Although it's about english of mathematics, but for the first time I want to write about vocabularies which often we used. We often get difficulties to translate or know the meaning of them. Pay attention!!
we know that the meaning of break is "patah", but.. please read it!
break away : lolos break down : memerinci
break in : mendobrak break open : membuka, membongkar
broken down : rusak (ks) broken hearted : patah hati
broken with : memutuskan hubungan
Come
come about : terjadi come across : menemukan
come after : menjemput come along : berjalan
come round : mampir come before : menghadap
come between : memisahkan come down : datang
come in for : mendapat come into : mewarisi
come through : lewat come within : tercakup
go
go for : menyerbu go down : turun
go by : melewati go through : mengalami
take
take about : membawa take for : mengira
take down : melepas take of : keberangkatan (plane)
Yeah, it's my new vocabularies. from one word but can be made more meaning, depend the contex.
Now it is my small dictionary of mathematics
segitiga siku-siku : right triangle
One of the angle of right triangle is ninety degree.
segitiga sebarang : scalene triangle
The sum of the angle of scalene triangle is one hundred and eighty degree.
segitiga samakaki : isosceles triangle
The isosceles triangle have two same sides.
lancip : acute
the acute angle has measure more than zero but less than ninety degree.
FPB : the greatest common divisor (GCD)
the GCD of two and four is two.
KPK : the least common multiple (LCM)
The LCM of two and four is four.
keliling : circumference, perimeter.
If we have a picture,the length is 20 cm and its width is 10 cm. so the perimeter of the picture is 60 cm.
Bilangan asli : natural number
the natural number is started by one.
Garis bilangan : number line
for early study about integer we can use number line to helping us find the solution/answer.
pengetian : concept
Before we study, we should know its concept.
Jari-jari : radius
the radius of the circle is 7cm, then the area of circle is 154 cm^2.
busur derajat : protactor
what is protactor, what's for?
sejajar : parralel
the parallel line don't have common point.
berimpit : superimpose
the superimpose line have infinite solution because it has infinite common point.
himpunan kosong : empty
The set of cows which have five legs is empty.
The above is small dictionary of mathematics (use sentences) and now, it is small dictionary without sentences
suku sejenis : like term
gabungan himpunan : union
berpotongan : intersection
titik persekutuan : common point
segiempat : quadrilateals
garis bagi : bisector
garis berat : median
garis sumbu : perpendicular bisector
pembilang : numerator
penyebut : denominator
titik singgung : tangent
titik kuasa : power of point
garis potong : secant
sudut pusat : central angle
talibusur : chord
sebanding : proporsional
bola : sphere
kongruen : congruent
jajargenjang : parallelogram
alas :base
trapesium : trapezoid
sebangun : similar
bersilangan : cross
aneh : strange
sering muncul : modus
nama samaran : nickname
terkejut : surprised
sama dan sebangun : congruent
menjiplak : plagiarize
pembulatan : rounded
bingung : confused
kalem : calm
semboyan : maxim
pola : pattern
hakikat matematika : natural of mathematics
bangun datar : plane
bangun ruang : solid
acak : random
kabur : blur
pasrah : give up
clean up : menyelesaikan
varnish : menghapus
turmoil : kerusuhan
fate : nasib
rata-rata: mean, average
jiwa : soul
kecewa : dissapointed
menghindari : avoid
sempurna : perfect
garis lengkung : curve
barisan : sequence
permukaan : surface
cabang : branch
uang kertas :note
uang logam : coin
sebarang : scalene
konsisten : consistent
persegi : square
persegi panjang : rectangle
lingkaran :circle
tabung : sylinder
prisma : prism
penaksiran : estimation
mengungkap : uncover
anggapan : assumsed
Minggu, 24 Mei 2009
Senin, 13 April 2009
Test of English
1. How we get phi?
Circumference of a circle is a limit of polygon on its circle. Circumference of circle noticed by “s”. It has relationship with radius (r) , namely s divided two r equals phi (s:2r = phi)
Proportion s : 2r of circumference of a circle with radius is equal of all circle. Phi equals twenty two divided by seven or three point one four.
2. How we get abc formula?
Formula of quadratic equation is a square x plus bx plus c equals zero
Change koefisien x square to be x square plus bx divided by a plus c divided by a equals zero.
Miss the konstanta on left, so we get x square plus bx divided by a equals negative c divided by a.
Add both of the sides right and left with quadratic of a half koefisien, we get x square plus bx divided by a plus the square of b divided by 2a equals negative c divided by a plus the square of b divided by 2a.
