| Exam Board | AQA |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2010 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Trig Graphs & Exact Values |
| Type | Find general solution of trig equation |
| Difficulty | Moderate -0.3 This is a straightforward application of the general solution formula for cos θ = cos α, requiring students to recall that solutions are θ = ±α + 360n°. The algebraic manipulation to solve for x is minimal (adding 20° and dividing by 5). While it's from FP1, this particular question is more routine than typical Further Maths content, being slightly easier than an average A-level question due to its direct application of a standard formula with no conceptual complications. |
| Spec | 1.05o Trigonometric equations: solve in given intervals |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(5x - 20 = \pm 40 + 360n°\) | M1 | Using \(\cos A = \cos B \Rightarrow A = \pm B + 360n°\) |
| Case 1: \(5x - 20 = 40 + 360n°\) | M1 | Correct split into two cases |
| \(5x = 60 + 360n°\) | ||
| \(x = 12 + 72n°\) | A1 | Correct first family |
| Case 2: \(5x - 20 = -40 + 360n°\) | ||
| \(5x = -20 + 360n°\) | ||
| \(x = -4 + 72n°\) | A1 | Correct second family |
| Both answers expressed with \(n\) as integer | A1 | General solution fully correct |
# Question 3:
| Answer/Working | Mark | Guidance |
|---|---|---|
| $5x - 20 = \pm 40 + 360n°$ | M1 | Using $\cos A = \cos B \Rightarrow A = \pm B + 360n°$ |
| Case 1: $5x - 20 = 40 + 360n°$ | M1 | Correct split into two cases |
| $5x = 60 + 360n°$ | | |
| $x = 12 + 72n°$ | A1 | Correct first family |
| Case 2: $5x - 20 = -40 + 360n°$ | | |
| $5x = -20 + 360n°$ | | |
| $x = -4 + 72n°$ | A1 | Correct second family |
| Both answers expressed with $n$ as integer | A1 | General solution fully correct |
---3 Find the general solution, in degrees, of the equation
$$\cos \left( 5 x - 20 ^ { \circ } \right) = \cos 40 ^ { \circ }$$
\begin{center}
\includegraphics[max width=\textwidth, alt={}]{763d89e4-861a-4754-a93c-d0902987673f-04_2228_1705_475_155}
\end{center}
\hfill \mbox{\textit{AQA FP1 2010 Q3 [5]}}