I was a student who has a goal to become a teacher. Among the lessons that I can from my small step to senior high school, I remember the most is like math. Because the integration between ideals and things that I like, then I strengthen myself, stick my ideals and desires to become a teacher of mathematics. But I do not want to become a mathematics teacher who always, but I must be a mathematics teacher who was amazing. Namely teachers who are global, a noble personality, mathematic experts in the field, has an ability that is capable of a global challenge (especially English). So I became a teacher not only has the ability of local, but global conception of teachers who are not override local capability. So that I can be inspiring teacher. Therefore, I entered college that has facilities such case, which later will be easier for me reach my dream of most people agree that it is glorious. So mathematic education is the right path to achieve that dream.
Learning science in mathematics and science education, with the convenience is a must if you want to become a good mathematics teacher. But that is not enough, there must be things that I have to dominating study and learn the English language. I have to learn the English language lessons for mathematic education.
A competence that I must be have of English for mathematic education are as follows:
1. I must have a clean soul. A good lesson and pure will not be embedded in a dirty soul.
2. I must have a spirit of abstinence give up and curiosity that high.
3. I must have the basic ability of the English language is adequate. This is quite important to measure the ability of basic English that I have so I know where I will start. In this case, the TOEFL can be a reference to find out how far the ability to speak English that I have.
4. I have to take a lot of vocabulary
5. I must have the courage to utter the English language use in daily life. This is important, so I used to use in the English language. Thus, I will be easy to use in teaching English.
6. I must be able to solve math problems by using the English language.
7. I need to know the basic philosophy of mathematic education.
8. I must have the ability to develop capabilities that are in me and I should be able to develop mathematics in the scientific, as well as I should be able to develop my ability in teaching mathematics. This can be a sentence in the so-called innovation of mathematic education. This includes contextual mathematic, Proofing a formula, etc.
Below is a sample math problem solved by using the English language:
HOW TO DETERMINE THE ABC FORMULA
To determine the ABC formula, we have had the common square equation, that is a times x to the power of 2 plus b times x plus c equals 0. Afterwards the equation is we alter in the form of perfect square equation, coefficient of x to the power of 2 turned into 1, so, the equation become x to the power of 2 plus open bracket b over a close bracket times x plus open bracket c over a close bracket equals 0. Than, left internode and joint right added with open square bracket b over open bracket 2 times a close bracket close square bracket to the power of 2, so, the equation become x to the power of 2 plus open bracket b over a close bracket times x plus open square bracket b over open bracket 2 times a close bracket close square bracket to the power of 2 plus open bracket c over a close bracket equals open square bracket b over open bracket 2 times a close bracket close square bracket to the power of 2. Than, alter x to the power of 2 plus open bracket b over a close bracket times x plus open square bracket b over open bracket 2 times a close bracket close square bracket to the power of 2 become open square bracket x plus open bracket b over 2 times a in bracket close bracket close square bracket to the power of 2, and move the internode c over a, so, the equation become open square bracket x plus open bracket b over 2 times a in bracket close bracket close square bracket to the power of 2 equals b to the power of 2 in bracket over 4 times open bracket a to the power of 2 close bracket plus c over a. than alter b to the power of 2 in bracket over 4 times open bracket a to the power of 2 close bracket plus c over a become open bracket b to the power of 2 minus 4 times a times c close bracket over open bracket 4 times open bracket a to the power of 2 close bracket. Than alter the mentioned equation become x plus open bracket b over 2 times a in bracket close bracket equals plus minus square root of open bracket b to the power of 2 minus 4 times a times c close bracket over 4 times a to the power of 2 close bracket. The last, move b over open bracket 2 times a close bracket to joint right, the equation become x equals negative b over 2 times a plus minus 1 over 2 times a times square root of open bracket b to the power of 2 minus 4 times a times c close bracket, so, x equals negative b plus minus square root of open bracket b to the power of 2 minus 4 times a times c close bracket over 2 times a.
When all have been met and traveled well, insya Allah, I can be inspiring teacher of mathematic education. I can be a teacher who has insight and has a global capability. Of course it can be achieved with patience, perseverance, prayer, and tawakal.
Senin, 01 Juni 2009
Senin, 06 April 2009
EXERCISE IN ENGLISH PART 2 LESSON BY RIZAL AHMAD 08301244039 PMNR08
1. NATURES OF LOGARITHM
a to the power of m times a to the power of n equals a to the power of m plus n in bracket.
a to the power of m over a to the power of n equals a to the power of m minus n in bracket.
log base a of b equals n equivalent b equals a to the power of n
example :
question : log base g of a times b in bracket equals…
answer :
log base g of a equals x equivalent a equals g to the power of x
log base g of b equals y equivalent b equals g to the power of y
a times b equals g to the power of x in bracket times g to the power of y in bracket
a times b equals g to the power of x plus y in bracket
log base g of a times b in bracket equals log base g of g to the power of x plus y in bracket equals x plus y in bracket times log base g of g. Note : log base g of g equals 1. So, log base g of a times b in bracket equals x plus y. So, log base g of a times b in bracket equals log base g of a plus log base g of b.
a over b in bracket equals g to the power of x in bracket over g to the power of y in bracket, equivalent a over b in bracket equals g to the power of x minus y in bracket, equivalent log base g of a over b in bracket equals x minus y in bracket, equivalent log base g of a over b in bracket equals log base g of a minus log base g of b.
log base g of b to the power of n in bracket equals log base g of a times a times a times a times a no limit in bracket equivalent log base g of a to the power of n in bracket equals n times log base g of a.
