| Exam Board | OCR |
|---|---|
| Module | PURE |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Topic | Trig Proofs |
| Type | Logical implication symbols (⇒, ⇔, ⇐) |
| Difficulty | Standard +0.3 This question tests understanding of logical implication symbols through calculus and algebra examples. While it requires careful thinking about sufficiency and necessity, the individual parts are straightforward: (i) is standard differentiation checking bidirectionality, (ii) involves factoring a quintic with one real root, and (iii) requires properties of logarithms. The conceptual demand is moderate but execution is routine for A-level students. |
| Spec | 1.01b Logical connectives: congruence, if-then, if and only if |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(P \Rightarrow Q\) | B1 [1] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(P \Leftrightarrow Q\) | B1 [1] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(P \Rightarrow Q\) | B1 [1] |
# Question 3:
## Part (i)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $P \Rightarrow Q$ | B1 [1] | |
## Part (ii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $P \Leftrightarrow Q$ | B1 [1] | |
## Part (iii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $P \Rightarrow Q$ | B1 [1] | |
---3 In each of the following cases choose one of the statements
$$P \Rightarrow Q \quad P \Leftarrow Q \quad P \Leftrightarrow Q$$
to describe the relationship between $P$ and $Q$.\\
(i) $P : y = 3 x ^ { 5 } - 4 x ^ { 2 } + 12 x$\\
$Q : \frac { \mathrm { d } y } { \mathrm {~d} x } = 15 x ^ { 4 } - 8 x + 12$\\
(ii) $\quad P : x ^ { 5 } - 32 = 0$ where $x$ is real\\
$Q : x = 2$\\
(iii) $\quad P : \ln y < 0$\\
$Q : y < 1$
\hfill \mbox{\textit{OCR PURE Q3 [3]}}