PEMBELAJARAN :
1. Membentuk Persamaan Garis Lurus (y = mx + c)
SIAP UJIAN NASIONAL :
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1. Pembahasan Uji Kemampuan Diri 1 ( Download ) - Soal ( Download )
2. Pembahasan Uji Kemampuan Diri 2 ( Download ) - Soal ( Download )
3. Pembahasan Uji Kemampuan Diri 3 ( Download ) - Soal ( Download )
4. Pemantapan Ujian Nasional Sesuai SKL ( Download ) - Soal ( Download )
...
Minggu, 31 Oktober 2010
Penelitian Tindakan Kelas
MGMP Matematika SMP DKI Jakarta pada Hari Minggu, 30 Oktober 2010 di SMP Negeri 68 Jakarta, selain hari itu didakan Kompetisi Matematika SMP Ke-27 Babak Semi Final, Siang harinya juga mengadakan pelatihan Penelitian Tindakan Kelas PTK sebagai upaya untuk menjembatani teman-teman guru Matematika yang mau naik Pangkat/Golongan dari IVa ke IVb. Nara sumber Bapak Supardi, S.Pd, M.Pd. Berikut hasil dari pelatihan tersebut :
Rencana Pembelajaran
- Muatan Karakter ( Download )
- Standar Isi Matematika ( Download )
- RPP Berkarakter Kelas VIII Semester 2 ( Download )
- Format-Format Kelas VIII Semester 2 ( Download )
- RPP Berkarakter Kelas IX Semester 2 ( Download )
- Format-Format Kelas IX Semester 2 ( Download )
- RPP Berkarakter Terbaru Lengkap 2011/2012 ( Download )
- Format-format Kelas VII ( Download )
- Format-Format Kelas VIII ( Download )
- Format-Format Kelas IX ( Download )
- Silabus Berkarakter Kelas VII (Download)
- Silabus Berkarekter Kelas VIII ( Download)
- Silabus Berkarakter Kelas IX ( Download )
- RPP Matematika Kelas VII Semester 1 ( Download )
- RPP Matematika Kelas VII Semester 2 ( Download )
- RPP Matematika Kelas VIII Semester 1 ( Download )
- RPP Matematika Kelas VIII Semester 2 ( Download )
- RPP Matematika Kelas IX Semester 1 ( Download )
- RPP Matematika Kelas IX Semester 2 ( Download )
SOAL - SOAL
- Soal Pemantapan Ujian Nasional ( Download )
- Pembahasan Pemantapan Ujian Nasional ( Download )
- Soal Try Out Kelas IX ( Download )
- Pembahasan Try Out Kelas IX ( Download )
- Uji Coba UAS Kelas IX Sesuai Kisi-Kisi ( Download )
- Pembahasan Paket A ( Download )
- Pembahasan Paket B ( Download )
- Soal TUKPD Tahap I Paket A ( Download )
- Soal TUKPD Tahap I Paket B ( Download )
- Modul Ujian Nasional 2013 ( Download)
- Pembahasan Ujian Nasional
- Ujian Nasional 2011/2012 Paket A17 ( Download )
- Ujian Nasional 2011/2012 Paket AB29 ( Download )
- Ujian Nasional 2011/2012 Paket C32 ( Download )
- Ujian Nasional 2011/2012 Paket D45 ( Download )
- Ujian Nasional 2011/2012 Paket E57 ( Download )
- Soal Kenaikan Kelas VII ( Download )
- Soal Kenaikan Kelas VIII ( Download )
- TUKPD Tahap II 2012 Paket A ( Download )
- TUKD Tahap II 2012 Paket B ( Download )
- TUKPD Tahap I 2012 Paket A ( Download )
- TUKPD Tahap I 2012 Paket B ( Download )
- UAS Kelas VII Semester I Th 2011/2012 ( Download )
- UAS Kelas VIII Semester I Th 2011/2012 ( Download )
- UAS Kelas IX Semester I Th 2011/2012 ( Download )
- Ulangan Semester I Kelas IX Tahun 2009/2010 ( Download )
- Ulangan Semester I Kelas VII Tahun 2010/2011 ( Download )
- Ulangan Semester I Kelas VIII Tahun 2010/2011 ( Download )
- Ulangan Semester I Kelas IX Tahun 2010/2011 ( Download )
- Soal Latihan Tes Diagnostik Guru ( Download )
- Soal Model Seagames 26 ( Download )
- Olimpiade Sains Nasional 2011
- Tugas Matematika Kelas IX ( Download )
- Ulangan Kenaikan Kelas VII ( Download )
- Ulangan Kenaikan Kelas VIII ( Download )
- Uji Coba Ujian Nasional Paket AB 2010/2011 ( download )
- Soal TUKPD Tahap I ( Download )
- Pemantapan UN, sesuai SKL ( download )
- Uji Kemampuan Diri 1 ( download )
