| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2024 |
| Session | October |
| Marks | 6 |
| Topic | Standard trigonometric equations |
| Type | Factorization method |
| Difficulty | Standard +0.8 Part (a) is a standard factorisation by grouping exercise. Part (b) requires recognising the substitution pattern from part (a), then solving two transcendental equations (sin(x²)=1/2 and cos(e^(x/3))=3/4) numerically within a restricted domain. The conceptual leap and numerical work elevate this above routine questions, but it's still a structured multi-part problem with clear signposting. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem1.05o Trigonometric equations: solve in given intervals |
\begin{enumerate}[label=\alph*)]
\item Factorise $8xy - 4x + 6y - 3$ into the form $(ax + b)(cy + d)$ where $a, b, c$ and $d$ are integers
\item Hence, or otherwise, solve
$$8\sin(x^2)\cos\left(e^{\frac{x}{3}}\right) - 4\sin(x^2) + 6\cos\left(e^{\frac{x}{3}}\right) - 3 = 0$$
where $0° < x < 19°$, giving your answers to 1 decimal place.
\end{enumerate}
[6 marks]
\hfill \mbox{\textit{SPS SPS FM 2024 Q9 [6]}}