| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2015 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Trig Proofs |
| Type | Logical implication symbols (⇒, ⇔, ⇐) |
| Difficulty | Moderate -0.8 This C1 question tests understanding of logical implication symbols rather than mathematical computation. Students must identify counterexamples (e.g., a kite has perpendicular diagonals but isn't a square; x=√2 gives integer x²=2... wait, that's wrong; x=1.5 gives non-integer x²). While conceptually important, finding these counterexamples requires only basic reasoning, not complex calculations or proofs, making it easier than average A-level questions. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem1.02n Sketch curves: simple equations including polynomials1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| The diagonals of a rhombus also intersect at \(90°\) | B1 | oe for kite or other valid statement/sketch; B0 if eg rectangle or parallelogram etc also included as having diagonals intersecting at \(90°\); accept 'diamond' etc; 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 |
| ABCD is a square \(\Rightarrow\) the diagonals of quadrilateral ABCD intersect at \(90°\) | B1 | oe; B0 if no attempt at explanation (explanation does not need to gain a mark); Do not accept \(\rightarrow\) oe |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| eg 8 is an integer but \(\sqrt{8}\) is not an integer | B1 | oe with another valid number, or equivalent explanation; B1 for the square root of some integers is a surd/irrational number/decimal; 0 for 'the square root of some integers is a fraction' |
| \(x^2\) is an integer \(\Leftarrow\) \(x\) is an integer | B1 | B0 if no attempt at explanation; Do not accept \(\leftarrow\) oe |
## Question 9(i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| The diagonals of a rhombus also intersect at $90°$ | B1 | oe for kite or other valid statement/sketch; B0 if eg rectangle or parallelogram etc also included as having diagonals intersecting at $90°$; accept 'diamond' etc; 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 |
| ABCD is a square $\Rightarrow$ the diagonals of quadrilateral ABCD intersect at $90°$ | B1 | oe; B0 if no attempt at explanation (explanation does not need to gain a mark); Do not accept $\rightarrow$ oe |
## Question 9(ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| eg 8 is an integer but $\sqrt{8}$ is not an integer | B1 | oe with another valid number, or equivalent explanation; B1 for the square root of some integers is a surd/irrational number/decimal; 0 for 'the square root of some integers is a fraction' |
| $x^2$ is an integer $\Leftarrow$ $x$ is an integer | B1 | B0 if no attempt at explanation; Do not accept $\leftarrow$ oe |9 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 $\Leftrightarrow$ 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 2015 Q9 [4]}}