June 2024 Paper 1 Q1
1 A student states that \(1 + x^2 \lt (1+x)^2\) for all values of \(x\).
Using a counter example, show that the student is wrong. [2]
| Scheme | Marks | AO |
|---|---|---|
| When \(x = 0\) | M1 | 2.1 |
| \(1 + 0^2 = 1\) and \((1+0)^2 = 1\) Values are equal, which contradicts the statement \(1 + x^2 \lt (1+x)^2\) for all values of \(x\) [So the statement is false] | A1 | 2.1 |
| [2] |
Notes
M1: Using a negative value or zero
A1: Must see an explicit comparison between correct values (could be in words or symbols)