| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2006 |
| Session | June |
| Marks | 2 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Proof |
| Type | Logical statements and converses |
| Difficulty | Easy -1.2 This is a straightforward logic question testing understanding of implication symbols. Students only need to check simple cases: (i) factorising a quadratic shows x=1 or x=-2, so Q⇒P but not P⇒Q; (ii) testing y³>1 gives y>1 (since cube root is monotonic), making them equivalent. Requires minimal calculation and is more about notation than mathematical depth. |
| Spec | 1.01b Logical connectives: congruence, if-then, if and only if |
| Answer | Marks | Guidance |
|---|---|---|
| (i) \(P \subset Q\) | 1 mark | |
| (ii) \(P \Leftrightarrow Q\) | 1 mark | condone omission of P and Q |
| 2 marks |
(i) $P \subset Q$ | 1 mark |
(ii) $P \Leftrightarrow Q$ | 1 mark | condone omission of P and Q
| | 2 marks |In each of the following cases choose one of the statements
$$\text{P} \Rightarrow \text{Q} \qquad \text{P} \Leftrightarrow \text{Q} \qquad \text{P} \Leftarrow \text{Q}$$
to describe the complete relationship between P and Q.
\begin{enumerate}[label=(\roman*)]
\item P: $x^2 + x - 2 = 0$\\
Q: $x = 1$ [1]
\item P: $y^3 > 1$\\
Q: $y > 1$ [1]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C1 2006 Q4 [2]}}