1. Find solution of differential equation y’= єy – αy3 , є>0 and α>0 !
Answer:
y’= єy – αy3 , є>0 and α>0
Rewriting equation in the standard from
y’= єy – αy3 ,…………….(1) (left and right side divided by y3)
» y’/ y3= єy/ y3 – αy3 /y3………….(2)
» (1/ y3)dy/dt = є/ y2 – α ……………………..(3)
Suppose: u = 1/ y2 = y-2
du=-2/ y3 so, -1/2 du = dy/ y3
substitution dy/ y3 and y-2 in equation (3), we have
(du/-2dt) – є u = -α…………….(4)
(-1/2) u’ – є u = -α ……………..(5)
To find this solution,we first compute µ(t)
Left and right side of (5) multiply by -2 µ(t), we have
µ(t) u’ + 2єu µ(t) = 2αµ(t) ………..(6)
µ(t) u’ + µ’(t) u = (µ(t)u)’ ………..(7)
so that,equation (6) =(7)
µ’(t)u = 2єu µ(t)
µ’(t) = 2є µ(t)
µ(t) = e ∫2єdt
µ(t) = e 2єt+ c ,e c= k, constant
we have µ(t) = e2єt
substitution µ(t) = in equation (7), we obtain
e2єtu’ + u e2єt = (e2єtu)’ ……………(8)
and therefor (e2єtu)’ = ∫ 2α e2єtdt
so we have u = (α + c є e-2єt) / є
where u = 1/ y2, it follow that
y2 = 1/ u
y = ± √(1/u)
y = ± √(є/(α + c є e-2єt))
The solution becomes y = ± √(є/(α + c є e-2єt))

2. Prove if {an} konvergen and {bn} divergen , { an + bn }divergen!
Answer:
{an} konvergen, suppose : {an} = 1/n
{bn} divergen, suppose {bn} = n, n2
a 1-5 , where n = 1-5
b 1-5 ,where n = 1-5
a 1-5 = 1/1 , ½, 1/3, ¼,1/5,……..,1/n (1)
b 1-5 = 1, 2, 3, 4, 5, ………….,n (2)
____________________________________ _____ +
2, 5/2, 7/3, 17/4, 26/5,……, (n + 1/n)
{a 1-5 + b 1-5} = 2, 5/2, 7/3, 17/4, 26/5
So, , { an + bn }divergen if {an} konvergen and {bn} divergen
3. In triangle the measure of side is 30, 17, and 26. Determine measure of each angles !
Answer:
C



A B
The three of angles which will counted measure is α, β, γ.
AC = 17, AB = 30, BC = 26
α is angle of CAB, β is angle of ABC, γ is angle of BCA
a. For determine measures α, using cosine
BC2 = AC2 + AB2 – 2 AC.BC cos α
262 = 172 + 302 – 2.17.30 cos α
Cos α = 0,5029
Using calculator or table , value of α = 59,800
b. For determine measure of β, using sine
BC /sin α = AC / sin β
26/ sin 59,80 = 17/ sin β
Sin β = (17. Sin 59, 800)/26
Sin β = 0,5623
β = 34,210
c. Counting measure of γ angle
γ = 1800- (α+β)
γ = 1800- (59,800+ 34,210)
γ = 85,990

4. Prove if C bisector of PAQ angle and AP =AQ . So, APC angle congruent with AQC angle!
Answer:
Triangle APQ, AP ≈ (congruent) AQ
AP = line segment af AP
Angle APC ≈ angle AQC
• AP ≈ AQ (measure of AP = AQ)
• Э C € PQ ( exsistence one point in line segment )
• Э AC ( exsistence line segment from two point)
• Э < QAC and < PAC ( existence of angles)
• Э ! AC
< QAC ≈ < PAC ( existence bisector of angle)
• ∆ QAC and ∆ PAC (existence teiangle)

AP ≈ AQ (given)
AC = AC ( reflektif)
< QAC ≈ < PAC
• ∆ QAC ≈ ∆ PAC (existence side – angle - side)
• Because ∆ QAC ≈ ∆ PAC,
So, PC ≈ QC
< PCA ≈ < QCA
< APC ≈ < AQC
So, we can prove that APC angle congruent with AQC angle

