CAIE P1 2024 November — Question 2 2 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2024
SessionNovember
Marks2
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicStandard trigonometric equations
TypeTransformed argument solving
DifficultyChallenging +1.2 This question requires solving a non-standard trigonometric equation involving two different angles (x/6 and 2x) with different trig functions, which cannot be solved by standard algebraic manipulation. Students must recognize that trial of special angles is needed, testing values like x = π/12, -π/12, etc. While only worth 2 marks and having a small search space due to the restricted domain, the non-routine nature and need for strategic angle substitution makes it moderately harder than average.
Spec1.05o Trigonometric equations: solve in given intervals

Find the exact solution of the equation $$\cos\frac{x}{6} + \tan 2x + \frac{\sqrt{3}}{2} = 0 \text{ for } -\frac{1}{4}\pi < x < \frac{1}{4}\pi.$$ [2]

Question 2:
AnswerMarks
2 3
cos +tan2x+ =0  tan2x=− 3
AnswerMarks Guidance
 6 2M1 Making tan2xthe subject. tan2x=0 is M0.
Accept decimals and one sign error.
 
2x=− x=−
AnswerMarks Guidance
3 6A1 May come from non-exact working.
Ignore answers outside the given range.
2
AnswerMarks Guidance
QuestionAnswer Marks
Question 2:
2 |  3
cos +tan2x+ =0  tan2x=− 3
 6 2 | M1 | Making tan2xthe subject. tan2x=0 is M0.
Accept decimals and one sign error.
 
2x=− x=−
3 6 | A1 | May come from non-exact working.
Ignore answers outside the given range.
2
Question | Answer | Marks | Guidance
Find the exact solution of the equation
$$\cos\frac{x}{6} + \tan 2x + \frac{\sqrt{3}}{2} = 0 \text{ for } -\frac{1}{4}\pi < x < \frac{1}{4}\pi.$$ [2]

\hfill \mbox{\textit{CAIE P1 2024 Q2 [2]}}