Change side of left be perfect quadratic, so
the square of x plus b divided by 2a equals negative 4ac plus b square divided by four a square then x plus b divided by 2a equals the square root of negative four ac plus b square divided by four a square, after that we get x. x equals negative b divided by 2a plus minus one 2a the root of b square minus 4ac, finally, x equals negative b plus minus the square root of b square minus 4ac divided by 2a.
3. Determine the area which limited y equals x square and y equals x plus two
To find that solution, we can draw it but for the first, we should make table. We’ll use scalene number to convert x.
For example, if x is zero, y is zero
if x is plus minus one, y is one
If x is plus minus two, y is four
And if x is plus minus three, y is nine, etc
For the second equation, y equals x plus two
I’ll choose x is zero so that y is two. (zero,two)
If y is zero, x is negative two. (negative two, zero)
The next step is we search the intersection point,
x square equals x plus two, so we get x equals negative one or x equals two
The last step is we have to integral from negative one until two on x plus two minus x square. By counting the integral we get the area which limited by way equals x square and y equals x plus two
4. Determine the volume of cone
Most of the three dimension have a formula volume namely, base area multiplied by height. For example the formula of cube volume is cubic sides. It happened because the base of cube is square and it has congruen sides so the volume of cube id cubic sides. Meanwhile the volume of cube equals one third limas volume. Limas volume has similar with cone volume, it just difference in base. So the cone volume is one third area base multiplied by height of cone. Or one third multiplied by circle area multiplied by height of cone.
5. Prove that the sum of angle of scalene triangle is one hundred and eighty degree.
Triangle have three angles, and sum of the angle is one hundred and eighty degree. On Element’s Euclid book 1, propositions 1 27 through 1 32 establish the theory of parallels and prove that the sum of the angle of a triangle is equal to two right angles.
If we have the picture of triangle and we cut the three of angles. After that we arrange the piece of them, we’ll get straight line or the measure of angle is one hundred and eighty degree.
6. Determine the probability of sum number more than 6 from two dices by throwing once.
A dice has six sides namely, one , two, three, four, five, and six. There are two dices so there are thirty six probability. The question how many probability come sum of number more than six.
The probability are (one, six), (two,five),(two, six),(three,four), (three, five), (three, six), (four, three), (four, four), (four, five), (four, six), (five, two), (five, three), (five, four), (five, five), (five,six),(six,one), (six, two), (six, three), (six, four), (six, five), (six,six)
There are twenty one, so the probability come sum of number more than six is 21/36.
7. How we determine the equation which on ( ten, zero) and have segment of circle x square plus y square equals nine?
To solving this question, we use equation segment formula which follow point (a,b), namely x index once x plus y index once y equals the square of radius. So the equation can be searched by entering elements which known. x index one is ten, y index one is zero and the square of radius is nine.
By accounting the equation we can give solution that the equation is ten x minus nine equals zero.
8. How we prove the phytagoras ?
Imagine that!
I have drawn two pictures, the pictures were square. For the first square. It’s divided into six pieces, namely two squares and four right triangles congruent. The second square is divided into five pieces namely the square on the hypotenuse and four right triangles congruent. a, b, c are sides of square. c means hypotenuse. By subtracting equals from equals. It follows that the square on the hypotenuse is equal to the sum of the squares on the legs. It’s one of the proof to make sure that it’s right.
9. Determine the sum of two hundred odd number first!
Odd number is started from one, three, five, seven,…
The sum of odd number is one plus three plus five plus seven,…
Let’s we find the sum of the odd number with formula.
one plus three plus five equivalent with five plus three plus one, if we sum of them, the result is six plus six plus six, or six multiplied by n
So we can conclude that one plus three plus five equals (six plus six plus six) multiplied by two =nx6/2=a half multiplied by n(one plus four)=a half multiplied by n (a+un)
n means the many of odd number
a means first term
un means last term
Our duty is finding the solution for the sum of the odd number, two hundred first
so one plus three plus five plus…plus one hundred and ninety nine equals…
the difference from 1 to three is two, therefore we can find the value of n
un= one hundred and ninety nine
one hundred and ninety nine =a+(n-1)b
one hundred and ninety nine =1+(2n-2)
one hundred and ninety nine =2n-1
two hundred=2n
n=one hundred
The sum is a half multiplied by one hundred multiplied by (one plus one hundred and ninety nine)
a half multiplied one hundred multiplied by two hundred equals ten thousand
10. the step to draw the cube ( the element of cube known)
Before, let’s know about the elements of cube
· frontal plane means every parallel plane with drawing plane.
· Frontal line is every line or segment which located on frontal plane.