2. HOW TO FIND THE VALUE FROM PHI NUMBER
Calculating approach phi can be elaborated as follows. Since is ahead known that by the ratio of area of circle to its distance square and ratio circle the circle with its diameter is constant. But, initially not yet been known that second of the constanta is of equal. Ancient book use the different constanta to be second of the ratio. Calculation Phi draw attention since pre-christian epoch ( about 1650 SM, in ancient Egypt). Since then hitherto a lot of all saintis conducting calculation of either through analytic and also by using computer. In modern epoch now calculation phi have time to be made by one of test to measure sophisticated and also a logarithm.
Searching number phi got from measurement of area of circle that is open bracket 8 over 9 times d close bracket to the power of 2; by d is diameter, and d equals 2 times r; by r is radius. So that got by equation of area of circle (A) equals open bracket 8 over 9 times 2 times r close bracket to the power of 2, equivalent A equals 64 over 81 times 4 times r to the power of 2, equivalent A equals 256 over 81 times r to the power of 2, equivalent 3,16 times r to the power of 2. Considering formula look for the area of circle equals phi times r to the power of 2, so, value of phi is 3,16.
3. HOW TO DETERMINE THE ABC FORMULA
To determine the ABC formula, we have had the common square equation, that is a times x to the power of 2 plus b times x plus c equals 0. Afterwards the equation is we alter in the form of perfect square equation, coefficient of x to the power of 2 turned into 1, so, the equation become x to the power of 2 plus open bracket b over a close bracket times x plus open bracket c over a close bracket equals 0. Than, left internode and joint right added with open square bracket b over open bracket 2 times a close bracket close square bracket to the power of 2, so, the equation become x to the power of 2 plus open bracket b over a close bracket times x plus open square bracket b over open bracket 2 times a close bracket close square bracket to the power of 2 plus open bracket c over a close bracket equals open square bracket b over open bracket 2 times a close bracket close square bracket to the power of 2. Than, alter x to the power of 2 plus open bracket b over a close bracket times x plus open square bracket b over open bracket 2 times a close bracket close square bracket to the power of 2 become open square bracket x plus open bracket b over 2 times a in bracket close bracket close square bracket to the power of 2, and move the internode c over a, so, the equation become open square bracket x plus open bracket b over 2 times a in bracket close bracket close square bracket to the power of 2 equals b to the power of 2 in bracket over 4 times open bracket a to the power of 2 close bracket plus c over a. than alter b to the power of 2 in bracket over 4 times open bracket a to the power of 2 close bracket plus c over a become open bracket b to the power of 2 minus 4 times a times c close bracket over open bracket 4 times open bracket a to the power of 2 close bracket. Than alter the mentioned equation become x plus open bracket b over 2 times a in bracket close bracket equals plus minus square root of open bracket b to the power of 2 minus 4 times a times c close bracket over 4 times a to the power of 2 close bracket. The last, move b over open bracket 2 times a close bracket to joint right, the equation become x equals negative b over 2 times a plus minus 1 over 2 times a times square root of open bracket b to the power of 2 minus 4 times a times c close bracket, so, x equals negative b plus minus square root of open bracket b to the power of 2 minus 4 times a times c close bracket over 2 times a.
4. HOW TO PROOF A SQUARE ROOT OF 2 IS IRRATIONAL NUMBER
To prove the square root of 2 is irrational number, provable through contradiction verification. Verification of through contradiction at ancient Greek era is verification that square root of 2 representing irrational number ( cannot be expressed by as integer comparison). This statement is provable by assuming on the contrary that square root of 2 is rational number, so that can be expressed by as comparison of integer a divided by b in bracket in simplest fraction. But if a divided by b in bracket equals square root of 2, hence a times 2 equals 2 times b times 2. This means a times 2 is even number. Because square from anomalous number not possible to be even, hence a is even number. Because a divided by b in bracket is simplest fraction of anomalous sure b ( even divided even fraction cause still can be made moderate). But because a is even number ( assume the its 2 times r meaning is a times 2 open bracket 4 times r times 2) is fold number 4, and b times 2 is fold number 2 ( even). Matter of this means b also represent the even number, and this represent the contradiction to previous conclusion that anomalous sure b. Because assumption of early that square root of two is rational result the happening of contradiction, the assumption wrong surely, and denied ( that square root of 2 is irrational) representing real correct statement.
a to the power of m times a to the power of n equals a to the power of m plus n in bracket.
a to the power of m over a to the power of n equals a to the power of m minus n in bracket.