- Uji Kemampuan Diri 2 ( download )
- Uji Kemampuan Diri 3 ( download )
- Pembahasan Uji kemampuan Diri 1
- Pembahasan Uji kemampuan Diri 2
- Pembahasan Uji kemampuan Diri 3
- Matematika 7 Ulangan Semester 1 ( download )
- Matematika 8 Ulangan Semester 1 ( download )
- Matematika 9 Ulangan Semester 1 ( download )
- Soal Kompetisi Matematika 27 Kelas 7 Babak Penyisian ( download )
- Soal Kompetisi Matematika 27 Kelas 8 Babak Penyisian ( download )
- Soal Kompetisi Matematika 27 Kelas 9 Babak Penyisian ( download )
- Ujian Nasional 2009/2010 Soal A ( download )
- Ujian Nasional 2009/2010 Soal B ( download )
- Kompetisi Matematika 26 Kelas VII ( download)
- Kompetisi Matematika 26 Kelas VIII ( download )
- Kompetisi Matematika 26 Kelas IX ( download )
- Aritmetika Sosial ( download )
- Himpunan ( download )
- Bangun Datar ( download )
- Bangun Ruang ( download )
- Perbandingan dan Kesebangunan ( download )
- Bilangan ( download )
- Garis-garis Sejajar( download )
- Kesebangunan ( download )
- Kubus dan Balok( download )
- Segitiga ( download )
- Operasi Bentuk Aljabar( download )
- Persamaan Garis Lurus ( download )
- Persamaan Kuadrat ( download )
- Persamaan Linear Dua Peubah ( download )
- Persamaan dan Pertidaksamaan Satu Variabel ( download )
- Lingkaran ( download )
- Pangkat Tak Sebenarnya ( download )
- Prisma dan Limas ( download )
- Relasi dan Fungsi ( download )
- Statistika ( download )
- Peluang ( download )
- Teorema Pythagoras ( download )
- Jambore Matematika I ( download )
- Jambore Matematika II ( download )
- Jambore Matematika III ( download )
- Latihan Ulum Smt 2 Kelas VII ( download )
- Latihan Ulum Smt 2 Kelas VIII ( download )
- Latihan Ulum Smt 2 Kelas IX ( download )
- Uji Coba Ujian Nasional Soal A ( download )
- Uji Coba Ujian Nasional Soal B ( download )
- Uji Coba Ujian Nasional Tahap I ( download )
- Ujian Nasional 2008/2009 ( download )
- Kompetisi Matematika ( download )
Kebijakan
- Permendiknas No.30 Tahun 2011 Download
- Permendiknas No.39 Tahun 2009 Download
- Permenpan No. 16 Tahun 2009 Lihat
- Permenpan No. 16 Tahun 2009 Download
- Kep. MenPan No. 84 Tahun 1993 Download
- Permen No. 75 Tahun 2009 Download
- Lampiran Permen No 75/2009 Download
- Permendiknas No. 22 Tahun 2006 ( SI ) Download
- Permendiknas No. 22 Tahun 2006 ( SKL ) Download
- Permendiknas No. 6 Tahun 2007 Download
- Permendiknas No. 24 Tahun 2007 Download
- Permendiknas No. 12 Tahun 2007 ( Pengawas) Download
- Permendiknas No. 12 Tahun 2007 (Lampiran) Download
- Permendiknas No. 13 Tahun 2007 (Kepala Sekolah) Download
- Permendiknas No. 13 Tahun 2007 (Lampiran) Download
- Permendiknas No. 16 Tahun 2007 (Kualifikasi Pendidikan ) Download
- Permendiknas No. 16 Tahun 2007 (Lampiran) Download
- Permendiknas No. 18 Tahun 2007 (Sertifikasi Guru) Download
- Panduan Penyusunan Sertifikasi Guru Download
- Permendiknas No. 19 Tahun 2007 (Pengelolaan) Download
- Permendiknas No. 20 Tahun 2007 (Penilaian) Download
- Permendiknas No. 20 Tahun 2007 (Power Point) Download
- Permendiknas No. 41 Tahun 2007 (S. Proses) Download
- Permendiknas No. 41 Tahun 2007 (Power Point ) Download
- Permendiknas No. 39 Tahun 2009 (Beban Kerja Guru) Download
- PP No. 74 Tahun 2008 (Guru) Download
The Mobius strip
I blogged many times about the Mobius strip, a fascinating object and superb to introduce mathematics to the uninitiated. Algebraic Geometry is the field of mathematics where they try ( more often do ) to catch these objects in polynomial equations. A quick browse ( or read ) of this PDF may give you an idea of the field.
