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 49
Tuesday 22 September 2020
30 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 $a * b=\left\{\begin{array}{ll}a+b | \text { if } a+b<6 a+b-6 | \text { if } a+b \geq 6\end{array}\right.$, and it is defined on the set $\{0,1,2,3,4,5\}$.
(i) Construct the operation table for *.
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(ii) Determine whether $*$ forms a group or not.
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2. Given that the area of the shaded region is $(2 \pi-4) c m^{2}$, find the radius of the whole sector.
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3. A manufacturing company needs to create a square-based rectangular box with a volume of $32000 \mathrm{~cm}^{3}$ at the lowest possible cost. The cost of material for the sides of the box cost $$ 0.25 / \mathrm{cm}^{2}$, while the cost of material for the top and the bottom of the box cost $$ 1 / c m^{2}$. What are the dimensions of the box that would minimise the cost of each box?
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4. The complex number $z$, where $z=x+i y$, satisfies the relation $|2 z+3 i| \leq|2 z+5|$. Sketch and shade on an Argand diagram the region represented by this inequality. State the Cartesian equation of this locus.
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5. Write down the real part of $(\sqrt{3}+i)^{7}$ using the DeMoivres theorem.
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6. Show that the following points are collinear: $A(3 \boldsymbol{i}+4 \boldsymbol{j}-2 \boldsymbol{k}), B(7 \boldsymbol{i}+8 \boldsymbol{j}-8 \boldsymbol{k})$ and $C(13 \boldsymbol{i}+14 \boldsymbol{j}-17 \boldsymbol{k})$.
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