| Exam Board | CAIE |
|---|---|
| Module | P2 (Pure Mathematics 2) |
| Year | 2024 |
| Session | November |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Standard trigonometric equations |
| Type | Solve using given identity |
| Difficulty | Moderate -0.3 This is a straightforward application of solving a quadratic in cosec²θ (from earlier parts of the question), then taking square roots and finding inverse trig values within a restricted domain. It requires basic manipulation and knowledge of cosecant, but is a standard textbook exercise with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.05h Reciprocal trig functions: sec, cosec, cot definitions and graphs1.05o Trigonometric equations: solve in given intervals |
| Answer | Marks | Guidance |
|---|---|---|
| 4(a) | Substitute x=−2, equate to zero and attempt solution | M1 |
| Obtain a=4 | A1 |
| Answer | Marks |
|---|---|
| 4(b) | Divide by x+2at least as far as k x2 +k x |
| 1 2 | M1 |
| Obtain 4x2 −12x+9 | A1 |
| Obtain(x+2)(2x−3)2 or equivalent with integer coefficients only | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Question | Answer | Marks |
| Answer | Marks | Guidance |
|---|---|---|
| 4(c) | Equate sin2 to appropriate value from factorised form and attempt solution | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| Obtain 54.7 | A1 | Or greater accuracy. |
| Obtain –54.7 | A1 | Or greater accuracy. |
| Answer | Marks | Guidance |
|---|---|---|
| Question | Answer | Marks |
Question 4:
--- 4(a) ---
4(a) | Substitute x=−2, equate to zero and attempt solution | M1
Obtain a=4 | A1
2
--- 4(b) ---
4(b) | Divide by x+2at least as far as k x2 +k x
1 2 | M1
Obtain 4x2 −12x+9 | A1
Obtain(x+2)(2x−3)2 or equivalent with integer coefficients only | A1
3
Question | Answer | Marks | Guidance
--- 4(c) ---
4(c) | Equate sin2 to appropriate value from factorised form and attempt solution | M1 | 2
Usingtheir .
3
Obtain 54.7 | A1 | Or greater accuracy.
Obtain –54.7 | A1 | Or greater accuracy.
No others in −9090.
3
Question | Answer | Marks | Guidance\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Solve the equation $\text{p}(\cos ec^2 \theta) = 0$ for $-90° < \theta < 90°$. [3]
\end{enumerate}
\hfill \mbox{\textit{CAIE P2 2024 Q4 [3]}}