Easy -1.8 This requires only finding a single counterexample (n=2 gives 18, which is even) to disprove the statement. It's a straightforward task with minimal calculation and no sophisticated proof techniques needed—well below average A-level difficulty.
which is not odd, so the statement must be false (counterexample)
A1 [2] (AO 2.2a)
Complete argument must include a clear conclusion that statement is false
## Question 1:
| Answer | Marks | Guidance |
|--------|-------|----------|
| When $n=2$, $2^2 + 2\times2 + 10 = 18$ | M1 (AO 2.1) | Use of $n=2$ seen |
| which is not odd, so the statement must be false (counterexample) | A1 [2] (AO 2.2a) | Complete argument must include a clear conclusion that statement is false |
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1 Celia states that $n ^ { 2 } + 2 n + 10$ is always odd when $n$ is a prime number.
Prove that Celia's statement is false.
\hfill \mbox{\textit{OCR MEI AS Paper 1 2020 Q1 [2]}}