CAIE FP2 2018 November — Question 1 3 marks

Exam BoardCAIE
ModuleFP2 (Further Pure Mathematics 2)
Year2018
SessionNovember
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicSimple Harmonic Motion
TypeSpeed at given displacement
DifficultyModerate -0.5 This is a straightforward SHM problem requiring direct application of the standard velocity formula v² = ω²(a² - x²). Students need to identify amplitude (3m), calculate ω from period (ω = 1/2), determine displacement from centre (1m), then substitute. It's more routine than average A-level questions since it's purely procedural with no conceptual challenges or multi-step reasoning.
Spec4.10f Simple harmonic motion: x'' = -omega^2 x

A particle \(P\) oscillates in simple harmonic motion between the points \(A\) and \(B\), where \(AB = 6\) m. The period of the motion is \(4\pi\) s. Find the speed of \(P\) when it is 2 m from \(B\). [3]

Question 1:
AnswerMarks Guidance
1ω = 2π/T = 4 B1
v = ω√(a2 – x2) = 4√(32 – 12) = 8√2 or 11.3 [m s–1]M1A1 Find speed v when BP = 2
3
AnswerMarks Guidance
QuestionAnswer Marks
Question 1:
1 | ω = 2π/T = 4 | B1 | Find ω from period T (may be implied)
v = ω√(a2 – x2) = 4√(32 – 12) = 8√2 or 11.3 [m s–1] | M1A1 | Find speed v when BP = 2
3
Question | Answer | Marks | Guidance
A particle $P$ oscillates in simple harmonic motion between the points $A$ and $B$, where $AB = 6$ m. The period of the motion is $4\pi$ s. Find the speed of $P$ when it is 2 m from $B$. [3]

\hfill \mbox{\textit{CAIE FP2 2018 Q1 [3]}}