log base a of b equals n equivalent b equals a to the power of n
example :
question : log base g of a times b in bracket equals…
answer :
log base g of a equals x equivalent a equals g to the power of x
log base g of b equals y equivalent b equals g to the power of y
a times b equals g to the power of x in bracket times g to the power of y in bracket
a times b equals g to the power of x plus y in bracket
log base g of a times b in bracket equals log base g of g to the power of x plus y in bracket equals x plus y in bracket times log base g of g. Note : log base g of g equals 1. So, log base g of a times b in bracket equals x plus y. So, log base g of a times b in bracket equals log base g of a plus log base g of b.
a over b in bracket equals g to the power of x in bracket over g to the power of y in bracket, equivalent a over b in bracket equals g to the power of x minus y in bracket, equivalent log base g of a over b in bracket equals x minus y in bracket, equivalent log base g of a over b in bracket equals log base g of a minus log base g of b.
log base g of b to the power of n in bracket equals log base g of a times a times a times a times a no limit in bracket equivalent log base g of a to the power of n in bracket equals n times log base g of a.
2. HOW TO FIND THE VALUE FROM PHI NUMBER
Calculating approach phi can be elaborated as follows. Since is ahead known that by the ratio of area of circle to its distance square and ratio circle the circle with its diameter is constant. But, initially not yet been known that second of the constanta is of equal. Ancient book use the different constanta to be second of the ratio. Calculation Phi draw attention since pre-christian epoch ( about 1650 SM, in ancient Egypt). Since then hitherto a lot of all saintis conducting calculation of either through analytic and also by using computer. In modern epoch now calculation phi have time to be made by one of test to measure sophisticated and also a logarithm.
Searching number phi got from measurement of area of circle that is open bracket 8 over 9 times d close bracket to the power of 2; by d is diameter, and d equals 2 times r; by r is radius. So that got by equation of area of circle (A) equals open bracket 8 over 9 times 2 times r close bracket to the power of 2, equivalent A equals 64 over 81 times 4 times r to the power of 2, equivalent A equals 256 over 81 times r to the power of 2, equivalent 3,16 times r to the power of 2. Considering formula look for the area of circle equals phi times r to the power of 2, so, value of phi is 3,16.
3. HOW TO DETERMINE THE ABC FORMULA
To determine the ABC formula, we have had the common square equation, that is a times x to the power of 2 plus b times x plus c equals 0. Afterwards the equation is we alter in the form of perfect square equation, coefficient of x to the power of 2 turned into 1, so, the equation become x to the power of 2 plus open bracket b over a close bracket times x plus open bracket c over a close bracket equals 0. Than, left internode and joint right added with open square bracket b over open bracket 2 times a close bracket close square bracket to the power of 2, so, the equation become x to the power of 2 plus open bracket b over a close bracket times x plus open square bracket b over open bracket 2 times a close bracket close square bracket to the power of 2 plus open bracket c over a close bracket equals open square bracket b over open bracket 2 times a close bracket close square bracket to the power of 2. Than, alter x to the power of 2 plus open bracket b over a close bracket times x plus open square bracket b over open bracket 2 times a close bracket close square bracket to the power of 2 become open square bracket x plus open bracket b over 2 times a in bracket close bracket close square bracket to the power of 2, and move the internode c over a, so, the equation become open square bracket x plus open bracket b over 2 times a in bracket close bracket close square bracket to the power of 2 equals b to the power of 2 in bracket over 4 times open bracket a to the power of 2 close bracket plus c over a. than alter b to the power of 2 in bracket over 4 times open bracket a to the power of 2 close bracket plus c over a become open bracket b to the power of 2 minus 4 times a times c close bracket over open bracket 4 times open bracket a to the power of 2 close bracket. Than alter the mentioned equation become x plus open bracket b over 2 times a in bracket close bracket equals plus minus square root of open bracket b to the power of 2 minus 4 times a times c close bracket over 4 times a to the power of 2 close bracket. The last, move b over open bracket 2 times a close bracket to joint right, the equation become x equals negative b over 2 times a plus minus 1 over 2 times a times square root of open bracket b to the power of 2 minus 4 times a times c close bracket, so, x equals negative b plus minus square root of open bracket b to the power of 2 minus 4 times a times c close bracket over 2 times a.
4. HOW TO PROOF A SQUARE ROOT OF 2 IS IRRATIONAL NUMBER
To prove the square root of 2 is irrational number, provable through contradiction verification. Verification of through contradiction at ancient Greek era is verification that square root of 2 representing irrational number ( cannot be expressed by as integer comparison). This statement is provable by assuming on the contrary that square root of 2 is rational number, so that can be expressed by as comparison of integer a divided by b in bracket in simplest fraction. But if a divided by b in bracket equals square root of 2, hence a times 2 equals 2 times b times 2. This means a times 2 is even number. Because square from anomalous number not possible to be even, hence a is even number. Because a divided by b in bracket is simplest fraction of anomalous sure b ( even divided even fraction cause still can be made moderate). But because a is even number ( assume the its 2 times r meaning is a times 2 open bracket 4 times r times 2) is fold number 4, and b times 2 is fold number 2 ( even). Matter of this means b also represent the even number, and this represent the contradiction to previous conclusion that anomalous sure b. Because assumption of early that square root of two is rational result the happening of contradiction, the assumption wrong surely, and denied ( that square root of 2 is irrational) representing real correct statement.