http://data.imaginary-exhibition.com/IMAGINARY-Moebiusband-Stephan-Klaus.pdf
Found while surfing IMAGINARY.
http://data.imaginary-exhibition.com/IMAGINARY-Moebiusband-Stephan-Klaus.pdf
Found while surfing IMAGINARY.
Sabtu, 30 Oktober 2010
Silabus
Babak Semi Final Kompetisi Matematika 27
Kompetisi Matematika SMP ke-27 sudah memasuki Babak Semi Final. Pelaksanaan Kompetisi Matematika Babak Semi Final ini akan dilaksanakan di SMP Negeri 68 Jakarta.
Berikut peserta Kompetisi yang masuk ke Babak Semi Final :
Daftar Kompetisi yang masuk ke Babak Semi Final ( Download )
Berikut peserta Kompetisi yang masuk ke Babak Semi Final :
Daftar Kompetisi yang masuk ke Babak Semi Final ( Download )
Prakata
Selamat datang di Blog MGMP Matematika SMP DKI Jakarta. Blog ini terbentuk sejalan dengan tuntutan akan kemajuan Ilmu Teknologi dan Komunikasi.
Semoga dengan adanya Blog ini bisa menjembatani semua Guru Matematika SMP/Mts di DKI Jakarta sebagai sarana tukar informasi dan saling mengisi keterkaitan dengan peningkatan mutu Pembelajaran Matematika di DKI Jakarta.
Maju terus MGMP Matematika DKI Jakarta .......
Analytical function representing the Fibonacci series
The MST209 exam has a different format than MS221 and M208 have. In 2006, for example, the format was as follows:
Part A. 15 multiple-choice questions, 2 marks each = 30 points. ( 1 hour )
Part B. 8 questions, 5 marks each = 40 points. ( 1 hour 15 min )
Part C. 3 out of 7, 15 marks each = 45 points. ( 45 min )
Yes. Maximum score is 115. Scores above 100 are set to 100.
The exam looks doable. And again questions on eigenvalues and eigenvectors. That would be three in a row: MS221, M208 and MST209. Considering the fact that one can prove Binet's formula for the Fibonacci numbers with them it's worthwhile having it firm under your math-belt.
There is also an analytical function for the Fibonacci numbers which rounded, gives an exact Fibonacci number if the input variable is an integer. Here is the related math.
Let $F_n = F_{n-1} + F_{n-2}, F_0=0, F_1=1$, show that $Fa_n=\frac{1}{\sqrt{5}}e^{n \cdot \log{\phi}}$, where $\phi$ is the Golden Ratio or $\frac{1+\sqrt{5}}{2}$. ( Round $Fa_n$ to get $F_n$. )
If we define the elements $F_{n}$ and $F_{n+1}$ as the vector $s_n= \left(
\begin{array}{c}
F_{n+1}\\
F_{n}
\end{array}
\right)$
then $F_n$ simply becomes
$F_n= \left(
\begin{array}{cc}
1 & 1\\
1 & 0
\end{array}
\right)^n
\cdot s_{0}$.
We can calculate the power of a matrix by diagonalizing the matrix. And this is where eigenvalues and vectors come in. If $\lambda_1, \lambda_2$ are eigenvectors with respective eigenvectors $E= \left( e_1, e_2 \right)$ we get $F_n= E^{-1}
\cdot
\left(
\begin{array}{cc}
\lambda_1^n & 0\\
0 & \lambda_2^n
\end{array}
\right)
\cdot
E
\cdot s_{0}$
The eigenvectors are the roots of the characteristic equation $\left|
\begin{array}{cc}
1-\lambda & 1\\
1 & -\lambda
\end{array} \right| = 0$ and are thus $\frac{1}{2} + \frac{1+\sqrt{5}}{2}$ and $\frac{1}{2} - \frac{1+\sqrt{5}}{2}$.
