Sekolah Agama
Menengah Bestari,Jalan USJ 5/3 A,
47620
Subang Jaya,Selangor.
Curiculum Development Division Ministry
Additional Mathematics Project Work 2/2013
Name: Siti Nasyroha binti Abd Rahim
Teacher’s Name: Puan Husna binti
No.
|
Title
|
Page
|
1
|
Acknowledgement
|
|
2
|
Objective
|
|
3
|
Part 1
|
|
4
|
Part 2
|
|
5
|
Part 3
|
|
6
|
Part 4
|
|
7
|
Reflection
|
|
8
|
Reference
|
|
First
of all, I wish to express gratitude to Allah SWT for His guidance and also give
me strength and health to do this project work. Finally, the Additional
Mathematics Project Work 2 was successfully completed with inspiration, the
gift and the instructions were given by Him. Peace and blessings be upon our
Prophet Muhammad SAW and the family, next to his companions and tabi’in, the
gentlemen scholars until the servants of God who follow in their footsteps.
Not
forgotten to my parents who always make sure that I have been educating and
nurturing of small though this day in devotion to God Almighty. They also had
providing everything such as money , to buy anything that are related to this
project, their advice, which is the most needed for this project and facilities
such as internet, books, computers and all that. They also supported me and
encouraged me to complete this task so that I will not procrastinate in doing
it.
Then,
infinity of appreciation and gratitude goes to my teacher,Puan Husna for guiding
throughout this project. Even I had some difficulties in doing this task, but
she taught me patiently until we knew what to do. She tried and tried to teach
me until I understand what I am supposed to do with the project work.
Besides,
my friends who were doing this project with me. Even this project is
individually but we are cooperated doing this project especially in discussion
and sharing ideas to ensure our task will finish completely.
Last
but not least, any party which involved either directly or indirect in
completing this project work. May Allah give a great reward for all His
servants
that are always helpful
in upholding His religion. Thank you everyone.
1.
Every student taking Additional Mathematics is required to carry out a project work in Form 5.
2. The aims of
carrying out project work are:
a. to apply and adapt a variety of problem-
solving strategies to solve problems;
b. to improve
thinking skills;
c. to promote
effective mathematical communication;
d. to develop
mathematical knowledge through problem solving in a way that increases
students’ interest and confidence;
e. to use the
language of mathematics to express mathematical ideas precisely;
f. to provide
learning environment that stimulates and enhances effective learning;
g.
to develop positive attitude towards mathematics.
Measure
of change in a set of prices, consisting of a series of numbers arranged so
that a comparison of the values for any two periods or places will show the
change in prices between periods or the difference in prices between places.
Price indexes were first developed to measure changes in the cost of living in
order to determine the wage increases necessary to maintain a constant standard
of living. There are two basic types. Laspeyres-type indexes define a market basket
of goods in a base period, then use the prices for those goods to examine
change over space and time. In its simplest form, this is simply the ratio of
what those goods cost today to what they cost in the base period. The two most
familiar indexes of this type are the consumer price index (CPI) and the
producer price index (PPI). The CPI measures changes in retail prices in such
component parts as food, clothing, and shelter. The PPI (formerly called the
wholesale price index) measures changes in the prices charged by manufacturers
and wholesalers. Paschal-type indexes define a market basket of goods in the
current period, then use the prices of those goods from past periods. The most
familiar index of this type is the GDP deflator, used in the U.S. in the
national income accounting to differentiate amounts in constant dollars from
those in current dollars.
Weightage
means preference of one product in comparison to other product. On the other
hand we can say weightage means giving the value of the specific or particular
matter or subject higher or lesser than that of or in comparison to similar
one. The factors of weightage are The more risk, the more weightage, the longer
the period, more the risk, more the uses of Bank’s facility, less the weightage
and last but not least less the Uses of Bank’s facility, more the benefit
weightage and moral dimension or ethical values.
A
grouping of equities, indexes or other factors combined in a standardized way,
providing a useful statistical measure of overall market or sector performance
over time. Usually, a composite index has a large number of factors which are
averaged together to form a product representative of an overall market or
sector. For example, the Nasdaq Composite index is a market
capitalization-weighted grouping of approximately 5,000 stocks listed on the
Nasdaq market. These indexes are useful tools for measuring and tracking price
level changes to an entire stock market or sector. Therefore, they provide a
useful benchmark against which to measure an investor's portfolio. The goal of
a well diversified portfolio is usually to outperform the main composite
indexes.
b)
State four ways of weightage representations. Find the examples of
the representations using internet or any printed materials.
