ADDITIONAL MATHEMATICS PROJECT WORK
2012
PART
1
A
family is an important institution in a society. Everyone’s hope is to have a
happy family. A closely knitted family will ensure the well-being of the
community and hence the nation.
Below
is an example of Zulkefli and Aminah’s family tree. Answer the questions below based
on the family tree given.
Diagram 1
a) Based on Diagram 1, list at least 5 different sets (Example : set of sons).
b) Based on Diagram 1, draw at
least three arrow diagrams to show the relation of the family. Hence,
i) determine
the domain,
codomain, objects, images and range.
ii) recognise the type of
relation.
iii) represent each relation
above using other methods.
c) Based on (b), which
relation is a function? State your reason.
Part 2
a) You are required to come
out with an attractive and creative card. Your card must have the following
information.
i) a family photo
ii) a family tree
b) Write a short description
about your family in not more than 150 words.
Part 3
Based
on Diagram 3, answer the following questions.
 |
Diagram 3
Find
a)
function
and function 
.
and function .
b)
the
inverse function and .
and .
c)
composite
function 
, 
, 
and 
.
, , and .
d)
function
and 
. Is = ?
and . Is = ?
e)
What
can you deduce from the following composite function?
and 
Hence, deduce the value of 
.
.
Further
Exploration
a)
The
function g is defined by 
. Find
. Find
i)
,
, 
, 
, 
and 
.
,
, , , and .
ii)
Hence, state the function 
and 
, where n
is a positive integer.
and , where n
is a positive integer.
b)
Given
the function is defined by 
. Find 
. Therefore deduce the
inverse functions for the followings. Check your answers using another method.
is defined by . Find . Therefore deduce the
inverse functions for the followings. Check your answers using another method.
i)
ii)
iii)
Reflection
While you were carrying out this project, what did you
learn? What moral values did you put into practice? Represent your opinion or
feelings creatively by using symbols, illustrations, paintings or songs.
END OF PROJECT
PAPER
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