( TO BE CONTINUED ... )
Part A. 15 multiple-choice questions, 2 marks each = 30 points. ( 1 hour )
Part B. 8 questions, 5 marks each = 40 points. ( 1 hour 15 min )
Part C. 3 out of 7, 15 marks each = 45 points. ( 45 min )
Yes. Maximum score is 115. Scores above 100 are set to 100.
The exam looks doable. And again questions on eigenvalues and eigenvectors. That would be three in a row: MS221, M208 and MST209. Considering the fact that one can prove Binet's formula for the Fibonacci numbers with them it's worthwhile having it firm under your math-belt.
There is also an analytical function for the Fibonacci numbers which rounded, gives an exact Fibonacci number if the input variable is an integer. Here is the related math.
Let $F_n = F_{n-1} + F_{n-2}, F_0=0, F_1=1$, show that $Fa_n=\frac{1}{\sqrt{5}}e^{n \cdot \log{\phi}}$, where $\phi$ is the Golden Ratio or $\frac{1+\sqrt{5}}{2}$. ( Round $Fa_n$ to get $F_n$. )
If we define the elements $F_{n}$ and $F_{n+1}$ as the vector $s_n= \left(
\begin{array}{c}
F_{n+1}\\
F_{n}
\end{array}
\right)$
then $F_n$ simply becomes
$F_n= \left(
\begin{array}{cc}
1 & 1\\
1 & 0
\end{array}
\right)^n
\cdot s_{0}$.
We can calculate the power of a matrix by diagonalizing the matrix. And this is where eigenvalues and vectors come in. If $\lambda_1, \lambda_2$ are eigenvectors with respective eigenvectors $E= \left( e_1, e_2 \right)$ we get $F_n= E^{-1}
\cdot
\left(
\begin{array}{cc}
\lambda_1^n & 0\\
0 & \lambda_2^n
\end{array}
\right)
\cdot
E
\cdot s_{0}$
The eigenvectors are the roots of the characteristic equation $\left|
\begin{array}{cc}
1-\lambda & 1\\
1 & -\lambda
\end{array} \right| = 0$ and are thus $\frac{1}{2} + \frac{1+\sqrt{5}}{2}$ and $\frac{1}{2} - \frac{1+\sqrt{5}}{2}$.
( TO BE CONTINUED ... )
Mathematical Deceptions - ( Coast to Coast AM 21-oct-2010 )
C2CAM had a 3 hour during interview with Prof. C. Seife on mathematics
For subscribers: http://www.coasttocoastam.com/show/2010/10/21
Otherwise: http://www.demonoid.com/files/details/2427492/2340388/ ( Opera Browser has a built-in BitTorrent Client )
Prof. Charles Seife discussed the art of using pure mathematics for impure ends. He used the term "proofiness," (an analogue of Stephen Colbert's term "truthiness") to describe how people use numbers to prove things that they believe in their hearts are true, even if they're not factually true. People often lie in polls to make themselves feel better, he reported. For instance, in surveys men will typically overestimate the number of sexual partners they have had, while women will underestimate the number.
Advertising often uses numbers fabricated out of whole cloth, like saying a moisturizer delivers 70% more moisture in every drop. Ads are just "larded with...completely meaningless numbers that are supposedly backed by some sort of research which is either dubious or non-existent," he declared. Politicians sometimes manipulate the scale of graphs to make it appear like a dramatic effect or change is occurring, such as with tax cuts or budgets. Al Gore, in his film An Inconvenient Truth, exaggerated climate projections, as a way to further his agenda, Seife added.
Numbers are often inflated to make a person or organization seem more important, such as the number of people in attendance at a rally, or the circulation of readers for newspapers and magazines, he noted. Seife also discussed various developments in science, such as the Large Hadron Collider experiments at CERN. If "a certain pattern of missing energy turns up, it could be a very good sign that we have found another dimension beyond our own," he reflected.
For subscribers: http://www.coasttocoastam.com/show/2010/10/21
Otherwise: http://www.demonoid.com/files/details/2427492/2340388/ ( Opera Browser has a built-in BitTorrent Client )
Jumat, 29 Oktober 2010
Bernouilli equations
I watched approximately half of video lecture 4 of 18.03 today. Topic of lecture 4 is solving differential equations by direct or indirect substitution.