We often hear
complaints from the public about inflation. It causes an increase in the
household expenditure in a family.
The household
expenditure for every family is different.
a) Complete
Table 1 for your family’s monthly expenditure for the year 2013
Item
|
Average
Monthly Expenditure for the year 2013(to the nearest RM)
|
Percentage
monthly expenses (to the nearest %)
|
FOOD
|
1900
|
31
|
ACCOMODATION
(RENTAL/LOAN)
|
700
|
11
|
TRANSPORTATION
(PETROL/LOAN/BUS FARE ETC)
|
800
|
13
|
CLOTHING
|
300
|
5
|
EDUCATION
|
1500
|
25
|
RECREATION
|
100
|
2
|
UTILITIES
(WATER/ELECTRICITY/TELEPHONE)
|
250
|
4
|
MEDICATION
|
150
|
2
|
MISCLLANEOUS
|
400
|
7
|
TOTAL
|
6100
|
100
|
My family used
up money on education as education is important in our life. My family often
buys new books every weeks as for us reading is the key to success in life no
matter how much the cost of the book. Instead, my family used least money on
recreation due to busy of works and studies.
b)If we want to
compare the cost of living from one year to another, we have to calculate the
price index that involves some of the items mentioned above.
i. In order to
calculate the price index of all the items above, we have to consider the
average monthly expenses of any previous year as the base year. Select the
appropriate year as the base year.
(b)(i) I have
chosen the year 2011 as the base year to calculate the price index
ii. Hence,
complete Table 2 below :
Item
|
Average Monthly Expenditure for
the year 2011 as the base year (RM)
|
Average Monthly Expenditure for
the year 2013 (RM)
|
FOOD
|
1600
|
1900
|
ACCOMODATION
(RENTAL/LOAN)
|
700
|
700
|
TRANSPORTATION
(PETROL/LOAN/BUS
FARE ETC)
|
550
|
800
|
CLOTHING
|
200
|
300
|
EDUCATION
|
1300
|
1500
|
RECREATION
|
100
|
100
|
UTILITIES
(WATER/ELECTRICITY/TELEPHONE)
|
155
|
250
|
MEDICATION
|
95
|
150
|
MISCLLANEOUS
|
300
|
400
|
TOTAL
|
5000
|
6100
|
c.
𝑖) 𝐶𝑜𝑚𝑝𝑙𝑒𝑡𝑒 𝑇𝑎𝑏𝑙𝑒 3 𝑏𝑎𝑠𝑒𝑑 𝑜𝑛 𝑡ℎ𝑒 𝑎𝑏𝑜𝑣𝑒 𝑖𝑛𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛.
Item
|
Price Indices for the year 2013 based on the
year 2011
|
Weightage
|
FOOD
|
119
|
31
|
ACCOMODATION
(RENTAL/LOAN)
|
100
|
11
|
TRANSPORTATION
(PETROL/LOAN/BUS FARE ETC)
|
145
|
13
|
CLOTHING
|
150
|
5
|
EDUCATION
|
115
|
25
|
RECREATION
|
100
|
2
|
UTILITIES
(WATER/ELECTRICITY/ TELEPHONE)
|
161
|
4
|
MEDICATION
|
158
|
2
|
MISCLLANEOUS
|
133
|
7
|
TOTAL
|
1181
|
100
|
ii) Hence,
calculate the composite index for the average monthly expenditure in the year 2013
based on the selected base year.
= 119(31)+100(11)+145(13)+150(5)+115(25)+100(2)+161(4)+158(2)+133(7)
d) Make a
conclusion about your family’s expenditure based on your findings.
From the
findings, I can see the increasing of my family’s expenditure especially on
transportation. When all of us are bigger, more place that we need to
go.Although,I am staying at hostel and I go home every 2 weeks.My brothers is
studying at three different schools.It takes a big cost.
Your family is
planning to buy a new television set.
a) You have
conducted a survey on the price of the television for two different brands from
three different shops. You would like to make a comparison between two modes of
payment, namely, cash payment and payment by installment.
Table 4(a)
shows the prices of televisions by cash payment in three different shops
whereas Table 4(b) shows the prices of televisions by installment. Complete
Table 4(a) and 4(b) using the data you obtained.
