Contoh soal ujian Nasional SMP

I.         Pilihlah salah satu jawaban yang paling tepat!

1.        Apabila a = 3; b = 0; dan c = -3, maka nilai dari  { a x (b + c – a)} x ( b + c ) = ……

a.        - 54                          c. 45

b.       - 45                          d. 54

Pembahasan :

Diketahui a = 3; b = 0; dan c = -3

Nilai dari                { a x (b + c – a)} x ( b + c )

                      =        {3 x ( 0 + (-3) – 3)} x ( 0 + (-3)

                      =        { 3 x ( 0 – 3 – 3 )} x ( 0 – 3 )

                      =        ( 0 – 9 – 9 ) x ( - 3 )

                      =        0 + 27 + 27

                      =        54                                                                                            Jawaban :  D        

2.        Jumlah dua bilangan pecahan saling berkebalikan adalah  ³⁴/15 . Jika salah satu penyebut bilangan itu adalah 5. salah satu bilangan tersebut adalah ……..

a.        2/5                           c. 5/4

b.       3/5                           d. 5/6

Pembahasan  :

-    Faktor dari yg penyebutnya 15 adalah 3 dan 5

-    Sehingga dapat dinyatakan ^x/3 dan ^x/5

-    Jika kedua pecahan saling berkebalikan maka jumlahnya ³⁴/15

-    Jadi :  ^x/3 + ^x/5 = ³⁴/15

^5x/15 + ^3x/15 = ³⁴/15

-    Dari pernyataan diatas dapat ditetukan pembilangnya adala 5 dan 3

3.        Karang Taruna Desa Kerta Jaya melaksanakan kerja bakti di sebuah lading berbentuk persegi panjang dengan ukuran 200 m x 150 m. ditepian tanah ditanami pohon mahoni dengan aturan jarak tanam antar pohon 2 m, maka banyaknya pohon yang harus disediakan adalah …..

a.        350 pohon                             c. 701 pohon

b.       700 pohon                             d. 351 pohon

Pembahasan :

Keliling  persegi panjang =  2 (panjang + lebar)

                                             = 2 (200 + 150)

                                             = 700 m

Karena keliling kebun tersebut 700 m dan ditanami pohon mahoni tiap 2 m, banyak pohon mahoni yang diperlukan sebanyak

Keliling kebun   =     700m

         2m                      2

                              =    350 pohon

                                                                   Jawaban  :  A

4.        Koperasi Tani Makmur memberikan layanan pinjaman kepada anggotanya dengan mengambil bunga 18% pertahun utuk 20 kali cicilan dan 12% pertahun untuk 8 kali cicilan. Jika terdapat dua orang pinjam masing-masing Rp. 20.000.000,00 untuk 20 kali cicilan dan Rp. 12.000.000,00 untuk 8 kali cicilan, maka keuntungan koperasi tersebut adalah …

a.        Rp. 1.600.000,00                    c.  Rp. 3.040.000,00

b.       Rp. 1.400.000,00                    d.  Rp.  6.960.000,00

Pembahasan  :

- Rp. 20.000.000,00 x 18%    =   Rp. 3.600.000,00

- Rp. 12.000.000,00 x  12%   =   Rp. 1.440.000,00  +

Keuntungan koprasi                     Rp.5.040.000,00

5.        Hasil perkalian (2x – 1) (3x + 4) adalah ……

a.        6x² +5x – 4                              c.  6x²  +  11x – 4

b.       6x²  – 5x  – 4                           d.  6x² – 11x  –  4

Pembahasan  :

  (2x – 1)  (3x + 4)

=  6x² + 8x – 4 – 3x

=  6x² + 8x – 3x –  4

=  6x² + 5x –  4                                       Jawaban  :  A

6.        Jumlah uang Ratih dan Jaka adalah Rp. 56.000,00. Uang Ratih Rp. 600,00 lebih banyak dari pada uang Jaka. Banyaknya uang Ratih adalah ….

a. Rp. 27.100,00                c.  Rp. 28.300,00

b. Rp. 27.700,00                d.  Rp. 28.900,00

Pembahasan :

-          jumlah uang Ratih dan Jaka  –  Rp. 600,00

=   Rp 56.000,00 –  Rp. 600,00

=   Rp 55.400,00

Sekarang jumlah uang Ratih dan Jaka sama banyak.

-          Jumlah uang Ratih dan Jaka di bagi dua untuk mengetahui besar uang Ratih dan Jaka

Rp. 55.400,00  : 2   =   Rp.  27.700,00

-          Sekarang sudah diketahui besar uang Ratih Rp. 27.700,00 dan uang Jaka Rp. 27.700,00, karena uang Ratih lebih banyak Rp. 600,00 dari uang Jaka, maka uang Ratih adalah:

Rp. 27.700,00 + Rp. 600,00 = Rp. 28.300,00

HOW ??

every children in this world have different characteristic each..
How to learn mathematics easy and make the learning processes fun is different to everybody
child or adult, all of them have many characteristic,
we know that there is multiple intelligences

• Linguistic intelligence ("word smart")
• Logical-mathematical intelligence ("number/reasoning smart")
• Spatial intelligence ("picture smart")
• Bodily-Kinesthetic intelligence ("body smart")
• Musical intelligence ("music smart")
• Interpersonal intelligence ("people smart")
• Interpersonal intelligence ("self smart")
• Naturalist intelligence ("nature smart")

and then how we can use multiple intelligence  in learn math for each children is different...
every child has all of the multiple intelligence but just one or two that look dominan...
just learning with your way,it means that you must learning in confident and also you feel comfort..

