Trigon Bearing Classified
Trigon Bearing Classified
Trigon Bearing Classified
2002 2011
CLASSIFIEDS TRIGOnBEARING
Compiled & Edited
By
Dr. Eltayeb Abdul Rhman
www.drtayeb.wordpress.com
First Edition
2011
7
13
T
North
B
NOT TO
SCALE
A
76
O
[2]
Answer(b)
[2]
UCLES 2011
0580/22/O/N/11
10
21
North
2.7
km
North
NOT TO
SCALE
4.5 km
A
5 km
[4]
Answer(b)
[1]
UCLES 2011
0580/23/O/N/11
10
6
C
26
95 m
79 m
NOT TO
SCALE
77
D
120 m
[4]
(b) Calculate the size of the obtuse angle ABC.
UCLES 2011
0580/41/O/N/11
[4]
11
(c) A straight path is to be built from B to the nearest point on the road AC.
Calculate the length of this path.
Answer(c)
m [3]
Answer(d)
UCLES 2011
0580/41/O/N/11
[4]
16
8
NOT TO
SCALE
C
5m
45
3m
[4]
(ii) Calculate angle BCA.
UCLES 2011
0580/42/O/N/11
[3]
17
(b) AC = CD and angle CDA = 52.
(i) Find angle DCA.
[1]
m2 [3]
Answer(b)(ii)
(c) Parvatti uses the canvas to give some shade.
She attaches corners A and D to the top of vertical poles, AP and DQ, each of height 2 m.
Corners B and C are pegged to the horizontal ground.
AB is a straight line and angle BPA = 90.
D
A
3m
2m
2m
B
NOT TO
SCALE
C
Q
UCLES 2011
0580/42/O/N/11
[2]
10
21
NOT TO
SCALE
95
6m
9m
C
The triangular area ABC is part of Henris garden.
AB = 9 m, BC = 6 m and angle ABC = 95 .
Henri puts a fence along AC and plants vegetables in the triangular area ABC.
Calculate
(a) the length of the fence AC,
[3]
[2]
8
18
Rotterdam
NOT TO
SCALE
North
Bruges
83 km
Antwerp
Calculate
(a) the distance between Bruges and Rotterdam,
Answer(a)
km [2]
(b) the bearing of Rotterdam from Bruges, correct to the nearest degree.
Answer(b)
UCLES 2004
[3]
10
20 A plane flies from Auckland (A) to Gisborne (G) on a bearing of 115o.
The plane then flies on to Wellington (W). Angle AGW = 63o.
North
o
A 115
North
63o
410 km
NOT TO
SCALE
400 km
Answer (a)
[2]
Answer (b)
UCLES 2005
[4]
5
4
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]
Answer(b)(i)
[1]
Answer(b)(ii)
[2]
(ii) A from B.
UCLES 2009
0580/04/M/J/09
730 m
37.1
B
(a) The length of the cable from the bottom, B, to the top, T, is 730 metres.
The angle of elevation of T from B is 37.1.
Calculate the change in altitude, h metres, from the bottom to the top.
Answer(a)
m [2]
(b) The lift travels along the cable at 3.65 metres per second.
Calculate how long it takes to travel from B to T.
Give your answer in minutes and seconds.
Answer(b)
UCLES 2010
min
0580/22/M/J/10
s [2]
10
21
North
North
NOT TO
SCALE
140
North
50 m
R
100 m
P
[3]
Answer(b)
[2]
UCLES 2010
0580/23/M/J/10
D
30
C
NOT TO
SCALE
24 cm
40
40
A
26 cm
Answer(a)
cm2
[2]
Answer(b)
cm
[4]
Answer(c)
cm
[4]
cm
[2]
(d) Calculate the shortest distance from the point C to the line BD.
Answer(d)
UCLES 2010
0580/41/M/J/10
North
NOT TO
SCALE
180 km
115 km
90 km
30
70
R
The diagram shows some straight line distances between Auckland (A), Hamilton (H), Tauranga (T)
and Rotorua (R).