· Orthogonal line is every line which located perpendicular on frontal plane.
· Surut angle means the angle which located between horizontal frontal segment to right and orthogonal segment to behind.
· The compare of projection or compare of orthogonal means the propotion between length of the map with the real length.
For example:
Draw ABCDEFGH cube. Given, the length of side is 3 cm, ABFE is frontal plane, sudut simpang 30’ and proportion of projection is one third.
First, make AB segment which length 3 cm. At point A make angle of 30’,so there is AD segment the length of AD is one third multiplied by 3 cm equals one cm. Because the projection of ABCD parallelogram, then the base can be done. The middle of side is vertical segment, therefore E, F, G and H can be drawn.
Circumference of a circle is a limit of polygon on its circle. Circumference of circle noticed by “s”. It has relationship with radius (r) , namely s divided two r equals phi (s:2r = phi)
Proportion s : 2r of circumference of a circle with radius is equal of all circle. Phi equals twenty two divided by seven or three point one four.
2. How we get abc formula?
Formula of quadratic equation is a square x plus bx plus c equals zero
Change koefisien x square to be x square plus bx divided by a plus c divided by a equals zero.
Miss the konstanta on left, so we get x square plus bx divided by a equals negative c divided by a.
Add both of the sides right and left with quadratic of a half koefisien, we get x square plus bx divided by a plus the square of b divided by 2a equals negative c divided by a plus the square of b divided by 2a.
Change side of left be perfect quadratic, so
the square of x plus b divided by 2a equals negative 4ac plus b square divided by four a square then x plus b divided by 2a equals the square root of negative four ac plus b square divided by four a square, after that we get x. x equals negative b divided by 2a plus minus one 2a the root of b square minus 4ac, finally, x equals negative b plus minus the square root of b square minus 4ac divided by 2a.
3. Determine the area which limited y equals x square and y equals x plus two
To find that solution, we can draw it but for the first, we should make table. We’ll use scalene number to convert x.
For example, if x is zero, y is zero
if x is plus minus one, y is one
If x is plus minus two, y is four
And if x is plus minus three, y is nine, etc
For the second equation, y equals x plus two
I’ll choose x is zero so that y is two. (zero,two)
If y is zero, x is negative two. (negative two, zero)
The next step is we search the intersection point,
x square equals x plus two, so we get x equals negative one or x equals two
The last step is we have to integral from negative one until two on x plus two minus x square. By counting the integral we get the area which limited by way equals x square and y equals x plus two
4. Determine the volume of cone
Most of the three dimension have a formula volume namely, base area multiplied by height. For example the formula of cube volume is cubic sides. It happened because the base of cube is square and it has congruen sides so the volume of cube id cubic sides. Meanwhile the volume of cube equals one third limas volume. Limas volume has similar with cone volume, it just difference in base. So the cone volume is one third area base multiplied by height of cone. Or one third multiplied by circle area multiplied by height of cone.
5. Prove that the sum of angle of scalene triangle is one hundred and eighty degree.
Triangle have three angles, and sum of the angle is one hundred and eighty degree. On Element’s Euclid book 1, propositions 1 27 through 1 32 establish the theory of parallels and prove that the sum of the angle of a triangle is equal to two right angles.
If we have the picture of triangle and we cut the three of angles. After that we arrange the piece of them, we’ll get straight line or the measure of angle is one hundred and eighty degree.
6. Determine the probability of sum number more than 6 from two dices by throwing once.
A dice has six sides namely, one , two, three, four, five, and six. There are two dices so there are thirty six probability. The question how many probability come sum of number more than six.
The probability are (one, six), (two,five),(two, six),(three,four), (three, five), (three, six), (four, three), (four, four), (four, five), (four, six), (five, two), (five, three), (five, four), (five, five), (five,six),(six,one), (six, two), (six, three), (six, four), (six, five), (six,six)
There are twenty one, so the probability come sum of number more than six is 21/36.
7. How we determine the equation which on ( ten, zero) and have segment of circle x square plus y square equals nine?
To solving this question, we use equation segment formula which follow point (a,b), namely x index once x plus y index once y equals the square of radius. So the equation can be searched by entering elements which known. x index one is ten, y index one is zero and the square of radius is nine.
By accounting the equation we can give solution that the equation is ten x minus nine equals zero.
8. How we prove the phytagoras ?
Imagine that!
I have drawn two pictures, the pictures were square. For the first square. It’s divided into six pieces, namely two squares and four right triangles congruent. The second square is divided into five pieces namely the square on the hypotenuse and four right triangles congruent. a, b, c are sides of square. c means hypotenuse. By subtracting equals from equals. It follows that the square on the hypotenuse is equal to the sum of the squares on the legs. It’s one of the proof to make sure that it’s right.
