root : akar
presumption : asumsi dasar
cuboids : balok
plane : bangun datar
rhombus : belah ketupat
scientific notation : bentuk baku
superimpose : berimpit
intersection : berpotongan
cross : bersilangan
integer : bilangan bulat
whole : bilangan cacah
base : dasar
row : deret
shadow : bayangan
odd : ganjil
median : garis berat
apothem : garis miring
bisector : garis sumbu
diameter : garis tengah
altitude /high line : garis tinggi
even : genap
set : himpunan
subset : himpunan bagian
relation : hubungan
slice : irisan
intersection : irisan himpunan
parallelogram : jajar genjang
sum : jumlah
inverse : kebalikan
perimeter : keliling
multiply : kelipatan
cone : kerucut
truncated : kerucut terpancung
square : kuadrat
cube : kubus
cute : lancip
direct : langsung
area : luas
complement : melengkapi
comparing : membandingkan
ungroup : menguraikan
simplifying : menyederhanakan
natural : murni
power : pangkat
fraction : pecahan
division : pembagian
numerator : pembilang
round up : pembulatan
mapping : pemetaan
estimation : penaksiran
elimination : penghilangan
substitution : pengubah
subtraction : pengurangan
sum : penjumlahan
denominator : penyebut
solving /solution : penyelesaian
proportion : perbandingan
equation : persamaan
inequalities : pertidak samaan
pattern : pola
average /mean : rata-rata
congruent : sama dan sebangun
equivalent : sama dengan
similar : sebangun
collinear : segaris
triangle : segitiga
isosceles : segitiga sama kaki
equilateral : segitiga sama sisi
balance : seimbang
difference : selisih
ground : landasan
try : latihan
clue : petunjuk
exercise : latihan
rehearsal : latihan
record : mencatat
Senin, 22 Juni 2009
It is a Must That I Have a Competence in English for Mathematics Education
In this globalization era, English as a universal language is very important for every think especially to communicate with other. Me as a student in Mathematics Education is very need to teach English. English is a important because a lot of references use English, such as the original book from abroad or the reference from Internet is also use English too. Some lecturers use English to give their subject. And English is also a language in mathematics test at my academy.
English is also need in job activity, relating to Internet, computer, international corresponded, international interaction, etc. Beside that when I graduate from mathematics education I would find a job as a mathematics teacher or an official.
Before I get the job I must have a TOEFL test, to evaluate my English capability And If I teach in international school, of course I must be able in English spoken to explain the subject and written to give handout and written test. As an official I use English to operate computer, in the internet interaction. My English must be active international interaction. Now many company searching officer capable to speak, write and read English to support their company.
Beside that to operate the electronic gadget we must be able to read or learn English because the instruction to operate the gadget is in English. And sometime in conversation, the people use English and I have to know meaning of the people say, so I must to can speak English too. Or if I want to read novel which not yet been translated in Indonesian language I also should be able to read English. Beside that If I listening English song. I must know the meaning of the song. And I write the lyrics and try to translate in Indonesian language. So English is very important for every one in this globalization era including too mathematics education.
English is also need in job activity, relating to Internet, computer, international corresponded, international interaction, etc. Beside that when I graduate from mathematics education I would find a job as a mathematics teacher or an official.
Before I get the job I must have a TOEFL test, to evaluate my English capability And If I teach in international school, of course I must be able in English spoken to explain the subject and written to give handout and written test. As an official I use English to operate computer, in the internet interaction. My English must be active international interaction. Now many company searching officer capable to speak, write and read English to support their company.
Beside that to operate the electronic gadget we must be able to read or learn English because the instruction to operate the gadget is in English. And sometime in conversation, the people use English and I have to know meaning of the people say, so I must to can speak English too. Or if I want to read novel which not yet been translated in Indonesian language I also should be able to read English. Beside that If I listening English song. I must know the meaning of the song. And I write the lyrics and try to translate in Indonesian language. So English is very important for every one in this globalization era including too mathematics education.
WHAT I HAVE DONE AND WHAT I WILL DO ABOUT ENGLISH FOR MATHEMATICS
The big question for me about English for mathematics is what I have done and what I will do about English for mathematics? I fell confused to answer this question because I fell not yet do anything is important about English for mathematics.
Now I was study about English for mathematics at Mr. Marsigit class that is English Part II Class. Besides of study about English for mathematics I also get more knowledge from his experience in international. He always given his experience even he teaching in his class and he can be an inspiration for his student. He always tells about his conception and international conception about education in Indonesian.
Maybe I need more much of time for me to can do something for English for mathematics. Which I can do now is must study hard so that I can develop mathematics education in Indonesian and than it can to be equal with international standard.
To proof the progressive education in Indonesian, the government has prepare the facility such as the school with international based and also the teacher which must be understand about English. And to proof this program UNY has open the international class to prepare the teacher so that they ready to teaching in international school.
My hope at the future is can join in this program to make education in Indonesian can be equable with education in other country, because by naturally education in other country is same. That’s all my opinion about what I have done and what I will do about English for mathematics. Thanks for your attentions.
