CAIE IGCSE Mathematics Extended E5.5 Compou…hapes

Covered syllabus points

E5.5.1 Carry out calculations and solve problems involving perimeters and E5.5.2 Carry out calculations and solve problems involving surface areas and

[Maximum number: 4]

Figure for Question 1 — 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 total area of the shape.

94.2 or 94.3 or 94.15 to 94.27... nfww
M1 for $\frac12\times6\times\text{their }OD\times\sin135$ oe
M1 for $\frac12\times6\times2\times\sin(90-19.5)$ oe or for $\frac12\times\text{their }OC\times2$
M1dep for their (a)(ii) + their two triangle areas

[Maximum number: 3]

NOT TO SCALE

The diagram shows a solid sphere with radius 6 cm inside a cube with side length 20 cm.
The cube contains water to a depth of 15 cm.
The sphere is removed.
Calculate the new depth of water in the cube.
[The volume, V, of a sphere with radius r is V=4/3 r^3.]

12.7 or 12.73 to 12.74
B2 for 2.26 or 2.261 to 2.262... soi
or M2 for $\frac{20^2\times15-\frac43\pi\times6^3}{20^2}$ oe, or $15-\frac{\frac43\pi\times6^3}{20^2}$ oe
or M1 for $20^2\times15-\frac43\pi\times6^3$ oe or $20^2D=\frac43\pi\times6^3$ oe
If 0 scored, SC1 for answer 11[.0] or 10.97 to 10.98

[Maximum number: 4]

Figure for Question 3 — CAIE IGCSE Mathematics Extended

NOT TO SCALE

The diagram shows a shape ABQP made from three straight lines and an arc of a sector of a circle. The sector has centre O and angle $90^{\circ}$ .
POQ is a straight line and $A P=P O=O Q=Q B=5 \mathrm{~cm}$ .
Find the area of ABQP.
Give your answer in the form $a+k \pi$ .
$\mathrm{cm}^{2}$

$25+\frac{25\pi}{2}$
M2 for $\frac{90}{360}\times\pi\times(\sqrt{5^2+5^2})^2$
or M1 for $\text{radius}^2=5^2+5^2$
M1 for triangle area $[2\times]\frac{1}{2}\times5\times5$ oe

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CAIE IGCSE Mathematics Extended E5.5 Compound Shapes and Parts of Shapes Topic Practice

Covered syllabus points

Question 1

Question 2

Question 3