Question 3 - A-Level Maths

CAIE P1 2019 June — Question 3 4 marks

Exam Board	CAIE
Module	P1 (Pure Mathematics 1)
Year	2019
Session	June
Marks	4
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Circles
Type	Sector and arc length
Difficulty	Moderate -0.8 This is a straightforward application of standard circle formulas (A = ½r²θ, perimeter = 2r + rθ) requiring only algebraic manipulation to express θ in terms of A and r, then substitute. It's simpler than average A-level questions as it involves just one concept and minimal steps.
Spec	1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta

3 A sector of a circle of radius \(r \mathrm {~cm}\) has an area of \(A \mathrm {~cm} ^ { 2 }\). Express the perimeter of the sector in terms of \(r\) and \(A\).

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Question 3:

Answer	Marks	Guidance
Answer	Marks	Guidance
Uses \(A = \frac{1}{2}r^2\theta\)	M1	Uses area formula
\(\theta = \frac{2A}{r^2}\)	A1
\(P = r + r + r\theta\)	B1
\(P = 2r + \frac{2A}{r}\)	A1	Correct simplified expression for \(P\)

## Question 3:

| Answer | Marks | Guidance |
|--------|-------|----------|
| Uses $A = \frac{1}{2}r^2\theta$ | M1 | Uses area formula |
| $\theta = \frac{2A}{r^2}$ | A1 | |
| $P = r + r + r\theta$ | B1 | |
| $P = 2r + \frac{2A}{r}$ | A1 | Correct simplified expression for $P$ |

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3 A sector of a circle of radius $r \mathrm {~cm}$ has an area of $A \mathrm {~cm} ^ { 2 }$. Express the perimeter of the sector in terms of $r$ and $A$.\\

\hfill \mbox{\textit{CAIE P1 2019 Q3 [4]}}

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