CAIE IGCSE Mathematics Extended E5.3 Circle…ctors

Covered syllabus points

E5.3.1 Carry out calculations involving the circumference and area of a circle.E5.3.2 Carry out calculations involving arc length and sector area as

[Maximum number: 3]

NOT TO SCALE

Points A, B, C and D lie on a circle.
ABCD is a square with area $72\,\text{cm}^2$ .

Calculate the area of the circle.
Give your answer as a multiple of $\pi$ .

Figure for Question 1 — CAIE IGCSE Mathematics Extended

$36\pi$ cao.

B2 for answer 113, or 113.0 to $113.1\ldots$ , or an answer in terms of $\pi$ which rounds to 113.
M1 for a correct first step for finding d or r, e.g. $72+72=d^2$ oe, $72=r^2+r^2$ oe, $(\frac{\sqrt{72}}{2})^2+(\frac{\sqrt{72}}{2})^2=r^2$ oe, $\sqrt{72}=\frac{r}{\sin45^\circ}$ oe, or $\frac12 r^2=\frac{72}{4}$ oe.

[Maximum number: 3]

Figure for Question 2 — CAIE IGCSE Mathematics Extended

The diagram shows a shape made from a major sector AOB and triangles OBC and AOD. $O B=6 \mathrm{~cm}, B C=2 \mathrm{~cm}$ , obtuse angle $A O C=135^{\circ}$ and angle $B C O=90^{\circ}$ .

Calculate the area of the major sector AOB.

64.6 or 64.55 to 64.58
M2 for $\frac{360-135-19.5}{360}\times\pi\times6^2$ oe
or M1 for $\frac{k}{360}\times\pi\times6^2$ oe

[Maximum number: 3]

ABCDEFGH is a regular octagon with sides of length 6 cm. The diagram shows part of the octagon.
O is the centre of the octagon and M is the midpoint of AB.

Figure for Question 3 — CAIE IGCSE Mathematics Extended

NOT TO SCALE

Find the area of the circle that passes through the vertices of the octagon.
$\mathrm{cm}^{2}$

193 or 193.0 to 193.1
M2 for $\pi\left(\frac3{\cos67.5^\circ}\right)^2$ oe
or M1 for $\frac3r=\cos67.5^\circ$ or $\frac{\sin45^\circ}{6}=\frac{\sin67.5^\circ}{r}$

All question bank results loaded

CAIE IGCSE Mathematics Extended E5.3 Circles Arcs and Sectors Topic Practice

Covered syllabus points

Question 1

Question 2

Question 3