Question 1 — IGCSE 0580 May/June 2023 Paper 42
Cambridge IGCSE Mathematics 0580, Extended tier, calculator. Topic: Geometry · Geometrical terms and vocabulary. Worth 18 marks.
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Question text
1 (a)
42°
NOT TO
SCALE
x°
The diagram shows an isosceles triangle with the base extended.
Find the value of x.
x = ................................................ [3]
(b) The diagram shows three lines meeting at a point.
The ratio a : b : c = 3 : 4 : 5.
Find the value of c.
a°
NOT TO
c°
b° SCALE
c = ................................................ [3]
(c) A regular pentagon has an exterior angle, d.
A regular hexagon has an interior angle, h.
d
Find the fraction .
h
Give your answer in its simplest form.
................................................. [4]
© UCLES 2023 0580/42/M/J/23
3
(d)
S R
x° (x+20 ) °
NOT TO
SCALE
(3x – 40 ) °
Q
(2x –5 ) °
P
Show that PQRS is a cyclic quadrilateral.
[5]
(e)
B
A
50°
9 cm NOT TO
O SCALE
The diagram shows a circle of radius 9 cm, centre O.
The minor sector AOB, with sector angle 50°, is removed from the circle.
Calculate the length of the major arc AB.
............................................ cm [3]
© UCLES 2023 0580/42/M/J/23 [Turn over
4
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