Maths Trail 2012

SECONDARY TWO

2012

Name:

Class:

Group:

Score:

TRAIL OBJECTIVES

1.

To offer an opportunity to help students see the relevance of Mathematics outside their classroom.

2.

To encourage students to see how Mathematics is used to interpret the world we live in.

3.

To emphasize the practical applications in Mathematics.

4.

To complement the content of Mathematics taught in the classroom by infusing National Education objectives.

5.

To allow students to practise their SEL skills in a group/team setting.

CONTENTS 1

WATER, WATER EVERYWHERE

4

2

SWEET, SIX-SIDED SHAPES

6

3

UNIVERSAL STUDIOS SINGAPORE

8

4

KNOW YOUR SINGAPORE

10

5a

TALKING BREAD

11

5b

WEIGHT FLOSS

12

6

THE MERLION

14

REFLECTIONS

16

MAP OF RESORTS WORLD SENTOSA

17

ACKNOWLEDGEMENTS

18

3

1 WATER, WATER EVERYWHERE

You will see many different fountains and water features around Resorts World Sentosa. Have you ever wondered how much water is being used for all these water features? Does replacing water in these features cost a lot of money and time? Let’s find out!

Task 1 In front of you is a huge water container in the shape of a cuboid. Take its measurements using the measuring tape provided.

Depth/ Height Breadth Length cm

cm

Task 2 Based on the measurements taken, calculate the volume of this container, assuming that it is a solid cuboid.

4

cm

Task 3 Assume that the water in the container needs to be changed daily. Given that water in Singapore cost $1.62 per m続, calculate the cost of changing the water in the container daily over a period of 4 weeks. Correct your answer to the nearest cent.

Now you are given additional measurements, in cm, of the water container. Find the amount of water this water container can hold (indicated by the dotted line) if it is filled to the brim.

25.5

25.5

19

A water pipe, capable of ejecting 30 cm続/s, is left to run continuously for 6 hours daily to fill up similar water containers. How many of such containers can be fully filled in 4 weeks?

5

2 SWEET SIX-SIDED SHAPES

Hexagons! The word “hexagon” is made up of the Greek words hex (six) and gonia (angle). A regular hexagon has six sides of the same length. It is a shape that appears in nature and manmade objects. Can you spot any around you?

Task 1

Edge length m

Shortest width m

Longest width m

Task 2 Based on the measurements taken, find the area of the hexagon.

HINT!

6

a h

b

Area of trapezium 1 = × (a+b) × h 2

Task 3 Honey is sometimes used to make caramel popcorn. Honey is obtained from honeycombs which are made by bees. People farm honey by getting bees to build their honeycombs on trays.

Imagine that you are a beekeeper and you want to extract honey to make popcorn.

You know that there are 500 cells in one honeycomb and the dimensions of each cell is as shown. Find out the volume of honey you will get from one honeycomb.

1 cm 0.5 cm 0.866 cm

12 cm

Volume of prism = base area Ă— height

HINT!

7

3 UNIVERSAL STUDIOS SINGAPORE The Universal Studios Singapore (USS) theme park is the first of its kind to open in Southeast Asia. The park is divided into 7 zones: Hollywood, New York, Sci-Fi City, Ancient Egypt, The Lost World, Far Far Away, and Madagascar. There are 20 rides in total, with 5 roller coasters and 2 water rides. The park opened in March 2010 and has since attracted more than 9 million visitors.

Task 1 Find out the cost of a One Day Peak Pass for the different categories at the ticketing counters and fill in the table below.

Ticket Type

A dult (A ges 13 to 64)

Child (A ges 4 to 12)

Senior (Age 65 and above)

One Day Non -Peak Pass

66

48

32

One Day Peak Pass

______

______

______

Two Day Pass Annual Pass Fun Pass Annual Pass Action Pass Annual Pass Superstar Pass

118

88

58

338

258

208

48 8

408

358

638

558

508

Task 2 You are planning a trip for your family to USS during the school holidays. Find the total cost of One Day Peak Passes for 2 adults and 3 children.

8

Another family consists of ( +2) adults and ( -1) children. Find an expression for the total cost of One Day Peak Passes for the whole family, in terms of and .

Task 3 There are two tour groups entering USS. There are adults in Group A and adults in Group B. The groups want to purchase One Day Peak Passes for both groups. Only Group A wants to purchase the Universal Express.

Find an expression for the total cost of tickets, in terms of and , and factorise the expression.

Ticket Type Universal Express (In addition to your admission ticket)

OffPeak

Peak

30

50

Task 4 The total cost of One Day Non-Peak passes for same as the total cost for ( + 3 ) children.

Write an equation in

adults is the

to represent the above information.

Solve the equation to find the number of adults.

