Study Pure Mathematics worksheet for A-Level. Useful for revision, homework, and exam preparation in Zimbabwe.
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This is the A-Level Pure Mathematics worksheet from August 2020. It is a free worksheet for revision.
Upper $6{ }^{\text {th }}$
LOCKDOWN PURE MATHS TEST 21
Thursday 13 August 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. Solve the inequality $|x-2|<2 x-3$
[4]
2.
The variables $x$ and $y$ satisfy the equation $y=K x^{p}$, where $K$ and $p$ are constants.
The graph of Iny against Inx is a straight line passing through the points (1.28; 3.69) and(2.11; 4.81), as shown in the diagram. Find the values of $K$ and $p$ correct to 2 decimal places.
[6]
3. Use the iterative formula
\[
x_{n+1}=\frac{2\left(x_{n}{ }^{3}+1\right)}{3 x^{2}{ }_{n}},
\]
where $x_{0}=1$, to calculate $x_{1}, x_{2}$ and $x_{3}$. Give your answers to 6 decimal places.
[4]
Given that the iteration converges, find and simplify an equation in $x$ whose real root is being approximated by this iteration.
[2]
Hence write down the exact value of this root. Find the absolute errors $e_{1}, e_{2}$ and $e_{3}$, in the first three approximations $x_{1}, x_{2}$ and $x_{3}$, giving your answers to 6 decimal places.
[4]
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