Salam dari redaksi tunggal
^_^ 

Euclid And fibonacci

EUCLID

Disappointingly little is known about the life and personality of Euclid except that he was a professor of mahtematics at the University of Alezandria and apparently the founder of the illustrious and long-lived Alezandrian School of Mathematics.  Even hes dates and his virthplacal training in the Platonic school at Athens.  Many years later, when comparing Euclid with Apollonius, to the latter's discredit, Pappus praised

Euclid for his modesty and consideration of others.  Pappus augmented his Eudemian Summary with the frequently told story of Euclid's reply to Ptolemy's request for a short cut to geometric know ledge that "there is no royal road in geometry."   But the same story has been told of Menaechmus when he was serving as instructor to Alexander the Great.   Stobaeus told another story of a student studying geometry under Euclid who questioned what he would get form learning the subject, whereupon Euclid ordered a slave to give the fellow a penny, "since he must make gain from what he learns." Source   FIBONACCI, L.(ca.1175-1250)     known as Leonardo of Pisa (or Leonarde Pisano), Fibonacc was born in the commercial center of Pisa, where his father was connected with the mercantile business.  Many of the large Italian businesses in those days maintained warehouses in various parts of the Medterranean world.  It was in this way, when his father was serving as a customs manager, that young Leonardo was brought up in Bougie on the north coast of Africa.  The father's occupation early roused in the boy an interest in arithmetic, and subsequent extended trips to Egypt, Sicily, Greece, and Syria btought him in contact with Eastern and Arabic mathematical practices.     Thoroughly convinced of the practical superiority of the Hindu-Arabic methods of calculation, Fibonacci, in 1202, shortly after his return home, published his famous work called the Liber abaci.     In 1220, Fibonacci's Practica geometriae appeared, a vast collection of material on geometry and trigonometry treated skillfully with Euclidean rigor and some originality.  About 1225, Fibonacci wrote his Liber quadratorum, a brilliant and original work on indeterminate analysis, which has marked him as the outstanding mathematician in this field, betweem Diophantus and Fermat.   These works were beyond the abilities of most of the contemporary scholars. source

PYTHAGORAS(ca.585-ca.500) & ERATOSTHENES(ca. 203 B.C)

The next outstanding Greek mathematician mentioned in the Eudemian Srmmary(these lost works was a resume of an apparently full history of Greek geometry, already lost in SProclus' time, sovering the period prior to 335 B.C., written by Eudemus, a pupil of Aristotle) is Pythagoras, whom his followers enveloped in wuch a mythical haze that very little is known about him with any degree of certainty.  It seems that he was born about 572 B.C. on the Aegean island of Samos.  Being about fifty years younger than Thales

and living so near Thales' home city of Miletus, it may be that Phthagoras studied under the older man.  He then appears to have sojourned in Egypt and may even have indulged in more extensive travel.       Returning home, he found Samos under the tyranny of Polycrates and ionia under the dominion of the Persians; accordingly, he migrated to the Greek seaport of Crotoma, located in southern Italy.  There he founded the famous Pythagorean school, which, in addition to beong an academy for the study of philosophy, mathematics, and natural science, developed onto a closely knit brotherhood with secret rites and observances.  In time, the influence and aristocratic tendencies of the brotherhood became so great that the democratic forces of southern Italy destroyed the buildings of the school and caused the society to disperse.  According to one report, Pythagoras fled to Metapontum where he died, maybe murdered, at an advanced age of seventy-five to eighty.   The brotherhood, although scattered, continued to exist for at least two centuries more. source ERATOSTHENES(ca. 203 B.C)     Eratosthenes was a native of Cyrene, on the south coast of the Mediterranean Sea, and was only a few uears younger than Archimedes.  He spent many years of his early life in Athens and, at about the age of forty, was invited by Ptolemy ¥² of Egypt to come to Alexandria as turor to his son and to serve as chief librarian at the University there.  It is told that in old age, about 194 B.C. he became almostblind from lphthalmia and committed suicide by voluntary stavation.     Eratosthenes was singularly gifted in all the branches of knowledge of his time.  He was distinguished as a mathemarician, an astronomer, a tgeographer, an historian, a philosopher, a poet, and an athlete. It is said that the students at the University of Alexandria used to call himpentathlus, the champion in five athletic sports.  He was also called Beta, and some speculation has been offered as to the possible origin of this nickname.  some believe that it was because his broad and brilliant knowledge caused him to be looked upon as a second Plato.   A less kind explanation is that, although he was gifted in many field in many fields, he always failed to top his contemporaries in any one brach; in other words, he was always second best.  Each of these explanations weakens somewhat when it is learned that certain astronomer Apollonius (very likely Apollonius of Perga) was called Epsilon.  Because if this, the historian James Gow has suggested that perhaps Beta and Epsilon arose simply fron the Greek numbers (2 and5) of certain offices or lecture rooms at the University particularly associated with the two men. On the other hand, Ptolemy Hephaesitio claimed that Apollonius was called Epsilon because he studied the moon, of which the letter e symbol.     In arithmetic, Eratosthenes is noted for a device known as the sieve, which is used for finding all the prime numbers less than a given number n.  One writes down, in order and starting with 3, all the odd numbers less than n.  The composite numbers in the sequence are then sifted out by crossing off, from 3, every third number, then from the next remaining number, 5, every fifth number, then from the next remaining number,7, every seventh number, from the next remaining number, 11, every eleventh number, and so on.  In the process some number will be crossed off more than once. All the remaining number along with the number 2, constitute the list of primes less than n. source