EXPRESSING THE VIDEO WHICH I HAVE SEEN IN ENGLISH PART 2 LESSON BY RIZAL AHMAD 08301244039 PMNR08
VIDEO 1
DO YOU BELIEVE
After seeing video entitling do you believe, I embrace some of words said by the remarkable speaker is which still occupy the class of fifth elementary school
Do you believe?
I can do anything, dream anything, and become anything.
I can do anything, dream anything, and become anything because you believe me.
Let’s me ask you a question that’s easy.
Do you believe on my classmate.
Do you believe that every singles can graduate where classmate, school, and collage.
You better, because next week, I join with your school.
Believe yourself, trust yourself, and mean yourself.
Because, we need you.
Please, believe yourself!
VIDEO 2
WHAT YOU KNOW ABOUT MATH
There's a lot of existing subject mater is which is the included in coverage of mathematics lesson. From the video, only mentioning just some of items or matter any kind of learned in mathematics study. There are some significant figure in math, that is the equals sign, the of plus sign, the multiplication sign, and the division sign. In mathematics there'is also ln open bracket x close bracket of is so-called number natural. then limit x come near do not till. And there's also how to make moderate a function. Others there's also lesson of trigonometry etc., there's also form of the graph of sine, and graph of exponential function.
VIDEO 3
SOLVING PROBLEM GRAPH
Let he function f be defined by f open bracket x close bracket equals x plus 1, if 2 times f open bracket p close bracket equals 20, what is the value of f open bracket 3 times p close bracket.
What is f when x equals 3 times p?
f open bracket x close bracket equals x plus 1, equivalent 2 times f open bracket p close bracket equals 20, equivalent f open bracket p close bracket equals p plus 1, equivalent p plus 1 equals 10, equivalent p equals 9. Insert p equals 9 into x equals 3 times p, so, x equals 3 times 9, x equals 27. f open bracket 27 close bracket equals x plus 1, f open bracket 27 close bracket equals 27 plus 1, f open bracket 27 close bracket equals 28.
In the x times y co-ordinate plane, the graph of x equals y to the power of 2 minus 4 intersects line l at open bracket o comma p close bracket and open bracket s comma t close bracket.
x equals y to the power of 2 minus 4,
line l : m equals open bracket y2 minus y1 close bracket over open bracket x2 minus x1 close bracket equals open bracket t minus p close bracket over open bracket s minus o close bracket.
make the assistive dot, if x equals o hence y equals p, and if x equals s hence y equals t.
hence its graph can be made.
VIDEO 4
PROPERTIES OF LOGARITHMS
log base b of x equals y equivalent b to the power of y equals x
notation : log base 10 of x equals log x; log base e of x equals ln x, ln x is natural logarithm.
Example :
1. log base 10 of 100 equals x, value of x is …
log base 10 of 100 equals x equivalent 10 to the power of x equals 100, equivalent 10 to the power 2 equals 100, so, the value of x is 2.
2. log base 2 of x equals 3, value of x is …
log base 2 of x equals 3 equivalent 2 to the power 3 equals x, equivalent 8 equals x, so, the value of x is 8.
3. log base 7 of open bracket 1 over 49 close bracket equals x, value of x is …
log base 7 of 1 over 49 equals x, equivalent 7 to the power of x equals 1 over 49, equivalent 7 to the power of x equals 1 over open bracket 7 to the power 2 close bracket, equivalent 7 to the power of x equals 7 to the power of negative 2, so, the value of x is negative 2.
log base b of m times n equals log base b of m base b plus log n
log base b of m over n equals log base b of m minus log base b of n
log base b of x to the power of n equals n times log base b of x
expand :
log base 3of open bracket x to the power of 2 times open bracket y plus 1 close bracket over z to the power of 3 close bracket,
equivalent log base 3 of open bracket x to the power of 2 times open bracket y plus 1 close bracket close bracket minus log base 3 of 2 to the power of 3,
equivalent log base 3 of x to the power 2 plus log base 3 of open bracket y plus 1 close bracket minus log base 3 of z to the power of 3.
VIDEO 5
GRAPH OF A RATIONAL FUNCTION
can have discontinuities
has a polynomial in the dominator
off limit
f open bracket x close bracket equals open bracket x plus 2 close bracket over open bracket x minus close bracket, when x equals 1, hence f open bracket x close bracket equals 3 over 0, that’s no good, bad, bad, bad.
Bad choice, break in function graph, insert x equals 0, hence f open bracket 0 close bracket equals open bracket 0 plus 2 close bracket over open bracket 0 minus 1 close bracket (rational). Insert x equals 1, hence f open bracket 1 close bracket equals open bracket 1 plus 2 close bracket over open bracket 1 minus 1 close bracket, equivalent 3 over 0(no rational).
