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Radian measure, arcs and sectors

37 questions

Additional Mathematics/Paper 2/Circular measure

CAIEO-Level4037-o · Paper 2

Circular measure

37 questions· page 1 of 4

Q82026 May/Jun·P213 partsMediumCircular measure

(a)

Show that the value of $\theta$ is 0.885 radians correct to 3 decimal places.

(b)

Find the length of the arc $AB$ .

(c)

Find the area of the sector $ACB$ .

Q22025 Oct/Nov·P223 partsMediumCircular measure

(a)

Find the obtuse angle $AOB$ .

Give your answer in radians.

(b)(i)

the perimeter of the shaded region

(b)(ii)

the area of the shaded region.

Q82025 Oct/Nov·P232 partsMedium-EasyCircular measure

(a)

Find the exact value of angle $AQB$ in radians.

(b)

Hence find the area of the shaded region. Give your answer in terms of $\pi$ .

Q112024 May/Jun·P217MMediumCalculus

In this question all lengths are in centimetres.

The diagram shows a rectangle $ABCD$ with $BC = x$ .
The area of the rectangle is $400\text{ cm}^2$ .

Two identical quarter-circles of radius $\frac{x}{2}$ , with centres $A$ and $C$ , are removed from the rectangle to make the shaded shape.

Given that $x$ can vary, find the value of $x$ that gives the minimum value of the perimeter of the shaded shape and hence find this minimum value.

Similar questions

Q42024 Oct/Nov·P232 partsMedium-EasyCircular measure

(a)

Show that the perimeter, $P\text{ cm}$ , of the logo is given by

P = 2r + \frac{18}{r}

(b)

Given that $r$ can vary, find the stationary value of $P$ and determine its nature.

Q32023 Oct/Nov·P224MMedium[Legacy] Indices and surds

DO NOT USE A CALCULATOR IN THIS QUESTION.

A cylinder has base radius $(2 + \sqrt{3})\,\text{m}$ and volume $\pi(16 + 9\sqrt{3})\,\text{m}^3$ . Find the exact value of its height, giving your answer in its simplest form.

Similar questions

Q92022 May/Jun·P222 partsMediumCircular measure

(a)

In the case when the area of the sector $OPQ$ is equal to the area of the shaded region, show that $\tan\phi = 2\phi$ .

(b)

In the case when the perimeter of the sector $OPQ$ is equal to half the perimeter of the shaded region, find an expression for $\tan\phi$ in terms of $\phi$ .

Q72021 May/Jun·P222 partsMediumCircular measure

(a)

Find the perimeter of the shaded region.

(b)

Find the area of the shaded region.

Q112020 May/Jun·P222 partsMediumCircular measure

(a)

Given that the perimeter of the shaded region is $4\pi\,\text{cm}$ , find the value of $r$ .

(b)

Find the exact area of the shaded region.

Q82019 May/Jun·P212 partsMediumCircular measure

(i)

Find the area of the shaded region.

(ii)

Find the perimeter of the shaded region.