Explain why neither \(x\) nor \(y\) can be zero. [1]
(ii) On the axes below, sketch the graph of \(y = \dfrac{1}{x}\). [2]
(iii) Complete this sentence about the graph you have drawn. [1]
The graph shows ‘\(y\) is ……………… proportional to \(x\)’.
(b) The variables \(V\) and \(p\) are connected by the equation \(\dfrac{V}{p^2} = 5\).
Find the value of \(V\) when \(p = 0{\cdot}1\). [2]
Mark scheme (a)
Scheme
Marks
Comments
(i) Valid explanation e.g. ‘There is no value for which 0 × .... = 1’ or ‘1 cannot be divided by 0’ or ‘Because if one of them is zero, the product would be zero not 1’.
E1
Allow e.g. ‘\(x = \frac{1}{y}\), \(y = \frac{1}{x}\) if \(x\) or \(y\) can be zero these have no value’
Do not allow e.g. ‘Because then the value could not be 1’ without further explanation
(ii) Correct graph: One branch in 1st quadrant, not touching either axis and correct shape One branch in 3rd quadrant, not touching either axis and correct shape
B2
For 2 marks, must be 2 distinct curves; allow some slight curving back at ends B1 for either branch correct
If no marks, SC1 for both branches correct but joined e.g. with a straight line.
(iii) inversely
B1
allow poor spelling; allow ‘inverse’ or ‘not directly’ or ‘not in direct’ or ‘not direct’ or ‘not’ or ‘indirectly’
Do not allow e.g. ‘invertional’ or ‘inversamental’
Mark scheme (b)
Scheme
Marks
Comments
5 × 0.12 oe, si
M1
Substitutes and rearranges; may be in stages; implied by e.g. \(\dfrac{V}{0.1^2} = 5\), \(\dfrac{V}{0.2} = 5\), \(V = 5\times0.2\) (must be clear that ‘0.2’ is what they think is 0.12)
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