9. Determine the sum of two hundred odd number first!
Odd number is started from one, three, five, seven,…
The sum of odd number is one plus three plus five plus seven,…
Let’s we find the sum of the odd number with formula.
one plus three plus five equivalent with five plus three plus one, if we sum of them, the result is six plus six plus six, or six multiplied by n
So we can conclude that one plus three plus five equals (six plus six plus six) multiplied by two =nx6/2=a half multiplied by n(one plus four)=a half multiplied by n (a+un)
n means the many of odd number
a means first term
un means last term
Our duty is finding the solution for the sum of the odd number, two hundred first
so one plus three plus five plus…plus one hundred and ninety nine equals…
the difference from 1 to three is two, therefore we can find the value of n
un= one hundred and ninety nine
one hundred and ninety nine =a+(n-1)b
one hundred and ninety nine =1+(2n-2)
one hundred and ninety nine =2n-1
two hundred=2n
n=one hundred
The sum is a half multiplied by one hundred multiplied by (one plus one hundred and ninety nine)
a half multiplied one hundred multiplied by two hundred equals ten thousand
10. the step to draw the cube ( the element of cube known)
Before, let’s know about the elements of cube
· frontal plane means every parallel plane with drawing plane.
· Frontal line is every line or segment which located on frontal plane.
· Orthogonal line is every line which located perpendicular on frontal plane.
· Surut angle means the angle which located between horizontal frontal segment to right and orthogonal segment to behind.
· The compare of projection or compare of orthogonal means the propotion between length of the map with the real length.
For example:
Draw ABCDEFGH cube. Given, the length of side is 3 cm, ABFE is frontal plane, sudut simpang 30’ and proportion of projection is one third.
First, make AB segment which length 3 cm. At point A make angle of 30’,so there is AD segment the length of AD is one third multiplied by 3 cm equals one cm. Because the projection of ABCD parallelogram, then the base can be done. The middle of side is vertical segment, therefore E, F, G and H can be drawn.
Minggu, 12 April 2009
Nature of mathematics
Nature of mathematics
Nature of mathematic consist of something, they are relationship, problem solving, research and tool of communication.1. Relationship
In mathematics must has a relationship. It is impossible single, something of mathematics has relationship with other. For instances, there is two dimensionIt can be relationship with square, triangle, circle, etc
2. Problem Solving
Mathematic is problem solving. Many difficulties in our life can be finish by mathematics. Every activities use mathematics.For example:I have one thousand rupiah, I want to buy five candies, the price of each candy is one hundred rupiah.With mathematic, we know, we should pay five hundred rupiahs.
3. Research
Mathematics can definitied by research. Because the importantance of mathematic is finding something use logical. We observate something, give definition, teorema and make a concliution.
4. Tool of communicationMathematics is one of tool of communication. So mathematic is very important.For example: ihave many books, magazines, story books, novels and comics. Other people know we have them if we communicate with other. Other peoples will asked how many book you have . we answer their question use mathematic, for example I answer that I have ten story books, eight comics, twenty magazines, etc
Wat to say it
Way to say it
in mathematics we should know how we say the sentence of mathematics. for example in addition, subtractions, fractions, etc.
FractionsFractions or in bahasa Indonesia known as pecahan. Are divided two variant; ordinal fractions and decimal fractions. On ordinal fractions can be divided again to be three kinds, namely proper fractions, improper fractions and mixed fractions. But how to read?
Pay close attension to the following examples:
Ordinal fraction
1/2= one second or a half
1/8= one eight or an eight
2/3=two thirds
1 5/9=one and five ninths
Decimal fractions
0,5 = point five or zero point five
3,25 = three point two fivePower
8^2 = 64
The second power of 8 is 64
Or
eight to the second power is 64
Or eight square is 64
The second exponent of 8 is 64
Rootv144 = 12
The square root of 144 is 12
?27 = 3The cubic of 27 is 3, or
The cube root of 27 is 3v16 =….
What is the square root of 16?
Additions
2 + 2 = 4
Two and two are four. It is in small additions but if in larger additions and in more formal style additions, we use plus or added For example:
712 + 145 = 857
Seven hundred twelve plus one hundred forty- five is or equals eight hundred and fifty-seven.
Subtractions
In conversational style, for the operation7-3 = 4, we say:Three from seven leaves / is four
Or
seven takes away three leaves / is four.