Break discontinuity
Rational function don’t always work this way
Rational function denominator can be zero
Polynomial (smooth unbroken curve)
There is no value for the function
Break in the graph
Missing point on the graph
y equals x to the power of 2 minus x minus 6 in bracket over x minus 3, if we insert x equals 3, hence the graph is not possible, not feasible, and not allowed. This is missing point syndrome.
to overcome it, factor top and bottom
y equals open bracket x minus 3 close bracket times open bracket x plus 2 close bracket in square bracket over open bracket x minus 3 close bracket, so that y equals x plus 2, so that if we insert x equals 3, y equals 3 plus 2 equals 5.
VIDEO 6
TRIGONOMETRY
There is a special triangle with angle is phi. To look for the sine, cosines or tangent from a the special triangle can use the way of knocking by heart its formula easier, that is soh cah toa; by o is opposite, that is length mark with lines in a the triangle which ahead time angle is phi, h is hypotenuse, that is hypotenuse from a the special triangle, and a is adjacent, that is side residing in side from angle phi. Intend the soh is sine of phi equals opposite over hypotenuse. And intend from cah is cosines equals adjacent over hypotenuse. And intend from toa is tangent equals opposite over adjacent.
example:
There is a triangle with the angle phi and opposite is equals 4, hypotenuse equals 5, and adjacent equals 3. Look for the value from sin phi, cosines phi, and tangent phi.
Soh; sinus phi equals opposite over hypotenuse, sinus phi equals 4 over 5.
Cah; cosines phi equals adjacent over hypotenuse, cosines phi equals 3 over 5.
Toa; tangent phi equals opposite over adjacent, tangent phi equals 4 over 3.
DO YOU BELIEVE
After seeing video entitling do you believe, I embrace some of words said by the remarkable speaker is which still occupy the class of fifth elementary school
Do you believe?
I can do anything, dream anything, and become anything.
I can do anything, dream anything, and become anything because you believe me.
Let’s me ask you a question that’s easy.
Do you believe on my classmate.
Do you believe that every singles can graduate where classmate, school, and collage.
You better, because next week, I join with your school.
Believe yourself, trust yourself, and mean yourself.
Because, we need you.
Please, believe yourself!
VIDEO 2
WHAT YOU KNOW ABOUT MATH
There's a lot of existing subject mater is which is the included in coverage of mathematics lesson. From the video, only mentioning just some of items or matter any kind of learned in mathematics study. There are some significant figure in math, that is the equals sign, the of plus sign, the multiplication sign, and the division sign. In mathematics there'is also ln open bracket x close bracket of is so-called number natural. then limit x come near do not till. And there's also how to make moderate a function. Others there's also lesson of trigonometry etc., there's also form of the graph of sine, and graph of exponential function.
VIDEO 3
SOLVING PROBLEM GRAPH
Let he function f be defined by f open bracket x close bracket equals x plus 1, if 2 times f open bracket p close bracket equals 20, what is the value of f open bracket 3 times p close bracket.
What is f when x equals 3 times p?
f open bracket x close bracket equals x plus 1, equivalent 2 times f open bracket p close bracket equals 20, equivalent f open bracket p close bracket equals p plus 1, equivalent p plus 1 equals 10, equivalent p equals 9. Insert p equals 9 into x equals 3 times p, so, x equals 3 times 9, x equals 27. f open bracket 27 close bracket equals x plus 1, f open bracket 27 close bracket equals 27 plus 1, f open bracket 27 close bracket equals 28.
In the x times y co-ordinate plane, the graph of x equals y to the power of 2 minus 4 intersects line l at open bracket o comma p close bracket and open bracket s comma t close bracket.
x equals y to the power of 2 minus 4,
line l : m equals open bracket y2 minus y1 close bracket over open bracket x2 minus x1 close bracket equals open bracket t minus p close bracket over open bracket s minus o close bracket.
make the assistive dot, if x equals o hence y equals p, and if x equals s hence y equals t.
hence its graph can be made.
VIDEO 4
PROPERTIES OF LOGARITHMS
log base b of x equals y equivalent b to the power of y equals x
notation : log base 10 of x equals log x; log base e of x equals ln x, ln x is natural logarithm.
Example :
1. log base 10 of 100 equals x, value of x is …
log base 10 of 100 equals x equivalent 10 to the power of x equals 100, equivalent 10 to the power 2 equals 100, so, the value of x is 2.
2. log base 2 of x equals 3, value of x is …
log base 2 of x equals 3 equivalent 2 to the power 3 equals x, equivalent 8 equals x, so, the value of x is 8.
3. log base 7 of open bracket 1 over 49 close bracket equals x, value of x is …
log base 7 of 1 over 49 equals x, equivalent 7 to the power of x equals 1 over 49, equivalent 7 to the power of x equals 1 over open bracket 7 to the power 2 close bracket, equivalent 7 to the power of x equals 7 to the power of negative 2, so, the value of x is negative 2.
log base b of m times n equals log base b of m base b plus log n
log base b of m over n equals log base b of m minus log base b of n
log base b of x to the power of n equals n times log base b of x
expand :
log base 3of open bracket x to the power of 2 times open bracket y plus 1 close bracket over z to the power of 3 close bracket,
equivalent log base 3 of open bracket x to the power of 2 times open bracket y plus 1 close bracket close bracket minus log base 3 of 2 to the power of 3,
equivalent log base 3 of x to the power 2 plus log base 3 of open bracket y plus 1 close bracket minus log base 3 of z to the power of 3.
