Example:
Permutation Cycles
123 (1)(2)(3)
132 (1)(23)
213 (12)(3)
231 (123)
312 (132)
321 (13)(2)
Thus:
S1[3,1]=2
S1[3,2]=-3
S1[3,3]=1
Tes Online dibawah ini ditujukan bagi siswa-siswi SD/SMP/SMA yang ingin menguji sudah sampai sejauh mana pemahaman mereka dalam menguasai materi pelajaran yang diberikan oleh bapak/ibu guru di dalam kelas selama 6 tahun (SD) / 3 tahun (SMP/SMA) belajar di sekolah.
Mudah-mudahan bermanfaat dalam persiapan menghadapi Ujian Nasional nanti.
Berikut ini adalah link untuk mengikuti soal ujian online. Silakan klik mata pelajaran yang dituju.
Untuk SMP/MTs ada 4 mata pelajaran yang dimasukkan, yaitu Matematika, IPA, Bahasa Indonesia, dan Bahasa Inggris
Untuk SD/MI ada 4 mata pelajaran yang dimasukkan, yaitu Matematika, IPA, Bahasa Indonesia, dan Bahasa Inggris.
Untuk SMA/MA ada 10 mata pelajaran yang dimasukkan, yaitu Matematika, Fisika, Kimia, Biologi, Bahasa Indonesia, Bahasa Inggris, Ekonomi, Sosiologi, PKn, dan Sejarah.
| Tahun 2008 | Matematika | Fisika | Kimia | Biologi | Indonesia | B. Inggris | Ekonomi | Sosiologi | P Kn | Sejarah |
| Tahun 2007 | Matematika | Fisika | Kimia | Biologi | Indonesia | B. Inggris | Ekonomi | Sosiologi | P Kn | |
| Tahun 2006 | Matematika | Fisika | Kimia | Biologi | Indonesia | B. Inggris | Ekonomi | Sosiologi | P Kn | |
| Tahun 2005 | Matematika | Fisika | Kimia | Biologi | Indonesia | B. Inggris | Ekonomi | P Kn | ||
| Tahun 2004 | Matematika | Fisika | Kimia | Biologi | Indonesia | B. Inggris | Ekonomi | P Kn | ||
| Tahun 2003 | Matematika | Fisika | Kimia | Biologi | B. Indonesia | B. Inggris | Ekonomi | P Kn |
Part 1: Algebraic Preliminaries
Chapter 3: Permutations
In chapter 3 the concept of a permutation is explained and how they form groups.
Definition: A permutation is a one-to-one map from a set to itself.
Example 1:
Given the set {1,2} the possible one-to-one maps ( permutations ) are:
1->1, 2->2 and
1->2, 2->1.
Example 2:
For sets of three elements there are 6 = 3! possible permutations.
If we put all the permutations of a set in a set by itself and add the composition of permutations as the operation then this set becomes a group. Permutation groups are among the most important objects in group theory because every finite group is a subgroup of some permutation group.
There are two possible ways of notation when it comes to permutations. Let's consider the set {1,2,3,4} which has 24 possible permutations.
The permutation 1->1, 2->2, 3->4 and 4->3 can be written as [1 2 4 3] and also as (1)(2)(3 4) or short (3 4) this is the so called cycle notation. Thus (1 2 3) and [2 3 1] represent the same permutation. Clearly the cycle notation is more efficient, especially when considering permutations of large sets.
The composition of permutations means permuting one after the other. Unfortunately in some books it is done from left to right, in others from right to left.
Exercise 1:
Show that (ab)(cde)*(ae)(bc)(d)=(ac)(bde).
( I would solve it as follows: )Right hand side:
A B C D E
_ D _ E B Apply (bde)
C D A E B Apply (ac)
Left hand side:
A B C D E
_ _ _ D _ Apply (d)
_ C B D _ Apply (bc)
E C B D A Apply (ae)
E C B D A
C D _ E _ Apply (cde)
C D A E B Apply (ab)
And it shows that LHS = RHS
Sets of permution form a group under composition because:
- composition leads to a new permutation ( closure )
- the neutral element is the do-nothing permutation, i.e. (1)(2)(3).
- every permutation has an inverse because it can be permuted back to the original positions.
- composition of permutations is associative.
Note that the composition of permutations is NOT ( always ) commutative.
JAKARTA, KOMPAS.com - Kementerian Pendidikan dan Kebudayaan akan mempercepat waktu pemberian kisi-kisi soal ujian nasional (UN) 2012. Kisi-kisi soal akan diberikan pada akhir tahun 2011 ini. Kepala Badan Penelitian dan Pengembangan Kemdikbud Khairil Anwar Notodiputro mengatakan, hal itu dilakukan untuk membantu sekolah dan para siswa lebih siap menghadapi UN tahun depan. Khairil menjelaskan, rencana tersebut merupakan langkah untuk meningkatkan akseptabilitas, dan juga merupakan jawaban atas banyaknya masukan terkait penyelenggaraan UN. Dari sekian banyak masukan, yang kemudian dijadikan fokus oleh Balitbang Kemdikbud adalah akseptabilitas, kualitas, dan efektifitas penyelenggaraan UN.
