4400 Higher June 2004 Paper 4 Q18
18
(a) Complete the table of values for \(y = x^3 - 3x^2 + 2\)
(2)
| \(x\) | −2 | −1 | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|---|---|
| \(y\) | −2 |
(b) On the grid, draw the graph of \(y = x^3 - 3x^2 + 2\)
(c) Use your graph to find estimates, correct to 1 decimal place where appropriate, for the solutions of
(i) \(x^3 - 3x^2 + 2 = 0\)
(ii) \(x^3 - 3x^2 - 4 = 0\) (4)
| Scheme | Marks |
|---|---|
| −18, (−2), 2, 0, −2, 2, 18 | B2 |
| (2) |
Notes
B2: for all correct
(B1 for 4 or 5 correct)
| Scheme | Marks |
|---|---|
| Points plotted | B1 |
| Curve | B1 |
| (2) |
Notes
B1: ± ½ sq ft if at least B1 in (a)
B1: ft if awarded B1 for points
| Scheme | Marks |
|---|---|
| (i) Answer: −0.7, 1, 2.7 | B2 |
| (ii) indication that \(y = 6\) used or \(x^3 - 3x^2 + 2 = 6\) or \(y = 6\) seen | M1 |
| 3.4 | A1 |
| (4) | |
| (8 marks) |
Notes
B2: ft if awarded \(\geqslant\) B1 in (b)
(B1 for 2 correct)
M1: eg line, mark on graph
A1: ft if awarded \(\geqslant\) B1 in (b)