Core Math Investigation

Core Math Investigation

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Core Math Investigation

1) When x is more than 0 and increases (e.g. from 5 to 6), y increases
at a much faster rate and becomes very big. When x increases when it
is less then 0 (e.g. from –10 to –9), y increases very slowly.

2) (i) The value of a affects the value of x proportionally. For
example we can compare the equations y = 1 + 2x and y = 5 + 2x. In the
second equation, the value of a has been change to 5. As we can see
from the results in Tables 1 and 2, all the values of y for y = 5 + 2x
are greater by 4, when x is the same.

(ii) As we have seen in (i), the effect of a does not affect the value
of y, as it is a constant added to the solution of 2x . Hence, the
value of a affects x proportionally, no matter what the value of x is.

3) (i) For b = -1, b causes the value of y decrease rapidly as x
increases. This is because when x becomes larger, bx will be a very
small number as bx will be small as b is negative while x is positive.
For b = 0, y remains constant throughout, no matter what the value of
x is. This is because 0x will always give 0. For b = 1, the
relationship is the same as in (1), as 1x will always lead to a rapid
rate of increase for y when x> 0.

(ii) For b = -1, b causes y to increase greatly when x gets smaller,
as b is a negative number and so bx will give a large number when both
b and x are negative. For b = 0, y remains constant throughout, no
matter what the value of x is. This is because 0x will always give 0.
For b = 1, the relationship is the same as in (1), as 1x will always
lead to a very slow rate of increase for y when x <0.

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Mathematical Article
====================

Title of Article: Birth rate falls in developing world

Source: The Straits Times

Date of Publish: 28 Jan 2005

Summary: This article is basically about birth rates, and how they
have decreased in developing countries. It goes on to give possible
reasons for and explain why this sudden decrease has occurred, e.g.
increased use of contraception in both developed and developing
countries as well as later marriages and thus later parenthood. The
article also points out what possible consequences this trend might
have, and what measures the Singapore government has taken to combat
the problem. [Total: 75 words]


Mathematical Content

This article has provided readers with important numbers on the
average fertility rate, the percentage of those single and the
percentage of those who use contraception and practice family
planning. These numbers clearly show that there is a strong
correlation between lowered fertility rate, increased percentage of
singles, increased number of late marriages and increased use of
contraception. As the number of people practicing contraception and
number of couples marrying later in life increase, the fertility rate
naturally decreases.


Strengths and Weaknesses

I was quite impressed by the article and the graphs provided. The
graphs are clear and well-labeled, two important characteristics of a
good graph. The graphs also made good use of colour to compare the
differences between 1970 and 2000. The graphs were also captioned with
appropriate headings, and the key and scale used were accurate and
adequate, which are another two features of a good graph. The
information presented was also well-researched and it also came from a
trustworthy source, the United Nations’ World Fertility Report of
2003. The only possible improvement that I could think of would be to
enlarge the graphs as they are a bit on the small side. However, this
may not be too feasible, as the graphs are still readable and the
larger graphs may not fit or take up too much space.


What can we see from the graphs?
--------------------------------

From the graphs, we can see that the general total fertility around
the world has dropped substantially in both developed and developing
countries during the time frame from 1970 to 2000. We can see from the
second graph that the fertility rates have dropped more drastically in
Asia and Latin America than in Africa and Europe. We can also see that
Europe has quite a low fertility rate while Africa’s is very high.
From the third and fourth graphs, we can see that Singapore’s
fertility rate has dropped significantly since 1970. We can also see
that the age-specific fertility rate for all age groups has dropped,
most notably in the 20-24 and 25-29 year age groups.


Real-world application

Through this article, I have gained more insight into why the
population explosion anticipated years ago has not happened, and
instead declining birth rates have come up. This decline in fertility
and birth rates has been a result of increase in use of contraception,
later marriages and government policy. For example, we can see that
the Singapore government’s two-child policy has resulted in an
irreversible trend of lowering fertility rates. This indicates that
the government was perhaps too successful in its goals, and maybe it
should consider more closely the next time it decides to embark on a
campaign.


Why I chose this article
------------------------

I found this article very interesting, because it is relevant to
Singapore today, as it experiences a low fertility rate. I was also
attracted to it due to the wide range of graphs presented (4 in total,
each of a different type).
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