4400 Higher November 2006 Paper 4 Q18
18
(a) Complete the table of values for \(y = x^2 - \dfrac{3}{x}\)
(2)
| \(x\) | 0.5 | 1 | 1.5 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|---|
| \(y\) | −5.75 | −2 | 24.4 |
(b) On the grid, draw the graph of \(y = x^2 - \dfrac{3}{x}\) for \(0.5 \leqslant x \leqslant 5\)
(c) Use your graph to find an estimate for a solution of the equation \[x^2 - \frac{3}{x} = 0\] (1)
(d) Draw a suitable straight line on your graph to find an estimate for a solution of the equation \[x^2 - 2x - \frac{3}{x} = 0\] (2)
| Scheme | Marks |
|---|---|
| 0.25, 2.5, 8, 15.25 | B2 |
| (2) |
Notes
B2: Accept rounding or truncating
B1 for 2 or 3 correct
| Scheme | Marks |
|---|---|
| Points | B1ft |
| Curve | B1ft |
| (2) |
Notes
B1ft: Allow ± ½ square
Condone 1 error or omission
ft if at least B1 in (a)
B1ft: ft if at least B1 in (a)
| Scheme | Marks |
|---|---|
| 1.4 − 1.47 | B1 |
| (1) |
| Scheme | Marks |
|---|---|
| \(x^2 - \dfrac{3}{x} = 2x\) or indication of \(y = 2x\) | M1 |
| ~2.5 | A1 |
| (2) | |
| (7 marks) |
Notes
M1: indication may be mark or line on graph
Must see \(2x\) or indic’n of line \(y = 2x\)
A1: ft if at least B1 in (b)