25 December 2008

Many attitude in my class at Vincent Study Center

Tell About My course : Vincent's Study Center....
Facilities : Comfort Class Room, activity Learning - Discuss and Exercise for Junior High School and Senior High School for Group n Private Course (Math, Physics, Chemistry). Student Center Teaching.



Many activities in my course at Vincent Study Center....
They come as their schedule, and go home, and another students come and go.....
There are many activities :




















Listening when I teach them, practice the exercises Maths, or Physics or Chemistry....
Ask n answer....


They are discussing about math, Physics, and Chemistry....Do they exercise....

Sometimes they feel hopeless to solve the exercise....Like this photo :



After their schedule they sometime wait their parents to pick them up...
Sometimes they play jokes, listening the music from their cell phone, sometimes they tell about film, about the subjects in school, tell about music, tell about their friends or teacher whom they hate or like, tell about terms n conditions at their school, tell about exam, etc...

Closing with them, make me feel young, and know what they need, what they want, and what they think, know their world which is different with us....

Sometimes I want to laugh, surprised, and I don't know what to tell about....Sometimes they attitude so kind, so rude, not control what they say or what they do, but sometimes they look funny, georgeous, innocent and salute with their achievement.

Sometimes they no attention with exercise, blank mind, or sometimes they encourage each other...sometimes they look so tired, boring, and hopeless...
But they are our students..I must encourage day to day....

These are some photoes :


































I am explain to my private student...

That's my little story about my course and about my students.....
I'm proude to be their teacher....

15 December 2008

Ask n Answer...

A Few days ago, somebody ask me how to selve the problem :

I try to answer....

Remember the formula :




So you can solve with this way :
I hope ypou can understand now....
Thank you....

29 November 2008

FINAL TEST 1st SEMESTRY ON HIGH SCHOOL

If you are a student at High School for First Class in Indonesia, you can download this exercise to prepare your Final Test at December 2008 at Subject : Maths..
Exercise Final Test Mathematics Grade 1 on Senior High School

Or, yuo can download for Multiple Choice Type here :
Excercise Multiple Choice Type of Mathematics Final Test

16 November 2008

Another Probability

I've made exercise for Probability 2...
For anybody who need this excercise for increase your ability, please download :

Exercise Probability 2

Wow.....I Got Award......


I Got Award....

Wow, I Got Award.....
This Award I got from another Blogger in Indonesia....
Thanks, Mr. Budiawan Hutasoit....
Really...really...surprised to me....

06 November 2008

Just for Fun......

  1. Johny, Leo, Vincent, James and Fanny undertake to paint a house. It will take Johny, Leo, and Vincent 7 1/2 days to complete the job. When Johny, Vincent and Fanny work together, it will take them 5 days to complete. When Johny, Vincent and James work together, it will take them 6 days to complete. And when Leo, James, and Fanny work together, it will only take them 4 days to complete the paiting job. How long will it take Johny, Leo, James, and Fanny to complete the job if they all worked together...?
  2. Mr Harry brought home a bag of sweets for his grandchildren. He gave the first grandshild 2 sweets plus 1/13 of the remaining sweets. He then gave the second grandchild 4 sweets plus 1/13 of the reminder. To the third grandchild, Mr Harry gave 6 sweets plus 1/13 of the reminder. He continued the methode by giving the next grandchild extra sweets than the previous one and 1/13 of the reminder. The last of Mr Harry's grandchild took his share and found that there was no more reminder.Given that each of Mr Harry's grandchildren receives an equal number of sweets, how many grandchildren does Mr. Harry have. Also find the number of sweets each grandchildren receives...?
  3. Three men are placed one behind another in front of a wall. The men are blindfolded and told that a hat will be placed on their head taken from a bin conmtaining 3 white and 2 black hats.
  4. The blindfolder is then removed and each man is asked to determine the colour of the hat he is wearing. The third man who is furthest from the wall sees the other two men's hat and says, "I cannot tell what colur hat I am wearing." The second man who hears the third man's reply and sees the colour of the hat the first man is wearing says the same thing. The first man after hearing the replies of the other two men says, " I know the colour of the hat I am wearing." Do you know how he came to this conclusion and what is the colour is..?
  5. A man with a dog, a rabbit and a bunch of lettuce came to a riverbank. There is only a small boat that can carry the man and one of the animals or the lettuce. The problem for the man is, : If left alone together, the dog will eat the rabbit and the rabbit will eat the lettuce. How can you help the man to transport his animals and his lettuce safely to the other side of the river...?