Brand
|
Size of
Television (inches)
|
Price(RM)
|
Mean
Price (RM)
|
Standard
Deviation (RM)
|
COURTS
MAMMOTH
|
TESCO
|
GIANT
|
TOSHIBA
|
24
|
599
|
575
|
580
|
584.67
|
10.15
|
32
|
899
|
888
|
899
|
895.33
|
5.73
|
40
|
1799
|
1488
|
1499
|
1595.33
|
144.12
|
SAMSUNG
|
24
|
588
|
590
|
620
|
599.33
|
14.77
|
32
|
888
|
869
|
999
|
918.67
|
57.28
|
40
|
1585
|
1590
|
1599
|
191.33
|
56.72
|
|
|
|
|
|
|
|
Table 4
(a)
|
|
|
|
|
|
|
Brand
|
Size of
Television (inches)
|
Price(RM)
|
Mean
Price (RM)
|
Standard
Deviation (RM)
|
|
COURTS
MAMMOTH
|
TESCO
|
GIANT
|
|
TOSHIBA
|
24
|
780
|
695
|
735
|
736.67
|
34.65
|
|
32
|
1080
|
1008
|
1054
|
1047.33
|
29.89
|
|
40
|
1980
|
1608
|
1654
|
1747.3
|
165.62
|
|
SAMSUNG
|
24
|
688
|
725
|
780
|
731
|
37.79
|
|
32
|
988
|
1004
|
1159
|
1050.33
|
77.16
|
|
40
|
1685
|
1725
|
1759
|
1723
|
30.25
|
|
|
|
|
|
|
|
|
|
b) Determine
the brand and size of the television that you have decided to buy. Give your
reasons based on the findings from part (a) above.
I have decided
to buy television Samsung from TESCO with the size of ’32 inch. The reasons of
my choice are because the prices for Samsung are more cheaper than Toshiba paid
by cash nor installment. We can see it from my findings as the measure of
dispersion for Samsung is more reasonable.The price of the products are very reasonable because
its mean price and its standard deviation is equal to the other brands.So,
I strongly choose television Samsung from TESCO with the size ’32 inch.
c) The Ministry
of Domestic Trade and Consumer Affairs wishes to present the Fair Prices Shop
Award for one of the above shops. If you are one of the panels for this award,
determine the shops that deserve the award. Do you consider the value of mean
and the value of standard deviation in making your decision? Give your
justification.
If I was the panel, I would have chosen TESCO as the shop that deserves the award This is because the prices of the products are
cheapest compared to the rest. I did not consider the mean and the standard
deviation in making my decision because the mean and standard deviation
involves all the three shops.
a) Your family
has a fixed monthly income. In order to buy the television, your family needs
to make some adjustment on the various types of expenditure.
[You can choose
to pay by cash or by installment]
Show the
average monthly expenditure that you have modified in a table.
Item
|
Average Monthly Expenditure for
the year 2013(to the nearest RM)
|
FOOD
|
1500
|
ACCOMODATION
(RENTAL/LOAN)
|
700
|
TRANSPORTATION
(PETROL/LOAN/BUS
FARE ETC)
|
620
|
CLOTHING
|
200
|
EDUCATION
|
1450
|
RECREATION
|
100
|
UTILITIES
(WATER/ELECTRICITY/TELEPHONE)
|
231
|
MEDICATION
|
110
|
MISCLLANEOUS
|
320
|
TELEVISION
|
869
|
TOTAL
|
6100
|
b)Assuming you
has just started working with a monthly salary of RM 2500. You intend to save
10% of your salary every month.
Plan your
monthly expenditure as in Table 1 above and add other items such as savings and
contributions to your parents.
Item
|
Average
Monthly Expenditure for the year 2013(to the nearest RM)
|
FOOD
|
300
|
ACCOMODATION
(RENTAL/LOAN)
|
800
|
TRANSPORTATION
(PETROL/LOAN/BUS FARE ETC)
|
350
|
CLOTHING
|
200
|
RECREATION
|
100
|
UTILITIES
(WATER/ELECTRICITY/TELEPHONE)
|
100
|
MEDICATION
|
100
|
SAVINGS
|
250
|
PARENTS
|
150
|
MISCLLANEOUS
|
150
|
TOTAL
|
2500
|
Siti Nasyroha Abd Rahim
