7 Here is a table of values for \(y = \frac{6}{x} - 2x\).
\(x\)
\(-4\)
\(-3\)
\(-2\)
\(-1\)
1
2
3
4
\(y\)
6.5
4
1
\(-4\)
4
\(-1\)
\(-4\)
\(-6.5\)
(a) Draw the graph of \(y = \frac{6}{x} - 2x\) for \(-4 \leqslant x \leqslant 4,\ x \ne 0\).[3]
(b) Use your graph to find the positive solution of \(\frac{6}{x} - 2x = 0\).
Give your answer to 1 decimal place. [1]
Mark scheme (a)
Answer
Marks
Part marks and guidance
Two accurate curves
3
B2 for 7 or 8 points plotted accurately
or
B1 for 5 or 6 points plotted accurately
Ignore the curve beyond points but the curve must not cross or touch the \(y\)-axis
tolerance ± \(\frac{1}{2}\) small square from correct points radially
no excessive feathering, no ruled lines, no excessive ‘tram lines’
overlay gives guidance only
Mark scheme (b)
Answer
Marks
Part marks and guidance
A correct and accurate reading from their graph
1FT DEP.
Dep. on a graph in (a) with at least one positive solution and strict FTtheir curve.
If curve crosses \(x\)-axis between two grid lines accept either grid line value as correct answer If their curve has more than one positive solution accept any of their correct solutions
Do not accept answers to more than 1d.p., \(\sqrt{3}\) or answers clearly rounded from this. CONDONE whole numbers where appropriate e.g. 2 for 2.0 Do not accept 0 as positive.