It's just for funny....Hemmmm....Yummy...spent the time to joke with your friend....

Question This Week.....

There are two questions coming from my visitor :

1.

Tg ( p + q) = ½....(1)

Tg (p – q) = 1/3........(2)

Tg 2p = ...?

Answer

:

If : p + q = A  and p – q = B

With elimination we find :

2p = A + B

Tangen1

Tg 2p = Tg (A + B) = Gbr 1

= Gbr 2

2.

Sin (3x + 2y) = 1/8......(1)

Sin ((3x – 4y) = ¼ .....(2)

Sin 6y = ....?

Sinus1

Answer :

Misalkan

(3x + 2y) = A ® Sin A = 1/8

(3x – 4y) = B ® Sin B = ¼

With elimination we find :

6y = A - B

So sin 6y = sin (A – B)

Sin (A – B) = sin A cos B – cos A sin B

= Gbr 3

I hope my explanation make you clear and can understand.....

21 October 2008

EDUCATION EXPO DI SMAK BINA BAKTI BANDUNG

EXPO SMAK 1 BINA BAKTI Bandung, 16 - 18 Oktober 2008

Anuual Education Expo hold by Bina Bakti 1 High School Bandung for this year is different with another years ago. The Educatio Expo which located at Jl. Bima 9 Bandung is show many attraction an proggramme such as ::

  • Seminar Mathematics Teacher ; Teaching Mathematics Strategies for Mathematics Teachers region West Java, with speaker by Mr. Ramir S. Austria, MAEA (Dari Philipina - Bimus University)
  • Education Fair, followed by many favourite University such as ENHAII, UNPAR, U. MARANATHA, ITHB, BINUS, LIKMI, IDP, MEC, ISS, IELTS, ICAT, Unistart, Vista, Edlink-Cponnex, and Education Insurance Prudential
  • Science Fair, shows many students masterpiece in Science (Physics, Biology, Chemistry) at Bina Bakti High School Bandung for supporting learning activity at school.
  • Bazaar, which followed by several book publishers, foods products, kids products, etc.
  • Talk Show University; by lecturer of Institute of Technology Bandung, Parahyangan University, Maranatha University, Padjajaran University, ENHAII
  • Mathematics Competition for Middlke School Region West Java, which is followed by SMPK BPK1 Penabur, SMPK BPK 5 Penabur, SMPK BPK 3 Cimahi, SMP Yos Sudarso Garut, SMPK Yos Sudarso Purwakarta, SMPK Babtis SMPK Yahya, SMPK 2 Bina Bakti, SMPK 1 Bina Bakti, SMP St. Mikael Cimahi
  • Dance Competition, followed by : SMPK BPK 5, SMP BPK Taman Holis, SMP Yos Sudarso, SMPK Bina Bakti, SMAK 1 Bina Bakti, SMAK 3 BPK, SMA St. Maria, SMAK PAulus, dan SMAK 2 BPK.
  • Art Presentation, such as Dancing , Choirs, and music band.
  • Games Arena by Bina Bakti High School Bandung

Please, enjoy some pictures below to describe the situation......

The Principal of Bina Bakti High School (Mrs Lily H. at right)IMG_0206

Bazaar..... Talk Show by Universities

DSCN0452 IMG_0274

Bina Bakti 1 High School Choir Science Fair........

IMG_0357

Seminar Math Teacher that makes us fresh to teach pupils........(by Mr. Ramir.....)

PA160144 IMG_0318

Thank You Mr. Ramir......

IMG_0328

Maths Competition for Middle High School Region West Java......