VIDEO 5
GRAPH OF A RATIONAL FUNCTION
can have discontinuities
has a polynomial in the dominator
off limit
f open bracket x close bracket equals open bracket x plus 2 close bracket over open bracket x minus close bracket, when x equals 1, hence f open bracket x close bracket equals 3 over 0, that’s no good, bad, bad, bad.
Bad choice, break in function graph, insert x equals 0, hence f open bracket 0 close bracket equals open bracket 0 plus 2 close bracket over open bracket 0 minus 1 close bracket (rational). Insert x equals 1, hence f open bracket 1 close bracket equals open bracket 1 plus 2 close bracket over open bracket 1 minus 1 close bracket, equivalent 3 over 0(no rational).
Break discontinuity
Rational function don’t always work this way
Rational function denominator can be zero
Polynomial (smooth unbroken curve)
There is no value for the function
Break in the graph
Missing point on the graph
y equals x to the power of 2 minus x minus 6 in bracket over x minus 3, if we insert x equals 3, hence the graph is not possible, not feasible, and not allowed. This is missing point syndrome.
to overcome it, factor top and bottom
y equals open bracket x minus 3 close bracket times open bracket x plus 2 close bracket in square bracket over open bracket x minus 3 close bracket, so that y equals x plus 2, so that if we insert x equals 3, y equals 3 plus 2 equals 5.
VIDEO 6
TRIGONOMETRY
There is a special triangle with angle is phi. To look for the sine, cosines or tangent from a the special triangle can use the way of knocking by heart its formula easier, that is soh cah toa; by o is opposite, that is length mark with lines in a the triangle which ahead time angle is phi, h is hypotenuse, that is hypotenuse from a the special triangle, and a is adjacent, that is side residing in side from angle phi. Intend the soh is sine of phi equals opposite over hypotenuse. And intend from cah is cosines equals adjacent over hypotenuse. And intend from toa is tangent equals opposite over adjacent.
example:
There is a triangle with the angle phi and opposite is equals 4, hypotenuse equals 5, and adjacent equals 3. Look for the value from sin phi, cosines phi, and tangent phi.
Soh; sinus phi equals opposite over hypotenuse, sinus phi equals 4 over 5.
Cah; cosines phi equals adjacent over hypotenuse, cosines phi equals 3 over 5.
Toa; tangent phi equals opposite over adjacent, tangent phi equals 4 over 3.
Minggu, 29 Maret 2009
Essence of school mathematics and Nature of student of mathematics by Rizal Ahmad PMNR08 08301244039
In lecturing, Dr. Marsigit have explained about mathematics of school and nature of student of mathematics. I also read some reference which deal with above context, so that I which can catch from lecturing or from the coresponding reference shall be as follows.
Essence of school mathematics
Mathematics is pattern
Meaning mathematics can put in the way of the student to conduct the activity of invention and investigation of mathematics pattern and earn also push the student to find the existence of sequence, difference, comparison, and subdividing.
Mathematics is communications
Meaning mathematics own the function can push the student reason the importance of explaining the nature of mathematics, reading and writing mathematics and others which deal with student communications.
Mathematics is investigation
Mathematics can form the student become the student owning to feel the high desire in enquiring to estimate. Others can push the student find the structure and design mathematics.
Mathematics is problem solving
Mathematics can push the student think out the mathematics by using its own way. And most importantly is can push the student to think logical and own the ability and skill think problem solving.
Nature of student of math
Student needs motivation
To more to improving of herself belief of so that more of the spirit and so that in mathematics study felt to please. Others motivate also can make the student to more readily to face the mathematics problem of in front of. Strong motivation is not got from outside, but emerging from within herself of each individual or in this case student.
Student is unique
In this world, there no from each that individual is equal, though them is twin one egg even if. For example twin baby one egg born to a world of one in holding by right hand, and which is one is again holded by left hand.
Mathematics student not all have the pattern or way of finishing problem or way of learning same, but in each that individual differ and own unique each.
Student have a competence
Student have a competence in herself of each, but that interest have to be dug and sharpened by so that stand-out instruct the membership area from every student.
Student is contextually
Student have a ability or nature of contextually, meaning to learn from external circumstance or about. In study, student learn the circumstance from outside existing context matching with study learned.
Essence of school mathematics
Mathematics is pattern
Meaning mathematics can put in the way of the student to conduct the activity of invention and investigation of mathematics pattern and earn also push the student to find the existence of sequence, difference, comparison, and subdividing.
Mathematics is communications
Meaning mathematics own the function can push the student reason the importance of explaining the nature of mathematics, reading and writing mathematics and others which deal with student communications.
Mathematics is investigation
Mathematics can form the student become the student owning to feel the high desire in enquiring to estimate. Others can push the student find the structure and design mathematics.
Mathematics is problem solving
Mathematics can push the student think out the mathematics by using its own way. And most importantly is can push the student to think logical and own the ability and skill think problem solving.
