| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Proof |
| Type | Logical statements and converses |
| Difficulty | Easy -1.8 This is a basic logic question testing understanding of odd/even integers and simple implications. All parts require only direct verification with no calculation or proof construction—students just need to recognize that 2n+1 is always odd, 3n+1 alternates, and apply elementary parity rules. This is significantly easier than typical A-level questions. |
| Spec | 1.01b Logical connectives: congruence, if-then, if and only if |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| (i) T, (ii) [blank], (iii) [blank], (iv) F | 3 | 3 for all correct, 2 for 3 correct, 1 for 2 correct |
## Question 5:
| Answer | Marks | Guidance |
|--------|-------|----------|
| (i) T, (ii) [blank], (iii) [blank], (iv) F | 3 | 3 for all correct, 2 for 3 correct, 1 for 2 correct |
---5 Given that $n$ is a positive integer, write down whether the following statements are always true (T), always false (F) or could be either true or false (E).\\
(i) $2 n + 1$ is an odd integer\\
(ii) $3 n + 1$ is an even integer\\
(iii) $n$ is odd $\Rightarrow n ^ { 2 }$ is odd\\
(iv) $n ^ { 2 }$ is odd $\Rightarrow n ^ { 3 }$ is even
\hfill \mbox{\textit{OCR MEI C1 Q5 [3]}}