It Is a Must That I have a Competent in English For Mathematic

Many people said in this era of globalization is essential to master at least the English language or other foreign languages. They said that without mastery of English is good, a country will not progress. English as a common language the world has a very important role. How not? all the things that we find in the Internet world and real world almost demands knowledge can be pro-English us. English is the language used in the international conversation, without the English language we can not afford to talk to people on other continents. So as students master the English language is a requirement that can not be denied again. Students, he should be able to speak English, because the student is a successor of the nation must be able to relate to people outside the country and the world must confronted in later. But sometimes international language has become part of the scourge for students understand the material and become a boomerang to develop themselves due to lack of knowledge in can speak English. that I experienced at this time.

I was a student of mathematics education majors. Of course, later on after I graduate will be a mathematics teacher, mathematics teacher is a teacher who must be able to converse in English. Because mathematics is a science that has been the world, knowledge that is needed around the world. Moreover, at this time many schools international. SBI is a problem that most pengantarnya in the form of the English language. For that time I became a teacher, I should be able to speak English with quite smoothly, because tomorrow may be my disciple English language than me, so I have to master English so that students can face like that.

I currently lecture in UNY, UNY the university to become a pioneer international universities, especially in mathematics education and accountant education. So starting this semester 2, mathematics education be split into 2 first-class mathematics education and regular education mathematics class bilingual. Those who are in bilingual classes must master the English language well. Although not a bilingual class annggota I have to learn English well, should be able to master the English language and speak in English, although I very weak in English. But I will try to continue so that I can speak English well, because it is my obligation as a student in mathematics education UNY.

Learning English is believed will be able to make the increased employee performance. More than that, learn the English language will also be able to create a nation will be able to progress and develop in the era of globalization which we call the era of globalization. The point is not English are considered and will not be capable of achievement in their job. Certainly because this is the English language is required in looking for work, there are test in the form of the English language, especially in the CPNS test. So that it is compulsory for students such as this I must master the English language. Ability to speak English well is a plus value for someone. People able to speak English he would be easier to find a job. An agency will seek applicants who are able to speak English. For prospective teachers in mathematics if I can master English well, will be teaching classes in international obstacles easily without the means. In addition, may also be a teacher to tutor the children abroad.

Presumably from the description above is not excessive if English is very much needed in this century contemporary. Each period is set by a particular system episteme. First English language is still a one antique now, but without the English language we can not relate to people in other countries. Control of English so one of the primary needs. Unfortunately, this need not be accompanied with a conscious sense of the students that were established as the successor of the nation, students should be required can speak English fluertly. Although it is not, a student must learn. Suppose the les-les in English, search for texts or songs in the English language. So there is no word for a student does not master the English language. Students are required over the English language. Without the English students can not seek to find a job easily. Without the English language student in mathematics education majors UNY will not be able to bring to mathematics education in the international class.

What I Have done and What I do English For Mathematics

English is the international language, which is often used someone is overseas, although they are not in the England. English is very muvh needed at this time in learning activities in class, especially if the class is a bilingual class. In bilingual classes, student are required to be able to speak in English.

Mathematics is the science of the very terms with the English language especially when we learn the history of mathematics. In the semester 1, I use the English language in mathematics is when I learn the history of mathematics. I will not know the history of mathematics if I do not use the English language, because information about the history of mathematics is written mostly in English.

Usage of English in mathematics among mathematics problems with completing the English language and mathematics. The use of difficult words in mathematics. Mathematics in the English language is different from the English language in general, example “akar” of the English language of mathematics is the root not radix. “Bola”, if translated into English to become general ball. But what happens if translated into English specifically mathematics? The ball is not there, there is even a sphere. Please note that there are lot of special vocabulary of English is very strange math heard.

In the future of English is a basic requirement. Without the English language we can not afford to communicate with the world community. So some day become a teacher if I may, I will apply a little or a lot of English in mathematics, example to create quizzes, quizzes on the difficult words in English and then translated in the language in indonesia, or vice versa. So this way the students are expected to be able to speak in English even if only in mathematics.

