Moderate -0.3 This is a straightforward trigonometric equation requiring basic algebraic manipulation (taking square roots) and knowledge of the tan function's periodicity. While students must find all solutions in the given range and work with the double angle 2θ, it's a standard AS-level exercise with no conceptual challenges beyond routine technique.
Question 4:
4 | Solves to find tan2θ (allow M1 even
if only +√3 given PI by any correct
final value of 𝜃) | AO1.1a | M1 | tan2θ = ±√3
tan2θ = √3 → 2θ = 60°, 240°, 420°,
600°
tan2θ = –√3 → 2θ = 120°, 300°, 480°,
660°
θ = 30°, 60°, 120°, 150°, 210°, 240°,
300, 330°
Obtains at least 3 correct final
values for 𝜃 ignore extra incorrect
terms or terms outside range | AO1.1b | A1
Obtains at least 3 correct final
values of θ from tan2θ = √3 and at
least 3 correct values from
tan2θ = –√3 ignore extra incorrect
terms or terms outside range | AO1.1a | M1
Obtains complete set of exactly 8
correct values for θ | AO1.1b | A1
Total | 4
Q | Marking Instructions | AO | Marks | Typical Solution
Solve the equation $\tan^2 2\theta - 3 = 0$ giving all the solutions for $0° \leq \theta \leq 360°$
[4 marks]
\hfill \mbox{\textit{AQA AS Paper 2 2018 Q4 [4]}}