Question 2 — IGCSE 0580 Oct/Nov 2024 Paper 31
Cambridge IGCSE Mathematics 0580, Core tier, calculator. Topic: Geometry · Angles using geometrical properties. Worth 9 marks.
Open in interactive question bank →
Question text
2 (a) In the diagram, BCG is a triangle.
ABCD and EF are parallel lines.
NOT TO
G SCALE
z°
E y° F
38°
x° 69°
A B C D
(i) Find the value of x.
Give a geometrical reason for your answer.
x = ................ because ........................................................................................................ [2]
(ii) Find the value of y.
Give a geometrical reason for your answer.
y = ................ because ........................................................................................................
............................................................................................................................................. [2]
(iii) Find the value of z.
z = ................................................ [2]
(cid:300)(cid:213)(cid:266)(cid:174)(cid:288)(cid:180)(cid:237)(cid:200)(cid:245)(cid:207)(cid:298)(cid:197)(cid:266)(cid:224)(cid:252)(cid:184)(cid:256)(cid:215)
© UCLES 2024 (cid:300)(cid:232)(cid:175)(cid:244)(cid:220)(cid:290)(cid:299)(cid:264)(cid:216)(cid:241)(cid:245)(cid:290)(cid:258)(cid:241)(cid:294)(cid:276)(cid:270)(cid:258) 0580/31/O/N/24
(cid:293)(cid:277)(cid:245)(cid:277)(cid:181)(cid:213)(cid:229)(cid:277)(cid:261)(cid:181)(cid:213)(cid:261)(cid:261)(cid:181)(cid:293)(cid:213)(cid:261)(cid:213)
M
SIHT
NI
ETIRW
TON
OD
NIGRAM
SIHT
NI
ETIRW
TON
OD
NIGRAM
SIHT
NI
ETIRW
TON
OD
NIGRAM
SIHT
NI
ETIRW
TON
OD
NIGRAM
SIHT
NI
ETIRW
TON
OD
* 0000800000005 *
5
(cid:44)(cid:1)(cid:1)(cid:1)(cid:1)(cid:9)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:6)(cid:44)
(b)
X
NOT TO
SCALE
T
O
S
Y
R
R, S and T are points on a circle, centre O.
Line XY touches the circle at T.
(i) Write down the mathematical name for the line XY.
................................................. [1]
(ii) Write down the mathematical name for the line SR.
................................................. [1]
(iii) Toby thinks shape RST is a right-angled triangle.
Give a geometrical reason why Toby is incorrect.
.............................................................................................................................................
............................................................................................................................................. [1]
© UCLES 2024 (cid:300) (cid:300) (cid:215) (cid:232) (cid:266) (cid:176) (cid:174) (cid:243) (cid:288) (cid:212) (cid:180) (cid:296) (cid:237) (cid:295) (cid:200) (cid:248) (cid:245) (cid:225) (cid:207) (cid:263) (cid:298) (cid:268) (cid:197) (cid:231) (cid:266) (cid:214) (cid:224) (cid:265) (cid:250) (cid:178) (cid:184) (cid:276) (cid:256) (cid:286) (cid:215) (cid:258) 0580/31/O/N/24 [Turn over
(cid:293)(cid:277)(cid:261)(cid:213)(cid:245)(cid:181)(cid:197)(cid:245)(cid:277)(cid:197)(cid:261)(cid:261)(cid:261)(cid:213)(cid:261)(cid:277)(cid:277)(cid:213)
NIGRAM
SIHT
NI
ETIRW
TON
OD
NIGRAM
SIHT
NI
ETIRW
TON
OD
NIGRAM
SIHT
NI
ETIRW
TON
OD
NIGRAM
SIHT
NI
ETIRW
TON
OD
NIGRAM
SIHT
NI
ETIRW
TON
OD
* 0000800000006 *
6
(cid:44)(cid:1)(cid:1)(cid:1)(cid:1)(cid:9)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:7)(cid:44)
NIGRAM
Mark scheme
