Before..I wanna say thanks you to Dian Tri Handayani because without her assignment I cannot improve my English about mathematics. 1. What is Jangka in English? Jangka in English is pair of compasses. I wanna give the example image of jangka. Look at this




2. What s bilangan genap and bilangan ganjil in English? Bilangan genap is even number and for example 2, 4, 6, 8, 10 etc. If in the calculus, we can find what a kind of number detailly. Maybe with curve or line in cartesius koordinate. And then bilangan ganjil is odd number, this is an all of number except an even number. For example 1, 3, 5, 7, 9. etc.

3. What is Luas Bangun in English? we can say area fot the meaning of luas bangun.
The area of a figure measures the size of the region enclosed by the figure. This is usually expressed in terms of some square unit. A few examples of the units used are square meters, square centimeters, square inches, or square kilometers.
• Area of a Square
If l is the side-length of a square, the area of the square is l2 or l × l.
Example:
What is the area of a square having side-length 3.4?
The area is the square of the side-length, which is 3.4 × 3.4 = 11.56.
• Area of a Rectangle
The area of a rectangle is the product of its width and length.
Example:
What is the area of a rectangle having a length of 6 and a width of 2.2?
The area is the product of these two side-lengths, which is 6 × 2.2 = 13.2.
• Area of a Parallelogram
The area of a parallelogram is b × h, where b is the length of the base of the parallelogram, and h is the corresponding height.
Example:
What is the area of a parallelogram having a base of 20 and a corresponding height of 7?
The area is the product of a base and its corresponding height, which is 20 × 7 = 140.
• Area of a Trapezoid
If a and b are the lengths of the two parallel bases of a trapezoid, and h is its height, the area of the trapezoid is
1/2 × h × (a + b) .
The figure formed is a parallelogram having an area of h × (a + b), which is twice the area of one of the trapezoids.
Example:
What is the area of a trapezoid having bases 12 and 8 and a height of 5?
Using the formula for the area of a trapezoid, we see that the area is
1/2 × 5 × (12 + 8) = 1/2 × 5 × 20 = 1/2 × 100 = 50.
• Area of a Triangle
Consider a triangle with base length b and height h.
The area of the triangle is 1/2 × b × h.
The figure formed is a parallelogram with base length b and height h, and has area b × ×h.
This area is twice that of the triangle, so the triangle has area 1/2 × b × h.
Example:
What is the area of the triangle below having a base of length 5.2 and a height of 4.2?
The area of a triangle is half the product of its base and height, which is 1/2 ×5.2 × 4.2 = 2.6 × 4.2 = 10.92..

Area of a Circle

The area of a circle is Pi × r2 or Pi × r × r, where r is the length of its radius. Pi is a number that is approximately 3.14159.
Example:

What is the area of a circle having a radius of 4.2 cm, to the nearest tenth of a square cm? Using an approximation of 3.14159 for Pi, and the fact that the area of a circle is Pi × r2, the area of this circle is Pi × 4.22 3.14159 × 4.22 =55.41…square cm, which is 55.4 square cm when rounded to the nearest tenth.


4. What is keliling bangun in English?
Round about form...

5. What is nilai ekstrim in English? nilai estrim is ekstrim value

We can know about it in calculus. If in calculus, we can know nilai tertinggi or the the top of curve with ekstrim value.

6. What is nilai mutlak in English?

Nilai mutlak is absolute value. We can know about it also in calculus for example the absolute value from -1 is 1 While if in matlab, we can write "abs" so we can know the absolute value directly.

7. What is Integral tentu in English? Integral tentu in English is a certain integral.

8. What is Integral tak tentu? Integral tak tentu in English is a uncertain integral

For example....
Power of x.
xn dx = x(n+1) / (n+1) + C
(n -1) Proof
1/x dx = ln|x| + C

Exponential / Logarithmic
ex dx = ex + C
Proof
bx dx = bx / ln(b) + C
Proof, Tip!

ln(x) dx = x ln(x) - x + C
Proof

Trigonometric
sin x dx = -cos x + C
Proof
csc x dx = - ln|CSC x + cot x| + C
Proof

