This activity is proudly organized,
sponsored and supported by:
• Kenneth Yuen 3O2(32),
• John Phua 3O2(18),
• Koh Tzehou 3O2(09),
• Math Department of HCI
• Singapore Tourism Board and
Committee
• Singapore nature Society
eMath Module
Rambling Walk Around
Singapore…
Introduction
To make this walk much more exciting and
fun-filled, you will not only be exploring the nature
side, parks as well as the cultural and historical
landmarks of Singapore, but at each stop, you will be
engaged in
In addition, the biggest takeaway would be to
learn about Singapore’s heritage and history in
Instructions
 The
rambling walk would be from 08:00 to 15:00.
 All together you would be exploring 6 (excluding the
final destination) stops in Singapore.
 There are also prizes waiting for you to take home in
addition to the treasures you find! Here are the
prizes:
Instructions
ATTRACTIVE PRIZES FOR JUST A
RAMBLING WALK?? YES IT’s
TRUE!!
 1st Prize: Attachment to Singapore Nature Society for
June Holidays 2011
 2nd Prize: 2 free tickets to the Singapore Math and
Algebra Museum
 3rd Prize: A Vanda Miss Joaquim plant
 To win the prizes, finish the activities at each stop and
reach the final stop first! Don’t miss this golden
opportunity!
Instructions
 All diagrams are not drawn to scale.
 The
tasks involve knowledge on trigonometry, such as
solving of 2D problems using sine rule, cosine rule,
bearings, area of triangle and simple trigonometry.
 The Geogebra applet that we have given you is to help
you get from one stop to another. You may need to zoom
in and out. We apologise for any inconveniences caused.
 For answers which are not exact, leave it to 3 significant
figures. For angles, leave it to 1 decimal place.
Instructions
Geogebra Applet
There are 4 maps available in the applet.
Please follow the instructions for the next 6
tasks and use the applet according to the
maps given.
Instructions
Items
needed:
 Geogebra Applet
(Laptop)
 Instructions + Activity Worksheet (This one)
 $10 (provided for lunch at Sixth Stop)
 A street directory book (in case you get lost)
Instructions
So…where to start?
 Start
 You will be starting at Hwa Chong Institution, Bukit
Timah.
 1st Stop Clue: Where is the founder of Singapore
standing at now?
First Stop
First Stop
 First Stop: Raffles Statue @ outside Victoria Concert
Hall, Raffles Place
 Geogebra Applet: Refer to Map 3 (Marina South)
First Stop
1. Read the following extract:
 Sir
Stamford Raffles was the first founder of
Singapore. He stepped on Singapore soil in 1819
and negotiated with the Temenggong then to
build a trading port here.
 Singapore was once a British colony till 1959,
whereby Singapore was granted self-governance.
 In 1965, when Singapore separated from the
Federation of Malaya, Singapore became
independent. This year marks the 46th birthday
of the young nation, Singapore.
First Stop
2. Task 1
A birthday cake for Singapore’s 46th Birthday was
reported lost near the Raffles Statue. Using satellite
imaging and technology, only the following information
about the location of the cake could be known:



Distance between Raffles Statue and the cake = 57m.
The bearing of the cake from Raffles Statue = x (less than
090°).
The following diagram was drawn. (Refer to next slide)
First Stop
3. Diagram 1
Find x. From there, you
should be able to find
the cake and your clue
for the next stop.
First Stop
4. Method and Answer for Task 1
 Concept tested: Sine and Cosine Rule
AC 2  BC 2  AB 2  2( AB)( BC ) cos ABC
AC 2  57 2  502  2(50)(57) cos 90
AC 2  5749
AC  75.822(5s. f .)
sin x sin 90

50
75.822
1 sin 90
x  sin (
 50)
75.822
x  41.257
x  41.3(1d . p.)
First Stop
5. 2nd Stop Clues
 2nd Stop Clue A