In a more formal style, we say minus for…. And equals.For instance:
619-428 = 191, six hundred and nineteen minus for hundred and twenty eight equals one hundred and ninety one.
Multiplication.
3 x 4 = 12Three fours are twelve.
6 x 7 = 42 Six sevens are forty two
3 x 71 = 213Three times seventy one makes two hundred and thirteen
Or three multiplied by seventy one equals two hundred and thirteen.
Division :
261 : 9 = 29Two hundred and sixty one divided by nine equals twenty-nine or two hundred and sixty one into nine goes twenty nine.
The form of quadratic equation is ax^2+bx+c=0
the find the root or solution from the quadratic equation, we can use :
# factor
# complete perfect quadratic
# abc formula
Minggu, 15 Maret 2009
English Class
Ladies and gentlement...
I am a student of Yogyakarta state of univercity and take mathematics department. Let's share our experience about English. Do you think English is important? what's your purpose learn English? Yeah..., English is very important for our life. It's international language. If we can't speak English what said the world for us? and how do you study English? what's your tips?? in order to our studying easier. Now, I want to share my first experience study English in my class. It is... Last Wednesday, exactly in March 11, 2009 was our first meeting English class. Mr Marsigit was our lecturer. Before class be started, we got a little difficult in finding classroom. Ugh what a pity we are. After surrounding exmat and RUB class, we got a classroom which no be used by student of univercity. Because it was first meeting, the first activity we did was introducing. Mr Marsigit asked us where we came from. After introducing he told us about his experience when he studied in abroad. He ever been studied in univercity of london. He described the condition of London and told about differences between indonesia and London culture.
Yeah... Now, I want to give my opinion about my lecturer. Before I have never seen him. I think he is briliant and discipline lecturer. honesly, I wished he would teach us about grammar and tenses. Actually he wouldnot do it. Although, I realized that my English of grammar is very bad. He gave us explanation that our class just 16 times so that it's impossible if we depended with him. because the time is't effective. Besides that he said that to mastering English 80% is from ourself whereas the rule of lecturer just 20%.Therefore, I could conclude that if we wanted master English and speak English fluently, we should study hard and practice our english with our friend, family and others. Our English could improve if we used it and please don't be afraid of making mistakes....
You had to beliefe with your ability that you can do it...
Based on our lecturer's explanation in studying English. We will master five skills. They are speaking, hearing, writing, understanding and translating. And remember to master English you have to enjoy it, without force.
That's right... Let's start practice English! I'm absolutely sure that learn English is very usefull. After graduating, we will seek a job and we have to face interview test. It's era globalization. Most of company use English to interview applycant. how we can competite with others if we can't speak English. master English will be a good capital for us to find a good job and improve our qualification...
I am a student of Yogyakarta state of univercity and take mathematics department. Let's share our experience about English. Do you think English is important? what's your purpose learn English? Yeah..., English is very important for our life. It's international language. If we can't speak English what said the world for us? and how do you study English? what's your tips?? in order to our studying easier. Now, I want to share my first experience study English in my class. It is... Last Wednesday, exactly in March 11, 2009 was our first meeting English class. Mr Marsigit was our lecturer. Before class be started, we got a little difficult in finding classroom. Ugh what a pity we are. After surrounding exmat and RUB class, we got a classroom which no be used by student of univercity. Because it was first meeting, the first activity we did was introducing. Mr Marsigit asked us where we came from. After introducing he told us about his experience when he studied in abroad. He ever been studied in univercity of london. He described the condition of London and told about differences between indonesia and London culture.
Yeah... Now, I want to give my opinion about my lecturer. Before I have never seen him. I think he is briliant and discipline lecturer. honesly, I wished he would teach us about grammar and tenses. Actually he wouldnot do it. Although, I realized that my English of grammar is very bad. He gave us explanation that our class just 16 times so that it's impossible if we depended with him. because the time is't effective. Besides that he said that to mastering English 80% is from ourself whereas the rule of lecturer just 20%.Therefore, I could conclude that if we wanted master English and speak English fluently, we should study hard and practice our english with our friend, family and others. Our English could improve if we used it and please don't be afraid of making mistakes....
You had to beliefe with your ability that you can do it...
Based on our lecturer's explanation in studying English. We will master five skills. They are speaking, hearing, writing, understanding and translating. And remember to master English you have to enjoy it, without force.
That's right... Let's start practice English! I'm absolutely sure that learn English is very usefull. After graduating, we will seek a job and we have to face interview test. It's era globalization. Most of company use English to interview applycant. how we can competite with others if we can't speak English. master English will be a good capital for us to find a good job and improve our qualification...
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