Nature of student of math
Student needs motivation
To more to improving of herself belief of so that more of the spirit and so that in mathematics study felt to please. Others motivate also can make the student to more readily to face the mathematics problem of in front of. Strong motivation is not got from outside, but emerging from within herself of each individual or in this case student.
Student is unique
In this world, there no from each that individual is equal, though them is twin one egg even if. For example twin baby one egg born to a world of one in holding by right hand, and which is one is again holded by left hand.
Mathematics student not all have the pattern or way of finishing problem or way of learning same, but in each that individual differ and own unique each.
Student have a competence
Student have a competence in herself of each, but that interest have to be dug and sharpened by so that stand-out instruct the membership area from every student.
Student is contextually
Student have a ability or nature of contextually, meaning to learn from external circumstance or about. In study, student learn the circumstance from outside existing context matching with study learned.
Minggu, 22 Maret 2009
Difficult Words to Express Mathematical Ideas by Rizal Ahmad PMNR08 08301244039
I. Print Storming
30 difficult words from My friend,Samuel Afriando.
1. Cubic
2. Circle
3. Sphere
4. Cylinder
5. Width
6. Radius
7. Trapecium
8. Average
9. Resistance
10. Freezing point
11. Breaking strain
12. Diameter
13. Force
14. Rectangle
15. Square
16. Relation
17. Cross over
18. Inverse
19. Limit
20. Cube
21. Rectangular
22. Equals
23. Division
24. Minus
25. Multiplication
26. Cone
27. Hemisphere
28. Pyramid
29. Angle
30. Plus
II. Meaning and Application Difficult Words
1. Cubic
. Produced by multiplying length width and height.
. a . . . metre, having the shape of a cube; of a cube.
2. Circle
. (space enclosed by a) curved line, every point on which is the same distance from the centre
. Ring
. Move in a circle, especially in the air
. Draw a circle around something
3. Sphere
. Completely round solid shape
. Range of interests, activities, influence, etc.
4. Cylinder
. Long solid or hollow body with circular ends and straight sides
. Hollow tube in an engine, shaped like a cylinder, inside which the piston moves
5. Width
. Measurement from one side of something to the other; how wide something is
6. Radius
. (length of a) straigth line from the centre of a circle to the side
. Circular area measured from a central point
7. Trapecium
. Rectangle not be arranged
8. Average
. Result of adding several amounts together and dividing the total by the number of amounts
. Usual level
9. Resistance
. (action of) resisting something
. Opposing force
10. Freezing point
. Temperature at which a liquid, especially water, freezes
11. Breaking strain
12. Diameter
. Length of a straight line drawn from side to side throught the centre of a circle
13. Force
. Power or influence
. Authority
. Power that causes movement
ex: the force of gravity
14. Rectangle
. Flat foursided shape with four angles of 90`
15. Square
. Having four straight equal sides and four angles of 90`
. Forming an angle of 90`
. Equal to a square with sides of a stated length
ex: six metres square
square root number which when multiplied by itself gives a particular number
ex: the square root of 4 is 2
16. Relation
. Way in which two or more things are connected
17. Cross over
18. Inverse
. Opposite in amount or position to something else
. The direct opposite of something
19. Limit
. Point or line that may not or cannot be passed
20. Cube
. Solid figure with six equal square sides
. Result of multiplying a number by itself twice
. Multiply a number by itself twice
ex: 3 cubed is 27
21. Rectangular
. Adjective word frome rectangle
. Flat foursided shape with four angles of 90`
22. Equals
. The sane in size, number, value, etc.
. Be equal to something
23. Division
. Process or result of dividing or being divided
. Process of dividing numbers
24. Minus
. Preposition of less
ex: 15 minus 6 equals 9
25. Multiplication
. Multiply, add a number to itself the number of times that is mentioned
ex: 6 multiplied 5 is 30
26. Cone
. Solid body that narrows to a point from a circular flat base
27. Hemisphere
. One half of the earth
ex: the northern hemisphere
. Either half or the brain
. One half of sphere
28. Pyramid
. Structure with a square base and sloping sides meeting at a point, especially one built in ancient egypt
. Pile of object in the shape of a pyramid
29. Angle
. Space between two lines that meet
. Corner
. Point of view at an angle not straight
. Move or place something so that it is not straight or not directly facing something
30. Plus
. Preposition used when the two numbers or amounts mentioned are being added together
ex: one plus two is three
30 difficult words from My friend,Samuel Afriando.
1. Cubic
2. Circle
3. Sphere
4. Cylinder
5. Width
6. Radius
7. Trapecium
8. Average
9. Resistance
10. Freezing point
11. Breaking strain
12. Diameter
13. Force
14. Rectangle
15. Square
16. Relation
17. Cross over
18. Inverse
19. Limit
20. Cube
21. Rectangular
22. Equals
23. Division
24. Minus
25. Multiplication
26. Cone
27. Hemisphere
28. Pyramid
29. Angle
30. Plus
II. Meaning and Application Difficult Words
1. Cubic
. Produced by multiplying length width and height.