As a student who majors in mathematics education pioneer class international may be I will be more zealous to apply mathematics in English. Try the shoptalk in the level of English words is quite difficult. I will try to find the difficult words in English related to mathematics. Trying to be zealous use of English in mathematics.

A. Properties of Logarithm

1) a to the power of m times a to the power of n equals a to the power of m plus n in bracket.

2) a to the power of m over a to the power of n equals a to the power of m minus n in bracket.

3) Log b to the base of a equals n, means with b equals a to the power of n.

4) Log a to the base of g equal x, means with a equals g to the power of x.

5) Log b to the base of g equals y, means with b equals g to the power of y.

6) Log a times b in bracket to the base of g equals bla………bla……….bla……bla….

Example:

a. Log a to the base of g equals x, so a equals g to the power of x

b. Log b to the base of g equals y, so b equals g to the power of y.

a times b equals g to the power of x times g to the power of y.

a times b equals g to the power of x plus y in bracket.

Ø Log a times b in bracket to the base of g,

equals Log g to the power of x plus y in bracket to the base of g

equals x plus y in bracket times Log g to the base of g. Consider : Log g to the base g equals 1.

So, x plus y in bracket times Log g to the base of g equals 1.

So, Log a times b in bracket to the base of g equals Log a to the base of g plus Log b to the base of g.

Ø a over b equals g to the power of x over g to the power of y.

equivalen a over b equals g to the power of x minus in bracket.

equivalen Log a over b in bracket to the base of g equals Log g to the power of x minus y in bracket to the base of g.

equivalen Log a over b in bracket to the base of g equals x minus y in bracket times Log g to the base of g.

equivalen Log a over b in bracket to the base of g equals x minus y.

equivalen Log a over b in bracket to the base of g equals Log a to the base of g minus Log b to the base of g.

So, Log a over b in bracket to the base of g equals Log a to the base of g minus Log b to the base of g.

Ø Log a to the power of n to the base of g.

Log a to the power of n to the base of g equals Log a times a times a times a up to n factor,

Equivalen Log a to the power of n to the base of g equals Log a to the base of g plus Log a to the base of g plus Log a to the base of g plus bla…..bla…..bla….. plus Log a to the base of g plus Log a to the base of g.

Equivalen Log a to the power of n to the base of g equals n times Log a to the base of g

So, Log a to the power of n to the base of g equals n times Log a to the base of g.

B. Square Root of 2 is Irrational Number

Square root of 2 is the first irrational number is recognizedby Yunani people. They to say that long of diagonal from a right triangle with long of 2 side to form angled, one of them is irrational, from Phytagoras Theorem to get that long of triangle hypotenuse is a square root of 2.

So, How to prove that square root of 2 is irrational number?????????

Prove:

Square root of 2 is knowed by Yunani people that’s plane and that numeral is irrational. Supposing square root of 2 is rational, so must to be integer of x and y, so that square of 2 equals xper y, where y not zero. We can to confirm that x and y are not even (minimal one of them is a odd), because if both of them are even, we can to simplifying. In other meaning x per y we take the simplest. We get that x square per y square equals 2 or x square equals 2 times y square with other meaning x square is even. Because x square is even, so x is even, because that to be h even, so x equals 2 times h and thus

x square equals 2 times y square.

ð Open bracket 2 time h close bracket square equals 2 times y square.

ð 4 times h square equals 2 times y square,

ð y square equals 2 times h square.

Because y square is even, so that y is even too. This contradiction with we estimate that x and y cannot even, minimal one of them is odd, so that estimate is fllen and square root of 2 is irrational number.

(PROVED)

Prove with Math Logical, we use a implication.

If square root of 2 is irrational so that integer of x and y not zero, thus square root of 2 equal x per y. We are simboled square root of 2 is rational with p and statement of integer of x per y not zero so square root of 2 equals x per y with q, thus implication can be written with pèq, thus q wrong or –q right, because –qè-p equivalen with pèq, thus we get conclusion that p is wrong or square root of 2 is irrational number.

