4MA0 Higher June 2015 Paper 3 Q16
16
(a) Complete the table of values for \(y = \dfrac{1}{2}\left(x + \dfrac{9}{x}\right)\) (2)
| \(x\) | 1 | 1.5 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| \(y\) | 5 | 3.25 | 3.125 | 3.4 |
(b) Draw the graph of \(y = \dfrac{1}{2}\left(x + \dfrac{9}{x}\right)\) for values of \(x\) from 1 to 6 (2)
(c) Use the graph to find estimates for the solutions of the equation \(x + \dfrac{9}{x} = 7\) (2)
| Scheme | Marks | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| B2 | ||||||||
| (2) |
Notes
B2: all 3 correct
If not B2 then B1 for 2 correct
| Scheme | Marks |
|---|---|
Graph | M1 A1 |
| (2) |
Notes
M1 A1: M1 (ft if at least B1 scored in (a)) for at least 5 points plotted correctly \(\pm\tfrac{1}{2}\) square
A1 for correct curve between \(x = 1\) and \(x = 6\)
| Scheme | Marks |
|---|---|
| \(y = 3.5\) drawn | M1 |
| 1.7, 5.3 | A1 |
| (2) |
Notes
A1: ft graph which gives at least 2 roots
NB: Sight of just one correct solution with no method shown gets M0 A0