Now I was study about English for mathematics at Mr. Marsigit class that is English Part II Class. Besides of study about English for mathematics I also get more knowledge from his experience in international. He always given his experience even he teaching in his class and he can be an inspiration for his student. He always tells about his conception and international conception about education in Indonesian.
Maybe I need more much of time for me to can do something for English for mathematics. Which I can do now is must study hard so that I can develop mathematics education in Indonesian and than it can to be equal with international standard.
To proof the progressive education in Indonesian, the government has prepare the facility such as the school with international based and also the teacher which must be understand about English. And to proof this program UNY has open the international class to prepare the teacher so that they ready to teaching in international school.
My hope at the future is can join in this program to make education in Indonesian can be equable with education in other country, because by naturally education in other country is same. That’s all my opinion about what I have done and what I will do about English for mathematics. Thanks for your attentions.
Senin, 13 April 2009
Proof that Square Root of Two is Irrational Number
To proof that square root of two is irrational number, we assuming that square root of two is rational number, that is square root of two equals a over b where a and b as integer prime. So a equals b times square root of two or a square equals two times b square. Because a square is two times an integer number, so a square is integer, so that a is integer too. And than we assuming that a is two times c, so the equation is four times c square equals two times b square or two times c square equals b square. So that b square is integer and b is integer too. But it is impossible because a and b is impossible to integer because they are relative prime number. So assumption that square root of two is rational number has brought us to the impossibility and must be annulled. And it is proofed that square root of two is irrationals number.
Abc Formula to Solve a Square Equation
We know that square equation is a times x square plus b times x plus c equals zero. To get the Abc formula we need some step. Step one, we divide all by a, that is x square plus b over a times x plus c over a equals zero. Step two, we need to insert perfect square into that equation. That is x square plus b over a times x plus open bracket b over two of a close bracket square plus c over a equals b over two times a in bracket square. Step three is x plus b over two times a in bracket square equals b square over four times a square in bracket minus c over a equals b square four times a times c all over four times a square. Step four is x plus b over two times a equals about square root of b square four times a times c all over four times a square. Step five is x equals minus b over two times a about one over two times a in bracket times square root of b square four times a times c equals minus b about times square root of b square four times a times c all over two times a. so the formula is:
x equals minus b about times square root of b square four times a times c all over two times a
x equals minus b about times square root of b square four times a times c all over two times a
How to Find Phi
Egypt has found phi about at 200 BC and the value for phi is 3.16. They get that value from the formula of circles area that is square of open bracket diameter times eight over nine close bracket. We know that diameter or d equals two times radius (r), so we get the formula of circles area is open bracket eight over nine in bracket times two of r close bracket square equals sixty four over eighty one in bracket times four of r square equals three point one six times r square. Long time after that Archimedes at 250 BC using phi, but with a different value that is three point one four like which we use now.
Properties of Logarithm
First, a to the power of m in bracket times a to the power of in bracket equals a to the power of m plus n. Second, a to the power of m all over a to the power of n equals a to the power of m minus n. Third, Log b to the base of a equals n, so that b equals a to the power of n. Fourth, Log a to the base of g equals x, so that a equals g to the power of x. Fifth, Log b to the base of g equals y, so that g to the power of y.
Example:
What is the equivalence of Log a times b to the base of g?
Consequence Log a to the base of g equals x, so that a equals g to the power of x, and Log b to the base of g equals y, so that b equals g to the power of y. So a times b equals g to the power of x in bracket times g to the power of y equals g to the power of x plus y. So that Log a times b to the base of g equals Log g to the power of x plus y to the base of g equals x plus y in bracket times Log g to the base of g. If Log g to the base of g is one, so Log a times b to the base of g equals x plus y in bracket times one equals Log a to the base of g plus Log b to the base of g. So:
Log a times b to the base of g equals Log a to the base of g plus Log b to the base of g
What is the equivalence of Log a over b to the base of g?
Consequence a over b equals g to the power of x all over g to the power of y equals g to the power of x minus y. So than Log a over b to the base of g equals Log g to the power of x minus y to the base of g equals x minus y in bracket times Log g to the base of g equals x minus y in bracket times one equals Log a to the base of g minus Log b to the base of g. So:
Log a over b to the base of g equals Log a to the base of g minus Log b to the base of g
Example:
What is the equivalence of Log a times b to the base of g?
Consequence Log a to the base of g equals x, so that a equals g to the power of x, and Log b to the base of g equals y, so that b equals g to the power of y. So a times b equals g to the power of x in bracket times g to the power of y equals g to the power of x plus y. So that Log a times b to the base of g equals Log g to the power of x plus y to the base of g equals x plus y in bracket times Log g to the base of g. If Log g to the base of g is one, so Log a times b to the base of g equals x plus y in bracket times one equals Log a to the base of g plus Log b to the base of g. So:
Log a times b to the base of g equals Log a to the base of g plus Log b to the base of g
What is the equivalence of Log a over b to the base of g?
Consequence a over b equals g to the power of x all over g to the power of y equals g to the power of x minus y. So than Log a over b to the base of g equals Log g to the power of x minus y to the base of g equals x minus y in bracket times Log g to the base of g equals x minus y in bracket times one equals Log a to the base of g minus Log b to the base of g. So:
Log a over b to the base of g equals Log a to the base of g minus Log b to the base of g
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