Elimination Stage Final.......

PA160139 IMG_0572

Para Jury at Final Maths Competitions for Middle High School.....

IMG_0573

The Result is : 1st, 2nd, 3rd Ranks are from SMP BPK 1 Penabur Bandung, 4th, 5th are from BPK 5 Penabur Bandung. Congratulation....!!!!

Dance Competition......(Come On...!!!...!!!! Chayo !!!!)

IMG_0591 IMG_0596

The Result is.....: 1st Rank : SMAK 2 BPK, 2nd Rank : SMAK 1 Bina Bakti....

Congratulation...!!!!!

Education Fair.....(Good information....)

IMG_0263 IMG_0264

IMG_0293


Hm...there are so many picts that haven't hang here...buat these pics can describe us how relly lively at Education Expo of Bina Bakti 1 High School Bandung this year...

Congratulations for collegas, pupils and the participants.....

See You Next Year.....!!!!!

Permutations and Combinations

Perrmutations and Combinations

1. The multiplication principle or (r,s) principle

It states that if one operation can be performed in r ways, and a second operation can be performed in s ways, then the two operations can be performed in succession in r x s ways.

Note : The principle can be extended to any finite number of operations

2. Permutaion

(a). A permutaion is an ordered arrangement of all or part of a set of objects in a row.

(b). The umber of permutaion of n different objects taken all at a time (without repetition), is donated by nPn and nPn = n ! where n! = n(n – 1) (n – 2) ...x 3 x 2 x 1

(c). The number of permutations or arrangements of n different objects, taken r at a time (without repetition) is donated by nPr where clip_image002

(d). The number of permutations of n objects (not all distinc), taken all at a time, where thee are p objects alike of one kind, q objects alike of another kind and the rest are distinct, can be done in clip_image004. (This result can be exdtended to many finite number of groups of objects).

3. Combination

(a). A combination is a selection of objects in which the order of selection does not matter.

(b). The number of combinations or selections of n different objects, taken r at the time, is donated by clip_image006

Note : nCo = 1 ; nCn = 1 ; nCr = nCn- r

(c). The number of selections from n different objects, taking any number at a time is 2n - 1

EXERCISES

Calculus cartoon1. A sixth from contains the Head Boy, the Head Girl and 8 other students. The form is asked to send a group of 4 representatives to a conference. Calculate the number of different ways i which the group can be formed if it must be contain :

(i). both the Head Boy and the Head Girl

(ii). Either the Head Boy or the Head Girl, but not both

2. Calculate the number of ways in which :

(i). 5 children can be devided in to group of 2 and 3

(ii). 9 children can be devided into groups of 5 and 4

Hence calculate the number of ways in which 9 children can be devided into groups of 2, 3, and 4

3. A row of 10 houses is to be painted in 3 colours, 2 houses ae to be red, 3 to be blue and 5 to be white. Find the number of different ways in which the row of the houses can be painted :

(i). with no restrictions

(ii). Given that the first and the last houses in the row are blue

(iii). Given that the first and the last houses in the row are the same colour.

4. Find the total numbers of different permutations of all the letters of the word RESERVE.

Find the number of these permutations in which :

(i). E is the first letter.

(ii). The two Rs come together

(iii). S and V come at the ends of the permutations.

5. Find the number of ways in which a team of 6 batsmen, 4 bowlers and a wicket-keeper may be selected from a squad of 8 batsmen, 6 bowlers and 2 wicket-keeper.

Find the number of ways in which :

(i). this team may be selected if it is to include 4 specified batsmen and 2 specified bowlers

(ii). The 6 batsmen may be selected from the 8 available, given that 2 particular batsmen cannot be selected together.

6. Calculate the total number of different permutations of all letters A, B, C, D, E and F when :

(i). there are no restriction

(ii0. the letters A and B are to be adjacent to one another

(iii). The first leter is A, B, or C and the last letter is D, E, or F.

7. A tennis team of 4 men and 4 women is to be picked from 6 men and 7 women. Find the number of ways in which this can be done.