AT = 180 km, AH = 115 km and HT = 90 km.
(a) Calculate angle HAT.
Show that this rounds to 25.0, correct to 3 significant figures.
Answer(a)
[4]
(b) The bearing of H from A is 150.
Find the bearing of
(i) T from A,
Answer(b)(i)
[1]
Answer(b)(ii)
[1]
(ii) A from T.
UCLES 2010
0580/42/M/J/10
Answer(c)
km
[3]
Answer(d)
km
[3]
Answer(e) n =
2
. Find angle A.
A
NOT TO
SCALE
Answer Angle A =
UCLES 2010
0580/42/M/J/10
[2]
2
C
B
8 cm
NOT TO
SCALE
5 cm
3 cm
D
A
11 cm
Answer(a) BC =
cm
[2]
[4]
Answer(c)
UCLES 2010
0580/43/M/J/10
cm2
[3]
4
10
C
27
NOT TO
SCALE
12 cm
B
cm [2]
Answer AC =
11
D
C
12 cm
NOT TO
SCALE
B
9 cm
Answer BC =
cm [3]
Answer(a)
[1]
(b) Calculate 7.85 (2.366 102), giving your answer in standard form.
Answer(b)
UCLES 2011
0580/13/M/J/11
[2]
16
North
10 (a)
North
d
B
NOT TO
SCALE
120 m
53
A
B is 120 m from A on a bearing of 053.
Calculate
(i) the distance d,
Answer(a)(i) d =
m [2]
Answer(a)(ii)
[1]
(b)
F
NOT TO
SCALE
20 m
9m
24 m
angle FHA,
[2]
Answer(b)(ii) GA =
UCLES 2011
0580/31/M/J/11
m [3]
12
8
North
North
3 km
Answer(a)(i)
(ii) The journey from A to B takes him 30 minutes.
Calculate his average speed in kilometres per hour.
Answer(a)(ii)
km/h [1]
(b) From B, Manuel rows 3.5 kilometres in a straight line, on a bearing of 145, to a point C.
On the diagram, draw accurately this journey and label the point C.
UCLES 2011
0580/32/M/J/11
[2]
13
(c) Manuel then rows from C to A.
(i) Measure CA.
Answer(c)(i)
cm [1]
Answer(c)(ii)
km [1]
Answer(c)(iii)
[1]
(d) Two buoys, P and Q, are on opposite sides of the line AB.
Each buoy is 2 km from A and 1.5 km from B.
(i) On the diagram, construct and mark the positions of P and Q.
[2]
Answer(d)(ii)
cm [1]
Answer(d)(iii)
UCLES 2011
0580/32/M/J/11
km [1]
6
4
(a)
12 cm
NOT TO
SCALE
6 cm
14 cm
[4]
Answer(a)(ii)
UCLES 2011
0580/41/M/J/11
cm2 [2]
7
(b)
Q
18 cm
R
NOT TO
SCALE
12 cm
117
P
The diagram shows triangle PQR, with RP = 12 cm, RQ = 18 cm and angle RPQ = 117.
Calculate the size of angle RQP.
UCLES 2011
0580/41/M/J/11
[3]
4
3
(a)
North
C
North
The scale drawing shows the positions of two towns A and C on a map.
On the map, 1 centimetre represents 20 kilometres.
(i) Find the distance in kilometres from town A to town C.
Answer(a)(i)
km [2]
(ii) Measure and write down the bearing of town C from town A.
Answer(a)(ii)
[1]
[2]
[1]
Answer(a)(v)
UCLES 2011
0580/42/M/J/11
km2 [2]
5
(b) A plane leaves town C at 11 57 and flies 1500 km to another town, landing at 14 12.
