Higher June 2019 Paper 1 Q10
10 The number of items, \(n\), made in 1 hour by a machine is given by \(\quad n = \dfrac{60}{t}\)
\(t\) is the time in minutes the machine takes to make one item.
The value of \(t\) changes for different types of item.
Use your graph to estimate the value of \(n\). [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| Plots the points (1, 60), (2, 30), (3, 20) and (4, 15) | M1 | \(\pm \dfrac{1}{2}\) small square |
| Correct smooth curve through correct four points | A1 | \(\pm \dfrac{1}{2}\) small square |
Additional guidance
Ignore any calculations and mark the graph only
Points cannot be implied by a bar chart or vertical line graph, but condone crosses at the top of a vertical line graph for M1 and the correct curve superimposed for M1A1
For M1, ignore the curve outside the domain \(1 \leqslant t \leqslant 4\)
For A1, whether or not the curve extends outside the domain \(1 \leqslant t \leqslant 4\) it must not have a positive gradient at any point
If there is no curve, for M1 there must be no other points with \(x\)-coordinate 1, 2, 3 or 4
The curve should be a single line with no feathering
Unless it affects the shape of the curve (in which case A1 cannot be awarded), ignore incorrect evaluations of \(60 \div\) a non-integer value
eg \(60 \div 1.5 = \ldots\)
| Answer | Mark | Comments |
|---|---|---|
| Vertical line from \(3\dfrac{1}{2}\) minutes to their graph | M1 | \(\pm \dfrac{1}{2}\) small square implied by mark at correct place on the graph or on the vertical axis (but not on the horizontal axis) or by correct reading from their graph |
| Correct reading from their graph for \(t = 3.5\) | A1ft | ft their graph \(\pm \dfrac{1}{2}\) small square |
Additional guidance
| Correct reading for their graph, with or without evidence of using graph | M1A1 |
| No graph in (a) | M0A0 |
| To score any marks, their graph must be decreasing in the domain \(1 \leqslant t \leqslant 4\), but may be a straight line or series of connected straight lines | |
| Answer from \(60 \div 3.5\) with no graph, or which does not match graph | M0A0 |
| Reading from 3.3 | M0A0 |