9

4 KNOW YOUR SINGAPORE You are now standing at the heart of Singapore’s first integrated resorts. RWS is a casino resort offering attractions, hotels, spa, casino and meetings & incentive venues. This mega resort is located on Singapore's holiday island of Sentosa.

The S$6.59 billion must-see destination welcomed its first visitors at its soft opening in early 2010.

Task 1 From the graph, state the number of tourists arriving in Singapore in:

2006: 2007: 2008: 2009: 2010:

What is the percentage increase in tourists from 2009 to 2010?

Show your workings.

Suggest a reason why there is a sudden jump in number of tourists in 2010.

10

Task 2 The sixth National Education Message of Singapore is:

We have confidence in our future. “United, determined and well-prepared, we have what it takes to build a bright future for ourselves, and to progress together as one nation.�

By taking a good look at the achievements that Singapore has accomplished in the past 40 years, write down three of them in the spaces provided below and state how they contribute to Singapore’s economy: Hints: 1. Safe country 2. More places of interest 3. More jobs created 4. First class airport 5. First class port

Task 3 One of the most recent achievements of Singapore is the Integrated Resort (IR). In your opinion, state one advantage and one disadvantage of having an Integrated Resort with a Casino.

11

5a TALKING BREAD Task 1

Brad Tok bought a few cups of mixed fruit juice and iced coffee frappe for his friends, but he can’t seem to remember how many of each he bought. Let’s try to help him figure it out!

Find out the cost of each cup of mixed fruit juice and iced coffee frappe.

Cost of mixed fruit juice

$

Cost of iced coffee frappe

$

Task 2 Brad says, “Since I can’t remember the number of each, let’s represent the number of mixed fruit juices as x and the number of iced coffee frappes as y.”

Brad remembers the following things: 1. “The total number of mixed fruit juices and iced coffee frappes were 12.” Form an equation to represent this information.

2. “The total cost of the mixed fruit juices and iced coffee frappes were $38.” Form an equation to represent this information.

Task 3 Using any method you’ve learnt for solving simultaneous equations, find the number of mixed fruit juices and iced coffee frappes Brad bought for his friends.

Number of mixed fruit juices

12

Number of iced coffee frappes

5b WEIGHT FLOSS Task 1

Brad likes to eat a lot of chicken floss bread. However, he is very concerned about the nutritional value of his food. He searches for this online and finds this: 1 tablespoon chicken floss = 20 calories 1 tablespoon flavoured chicken = 60 calories 1 tablespoon mayonnaise = 130 calories 1 tablespoon cheese = 70 calories 1 mini sausage = 60 calories 1 average bun = 200 calories Find out how many calories his favourite chicken floss bun has if it contains: 3 tablespoons of chicken floss 1 tablespoon of mayonaise 1 average bun

Task 2 To keep fit and healthy, Brad needs at most 2500 calories a day. Any more, and he will become overweight.

Form an inequality involving the number of buns he is allowed to eat a day, if he does not want to be overweight.

Task 3 From Task 2, solve the inequality, and tell Brad how many of his favourite buns he is allowed to eat a day at most.

13

6 THE MERLION Take a good look at the stairs in front of you leading to the Merlion.

height

length

Task 1

What is the height of the staircase? Show your working below.

What is the length of the staircase? Show your working below.

Task 2 What is the gradient of the staircase?

Hint: Gradient =

14

vertical change horizontal change

or

rise run

Task 3

There are 5 Merlion statues recognized by Singapore Tourism Board located at: A. Sentosa (37 m tall), B. Merlion Park (known as the original Merlion built in 1972), C. Merlion Park (smaller statue standing behind the original Merlion), D. Tourism Court (near Grange Road), E. Faber Point on Mount Faber.

The ratio of the height of the Sentosa Merlion and the original Merlion at Merlion Park is 185 : 43. (a) Find the height of the original Merlion at Merlion Park in metres.

(b) If the ratio of height of the Sentosa Merlion to the smaller statue standing behind the original merlion is 37 : 2, find the ratio of the heights of the three merlions as follows: A : B : C Sentosa Merlion : Original Merlion : Smaller Merlion

15

REFLECTIONS

16

17

MAP OF RESORTS WORLD SENTOSA Basement 1

Level 1

18

ACKNOWLEDGEMENTS

Greenview Secondary School Mathematics Department would like to thank s /UR 0RINCIPAL AND 6ICE 0RINCIPALS FOR THEIR SUPPORT OF

the event, s

!LL 4EACHERS STUDENT HELPERS PARTICIPANTS AND THOSE who have contributed in one way or another towards THE SUCCESS OF OUR -ATHEMATICS 4RAIL

Š 2012 Greenview Secondary School