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This is the A-Level Pure Mathematics marking scheme from 2020. It shows how marks are awarded, so you can mark your own answers.
Upper $6{ }^{\text {th }}$
LOCKDOWN PURE MATHS TEST 50
Wednesday 23 September 2020
ANSWERS
30 MARKS
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. Solve the equation
\[
\left(\frac{3-i}{2+i}\right) z=\frac{5+5 i}{-1+2 i}
\]
giving your answer in the form $a+i b$.
[5]
\[
\begin{array}{l}
\left(\frac{3-i}{2+i}\right) z=\frac{5+5 i}{-1+2 i}
\Rightarrow z=\left(\frac{5+5 i}{-1+2 i}\right)\left(\frac{2+i}{3-i}\right)
\Rightarrow z=\frac{10+5 i+10 i+5 i^{2}}{-3+i+6 i-2 i^{2}}
\Rightarrow z=\frac{10+15 i-5}{-3+7 i+2}
\Rightarrow z=\frac{5+15 i}{-1+7 i}
\Rightarrow z=\left(\frac{5+15 i}{-1+7 i}\right)\left(\frac{-1-7 i}{-1-7 i}\right)
\Rightarrow z=\frac{-5-35 i-15 i-105 i^{2}}{(-1)^{2}+(7)^{2}}
\Rightarrow z=\frac{-5-50 i+105}{50}
\Rightarrow z=\frac{100-50 i}{50}
\therefore z=2-i
\end{array}
\]
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