COs x dx = sin x + C
Proof
sec x dx = ln|sec x + tan x| + C
Proof

tan x dx = -ln|COs x| + C
Proof
cot x dx = ln|sin x| + C
Proof

Trigonometric Result
COs x dx = sin x + C
Proof
CSC x cot x dx = - CSC x + C
Proof

sin x dx = COs x + C
Proof
sec x tan x dx = sec x + C
Proof

sec2 x dx = tan x + C
Proof
csc2 x dx = - cot x + C
Proof

Inverse Trigonometric
arcsin x dx = x arcsin x + (1-x2) + C

arccsc x dx = x arccos x - (1-x2) + C

arctan x dx = x arctan x - (1/2) ln(1+x2) + C

Inverse Trigonometric Result

dx
________________________________________
(1 - x2)
= arcsin x + C


dx
________________________________________
x (x2 - 1)
= arcsec|x| + C


dx
________________________________________1 + x2 = arctan x + C

Useful Identities
arccos x = /2 - arcsin x
(-1 <= x <= 1)
arccsc x = /2 - arcsec x
(|x| >= 1)
arccot x = /2 - arctan x
(for all x)

Hyperbolic
sinh x dx = cosh x + C
Proof
csch x dx = ln |tanh(x/2)| + C
Proof

cosh x dx = sinh x + C
Proof
sech x dx = arctan (sinh x) + C
tanh x dx = ln (cosh x) + C
Proof
coth x dx = ln |sinh x| + C
Proof


9. What is kuadrat in English?kuadrat in English is qudrate...
Fo example the quadrate of 4 is 16

10. What is lebih besar atau sama dengan in English?lebih besar ata sama dengan in English is bigger or equal..( >= )
11. What is akar in English?
Akar in English is root. Root in matematika is the antonym of quadrate. For example the root of 16 is 4. And the root n Biologi is the part of tree.
12. What is sumbu simetri inEnglish?Sumbu simetri in English is which of simetrims.
13. What is koordinat kartesius in English? Coordinate cartesius..
14. What is logika and himpunan? mix ang logical is himpunan dan logika..
This is one of subbab which studied in logical.
DISJUNGSI, CONJUNTION, IMPLICATION, BIIMPLIKASI AND
NEGASINYA
Occasionally, we are required to make a statement or menegasikan new indicate disavowal of the statement above, using perakit "Not" or "no". In addition, they must combine the two statements or
using more perakit "or", "and", "If ... then ....", and "if ...And only if .... ", known in mathematics as a conjunction, disjungsi, the implicationsand biimplikasi. This section will discuss these perakit-perakit
1.Negasi
If p is the "East Java capital of Surabaya.", Then negasi or from ingkaranstatement p is the p: "Singapore is not the capital of East Java." or"It is not true that the East Java capital of Surabaya.".
From the above examples seem clear that p is a correct statement of value Surabaya because in fact the capital of East Java.

2. Conjunction
Conjunction is a compound statement that uses perakit "and".
For example, Adi following statement:
"Fahmi eating rice and drinking coffee."The statement ekivalen with single following two statements: "Fahmi eatrice. "and" Fahmi drinking coffee. "
In the process of learning in the classroom, give the opportunity for students toask themselves, in which case the above statement Adi valuable correct and valuable in the case where one of four in the following cases,
namely:
(1) Fahmi the right to eat rice and he also drank coffee,
(2) Fahmi eat rice, but it does not
drinking coffee,
(3) Fahmi did not eat rice, but he drank coffee, and (4) does not Fahmi
eating rice and he does not drink coffee.:

In the first case, Fahmi is correct to eat rice and he also drank coffee. In cases like this, you probably will not say Adi earlier statement valuable one. The reason, according to earlier statements Adi with reality. In the case of second, Fahmi eat rice, but he does not drink coffee. In this case, of course you will that compound statement earlier Adi valuable because even if one Fahmi have to eat rice, but he does not drink coffee, as stated Adi.
Analogoushence, in the third case, Fahmi not eating rice, although he is drinking coffee. As the two earlier cases, you will read that statement compound Adi. Mentioned as a valuable Fahmi did not eat rice as stated Adi. Fahmi that eating rice and drinking coffee. Finally, the fourth case, not Fahmi eating rice and he does not drink coffee. In this case you will read that Adi compound statement before any value because there is no congruence between the expressed by the fact that indeed.
3. Disjungsi
Disjungsi is a compound statement that uses perakit "or".
For example, Adi following statement: "Fahmi eat rice or drink coffee." Now,to ask yourself, in which case the above statement will be Adi correct value in the following four cases, namely:
(1) Fahmi is correct to eat rice and he also drank coffee,
(2) Fahmi eat rice, but he does not drink coffee,
(3) Fahmi do not eat rice, but he drank coffee, and
(4) Fahmi did not eat rice and it does not drinking coffee.
In the first case, Fahmi is correct to eat rice and he also drank coffee. In cases like this, you probably will not say Adi earlier statement valuable one, as Adi earlier statement in accordance with reality. In the case of second, Fahmi eat rice, but he does not drink coffee. In this case, of course you will that compound statement earlier Adi value is correct because Fahmi correct eating rice, although he does not drink coffee, as stated Adi.
While in the third case, Fahmi not eat rice, but he drank coffee. As the two earlier cases, you will read that statement compound Adi correct value before because Fahmi not even eat rice, but he is drinking coffeeas stated Adi. Finally, the fourth case, not eating Fahmirice, and he does not drink coffee. In this case you will read that statementAdi valuable compound earlier because no one conformity between the stated with the fact that indeed. He says Fahmi eat rice or drink coffee, but the fact is, Fahmi not do so.
4. Implications
Suppose there are two statements p and q. Often come to the attention of scientists and is matematikawan show or prove that, if the p value will lead to correct q value is also true. To achieve these desires,diletakkanlah word "If" statement before the first ago placed the word "then" in statements between the first and second statements, so that a statement obtained compound called implications, conditional statements, conditional orhypothetical with notation "⇒" like this:
p ⇒ q
The above notation can be read with:
1) If p then q,
2) q if p,
3) p is a sufficient condition for q, or
4) q is a necessary condition for p.
Implication p ⇒ q is a compound of the most difficult to understand theSMU students. To help students understand the complex implications, and Mr. and Mrs. Teacher can start the learning process with berceritera
Adi says that the plural of the following:
If rainy days then I (Adi) bring an umbrella.In this case dimisalkan:
p: Day rain.
q: Adi bring an umbrella.
Give the opportunity for students to think, in the case where a statement Adi earlier will be valuable right or wrong for the following four cases, namely:
(1) Day really Adi rain and really bring an umbrella,
(2) Day really rain but Adi does not carry an umbrella,
(3) Day does not rain but Adi bring an umbrella, and
(4) Day Adi does not rain and no umbrella.

