Task English II

(My story about my experience to explain a topic in mathematics)

My Experience about Math and English

To development of mathematics and make us active in the English language communication lecturers to give exercise to explain a concept of mathematics to a friend. Noviana is my friend, he became my partner. We did experience in Novi’s house on Saturday, january 10, 2009.

Before I do the experience, I made a post about “cube”. My post is containing any posts about definitions, concepts, formulas, examples and exercises from cube. I am get reference from the internet and books. This is my following explanation of the topic.

The definition of cube is a three dimensional solid object bounded by six square faces, facets or sides, whit three meeting at each vertex. The cube can also be called a regular hexahedron. Normally, cube has same as edge length. The elements of cube there are face=6, vertex=8, edge=12 and have dihedral angle.

For a cube centered at the origin, with edges parallel to the axes and with an edge length of 2, the Cartesian Coordinates of the vertices while the interior consists of all point (x0, x1, x2) with -1 <>

For a cube of edge length a. Because the cube has 6 faces square so the formula of surface area is 6 multiply with area of square. In symbols A = 6 . a^2. As the volume of a cube is the third power of its sides a x a x a, third powers are called cubes, by analogy with squares and second powers. In symbols V = a^3.

The example:

1. A dies has 20mm in edge length. How is the surface area and volume of that cube?

Answers:

Edge length (a) = 10

A = 6 . a^2 V = a^3

= 6 . 20^2 = 20^3

= 6 . 400 = 8000

= 2400

So the surface area of dies is 2400mm^2 and volume is 8000mm^3

The Exercise:

1. A box with same as edge length has 125000cm^3 in volume. How is the edge length and surface area of the box?

When I was explaining to Noviana, she was attention my explanation. However I am feel difficult in explain my post, because I not yet fluent in English language communication. But I remain confident, so she can understand the meaning of my sentences. For me, she is more than smart in the use of the English language as a communication. She has very enthusiastic with my explanation. But she didn’t ask me a lot about my explanation, because the cube is a topic that is very easy to learn. She also can right answer from all question. And finally, I say many thanks to the English language lecturers 2 that he has encouraged me to be more active in the English communication.

Source:

http://en.wikipedia.org/wiki/Cube

Buku Pelajaran Matematika SMP, Erlangga 2000.

Nice Blog to Mathematic

In world of education, technology information is great influence. The technology information is important to student. Even though internet is greatest development of technology information. With internet we can get information easily. Internet have facilities, for example: email, chatting, friendster, blog, etc. From information blog is newest facility of internet. Now. I will explain to you about blog.

Blog is facility for internet which used to posting ideas, daily note, publication about business, our expression and all about our. Blog is like friendster but blog can accessed by all people.

OK,,
Now you know blog,,
And for me, blog can be a place to introduce me to other people. Introduce my ability, ideas, experience, task, daily note, etc. But I not yet increase blog because I am still studying it. And the next time I will use blog to show about me and my ideas or creation of mathematic. So, I can create my nice blog.

Blog have many advantage in learning English language for math student. The advantage to
1. Short time
a) Relation between student and lecture about task can be ease.
b) To posting our opinion or ideas about mathematic in English language.
c) We can look for information in other blog.
d) We or lecture can give comment to blog.
2. Middle time
a) To sharing with lecture about mathematic.
b) To searching many partner to learning mathematic and develop skill of English.
c) To searching information from other blog.
3. Long time
a) To develop of mathematic from global communication of English language.
b) If we being teacher, blog can be development of study mathematic.
c) To be active in English communication so we can good human in world.

From the explain above, we can take positive suggestion to develop our skill.
Let's we start to used blog to creation about mathematic. To be English as our language in world communication.
Don't be passive human!!!
We have facility,, So, we must to used it.
GOOD LUCK!!

Task English II
Tuesday, December 16 2008
(My writhed from explanation Mr. Marsigit in class English II)

About Our Communication

Communication…
What is communication???
Many people say communication is process to have contact other people. For example: to give information to another. So, communication is very important.

We are communicating with each language. Even though language offered different culture aspect, while we have local intelligence, there are emotional intelligence and spiritual intelligence. However, the culture aspect is resulting problem each other with heart of hearts.

In this moment, we are discussing about “How overcome the problem for individual”. Before we look for solution from this problem, we can classification about communication.

There are two kind of communication
1. Lowest Level, consist of :
Ø Material communication is relation human with thing, for example: the communication in cooking show.
Ø Normative communication is communication with other people in the days. So, we can relax with our communication. For example: talk with friends or talk with partner informal communication.
2. Highest Level, consist of :
Ø Formularize communication is formal communication, for example: talk formally, write formally like write in blog or formal letter.
Ø Spiritual communication is relation human with God. This communication about implementation of religion, for example: praying.

The psychology problem is influent by communication social. We can relation with other people use communication to give information. However, we need best communication. The kinds of unhealthy communication are passive vocal and univocal. And it can destroy the meaning of language.

What will we see in this moment???
ü To solve the problem for individual.

We get the solution if we can active in communication to develop our skill. So, we can be better one people.

