# Core Math Investigation

#### Essay Preview

More ↓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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### Related Searches

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).