| Exam Board | Edexcel |
|---|---|
| Module | P3 (Pure Mathematics 3) |
| Year | 2020 |
| Session | October |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Addition & Double Angle Formulae |
| Type | Solve equation with sin2x/cos2x by substitution |
| Difficulty | Moderate -0.3 This is a straightforward double angle equation requiring the standard substitution cos(2x) = 2cos²(x) - 1, leading to a quadratic in cos(x). The algebraic manipulation is routine, and finding solutions in the given range is standard A-level technique. Slightly easier than average due to its predictable structure and limited steps. |
| Spec | 1.05l Double angle formulae: and compound angle formulae1.05o Trigonometric equations: solve in given intervals |
$2\cos 2x - 1 = 7\cos x$ M1
$4\cos^2 x - 7\cos x - 2 = 0 \Rightarrow \cos x = -\frac{1}{4}$ M1 A1
$x = \arccos\left(-\frac{1}{4}\right) = 104.5°, 255.5°$ dM1 A1
(5 marks)\begin{enumerate}
\item Solve, for $0 \leqslant x < 360 ^ { \circ }$, the equation
\end{enumerate}
$$2 \cos 2 x = 7 \cos x$$
giving your solutions to one decimal place.\\
(Solutions based entirely on graphical or numerical methods are not acceptable.)\\
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\hfill \mbox{\textit{Edexcel P3 2020 Q1 [5]}}