Task English II
Tuesday, November 25, 2008
(My Created from listening video mathematics in English language)

Video 1
PRE CALCULUS
A. Graph of a rational function
Can have discontinuities has a polynomial in the denominator
Example:
f(x) = (x + 2)/(x - 1)
Is called Off Limit, when x = 1 because if x =1 substituted to function f the denominator can be 0.
f(1) = (1 + 2) /(1 - 1)
f(1) = 3 / 0
The function above is break function if insert 1.
If the function insert 0
f(0) = (0 + 2)/(0 – 1)
f(0) = 2 /(-1)
f(0) = -2
and not all rational function will give 0 in denominator and can be 0.

B. Break 2 ways in rational function:
1. Missing point is a loophole
Example:
y = (x^2 – x – 6)/(x – 3)
if x =1 substituted to function f not allowed because
y = (3^2 – 3 - 6)/(3 - 3)
= 0
Good choice from the function above
y = (x - 3)(x + 2)/(x - 3) (cancelled the factor)
= x + 2
2. Zero in denominator
Example: in function f(x) = (x + 2)/(x - 1) and insert 1.

Video 2
LIMIT by INSPECTION
1. x goes to positive or negative infinity
2. Limit involved a polynomial divided by a polynomial

Example 1:
lim (x^3 + 4) / (x^2 + x + 1)
x--~
(Polynomial over by polynomial with limit x approach infinity)
To solving limit above attention this:
- looking the power of x in the numerator and denominator
- must be dividing f polynomial if power of numerator highest than denominator, limit can be + positive or negative infinity
example above power of x in numerator highest than in denominator.
Example 2:
lim (x^2 + 3) / (x^3 + 1)
x--~
Its mean power of x in denominator highest than in numerator
Example 3:
lim (4x^3 + x^2 + 1) / (3x^3 + 4)
x--~
Limit above power of x in denominator = in numerator, so the solution of the limit is same of the coefficient from the highest power of x in denominator and in numerator it self. Solution of limit:
lim (x^3 + 4) / (x^2 + x + 1) = 3/4
x--~

Video 3
PROBLEM SOLVING ABOUT GRAPH MATH
1. The graph y = g(x) if the function is defined by h(x) = g(2x) + 2. What the value of h(0)?
Solution:
The functions is h(x) = g(2x) + 2. If h(0) is mean when h = 1, we substituted this to the functions
h(x) = g(2x) + 2
h(0) = g(2.0) + 2
= g(0) + 2
g(0) is mean g when x = 0, if we look the graph of y = g(x), we get g(0) = 3 because x = 0
and y = 3
So h(1)= g(0)+2
= 3 + 2
= 5
We get the value of h(0) is 5.
2. Let the function f be defined by f(x) = x + 3. If 3f(p) = 15, What is the value of f(2p)?
Solution:
The function is f(x) = x + 3
The value of f(2p) is mean f when x = 2p, we have 3f(p) = 15 because each edge have factors 3. So we can over by 3 and we get f(p) = 5
f(p) = 5 is mean f when x = p is 5, we can substituted this value to the function f(x) = x + 3 we get f(p) = p + 3 = 5
p = 5 - 3
p = 2
With move 1 to the left space between become we get the value of p.
So we can get f(2p) If p = 2 so 2p = 4 is mean f when 2p = 4 we substituted this value to the function f(x) = x + 3
f(4) = 4 + 1
= 5
We get the value of f(2p) is 5

3. In the xy coordinate x = y^2 – 9 intersects line at (p,-3) and (7,t).What is the greatest possible value of the slope of g?
The function x = y^2 – 9 intersects line at (p,-3) and (7,t). The formula of slope is m = (y2 – y1)/(x2-x1) the coordinate of g are (p,-3) and (7,t). That’s mean x1 = p, y2 = -3, x2 = 7, y2 = t, we substituted thus to the m
m = (y2 – y1)/(x2-x1)
= {t – (-3)} /(7 – p)
= (t +3)/(7 – p)
We get the greatest possible value of the slope g is the (t + 3) / (7 - p)

Video 4
INVERS FUNCTION
Notation by : F(x,y) = 0
Function y = f (x) is called VLT and x = g (y) is called HLT

A. Function x = g(y) : invertible
Example:
1. Line function y = 3x - 2 and y = x
y = 3x - 1
x = 3x – 1
1 + x = 3x
1 = 2x
x = 1/2
Substituted x = 1/2 in y = 3x - 2
y = 3.1/2 - 1
= 1/2
So, line function y = 3x - 2 and y = x intersect in (1/2,1/2)

3x – 2 = y
3x = y + 2
x = 1/3 (y + 2)
x = 1/3y + 2/3 and y = 1/3x + 2/3


in inverse function the line be write:
f(x) = 5x -2
g(x) = 1/5x + 2/5

f(g(x)) = 5(1/5x + 2/5) - 2
= x + 2 – 2
= x
g(f(x)) = 1/5(5x – 2) + 2/5
= x – 2/5+ 2/5
= x
From operation above can be conclusion:
g = f^(-1)
f(g(x)) = g(f^(-1) (x)) = x
g(x) = f^(-1) (f(x)) = x

2. Line function y = (x - 3)/(x + 5)
y(x + 5) =
yx – x = (- 3) – 5y
(y – 1)x = (- 3) – 5y
x = {(- 3) - 5y}/(y-1) and
y = {(- 3) – 5x}/(x-1)