It was decided that 2 of the 7 women must either be selected together or not selescted at all. Find how many possible teams could be selected in these circumstances.

The selected team is arranged into 4 pair, each consisting of a man an a woman.

Find the number of ways in which this can be done.

8. At an art exhibition 7 paintings are to be hung in a row along one wall. Find the number of possible arrangements

Given 3 paintings are by the same artist, find the number of arrangements in which :

(i). these 3 paintings are hung side by side.

(ii). Any one of these paintings in shung at the beginning of the row but neither of the other 2 is hung at the end of the row.

9. A shelf is to contain 7 different books, of which 4 were written by Dickens and 3 by Hardy. Find the number of aangements in which :

(i). no two books by the same author are adjacent

(ii0. the first two books at the left-hand end are by the same author.

10. A editor has space for 6 advertisements, one on each of the first 6 pages of the magazine. Of the 6 advertisements to be displayed, 4 ar for household goods, 1 for gardening equipment and 1 for sports equpipment. In how many different ways can the advertisements appear in the magazine if the 4 advertisements for household goods must appear on consecutive pages ?

Answers :

1. (i). 28 (ii). 112

2. (i). 10 126 ; 1 260

3. (i). 2 520 (ii). 168 (iii). 784

4. 420

(i). 180 (ii). 120 (iii). 20

5. 840, 72, 13

6. (i). 720 (i). 240 (iii). 216

7. 525, 225, 24

8. 5 040 (i). 720 (ii). 1 440

9. (i). 144 (ii). 2 160

10. 144

19 October 2008

The Great Mathematicians all Times


1. Leonhard Euler (1701 - 1783)

He was one of the greatest mathematicians of all time. Known as the "grandfather of Topology". He founded the "network theory" which is one of the most practical forms of topology. He wrote a whole library of outstnading, articles on all branches of mathematics. He was also responsible for the international adoption of many fundamental mathematical notations such as phi, e, i, and others.

The value of Special irrational number represented by " e" and the value e = 2.7193

The value e is often as the base in exponential equations as it often provides as a good model to many natural, social and economic phenomena.

Logarithm to the basic e, "loge x" is often abbreviated as " ln x". ln x is called Natural Logarithm or Napierian Logarithm (in honour of the Scottis Mathematician John Napier)

2. Pythagoras (about 585 - 500 B.C.)

He was a pupil if Thales is the best known for the relation between the sides of a right-angled triangle which bears his name.

He founded the "Order of Pythagoras" to study mathematics, music, science, philosophy and religion. The school was the first to exclusively and systematically apply deductive reasoning in solving mathematical problems.

The multiplication table that we know of today was also credited to them.They believed that the world was a stationary sphere and that it was the centre of the universe.


3. Thales (about 625 - 545 B.C.)

Thales was an outstanding Greek academican and merchant, was the first to use the idea of proofs in geometry, leading the way to abstract thinking.

He astounded the Egyptians by calculating the height of pyramid using proportionate right-angled triangles.

This helped to lay the foundation for the development of "Trigonometry"

4. Blaised Pascal (1623 - 1662)

He showed his great intellect by proving an important theorem in projective geometry at the age of 16. He devised the world's second mechanical calculating machine at age 19, (the world's first was made by Wilhelm Schickard in 1623)

In 1654, he and Pierre de Fermat laid the foundation of probability theory.






5. Joseph Louise Lagrange (1736 - 1813)

He made significant contributions to the mathematics of differential equations, analysis, number theory, analystical and celstial mechanics.

He headed the commitee that led to the adoption of the metric system by many countries. He also played an important role in verifying Newton's universal law of gravitation.

6. Geofrey Harold Hardy (1877 - 1947)

He was one of the best pure mathematicians that England has produced. He contributed in many fields of pure mathematics such as analysis and the number theory.

His book, "Pure Mathematics", revolutionised the teaching of mathematics i England in 1917. Hardy together with Ramanujan published an important piece of work on number theory.






7. Carl Friedrich Gauss (1777 - 1855)

He was born a prodigy ; he could operate with numbers even before he could talk. He opened new horizon in almost all fields of pure as well as applied mathematics.

