Question 4 — IGCSE 0580 May/June 2023 Paper 41
Cambridge IGCSE Mathematics 0580, Extended tier, calculator. Topic: Geometry · Angles using geometrical properties. Worth 14 marks.
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Question text
4 (a)
P
NOT TO
SCALE
8 cm
Q R
24 cm
(i) Calculate the area of triangle PQR.
......................................... cm2 [2]
(ii) Calculate angle PRQ.
Angle PRQ = ................................................ [2]
(b)
NOT TO
SCALE
11 cm
6 cm
The diagram shows a half-cylinder of radius 6 cm and length 11 cm.
Calculate the volume of the half-cylinder.
......................................... cm3 [2]
© UCLES 2023 0580/41/M/J/23
9
(c)
T T
D C C
44 ccmm
S S
O
NOT TO
15 cm
X X
SCALE
A B A B
20 cm
(i) ABCD is a rectangle with AB = 20 cm and BC = 15 cm.
S, X and T are points on a circle centre O, such that DSA and DTC are tangents to the circle.
The radius of the circle is 4 cm and TX is a diameter of the circle.
The shape DSXT is removed from the corner of the rectangle, leaving the shaded shape shown
in the second diagram.
Calculate the area of the shaded shape.
......................................... cm2 [5]
(ii) Calculate the perimeter of the shaded shape.
............................................ cm [3]
© UCLES 2023 0580/41/M/J/23 [Turn over
10
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