C. abc formula

a times x square plus b times x plus c equals zero is quadratic equation, so to find a roots of quadratic equation can search with abc formula.

This formula:

a times x square plus b times x plus c equals zero then both of articulations is overed with a.

Become:

x square plus b over a in bracket times x plus c over a equals zero.

Then c over a is transferred to right articulations and both of articulation plus with b over 2a in bracket square.

Become:

x square plus b over a in bracket times x plus b over 2a in bracket square equals b over 2a in bracket square minus c over a.

Then left articulation we can changed to perfect quadratic, become:

x plus b over 2a all in bracket square, then become:

x plus b over 2a all in bracket square equals b square over 4 times a square in bracket minus c over a, then right articulation equation of denominator become:

b square minus 4ac all over open bracket4 times a square close bracket, then become:

x plus b over 2a all in bracket square equals b square minus 4ac all over open bracket 4 times a square close bracket. Then both of articulation we root become:

x plus in bracket b over 2a close bracket equals plus minus square root of b square minus 4acall over open bracket 4 times a square close bracket.

Then we transfer b over 2a to right articulations, become:

x equals minus b over 2a plus minus square root of open bracket b square minus 4ac close bracket all over 2a.

So, x equals minus b plus minus square root of open bracket b square minus 4ac close bracket all over 2a.

D. Point of intersection

Find intersection of y equals x square minus 1 and y square plus x square equals 30.

Solving:

y square plus x square equals 30 is a circle has a radius of square root of 30 and centered in point (0,0) and y equals x square minus 1 is quadratic equation has vertex of -1. For to find a point of intersection we must to substitution y equal x square minus 1 to equation of y square plus x square equals 30.

è y equals x square minus 1 become y plus 1 equals x square then this equation we substitution to y square plus x square equals 30, become:

y square plus y plus 1 equals 30, then 30 we transfer to left articulation become:

y square plus y plus 1 minus 30 equals zero

y square plus y minus 29 equals zero

Then, we find y variable with abc formula, become:

y equals minus 1 plus minus square root of open bracket 1 minus 4 times 1times minus 29 close bracket all over 2

y equals minus 1 plus minus square root of 117 all over 2,

so, y₁ equals minus 1 plus square root of 117 all over 2

y₁ equals minus 1 plus 10 point 81 all over 2 equals 9 point 81 all over 2 equals 4 point 905

y₂ equals minus 1 minus square root of 117 all over 2

y₂ equals minus 1 minus 10 point 81 all over 2 equals minus 5 point 905

For y₁ equals 4 point 905, we substitution to x square equals y plus 1, become:

x square equals 4 point 905 plus 1

x square equals 5 point 905

x equals plus minus 2 point 43

For y₂ equals minus 5 point 905, we substitution to x square equals y plus 1, become:

x square equals minus 5 point 905 plus 1

x square equals minus 4 point 905, because x square minus so this not valid.

So, point of intersection are 2 point 905 comma 4 point 905 and minus 2 point 905 comma 4 point 905.

Summary of Video

Video 1:

From that video, I think that we have to believe with our ability. We have to certain that we be able to doing something. If we have a dream, so we must sure that we can to reach our dream. Without assureance from our heart, we incable to doing we anxious and we dream. So, we must believe with our ability.

Video 2:

In second video, I am more know about mathematics. Mathematics learned geometry, trigonometry, ln x, significant figure, limit x approach boundlessly, exponent, integral e power x and from this video, I know that value of phi is 3,145…………

Video 3:

The third video show about mathematic problem solving.

For example :

The graph of f(x) = x + 1 if 2f(p) = 20. How value of f(3p)?

Answer:

2f(p) = 20

f(p) = 10

f(x) = x + 1

we substitution p to f(x) = x + 1 become f(p) = p + 1

f(p) = p + 1 = 10

p = 10 – 1 = 9

f(3p)????