You are now at Marina South. (on Geogebra Applet Map
3)
The bearing of your next location should be 307-310° from
Marina South.
Note: Any deviations from the clue may end up giving you
a different location. Hence, clue B is given to you too as a
reference.
 2nd Stop Clue B: Find the flowers, the trees, and the
nature all over here! The largest garden of Singapore!
Second Stop
Second Stop
 Second Stop: Singapore Botanical Gardens
 Geogebra Applet: Refer to Map 3 (Bukit Timah)
Second Stop
1. Read the following extract:
 Sir Stamford Raffles, the founder
of Singapore and a
keen naturalist, established the first botanical and
experimental garden on Government Hill (Fort
Canning Hill) in 1822.
 The Gardens is geared towards entrenching itself as
a tropical botanical institution of international
renown, a key tourist destination and a flagship
park.
Second Stop
2. Task 2
You are required to help Singapore Botanical Gardens
to put up banners for an event. The event will be held
at the Symphony Lake. There are three banners of
different lengths. Only the lengths of 2 banners are
known and the bearing of B from C is 065°. Find ∠CAB.
From there, you should be able to put up all the
banners in the way like the diagram and get your next
clue from the staff.
Second Stop
3. Diagram 2
Symphony Lake
95m
65m
Second Stop
4. Method and Answer for Task 2:
 Concept tested: Sine Rule
sin CAB sin 65

65
95
sin 65
sin CAB 
 65
95
CAB  38.3(1d . p.)
Second Stop
5. 3rd Stop Clues
 3rd



Stop Clue A
You are now at Marina South. (on Geogebra Applet
Map 3)
The bearing of your next location should be 133-137°
from the “Bukit Timah”.
Note: Any deviations from the clue may end up giving
you a different location. Hence, clue B is given to you
too as a reference.
 3rd
Stop Clue B: We are going to say goodbye to this
place very soon.
Third Stop
Third Stop
 Third
Stop: KTM Station at Tanjong Pagar
 Geogebra Applet: Refer to Map 3 (Outram)
Third Stop
1. Read the following extract:
 The
train service carries passengers from Singapore
to Kuala Lumper, and from Kuala Lumper back to
Singapore.
 Recently, it has been announced that the KTM station
will be dismantled soon because it will be relocated
to Johor or Woodlands.
 Many people have since flocked to the station to take
photos for memories, or even buy the train tickets to
have a last train ride before it goes.
Third Stop
2. Task 3a:
Watch a train arrive at Tanjong Pagar KTM Station
from point X. After a train has arrived at the station,
watch the train return to the train depot. The train
should be travelling at an average speed of 21m/s
and take about 20s to enter the train depot. Given
that DX = 205m, XE = 315m, find angle DXE.
Third Stop
3. Diagram 3:
D: Train
Depot
E: KTM
Station
X
Third Stop
4. Task 3b:
The KTM Station is intending to paint the area covered
by DXE in black, but this proposal has been delayed
because nobody know how to calculate the area. Also,
it is too dangerous and inconvenient to measure the
height of the triangle because trains frequently pass
by DE. Give a try at calculating the area of DXE so that
you get your next clue from the station control
personnel.
Third Stop
5. Method and Answer for Task 3a:
 Concept tested: Cosine Rule
 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒
𝐷𝐸 = 𝑆𝑝𝑒𝑒𝑑 × 𝑇𝑖𝑚𝑒
 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒
𝐷𝐸 =
 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒
𝐷𝐸 = 420𝑚
21𝑚
𝑠
× 20𝑠
DX 2  XE 2  DE 2
cos DXE 
2( DX )( XE )
2052  3152  4202
cos DXE 
2(205)(315)
DXE  105.8(1d . p.)
Third Stop
6. Method and Answer for Task 3b:
 Concept tested: Sine Rule and Area of Triangle
 Construct an additional line FX perpendicular to
the line DE.
D: Train
Depot
F
X
E: KTM
Station
Third Stop
6. Method and Answer for Task 3b:
Read from left to right.
1
𝐴𝑟𝑒𝑎 = × 𝑏𝑎𝑠𝑒 × ℎ𝑒𝑖𝑔ℎ𝑡
2
1
𝐴𝑟𝑒𝑎 = × 𝐷𝐸 × 𝐹𝑋 − −(1
2
𝐹𝑋
sin∠𝐹𝐸𝑋 =
𝑋𝐸
𝐹𝑋 = 𝑋𝐸sin∠𝐹𝐸𝑋 − −(2
1
𝐴𝑟𝑒𝑎 = × 𝐷𝐸 × 𝑋𝐸sin∠𝐹𝐸𝑋
2
1
𝐴𝑟𝑒𝑎 = × 420 × 315sin∠𝐹𝐸𝑋
2
sin𝑋 sin𝐸
=
𝐷𝐸
𝐷𝑋
sin105.8 sin∠𝐹𝐸𝑋
=
420
205
sin105.8
sin∠𝐹𝐸𝑋 =
× 205
420
∠𝐹𝐸𝑋 = 28.0°(1𝑑. 𝑝.
1
𝐴𝑟𝑒𝑎 = × 420 × 315sin28.0
2
𝐴𝑟𝑒𝑎 = 31056𝑚2 (5𝑠. 𝑓
𝐴𝑟𝑒𝑎 = 31100𝑚2 (3. 𝑓.
Third Stop
7. 4th Stop Clues:
 4th Stop Clue A:



You are now at Outram. (on Geogebra Applet Map 3)
The bearing of your next location should be 075-078°
from the “Outram”.
Note: Any deviations from the clue may end up giving you
a different location. Hence, clue B is given to you too as a
reference.
 4th Stop Clue B: Singapore’s most iconic and historical
landmark, or more specifically Singapore’s mascot
Fourth Stop
Fourth Stop
 Fourth Stop: Merlion Park @ One Fullerton
 Geogebra Applet: Refer to Map 2 or Map 3
(Marina South)
Fourth Stop
1. Read the following extract:
 The
Merlion Park was originally located at the
Esplanade Bridge, but now when you come out
from One Fullerton/Fullerton Hotel, you will
notice this iconic landmark standing at the edge
spitting out water.
 The Merlion has become a famous landmark and
represents Singapore’s historical development –
from once a fishing village to a lion city, hence the
half-lion and half-mermaid Merlion.
Fourth Stop
2. Task 4





The government wants to build a shelter for the poor Merlion
who has to withstand rain and hot sun day in and out. The
shelter is to be triangular. However, the contractor is currently
having troubles with finding out the 3 angles of the shelter. He
only knows the following information:
The bearing of I from G is 099°.
The bearing of H from I is 230°.
The bearing of G from H is 015°.
Find 3 angles of the shelter. When you are done, call the
contractor at 65778990 and he will tell you the clue for your
next stop.
Fourth Stop
3. Diagram 4:
G
Merlion
H
I
Fourth Stop
4. Method and Answer for Task 4:
 Concept tested: Bearings and Basic Angle
Geometry
G 099°
015
°
H
Merlion
I
230
°
Fourth Stop
4. Method and Answer for Task 4:
KIH  360  230  130
LHI  180  130  50
GHI  50  15  35
GIK  180  99  81
HIG  360  230  81  49
HGI  180  35  49  96
 The
three angles are 35°, 49° and 96°.
Fourth Stop
5. 5th Stop Clues:
 5th Stop Clue A:



