Easy -2.0 This is a very straightforward algebraic inequality question requiring only basic expansion and a single counterexample (e.g., x=0 gives 1 < 1, which is false). It involves minimal calculation, no trigonometry despite the topic label, and tests only the most basic understanding of counterexamples—significantly easier than typical A-level questions.
\(1 + 0^2 = 1\) and \((1+0)^2 = 1\), values are equal, which contradicts the statement \(1 + x^2 < (1+x)^2\) for all values of \(x\)
A1
Must see an explicit comparison between correct values (could be in words or symbols)
[So the statement is false]
[2]
## Question 1:
| Answer | Marks | Guidance |
|--------|-------|----------|
| When $x = 0$ | M1 | Using a negative value or zero |
| $1 + 0^2 = 1$ and $(1+0)^2 = 1$, values are equal, which contradicts the statement $1 + x^2 < (1+x)^2$ for all values of $x$ | A1 | Must see an explicit comparison between correct values (could be in words or symbols) |
| [So the statement is false] | **[2]** | |
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1 A student states that $1 + x ^ { 2 } < ( 1 + x ) ^ { 2 }$ for all values of $x$.\\
Using a counter example, show that the student is wrong.
\hfill \mbox{\textit{OCR MEI Paper 1 2024 Q1 [2]}}