Assigment 5

1.Prove if C bisector of PAQ angle and AP =AQ . So, APC angle congruent with AQC angle!
Answer:
Triangle APQ, AP ≈ (congruent) AQ
AP = line segment af AP
Angle APC ≈ angle AQC
• AP ≈ AQ (measure of AP = AQ)
• Э C € PQ ( exsistence one point in line segment )
• Э AC ( exsistence line segment from two point)
• Э < QAC and < PAC ( existence of angles)
• Э ! AC
< QAC ≈ < PAC ( existence bisector of angle)
• ∆ QAC and ∆ PAC (existence teiangle)

AP ≈ AQ (given)
AC = AC ( reflektif)
< QAC ≈ < PAC
• ∆ QAC ≈ ∆ PAC (existence side – angle - side)
• Because ∆ QAC ≈ ∆ PAC,
So, PC ≈ QC
< PCA ≈ < QCA
< APC ≈ < AQC
So, we can prove that APC angle congruent with AQC angle

I am aware English is very IMPORTANT for communicating Mathematics at International Level

Now, I am Aware that English is very Important for Communicating Mathematics at International Level
English is considered to be the most important and common language of the world today. A great number of people understand and use English in every part of the world. Because of its importance I have chosen English as a second language after Indonesian.

English is the most useful language. Being good at English, we can travel to any place or any country we like. We shall not find it hard to make others understand what we wish to say.

In Fact, English has become the international language. Everywhere people talk English. Because of his popularity, innumerable books have been written in English. The English help to spread ideas and knowledge to all the corners of the world. There is no subject that cannot be learned in the English language. So one of my ways to improve my English is read books on variety of subjects: economics, philosophy, physiology, mostly books which linking to Mathematics such geometry, calculus,algebra, history of mathematics,etc.

To acquire correct and fluent English I should learn basic rules of English Grammar and practice speaking English. Like idiom:"Practice makes perfect". I should frequently listen to native speakers through videos, television, and radio. Taking action is better than waiting, even if it's just a small step.

Now I am aware that English is important. Being aware of the preeminence of the English language in every aspect of man's activity, I have been learning it great zeal and avidity. I remember the phrases: If you dream it, you can achieve it.

Now I am study in Mathematics study program. That's mean I should have communicated English for Mathematics. As we know, English has been used in all important meeting and conferences at International level. As a person who know English, easily get more knowledge from many parts of the world. It is for all these reasons that I want to improve my English. So...What will I do? The most frequently heard question in my life maybe "What will I do?". My answer to this question can start changes in my life. Then I am describing the how and why of what I will doing.

I will study more diligent to improve my English for Mathematics. That's the way to enter International level. Positive attitude and action will lead me to better life through Mathematics because Mathematics not isolated from part of our life.

Book Review "Mathematic for Junior High School Years IX" By Marsigit

Preface

First of all, reviewrs be grateful ot Allah SWT because we still given ability to review Mathematic for Junior High School IX by Marsigit. Thank’s to Mr. Marsigit who give us opportunity to review his book.We feel happy can review your’s book.
We get some benefit because review book. For examples,we know content of book,we know scheme of book, quality of book, method of writing, information and we get more knowledge.
We hope this review book useful. Especially to student and teachers of Junior High School before buy mathematic book.The book Mathematic for Junior High School by Marsigit is good,proper to use. The book completed two language (bilingual),Indonesian and English language. The content is complete,that use language don’t difficult to understand.
To release of the review book has been made possible due to the assistance and contributions of various people who cannot mention one by one. To all who involved in this preparation of this review book, I wouldlike to express my high appreciation.
Comment and suggestion,we always welcome. Thank you.





Scheme Of Book

My name is Ika Indriyati. I will review the book “Mathematic for Junior High School Years IX” by Mr. Marsigit from the aspect of Scheme of book. The scheme of book that is good. The book is attractive because of bilingual, Indonesian and English Language, so the student not only learn mathematic but also about English language in mathematic. Cover of this book, we can see a building that can let you know that the content of the book is in English. The book consist of five chapters. In each chapter served very interest,such us presented with full colour, so the students will be easier to understand and remember that content. Images that also provided good, even print the picture is also very clear and no picture is not clear or blur. The content of this book is presented detailedly and in face chapter accompanied by pictures. That picture is application of content it. In every chapter of this book is given basic competence. The scheme of book divided into definition, questions problem and problem solving is given in every chapter. And there are some examples of final exam, national exam. Then, in this book completed by more exercise,that’s variously.Finally,the book “Mathematic for Junior High School Years IX” by Mr. Marsigit is good, proper used by students and teachers in Junior High School Years IX.