"Dari sekian banyak rekomendasi yang disampaikan, yang paling banyak dipersoalkan adalah akseptabilitasnya," kata Khairil, kepada Kompas.com, Senin (7/11/2011), di Kemdikbud Jakarta.
Peningkatan akseptabilitas UN dinilai akan meminimalisir "ketakutan" para siswa dan guru saat akan menghadapi UN. Cara yang ditempuh adalah dengan melakukan dialog secara lebih intensif, dan memberikan kisi-kisi UN secepatnya.
Pemberian kisi-kisi UN juga bertujuan agar memudahkan pusat memberikan arahan kepada dinas pendidikan daerah dan guru-guru di sekolah agar pembuatan soal-soal ujian di sekolah merujuk dan disesuaikan dengan kisi-kisi UN yang diberikan.
"Ketakutan itu akan memicu penolakan. Untuk menekan itu, kita berencana menyampaikan kisi-kisi secepatnya. Jika dulu berbarengan, maka sekarang kisi-kisi UN 2012 akan kita berikan di tahun 2011, ini agar tercipta keselarasan soal dan membuat siswa terbiasa dengan soal yang akan diberikan" jelasnya.
Selain itu, hal lain yang akan dipertegas adalah memberikan pemahaman kepada seluruh masyarakat bahwa UN bukanlah satu-satunya penentu kelulusan. Meski proporsi penilaiannya membuat nilai UN mendominasi kelulusan, yaitu 60 persen nilai UN dan 40 persen nilai sekolah.
"Saya harap UN 2012 bisa lebih santai dan diterima. Secara politik, proporsi 60:40 itu sudah diterima, dan baru akan dievaluasi apakah tetap digunakan atau akan diubah setelah dua tahun digunakan, yaitu pada 2013," tuturnya.
"Nilai-nilai UN yang rendah juga dalam proses pengkajian. Ujungnya kita berharap ada kebijakan berdasarkan pengkajian mengapa nilainya menjadi rendah, apakah soal yang terlalu susah atau ada penyebab lain," tambah Khairil.
Sumber : KOMPAS.com
 |
| Rigor, Relevance, Relationships |
 |
| Fig 1.1 from this ASCD article |
So I brought the framework into class and asked them to classify the kind of lessons they saw in observation... 10 to 15 lessons over the course of the semester. I was seriously surprised how well distributed the X's were on the relevance framework, but not surprised by the low range of rigor. The students discussed how the ABCD was confusing, as D was the "best." They had quite an interesting discussion about whether math should be 'real world' or not. You all know the discussion: why do they ask us (math teachers)? Do they ask their history teacher? What about learning the math for math's sake? Sometimes the applications are so artificial. The students hate the applications so much, why make them do them?Our question is: how can we plan a lesson or lessons that will support our students in moving towards being able to make proofs, understanding the required angle content, and engaging them all the while?
Consider the following and please add your own:
a) a puzzle made from parallels and transversals
b) a map of city streets
c) a classic Japanese problem using these ideas
Where do these ideas fall on the rigor/relevance chart? How should we sequence them or structure class to get to our objective?
Explore the activities in your groups, or design your own, and then we’ll come back together to discuss the ideas.The puzzle: (Actually revised a bit from their use, based on play; changes were made to make it more accessible and focus on the mathematical properties. Click on the image for full size.)
Part 1: Algebraic Preliminaries
Chapter 2: Groups
Definition: A group G is a set with a composition defined on pairs of elements, as long as three axioms hold true:
1. For any three elements x,y,z in G: x*(y*z) = x*(y*z)
2. G contains an element e such that for all x in G: x*e = e*x = x.
3. For any element x in G, there is an element y in G such that x*y=e.
Example 1:
The group of rotations of the sphere in R3: SO(3) or the Special Orthogonal Group in 3 dimensions. -The set G is the collection of all rotational symmetries of the sphere, i.e. if we rotate the sphere by any angle, the sphere doesn't noticeably change. The group property basically means that if we rotate the sphere over any angle A, after this over an angle B, it is the same if we would have rotated it in one go, but over some different angle. Also any rotation has an inverse: rotating it over the opposite angle. This makes the rotations a group. SO(3) is in fact a Lie group because these rotations can be done arbitrary small which is not the case when considering the symmetry group of for example a cube. Lie groups capture the concept of "continuous symmetries".
