Easy -1.2 This requires finding a simple counterexample (e.g., p=-3, q=1) to disprove a statement about inequalities. It's a straightforward proof by counterexample with minimal steps, testing basic understanding of how squaring affects negative numbers rather than requiring sophisticated reasoning.
For example: \((-3)^2 = 9 > 2^2 = 4\) and \((-3) < 2\), so Beth is not correct
M1
Stating any pair of numbers where \(p^2 > q^2\) and \(p < q\). Also accept general statement about a negative number [for \(p\)]
Fully convincing argument – do not allow for only disproving the converse
E1 [2]
Fully convincing argument
## Question 1:
| Answer | Marks | Guidance |
|--------|-------|----------|
| For example: $(-3)^2 = 9 > 2^2 = 4$ and $(-3) < 2$, so Beth is not correct | M1 | Stating any pair of numbers where $p^2 > q^2$ and $p < q$. Also accept general statement about a negative number [for $p$] |
| Fully convincing argument – do not allow for only disproving the converse | E1 [2] | Fully convincing argument |
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1 Beth states that for all real numbers $p$ and $q$, if $p ^ { 2 } > q ^ { 2 }$ then $p > q$.
Prove that Beth is not correct.
\hfill \mbox{\textit{OCR MEI Paper 1 2021 Q1 [2]}}