Many of the mathematics of the 19th and 20th centuries had their beginnings in the works of Gauss.

At he page of 17, he gave the first exact proof of the fundamental theorm of algebra, a proof that the greatest mathematicians of previous ages had attempted without success.

Gauss was named "The Prince of Mathematics" and is widely regarded together with Newton and Archimedes, as one of the three greatest mathematicians in history.


8. Pierre de Fermat (1601 - 1665)

Pierre de Fermat is perhaps the most famous number theorist in history. What is less widely known is that for Fermat mathematics was only an avocation: by trade, Fermat was a lawyer.

He work on maxima and minima, tangents, and stationary points, earn him minor credit as a father of calculus.

Independently of Descartes, he discovered the fundamental principle of analytic geometry.

And through his correspondence with Pascal, he was a co-founder of probability theory.

But he is probably most well-known for his famous "Enigma".

Fermat's portrait is inscribed with this famous "Enigma", which is also known as Fermat's Last Theorem. It states that xn + yn = zn has no whole number solution when n > 2.

Fermat, having posed his theorem, then wrote

"I have discovered a truly remarkable proof which this margin is too small to contain."

The proof Fermat referred to was not to be found, and thus began a quest, that spanned the centuries, to prove Fermat's Last Theorem.

Fermat's image is also overlaid by Fermat's spiral. Fermat's spiral (also known as a parabolic spiral), is a type of Archimedean spiral, and is named after Fermat who spent considerable time investigating it.

9. Sir Isaac Newton (1642 [1643 New Style Calendar] - 1727)

Sir Isaac Newton stated that "If I have seen further it is by standing upon the shoulders of giants." Newton's extraordinary abilities enabled him to perfect the processes of those who had come before him, and to advance every branch of mathematical science then studied, as well as to create some new subjects. Newton himself became one of those giants to whom he had paid homage.

Newton's image is set against the cover of a tome easily recognizable to those familiar with the history of mathematics -- his Principia Mathematica, The Mathematical Principles of Natural Philosophy, first published in 1687.

Its first two parts, prefaced by Newton's "Axioms, or Laws of Motion", dealt with the "Motion of Bodies". The third part dealt with "The System of the World" and included Newton's writings on the Rules of Reasoning in Philosophy, Phenomena or Appearances, Propositions I-XVI, and The Motion of the Moon's Nodes.

Inscribed over Newton's image is Newton's binomial theorem, which dealt with expanding expressions of the form (a+b) n. This was Newton's first epochal mathematical discovery, one of his "great theorems". It was not a theorem in the same sense as the theorems of Euclid or Archimedes, insofar as Newton did not provide a complete "proof", but rather furnished, through brilliant insight, the precise and correct formula which could be used stunningly to great effect.

Newton is widely regarded as the inventor of modern calculus. In fact, that honor is correctly shared with Leibniz, who developed his own version of calculus independent of Newton, and in the same time frame, resulting in a rancorous dispute.

Leibniz's calculus had a far superior and more elegant notation compared to Newton's calculus, and it is Leibniz's notation which is still in use today.

Newton's portrait shares a color palette with Leibniz, the other acknowledged "inventor" of calculus, Lagrange, a pioneer of the "calculus of variations", and Laplace and Euler, two of those who built on what had been so ably begun.

10. Eukleides (Euclid) c. 330 - 275 B.C.E

Eukleides (Euclid of Alexandria), although little is known about his life, is likely the most famous teacher of mathematics of all time. His treatise on mathematics, The Elements, endured for two millennia as a principal text on geometry.

The Elements commences with definitions and five postulates. The first three postulates deal with geometrical construction, implicitly assuming points, lines, circles, and thence the other geometrical objects.

Postulate four asserts that all right angles are equal -- a concept that assumes a commonality to space, with geometrical constructs existing independent of the specific space or location they occupy.