By : IKA INDRIYATI
NIM :08305141020

English1

1.Factoring (memfaktorkan)
If a polynomial is written as a produc of other polynomials, then each of the latter polynomials is called a factor of original polinomial. The process of finding such a product is called factoring. Since x2-1 = (x + 1) (x -1), we know that x+1 and x-1 are factor of x2-1. The concept of factor can be extended to general algebraic expressions.Our main use for factoring,however,is in the simplification of expressions which are made up of polynomials.
Example : factor 6x2 -7x-3
Solution :If we write 6x2 -7x-3 = (ax + b)(cx + d), the product of a and c is 6, whereas the product of b and d is -3. Trying various possibilities, we arrive at the factorization 6x2 -7x-3 = (2x -3)(3x + 1)


2. Solution (penyelesaian)
Solution is a product or answer of questions.
Example : find solutions of 2x -5 = 3
Solution : 2x – 5 = 3
2x = 8
x = 4
Solution x = 4


3. Solution Set (himpunan solusi)
Solution set is a set with solutions. Symbol: HS = {….}.
Example : Find HS of 2x + 6 = 0 , x € R
Solution : 2x + 6 = 0
2x = -6
X = -3
HS = {-3}


4. System of Linier Equation (Sistem Persamaan Linier)
Linier equations with n variable x1, x2,…..,xn is a equations form:
a1x1 + a2x2 + …..+anxn = b,
with a1, a2, ….., an , b € R
System of linier equation with n variable x1, x2, ….., xn and m equations, is equations form:
a11x1 + a12x2 +…..a1jxj + …..+ a1nxn = b1
a21x1 + a22x2 +…..a2jxj + …..+ a2nxn = b2
am1x1 + am2x2 +…..amjxj + …+ amnxn = bm
with aij € R, i =1,2,….,m dan j = 1,2,….,n
Example :2x + 7y = 8
2x + 3y = 6


5. Cuadratic Form (bentuk form)
Quardratic form is a number degreed two (a2), a € R..
Example : Find quadratic form of 16
Solution :162 = 256


6. Tangent (garis singgung lingkaran)
If one distinct point are selected on the circumference of a circle is called tangent.
. tangent


7. Ekstrim of Point
General definition of the quadratic function is
f(x) = ax2 + bx + c
Ekstrim of point (-b/2a, -[b2- 4ac]/4a)


8. Base (bidang alas)
If we have a form, side in above is called base.
Example : base of conical is circle.


9. Completing the square….(melengkapkan kuadrat sempurna)
Completing the square is a way to solve equation system. We know that ax2 + bx + c = 0
May be written : a(x2 + b/a x+ c = 0
a(x + b/2a)2 + c – b2/4a = 0

11. Prove ( akan dibuktikan)
If we have theorm or something we must prove that.
Example : Theorm. For all a, b, c € R, a(b-c) = ab-ac
Proof : a(b-c) = a[b + (-c)] definition of subtraction
= ab + a(-c) distributive law
=ab – ac definition of subtraction


12. Inequality ( Pertidaksamaan)
If p and q are algebraic expressionsin variable x, the a statement of the form p < q or p > q, is called an inequality. If a true statement is obtained when x is replaced by a real number a,then a is called a solution of the inequality. Suppose p < q is an inequality, when p and q are algebraic expressions in a variable x. If r is another algebraic expressions in x, then
• The inequality p < q is equivalent to the inequality p + r < q + r
• If the value of r is positive for all value values of x , then the inequality p < q is equivalent to p r < q r
• If the value of r is negative for all value values of x , then the inequality p < q is equivalent to p r > q r
Example : solve 4x – 3 < 2x + 5
Solution :4x – 3 < 2x + 5
(4x – 3)+(3 – 2x)< (2x + 5)+(3 – 2x)
2x < 8
x < 4
The solution set HS = {x € R I x < 4}