3p = 3(9) = 27

f(x) = x + 1

f(3p) = 3p + 1 = 27 + 1 = 28

So value of f(3p) is 28

Video 4:

Video 4 about the properties of logarithm.

1. Log x to the base b equals y symmetry with b power y equal x

2. Log x to the base 10 equals Log x

3. Log x to the base natural numeral equasl Ln x (this natural logarithm)

Example :

1.Log 100 to the base 10 equals x. How value of x?

2. Log x to the base 2 equasl 3. How value of x?

3. Log 1 over 49 to the base 7 equals x. How value of x?

Answer :

1. Log 100 to the base 10 equals x, become 10 to the power of x equals 100, so x equal 2.

2. Log x to the base 2 equals 3, become 2 to the power of 3 equal x, so x equals 8.

3. Log 1 over 49 to the base 7 equals x, become 7 to the power of x equals 1 over 7 to the power of 2 in bracket. This similer with 7 to the power of x equals 7 to the power of minus 2, so x equal minus 2.

4. Log M times N in bracket to the base b equals Log M to the base 2 plus Log N to the base 2.

5. Log M over N in bracket to the base b equals Log m to the base 2 minus Log N to the base 2.

6. Log x to the power of n in bracket to the base b equals n times Log x to the base b.

Example:

How value of Log x to the power of 2 times y plus 1 in bracket all over open bracket z to the power of 3 close bracket in square bracket to the base 3?

Answer:

Log x to the power of 2 times y plus 1 in bracket all over open bracket z to the power of 3 close bracket in bracket to the base 3

equals Log x to the power 2 times open bracket y plus 1 close bracket in square bracket to the base 3 minus Log z to the power 3 in bracket to the base 3

equals Log x to the power 2 to the base 3 plus Log open bracket y plus 1 close bracket to the base 3 minus Log z to the power 3 to the base 3

equals 2 times Log x to the base 3 plus Log y plus 1 in bracket to the base 3 minus 3 times Log z to the base 3.

So, Log x to the power of 2 times y plus 1 in bracket over open bracket z to the power of 3 close bracket in bracket to the base 3 equals 2 times Log x to the base 3 plus Log y plus 1 in bracket to the base 3 minus 3 times Log z to the base 3.

Video 5:

About Graph of Rational Function.

Example:

Draw a function of f(x) equals x plus 2 in bracket over x minus 1 in bracket

Answer:

f(x) = ( x + 2 ) / ( x – 1 )

even x = 1 we find f (x) = 3 / 0 ( this wrong and imposible ), so graph of f(x) not be able nudge line x = 1.

And not all rational fuction denominator can be zero..

Video 6:

Video 6 consist obout Trigonometry.

Sine (Sin), Cosine (Cos), and Tangents (Tan) are trigonometric ratios.

Ratio of Sin is opposite per hypotenuse (soh)

Ratio of Cos is adjoin per hypotenuse (cah)

Ratio of Tan is opposite per adjoin (toa)

The other trigomometric rations are represented as follows:

Secant (Sec) is one cos

Cosecant (Cos) is one sin

Cotangents (Cot) is one tan

For example:

If the right triangle ABC right angled at B where AB = 3 cm, BC = 4 cm, CA = 5 cm (hypotenuse). P is angle front of BC and Q is front of BA. How value of all trigonometric ratio?

Answer:

1. Sin P = opposite/hypotenuse = 4/5

Cos P = adjoin/hypotenuse = 3/ 5

Tan P = opposite/ adjoin = 4 /3

Cosec P = one sin = 5/ 4

Sec P = one cos =5/ 3

Cot P = one tan = 3/ 4

2. Sin Q = opposite/ hypotenuse =3/ 5

Cos Q = adjoin/ hypotenuse = 4/ 5

Tan Q = opposite/ adjoin = 3/ 4

Cosec Q = one sin = 5/ 3

Sec Q = one cos = 5 /4

Cot Q = one tan =4/ 3