Calculate the average speed of the plane.
km/h [3]
Answer(b)
(c)
Q
NOT TO
SCALE
1125 km
790 km
P
1450 km
Answer(c)Angle PQR =
UCLES 2011
0580/42/M/J/11
[4]
6
4
8 cm
NOT TO
SCALE
6 cm
O
9 cm
[4]
(b) M is the midpoint of BC.
(i) Find angle BOM.
UCLES 2011
0580/43/M/J/11
[1]
7
(ii) Calculate the radius of the circle and show that it rounds to 4.59 cm, correct to 3 significant
figures.
Answer(b)(ii)
[3]
(c) Calculate the area of the triangle ABC as a percentage of the area of the circle.
Answer(c)
UCLES 2011
0580/43/M/J/11
% [4]
11
22
P
NOT TO
SCALE
8cm
O
5.5cm
3cm
Q
K
M
8cm
In the circle, centre O, the chords KL and PQ are each of length 8 cm.
M is the mid-point of KL and R is the mid-point of PQ. OM = 3 cm.
(a) Calculate the length of OK.
[2]
0580/2/O/N/02
[3]
North
B
17
NOT TO
SCALE
40
32 m
T
Felipe (F) stands 17 metres from a bridge (B) and 32 metres from a tree (T).
The points F, B and T are on level ground and angle BFT # 40.
(a) Calculate
(i)
[4]
[3]
[1]
(ii) F from T,
[1]
(iii) B from T.
[1]
(i)
0580/04/0581/04/O/N/03
[2]
6
5
North
North
NOT TO
SCALE
40 km
80
115
60 km
Island
C
To avoid an island, a ship travels 40 kilometres from A to B and then 60 kilometres from B to C.
The bearing of B from A is 080 and angle ABC is 115.
[3]
[1]
(ii) C from B.
[1]
[4]
[3]
[3]
UCLES 2008
0580/04/O/N/08
7
16
B
North
NOT TO
SCALE
3 km
North
3 km
C
85
A
A, B and C are three places in a desert. Tom leaves A at 06 40 and takes 30 minutes to walk directly
to B, a distance of 3 kilometres. He then takes an hour to walk directly from B to C, also a distance of
3 kilometres.
(a) At what time did Tom arrive at C?
Answer (a)
[1]
Answer (b)
km/h
[2]
UCLES 2009
0580/21/O/N/09
[1]
10
6
L
5480 km
D
NOT TO
SCALE
165
3300 km
The diagram shows the positions of London (L), Dubai (D) and Colombo (C).
(a) (i) Show that LC is 8710 km correct to the nearest kilometre.
Answer(a)(i)
[4]
(ii) Calculate the angle CLD.
UCLES 2010
0580/42/O/N/10
[3]
3
2
R
4 km
Q
NOT TO
SCALE
7 km
4.5 km
S
85
40
P
[4]
(b) Calculate the length of the road RS and show that it rounds to 4.52 km.
Answer(b)
[3]
(c) Calculate the area of the quadrilateral PQRS.
[Use the value of 110.7 for angle PQR and the value of 4.52 km for RS.]
Answer(c)
UCLES 2010
0580/43/O/N/10
km2
[5]
10
21
North
topicTrigonometry
NOT TO
SCALE
140 m
North
P
220 m
31
North
R
Theresa swims from P to Q, then from Q to R and then finally returns from R to P.
PQ = 140 m, RP = 220 m and angle PRQ = 31.
(a) Angle PQR is obtuse.
Calculate its size, to the nearest degree.
Answer (a) ......................................................
[4]
[1]
22
f: x a 3 2x
topicFunctions
(a) Find
and
x+1
g: x a ,
4
f( 34 ).
[1]
[2]
g1(x).
fg(x),
[2]
EXTENDED MATHEMATICS
2002 2011
CLASSIFIEDS TRIGOnBEARING
Compiled & Edited
By
Dr. Eltayeb Abdul Rhman
www.drtayeb.wordpress.com
First Edition
2011