(a) Complete the table of values for \(y = x^2 + \dfrac{2}{x}\)
\(x\)
0.1
0.2
0.5
1
1.5
2
3
4
\(y\)
20.01
10.04
3
3.58
5
9.67
(1)
(b) On the grid, draw the graph of \(y = x^2 + \dfrac{2}{x}\) for \(0.1 \leqslant x \leqslant 4\)(2)
(c) Use your graph to find estimates for the solutions of \(x^2 + \dfrac{2}{x} = 14\) in the interval \(0.1 \leqslant x \leqslant 4\) Give your estimates correct to 1 decimal place. (2)
(d) \(x = 1\) is one solution of the equation \(x^2 + \dfrac{2}{x} = mx\)
(i) Find the value of \(m\).
(ii) Draw a suitable straight line on your graph to find an estimate for the second positive solution of the equation \(x^2 + \dfrac{2}{x} = mx\) for the value of \(m\) found in part (d)(i). Give your estimate correct to 1 decimal place.
(3)
Mark scheme (a)
Scheme
Marks
4.25 16.5
B1
(1)
Notes
B1: for both values correct
Mark scheme (b)
Scheme
Marks
Points
B1
Curve
B1
(2)
Notes
B1: Allow ± ½ sq ft from their table
B1: ft from their points if at least 6 points plotted correctly
Mark scheme (c)
Scheme
Marks
0.1 to 0.2 and 3.7
B2
(2)
Notes
B2: B1 for each correct value ± ½ sq ft from their graph if at least 1 mark scored in (b) tol
Mark scheme (d)
Scheme
Marks
(i) 3
B1
(ii) Draw \(y = 3x\)
M1
approx 2.7
A1
(3)
Notes
B1: cao
M1: from \(x = 1\) to at least \(x = 3\)
A1: ft from their graph if at least 1 mark scored in (b) and dep on M1
