y=1$ when $x=1$ may be expressed in the form $x^{2}+y^{2}=2$.
Draw a sketch showing this particular solution and also the solution curve which passes through the point $(2,0)$.
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3. The position vectors of points $A, B$ and $C$ are $3 \boldsymbol{i}+2 \boldsymbol{j}, \boldsymbol{i}+\boldsymbol{j}+\boldsymbol{k}$ and $2 \boldsymbol{j}+2 \boldsymbol{k}$ respectively. Find the Cartesian equation of
(i) the plane which bisects the line $A B$ at right angles,
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(ii) the plane through the points $A, B$ and $C$.
[4]
4. The diagram shows the graphs of $y=|x|$ and $y=|x-2|+1$. The point $P$ is the minimum point of $y=|x-2|+1$, and $Q$ is the point of intersection of the two graphs.
(i) Write down the coordinates of $P$.
[1]
(ii) Verify that the $y$-coordinate of $Q$ is $1 \frac{1}{2}$.
[4]
Galatians 6:6 \& 6:9 ~ Tarakino N.P. (Trockers)
STUDY while others are sleeping, WORK while others are loafing, PREPARE while others
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