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0580/23/M/J/12
6
C
NOT TO
SCALE
9 cm
A
B
28°
15 cm
Calculate the area of triangle ABC.
cm2 [2]
Answer
0580/23/O/N/12
18
C
23°
A
6 cm
13 cm
NOT TO
SCALE
B
In triangle ABC, AB = 6 cm, BC = 13 cm and angle ACB = 23°.
Calculate angle BAC, which is obtuse.
Answer Angle BAC =
[4]
6
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0580/43/O/N/12
A
16 cm
NOT TO
SCALE
B
25 cm
C
The area of triangle ABC is 130 cm2.
AB = 16 cm and BC = 25 cm.
(a) Show clearly that angle ABC = 40.5°, correct to one decimal place.
Answer (a)
[3]
0580/41/O/N/14
7(b)
D
C
NOT TO
SCALE
30 m
37°
A
31°
B
In the diagram, BC represents a building 30 m tall.
A flagpole, DC, stands on top of the building.
From a point, A, the angle of elevation of the top of the building is 31°.
The angle of elevation of the top of the flagpole is 37°.
Calculate the height, DC, of the flagpole.
Answer(b) ............................................ m [5]
__________________________________________________________________________________________
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Page 3 of 6
5
4
For
Examiner's
Use
North
NOT TO
SCALE
North
A
126°
B
North
250 m
23°
P
The diagram shows three straight horizontal roads in a town, connecting points P, A and B.
PB =250 m, angle APB = 23° and angle BAP = 126°.
(a) Calculate the length of the road AB.
Answer(a) AB =
m [3]
(b) The bearing of A from P is 303°.
Find the bearing of
(i) B from P,
Answer(b)(i)
[1]
Answer(b)(ii)
[2]
(ii) A from B.
© UCLES 2009
0580/04/M/J/09
[Turn over
Page 4 of 6
12
21
For
Examiner's
Use
P
NOT TO
SCALE
5 cm
D
C
8 cm
M
A
8 cm
B
The diagram shows a pyramid on a square base ABCD.
The diagonals of the base, AC and BD, intersect at M.
The sides of the square are 8 cm and the vertical height of the pyramid, PM, is 5 cm.
Calculate
(a) the length of the edge PB,
Answer(a) PB =
cm [3]
(b) the angle between PB and the base ABCD.
Answer(b)
[3]
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.
University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of
Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
© UCLES 2012
0580/23/M/J/12
Page 5 of 6
7.!
Here is a graph of y = cos x for 0 ≤ x ≤ 360 , complete the curve
you have the space below to construct your table .
(2)
(4)
!
(a) Use your graph to solve cos x = 0.5 for 0 ≤ x ≤ 360.
........................................................
(2)
!
(b) Use your graph to solve cos x = −0.75 for 0 ≤ x ≤ 360.
........................................................
(2)
Page 6 of 6
7.!
Here is a graph of y = tan x for -90 ≤ x ≤ 270 , complete the
curve you have the space below to construct your table .
(1)
(4)
!
(a) Use your graph to solve tan x = 1.25 for -90 ≤ x ≤ 270.
........................................................
(2)
!
(b) Use your graph to solve sin x = −1.75 for -90 ≤ x ≤ 270.
........................................................
(2)