4400 Higher November 2008 Paper 3 Q13
13
(a) Complete the table of values for \(y = x + \dfrac{1}{x^2}\)
(2)
| \(x\) | 0.5 | 1 | 1.5 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|---|
| \(y\) | 2 | 2.3 | 5.0 |
(b) On the grid, draw the graph of \(y = x + \dfrac{1}{x^2}\) for \(0.5 \leqslant x \leqslant 5\)
(c) \(x = 1\) is a solution of the equation \(x + \dfrac{1}{x^2} = k\) where \(k\) is a number.
(i) Find the value of \(k\).
(ii) Use your graph to find an estimate for another solution of the equation\[x + \frac{1}{x^2} = k\]Give your estimate correct to 1 decimal place.
(2)| Scheme | Marks |
|---|---|
| 4.5 1.9 3.1 4.1 | B2 |
| (2) |
Notes
B2: for all correct (B1 for 2 or 3 correct)
| Scheme | Marks |
|---|---|
| Points | B1 |
| Curve | B1 |
| (2) |
Notes
B1: Allow \(\pm\frac{1}{2}\) sq ft from table if at least B1 scored in (a)
B1: ft from their points if at least 5 points are correct or ft correctly
| Scheme | Marks |
|---|---|
| (i) Answer: 2 | B1 |
| (ii) Answer: 1.6 or 1.7 | B1 |
| (2) | |
| (6 marks) |
Notes
B1: cao
B1: for answer which rounds to 1.6 or 1.7
ft from curve if B1 scored for curve in (b)
Condone >1 dp