(a) Complete the table of values for \(y = x + \dfrac{2}{x}\)
\(x\)
0.2
0.4
0.6
0.8
1
1.5
2
3
4
5
\(y\)
10.2
3.9
3
2.8
3.7
5.2
(2)
(b) On the grid, draw the graph of \(y = x + \dfrac{2}{x}\) for \(0.2 \leqslant x \leqslant 5\)(2)
(c) Use your graph to find estimates for the solutions of the equation \[x + \frac{2}{x} = 4\] (2)
The solutions of the equation \(2x + \dfrac{2}{x} = 7\) are the \(x\)-coordinates of the points of intersection of the graph of \(y = x + \dfrac{2}{x}\) and a straight line \(\mathbf{L}\).
(d) Find the equation of \(\mathbf{L}\). (2)
Mark scheme (a)
Scheme
Marks
5.4 3.3 3 4.5
B2
(2)
Notes
B2: for all 4 correct (B1 for 2 correct)
Mark scheme (b)
Scheme
Marks
Points
B1
B1
(2)
Notes
B1: dep on at least B1 in (a) for plotting at least 7 points which are correct or ft correctly ± ½ square
B1: dep on previous B1 for joining points with a smooth curve
Mark scheme (c)
Scheme
Marks
0.59, 3.41
B2
(2)
Notes
B2: B1 for each solution ft from graph Accept 1 or 2 dp