13. Determinant (determinan)
Associated with each square matrix A is a number called the d eterminant of A. Determinants of square matrices can be use to solve system of linier equations when the number of equations is the same as the number of variables.
The determinant of matric a11 a12
a21 a22
|A| = a11 a22 - a12 a21

Example : Find |A| of 2 -1
4 -3
Solution |A| = (2)(-3) – (4)(-1) = -2


14. Polynomials (Suku banyak)
A polynomial is any sum of monomials. A polynomials in a variable x (with real coefficiens) as any sum of the form axk , where a is a real number and k is non negative integer. Thus any such polynomial can be written:
anxn + an-1xn-1+ ……+ a1x + a0
where n is a nonnegative integer and the coefficient a0, a1,….., an are real number. Each akxk is called a term of the polynomials.
Example : x4 + 16x3 – 3x2 + 19x + 90


15. Have any Solutions (memiliki banyak penyelesaian)
In system of linier equations,that have any solution if each linier equations have a proportional of element same.
ax + by = c
px + q y = r
Have any solution if a/p = b/q = c/r


17. Permutation (Permutasi)
If we have a collection (set) of object, then each different ordering or arrangement which can be obtained by taking some or all of the objects is called permutations. Consider the three letter A, B, C. All permutations of these letter which can be obtained by taking two time appear in the following list:
(A,B), (B,A), (C,A)
(A,C), (B,C), (C,B)

18. Complement of…(Sekawan dari….)
Example: complement of x is –x

19. Hipotenusa (sisi miring)
In triangle,hipotenusa is longest line.

21. Truncated cone (kerucut terpancung)
If conical cross section of two segment called is truncated cone.

22. Space diagonal (diagonal ruang)

23. Root of….(akar dari…)
Example: Root of 16 is 4.
24. The biggest Factor ( FPB)
Example: FPB of 6 and 8 is 2.
25. Titik potong (cutting point)

1. Penyelesaian: Solution
2. Sistem Persamaan linier: linier equation system
3. Bentuk kuadrat:cuadratic form
4. Garis singgung (lingkaran): tangent
5. Bidang alas : base (base of......)
6. Akan dibuktikan: proof
7. Determinan: determinan
8. Suku banyak: polinom
9. Memiliki solusi banyak: have any solution
10. Himpunan solusi: solution set
11. Turunan fungsi: derivatif
12. Permutasi: permutation
    
13. Luas permukaan: surface area of.........
14. Kerucut: conical
15. Diagonal ruang: space diagonal
16. Akar dari: root of........
17. Berlainan pihak: in other side
18. Sudut berseberangan: cross angle
    

Introduction to English One

Assalamu'alaikum wr. wb.
At first, I will to introduce my self. My name is Ika Indriyati, i'm from Kebumen city. Now, i'm school in Yogyakarta State University, Mathematic and Science Faculty, Mathematic Education, Mathematic Reguler 2008.

My teach English is Mr. Marsigit. He very care with his student. He teach english different,so I'm very happy learn english with him. Thank you Mr. Marsigit. I'm proud with you. Mr. Marsigit teach me to make blog. How to make a blog? At first,we should have an email in.....@gmail.com. And then must open software blogger in http://blogger.com. He also told about his experience in foreign country.He inspirate me to get a good person.

I get many experience after study with his. Mr. Marsigit is a good teacher. He make me to get spirit. He inspiration me. He sport me to wide think, to get high knowledge. We must have high motivation, good behavior, and good communicate. We study mathematic with continually, consistenly. Realy meaning study mathematic is high motivation, high spirit, and good understanding with mathematic. How tobe a good student? A good student have a responsibility, independent learner and cooperate.

At last,Mr. Marsigit said "You don't say: "Mathematic beyond me" because mathematic is your mind. We can't understand mathematic, before we love that.". He told mathematic a part your life. So you must understand your self,if you will understand mathematic.
What is we competent after learn mathematic in english?
1. We get skill in talking, speaking, hearing, writing, understanding,translating,discussing.
2. We get experience.
How to be a mathematcers?
We must have mathematical thinking. Three component mathematical thinking is
1. Mathematic attitude
2. Mathematic method
3. Mathematic content
Three component them related each other.

Mathematic is my life. Mathematic is your life. Mathematic is our life. Everytime we need mathematic. Everywhere we need mathematic.
I LOVE MATHEMATIC.....
"Mathematic in English."