| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Proof |
| Type | Logical statements and converses |
| Difficulty | Moderate -0.8 This is a C1 question testing basic understanding of logical implications and counterexamples. Students only need to provide counterexamples (e.g., a rhombus for (i), x=√2 for (ii)) and identify the correct logical symbol. It requires minimal calculation and tests foundational logic concepts, making it easier than average A-level questions. |
| Spec | 1.01b Logical connectives: congruence, if-then, if and only if |
| Answer | Marks |
|---|---|
| B1 | The diagonals of a rhombus also intersect at \(90°\) |
| B1 | ABCD is a square \(\therefore\) the diagonals of quadrilateral ABCD intersect at \(90°\) |
| Answer | Marks |
|---|---|
| B1 | eg \(\sqrt{8}\) is an integer but \(\sqrt{8}\) is not an integer |
| B1 | \(x^2\) is an integer \(\therefore\) \(x\) is an integer |
# Question 1
## (i)
B1 | The diagonals of a rhombus also intersect at $90°$
B1 | ABCD is a square $\therefore$ the diagonals of quadrilateral ABCD intersect at $90°$
**Guidance:**
- Accept oe for kite or other valid statement/sketch
- Accept 'diamond' etc
- B0 if eg rectangle or parallelogram etc also included as having diagonals intersecting at $90°$
- oe; B0 if no attempt at explanation (explanation does not need to gain a mark)
- Reference merely to 'other shapes' having diagonals intersecting at $90°$ is not sufficient
- Sketches must have diagonals drawn, intersecting approx. at right angles but need not be ruled
- Do not accept $\rightarrow$ oe
## (ii)
B1 | eg $\sqrt{8}$ is an integer but $\sqrt{8}$ is not an integer
B1 | $x^2$ is an integer $\therefore$ $x$ is an integer
**Guidance:**
- B0 for 'the square root of some integers is a fraction'
- Do not accept $\leftarrow$ oe1 Explain why each of the following statements is false. State in each case which of the symbols ⟹, ⟸ or ⇔ would make the statement true.\\
(i) ABCD is a square ⇔ the diagonals of quadrilateral ABCD intersect at $90 ^ { \circ }$\\
(ii) $x ^ { 2 }$ is an integer $\Rightarrow x$ is an integer
\hfill \mbox{\textit{OCR MEI C1 Q1 [4]}}