WEIERSTRASS,K.T.W.(1815-1897) and RIEMANN,G.F.B.(1826-1866)

	A misdirected youth spent in studying the law and finane gave Weierstrass a late start in mathematics, and it was not until he was forty that he fonally emancipated himself from secondary teaching by obtaining an instructorship at the University of Berlin, and another eight years passed before, in 1864, he was awarded a full professorship at the university and could finally devote all his time to
advanced mathematics. Weierstrass never regretted the years he spent in elementary teaching, and he later carried over his remakable pedagogical abilities into his university work, becoming probably the greatest teacher of advanced mathematics that the world has yet known.     Weierstrass wrote a number of early papers on hyperelliptic integrals, Abelian functions, and algebraic differntial equations, but his widest known contribution to mathematics is his construcition of complex functions by means of power series.  This, in a sense, was an extension to the complex plane of the idea earlier attempted by Lagrange, but Weierstrass carried it through with absolrte rugor.     In algebra, Weierstrass was perhaps the first to give a so-called posrulational definition of a determinsant. He defuned the determinant of a square matrix Aas a polynomial in the elements of A, which is homogeneous and linear in the elements of each row of A, which merely changes sign when two rows of Aare permuted, and which reduces to I when A is the correspending identity matrix.   Weiestrass was a very influential teacher, and his meticulously prepared lectures established an ideal for many future mathmaticians;"Weierstrassean rigor" became synonymous with "extremely careful reasoning." weiestrass was "the mathemarical conscience par excellence," and he became known as "the father of modern analysis."  He died in Berlin in 1897, just one hrndred years after the furst publication, in 1797 by Lagrange, of an attempt to rigorize the calculus.
	Along with this rigorization of mathematics, there appeared a tendency toward abstract generalization, a process that has becomevery pronounced in present-day mathenatics.  Perhaps the German mathematician Georg Friedrich Bernhard Riemann influenced this feature of midern mathrmatics mire than any other nineteedth-century mathematician.  He certainly wielded a profound influence on a number of branches
of mathematics, particularly geometry and function theory, and few mathematicians have bequeathed to their successors a richer legacy of ideas for further develipment.     Riemann was born in 1826 in a small cillage in Hanover, the son of a Lutheran pastor.  In manner, he was always shy; in health, he was always frail.   In spote of the very modest cirsumstances of his father.  Riemann managed to decure a good education, first aty the University of Berlin and then at the University of Gottingen.  He took his dectoral degree at the latter institution with a brilliant thesis in the field of complex-function theory.  In this thesis, one finds the so-called Carahy-Riemann differential equations(Known, however, before Riemann's time) that guarantee the analyticity of a complex varible, and the highly fruitful cincept of a Riemann surface,ch introduced topological cinsiderations into analysis.  Riemann clarified the cincept of integrability by the definition of what we now knowas the Rirmann integral, which led, in the twentieth century, to the more general Lebesgue integral,and thence to futher generalizatiens of the integral.     Later, Albert Einstein and othera found Riemann's broad cincept of space and geometry the mathematical milieu needed for general relativity theory. Riemann himself contribrted in a number of directions to theoretical physics; he was the first, for example, to give a mathematical treatmint of shock waves.     Famius in mathematical literature are the so-called Riemann zeta function and associated Riemann hypotheses.  The latter is a celebrated unproved conjecture that is to classical analysis what Fermat'slast "theorem" is to number theory.     In 1857, riemann was appointed assistant prefessor at Gottingen, and then, in 1859, full professor, succeeding Dirichlet in the chair once occupied by Gauss.  Riemann died of tuberculosis in 1866, when only years of age, in nothern Italy, where he had gone to seek an improvement in his health. Source

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look at building above...
they made by many little things....
like mathematics that have many things...hopefully we can make a buiding from the beautifull of everything in math...
happy ENJOY!!!