Eukleides is pictured with what is perhaps his most famous postulate -- the fifth postulate, often cited as the "parallel postulate". The parallel postulate states that one, and only one, line can be drawn through a point parallel to a given line -- and it is from this postulate, and on this basis, that what has come to be known as "Euclidean geometry" proceeds.

It was not until the 19th century that Euclid's fifth postulate -- the "parallel postulate" was rigorously and successfully challenged.

The two parallel lines of Euclid meet and converge in the portrait of Johann Carl Friedrich Gauss -- whose work led to the emergence of non-Euclidean geometry, where Euclid's fifth postulate gave way to new mathematical universe, where 2 parallel lines could, in fact, meet.

The portrait of Gauss shares a common dominant color palette with the portrait of Euclid -- but two different conceptions of 'geometry'.

Pictured over Euclid's right shoulder is a small drawing which is taken from Euclid's proof of the right angled triangle which has come to be known as the theorem of Pythagoras. While very little is known about the lives of either Pythagoras or Eukleides, it is both plausible and likely that Euclid and Pythagoras independently discovered and "proved" this basic theorem. Euclid's proof of this theorem relies on most of his 46 theorems which preceded this proof.

Central to Euclid's portrait is a circle with its radius drawn. Euclid's geometry was one of construction, and the circle and radius were central elements to Euclid's constructions.

11. Gottfried Wilhelm Leibniz (1646 - 1716 )

Gottfried Wilhelm Leibniz was a philosopher, mathematician, physicist, jurist, and contemporary of Newton. He is considered one of the great thinkers of the 17th century. He believed in a universe which followed a "pre-established harmony" between mind and matter, and attempted to reconcile the existence of a material world with the existence of a supreme being.

The twentieth century philosopher and mathematician Bertrand Russell considered Leibniz's greatest claim to fame to be his invention of the infinitesimal calculus -- a remarkable achievement considering that Leibniz was self-taught in mathematics.

Leibniz is portrayed overlaid with integral notation from his calculus which he developed coincident with but independently of Newton's development of calculus.

Although the historical record suggest that Newton developed his version of calculus first, Leibniz was the first to publish. Unfortunately, what emerged was not fruitful collaboration, but a rancorous dispute that raged for decades and pitted English continental mathematicians supporting Newton as the true inventor of the calculus, against continental mathematicians supporting Leibniz.

Today, Leibniz and Newton are generally recognized as 'co-inventors' of the calculus.

But Leibniz' notation for calculus was far superior to that of Newton, and it is the notation developed by Leibniz, including the integral sign and derivative notation, that is still in use today.

Leibniz considered symbols to be critical for human understanding of all things. So much so that he attempted to develop an entire 'alphabet of human thought', in which all fundamental concepts would be represented by symbols which could be combined to represent more complex thoughts. Leibniz never finished this work.

Leibniz, who had strong conceptual differences with Newton in other areas, notably with Newton's concept of absolute space, also develop bitter conceptual differences with Descartes over what was then referred to as the "fundamental quantity of motion", a precursor of the Law of Conservation of Energy.

Much of Leibniz' work went unpublished during his lifetime. He died embittered, in ill health, and without achieving the considerable wealth, fame, and honor accorded to Newton.

Leibniz' diverse writings -- philosophical, mathematical, historical, and political -- were resurrected and published in the late 19th and 20th centuries.

But calculus -- with Leibniz notation still in use today -- remains his towering legacy.

12. Evariste Galois (1811 - 1832)

Évariste Galois (French pronunciation: [evaʁist ɡalwa]; October 25, 1811May 31, 1832) was a French mathematician born in Bourg-la-Reine. While still in his teens, he was able to determine a necessary and sufficient condition for a polynomial to be solvable by radicals, thereby solving a long-standing problem. His work laid the foundations for Galois theory, a major branch of abstract algebra, and the subfield of Galois connections. He was the first to use the word "group" (French: groupe) as a technical term in mathematics to represent a group of permutations. A radical Republican during the monarchy of Louis Philippe in France, he died from wounds suffered in a duel under murky circumstances[1] at the age of twenty.

Known for Work on the theory of equations and Abelian integrals