You are now at Merlion Park. (on Geogebra Applet
Map 2)
The bearing of your next location should be 072-078°
from the Merlion Park.
Note: Any deviations from the clue may end up giving
you a different location. Hence, clue B is given to you
too as a reference.
 5th Stop Clue B: The
I’m not kidding!
tallest Ferris Wheel on Earth.
Fifth Stop
Fifth Stop
 Fifth Stop: The
Singapore Flyer @ Marina Bay
 Geogebra Applet: Refer to Map 2 (Singapore
Flyer)
Fifth Stop
1. Read the following extract:
 Singapore Flyer was first conceived in early 2000s by
Patrick MacMahon of Melchers Project Management,
a subsidiary of German company Melchers.
 It is the tallest Ferris wheel in the world, taller than the
London Eye and Star of Nanchang.
 It has also become one of Singapore’s architectural
landmarks, together with Esplanade, Marina Bay Sands
and Gardens by the Bay.
Fifth Stop
2. Task 5:
Take a ride up the Singapore Flyer. When you reach the
top, you can look down at the Esplanade. Also, you get
a panoramic view of the Marina Barrage and the
Esplanade Bridge too. Your field of vision is illustrated
in the diagram below:
Fifth Stop
3. Diagram 5:
M: Singapore Flyer
062°
N: Suntec
City
P: Mandarin Oriental
Hotel
O: The Float@
Marina Bay
The distance between the Suntec City and the Float @
Marina Bay is 100m. The bearing of M from N is 062° and
the bearing of M from O is 312°. Points M, N, P and O are
points on the ground and N, P, O lie on a straight line
perpendicular to the North direction. Find the distance
between Suntec City and Mandarin Oriental Hotel.
Fifth Stop
4. Method and Answer for Task 5:
 Concept tested: Bearings,
Basic Trigonometry,
Algebraic Manipulation
MNO  90  62  28
MOP  312  270  42
MP
tan 28 
NP
MP
tan 42 
PO
Continued
on next slide
Fifth Stop
4. Method and Answer for Task 5:
Read from left to right.
MP
MP(tan 42  tan 28)  100(tan 28)(tan 42)
tan 28
100(tan 28)(tan 42)
MP 
MP
PO 
(tan 42  tan 28)
tan 42
MP  33.423m(5s. f )
MP
MP

 100
33.423
tan 28 tan 42
NP 
MP(tan 42)  MP(tan 28)
tan 28
 100
(tan 28)(tan 42)
NP  62.872m(5s. f .)
NP 
NP  62.9m(3s. f .)
Fifth Stop
5. 6th Stop Clues:
 6th Stop Clue A:



You are now at Marina East . (on Geogebra Applet Map
3)
The bearing of your next location should be 344-350°
from the Marina East.
Note: Any deviations from the clue may end up giving
you a different location. Hence, clue B is given to you
too as a reference.
 6th Stop Clue B: The
most unique park in Singapore,
with trees shaped like bottles.
Sixth Stop
Sixth Stop
 Sixth Stop: Bottle Tree
Park @ Yishun
 Geogebra Applet: Refer to Map 2 (Yishun)
Sixth Stop
1. Read the following extract:
 The
most unique thing about this park is that it grows
bottle trees! The picture above tells it all.
 Besides that, residents can also fish at the big lake
there and have a seafood feast at a seafood restaurant
nearby.
 Not only so, if you don’t like fishing, prawning is an
available alternative. This park definitely promises you
tons of fun and that’s the power of nature!
Sixth Stop
2. Task 6a:
 First and foremost, have your lunch!
We have provided
you $10 to have a good lunch at the Seafood
Restaurant there.
 The Bottle Tree Park Lake is circular in shape. Fishing
nets have been placed inside the circle to form a
square QRST. Another red fishing net is placed to
separate the two types of fishes that residents can fish.
U is a midpoint of RS. If the fishing net QR is 45m long,
find the following:



Angle
The radius of the circular lake
Sixth Stop
3. Diagram 6:
Sixth Stop
4. Method and Answer to Task 6a:
 Concept tested: Basic Trigonometry, Pythagoras
Theorem
45
tan  
22.5
  63.4(1d . p.)
Radius  (452  452 )
Radius  63.6m(3s. f .)
Sixth Stop
5. Task 6b:
 You are now at Bottle Tree. (on Geogebra Applet Map
4)
 Your next destination is Khatib MRT, but first you need
to measure the bearing of Khatib MRT from Bottle
Tree. A stationmaster would be present at your final
destination and request for the bearing value.
 Method and Answer for Task 6b:

Use Geogebra Applet Map 4 to help you. Your bearing is
34-38°.
Sixth Stop
6. THE FINAL DESTINATION:
Hwa Chong
Institution.
 Take bus 852 back to the school from Khatib MRT
Station.
 HURRY!! The prizes are waiting for you to come
back fast!
Seventh Stop
Seventh Stop
Debrief
 Congratulations, you have finished
the activity
Rambling Walk Around Singapore! Hope you have
enjoyed the walk while solving challenging but
fulfilling mathematical problems involving
trigonometry.
 P/S: As for the prizes, that will depend on whether
you are the first, second, third or last.
THE END
Have a nice day.