| Exam Board | OCR MEI |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2009 |
| Session | January |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Proof |
| Type | Counter example to disprove statement |
| Difficulty | Moderate -0.8 This question requires finding a counterexample to disprove a statement (e.g., p=1, q=-1) and stating a simple condition (both positive). It tests basic understanding of inequalities and reciprocals but requires minimal calculation and is more accessible than average A-level proof questions. |
| Spec | 1.01c Disproof by counter example |
| Answer | Marks | Guidance |
|---|---|---|
| \(p = 1\) and \(q = -2\) | M1 | Stating values of \(p, q\) with \(p \ge 0\) and \(q \le 0\) (but not \(p = q = 0\)) |
| \(p > q\) but \(\frac{1}{p} = 1 > \frac{1}{q} = -\frac{1}{2}\) | E1 | [2] showing that \(\frac{1}{p} > \frac{1}{q}\) - if 0 used, must state that \(\frac{1}{0}\) is undefined or infinite |
| Answer | Marks | Guidance |
|---|---|---|
| Both \(p\) and \(q\) positive (or negative) | B1 | or \(q > 0\), 'positive integers' |
## Part (i)
$p = 1$ and $q = -2$ | M1 | Stating values of $p, q$ with $p \ge 0$ and $q \le 0$ (but not $p = q = 0$)
$p > q$ but $\frac{1}{p} = 1 > \frac{1}{q} = -\frac{1}{2}$ | E1 | [2] showing that $\frac{1}{p} > \frac{1}{q}$ - if 0 used, must state that $\frac{1}{0}$ is undefined or infinite
## Part (ii)
Both $p$ and $q$ positive (or negative) | B1 | or $q > 0$, 'positive integers' | [1]
---6 (i) Disprove the following statement.
$$\text { 'If } p > q \text {, then } \frac { 1 } { p } < \frac { 1 } { q } \text {. }$$
(ii) State a condition on $p$ and $q$ so that the statement is true.
\hfill \mbox{\textit{OCR MEI C3 2009 Q6 [3]}}