. a . . . metre, having the shape of a cube; of a cube.
2. Circle
. (space enclosed by a) curved line, every point on which is the same distance from the centre
. Ring
. Move in a circle, especially in the air
. Draw a circle around something
3. Sphere
. Completely round solid shape
. Range of interests, activities, influence, etc.
4. Cylinder
. Long solid or hollow body with circular ends and straight sides
. Hollow tube in an engine, shaped like a cylinder, inside which the piston moves
5. Width
. Measurement from one side of something to the other; how wide something is
6. Radius
. (length of a) straigth line from the centre of a circle to the side
. Circular area measured from a central point
7. Trapecium
. Rectangle not be arranged
8. Average
. Result of adding several amounts together and dividing the total by the number of amounts
. Usual level
9. Resistance
. (action of) resisting something
. Opposing force
10. Freezing point
. Temperature at which a liquid, especially water, freezes
11. Breaking strain
12. Diameter
. Length of a straight line drawn from side to side throught the centre of a circle
13. Force
. Power or influence
. Authority
. Power that causes movement
ex: the force of gravity
14. Rectangle
. Flat foursided shape with four angles of 90`
15. Square
. Having four straight equal sides and four angles of 90`
. Forming an angle of 90`
. Equal to a square with sides of a stated length
ex: six metres square
square root number which when multiplied by itself gives a particular number
ex: the square root of 4 is 2
16. Relation
. Way in which two or more things are connected
17. Cross over
18. Inverse
. Opposite in amount or position to something else
. The direct opposite of something
19. Limit
. Point or line that may not or cannot be passed
20. Cube
. Solid figure with six equal square sides
. Result of multiplying a number by itself twice
. Multiply a number by itself twice
ex: 3 cubed is 27
21. Rectangular
. Adjective word frome rectangle
. Flat foursided shape with four angles of 90`
22. Equals
. The sane in size, number, value, etc.
. Be equal to something
23. Division
. Process or result of dividing or being divided
. Process of dividing numbers
24. Minus
. Preposition of less
ex: 15 minus 6 equals 9
25. Multiplication
. Multiply, add a number to itself the number of times that is mentioned
ex: 6 multiplied 5 is 30
26. Cone
. Solid body that narrows to a point from a circular flat base
27. Hemisphere
. One half of the earth
ex: the northern hemisphere
. Either half or the brain
. One half of sphere
28. Pyramid
. Structure with a square base and sloping sides meeting at a point, especially one built in ancient egypt
. Pile of object in the shape of a pyramid
29. Angle
. Space between two lines that meet
. Corner
. Point of view at an angle not straight
. Move or place something so that it is not straight or not directly facing something
30. Plus
. Preposition used when the two numbers or amounts mentioned are being added together
ex: one plus two is three
Minggu, 22 Februari 2009
My Preparation in Participating Marsigit Lesson of English part II
by: Rizal Ahmad 08301244039 PMNR08 UNY
first, I say Bismillah and prayer,than straighting my intention in my spirit (soul) that all of my activities live in the world just for Allah swt. in order to, all of my activities shaded Allah swt.
Than, I prepare my self, to be a good attitude, good in knowledge, skills, and experience. And I believe my teacher that is Dr. Marsigit help me for that, espesialy in English courses.
Dr. Marsigit was gave a courses of how to communicate mathematics education in English, that is:
in communicate, there is a some manner to learn that, that is: to hear, to talk, to write, to read and to translate.
in mathematics, we must powering about Algebra, Arithmatics, Geometry, Calculus, statistics, Trigonometry, and Computer/ICT. espesialy, we must knew translated or vocabulary of mathematics courses.
in mathematics education, there is a theacing learning process, that is motivation, competence, indicators, evaluation, preparation, lesson plan, student worksheet, discussion, classical teaching, paradigm, theory, and constructious.
in Dr. Marsigit's lesson, there is a several assignment, that is paper, internet, and blog. And class discussions become a plan, but if we have many time for this.
self effort, there is a text book, active learn, and reference seeker.
first, I say Bismillah and prayer,than straighting my intention in my spirit (soul) that all of my activities live in the world just for Allah swt. in order to, all of my activities shaded Allah swt.
Than, I prepare my self, to be a good attitude, good in knowledge, skills, and experience. And I believe my teacher that is Dr. Marsigit help me for that, espesialy in English courses.
Dr. Marsigit was gave a courses of how to communicate mathematics education in English, that is:
in communicate, there is a some manner to learn that, that is: to hear, to talk, to write, to read and to translate.
in mathematics, we must powering about Algebra, Arithmatics, Geometry, Calculus, statistics, Trigonometry, and Computer/ICT. espesialy, we must knew translated or vocabulary of mathematics courses.
in mathematics education, there is a theacing learning process, that is motivation, competence, indicators, evaluation, preparation, lesson plan, student worksheet, discussion, classical teaching, paradigm, theory, and constructious.
in Dr. Marsigit's lesson, there is a several assignment, that is paper, internet, and blog. And class discussions become a plan, but if we have many time for this.
self effort, there is a text book, active learn, and reference seeker.
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