Direct and indirect substitution originates from Calculus Integration, I suppose. Take for example, the integral:
$$\int{x \sin(x^2)\ dx}$$
requires the direct substitutions $y=x^2, dy=2x \ dx$ to solve. However, the integral
$$\int{\frac{1}{\sqrt{1-x^2}}\ dx}$$
requires the indirect substitution $x=sin(u), dx=cos(u) \ du$ to solve.
A Bernoulli equation is a DE of type:
$$y' = p(x) \cdot y + q(x) \cdot y^{n}$$
Rearrange as follows:
$$\frac{y'}{y^{n}} = p(x) \cdot \frac{y}{y^{n}} + q(x) \cdot \frac{y^{n}}{y^{n}}$$
$$\frac{y'}{y^{n}} = p(x) \cdot \frac{1}{y^{n-1}} + q(x) $$
Now substitute $v=\frac{1}{y^{n-1}}$, and thus $v' = (1-n) \frac{y'}{y^{n}}$:
$$\frac{v'}{1-n} = p(x) \cdot v + q(x)$$
$$v' + (n-1)p(x) \cdot v = (1-n)q(x) $$
The last equation is a linear ODE in standard form.
Direct and indirect substitution originates from Calculus Integration, I suppose. Take for example, the integral:
$$\int{x \sin(x^2)\ dx}$$
requires the direct substitutions $y=x^2, dy=2x \ dx$ to solve. However, the integral
$$\int{\frac{1}{\sqrt{1-x^2}}\ dx}$$
requires the indirect substitution $x=sin(u), dx=cos(u) \ du$ to solve.
A Bernoulli equation is a DE of type:
$$y' = p(x) \cdot y + q(x) \cdot y^{n}$$
Rearrange as follows:
$$\frac{y'}{y^{n}} = p(x) \cdot \frac{y}{y^{n}} + q(x) \cdot \frac{y^{n}}{y^{n}}$$
$$\frac{y'}{y^{n}} = p(x) \cdot \frac{1}{y^{n-1}} + q(x) $$
Now substitute $v=\frac{1}{y^{n-1}}$, and thus $v' = (1-n) \frac{y'}{y^{n}}$:
$$\frac{v'}{1-n} = p(x) \cdot v + q(x)$$
$$v' + (n-1)p(x) \cdot v = (1-n)q(x) $$
The last equation is a linear ODE in standard form.
Pembahasan Deret Geometri
Kalau pada postingan sebelumnya saya menampilkan pembahasan deret aritmetika, maka kali ini lanjutannya adalah pembahasan deret geometri. Buat anda yang mau download, silahkan KLIK DISINI.
Recipe for solving linear first order ODE
As I blogged before I am going to make more notes, summaries and stuff and store everything in a plex in a Personal Brain database. The following note basically summarizes 18.03 lecture 3.
$$a(x) \cdot y' + b(x) \cdot y = c(x)$$
$$y' + p(x) \cdot y = q(x)$$
$$e^{\int{p(x) \ dx}} \cdot y' + p(x) e^{\int{p(x) \ dx}} \cdot y = e^{\int{p(x) \ dx}} q(x) $$
$$( e^{\int{p(x) \ dx}} \cdot y )'= e^{\int{p(x) \ dx}} q(x) $$
$$e^{\int{p(x) \ dx}} \cdot y= \int{e^{\int{p(x) \ dx}} q(x) \ dx} $$
$$y= \frac{\int{e^{\int{p(x) \ dx}} q(x) \ dx}}{e^{\int{p(x) \ dx}}} + \frac{C}{e^{\int{p(x) \ dx}}}$$
( Would need some explanations but as a personal note it is clear to me. )
$$a(x) \cdot y' + b(x) \cdot y = c(x)$$
$$y' + p(x) \cdot y = q(x)$$
$$e^{\int{p(x) \ dx}} \cdot y' + p(x) e^{\int{p(x) \ dx}} \cdot y = e^{\int{p(x) \ dx}} q(x) $$
$$( e^{\int{p(x) \ dx}} \cdot y )'= e^{\int{p(x) \ dx}} q(x) $$
$$e^{\int{p(x) \ dx}} \cdot y= \int{e^{\int{p(x) \ dx}} q(x) \ dx} $$
$$y= \frac{\int{e^{\int{p(x) \ dx}} q(x) \ dx}}{e^{\int{p(x) \ dx}}} + \frac{C}{e^{\int{p(x) \ dx}}}$$
( Would need some explanations but as a personal note it is clear to me. )
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