In the case of the first day really rainy and Adi really bring an umbrellaas he reveal. How it may be stated in a lie this case? Thus clear that both components equally valuable true that statement has caused compound (implications) that Adi was stated earlier will be valued properly. In the second case, that day really rain but not Adi bring an umbrella as he should do as dinyatakannya, how Adi earlier statements may be properly assessed? With other components of value p, but not properly followed by the components of q should also correct value, will cause the compound statement (implications) that Adi stated earlier will be worth one.
Finally, for the third and fourth cases, where the day does not rain, of course You will not be called compound statements (implications) as Adi the statement is wrong, because it states that Adi is just something that is going to happen he will bring an umbrella if rain days.
5. Biimplikasi
Biimplikasi or bikondisional compound statement is a statement from the two p and q with the dinotasikan p ⇔ q value equal to (p ⇒ q) ∧ (q ⇒ p) so it can be read: "p if and only if q" or "p if and only if q."
Thus biimplikasi clear that the two statements p and q will only true value if the second statement tunggalnya worth the same. Biimplikasi example:
1.Triangle is a triangular carpenter's square if and only if the broad square in the
hipotenusanya with the same amount of square-wide on both sides of the square the other.

15. What is tegak lurus in English? Tegak lurus is upright..
16. What is kesebangunan? Kesebangunan is construction
17. What is jajar genjang? Jajar genjang is parallelogram
18. What is Belah Ketupat?Belah ketupat is a form like a square but a little different
19. What is barisan dan deretan? Barisan dan Deretan is formation and row
There is two kind of Formation and row in mathematics. That is Aritmatics and Geometry.
1. Aritmatics
Line arithmetic
U 1, U 2, U 3, U ....... n-1, U n is called the line arithmetic, if
U 2 - U 1 = U 3 - U 2 = .... = U n - U n-1 = constant
This difference is also called (b) = b = U n - U n-1
Tribe to line arithmetic n-a, a + b, a +2 b, ......... , A + (n-1) b
U 1, U 2, U 3 ............., U n
The formula to-n:
U n = a + (n-1) b = bn + (ab) ® Fu ngsi linier in n
Arithmetic progression
a + (a + b) + (a +2 b) +. . . . . . + (A + (n-1) b) called the arithmetic progression.
a = beginning of the race
b = different
n = many tribes
U n = a + (n - 1) b is-n to tribe
N the number of tribes
Sn = 1 / 2 n (a + U n)
= 1 / 2 n [2a + (n-1) b]
= 1/2bn ² + (a - 1/2b) n ® quadratic function (in n)
Description:
Difference between the two tribes that sequence is fixed (b = n S ")
Rows of arithmetic will be increased if b> 0
Arithmetic will be down the line if b <0
Valid relations U n = S n - S n-1, or Un = S n '- 1 / 2 S n "
If the number of odd tribe, the tribe of the
U t = 1 / 2 (U 1 + U n) = 1 / 2 (U 2 + U n-1) ff.
S n = 1 / 2 n (a + U n) = t ® U NU t = Sn / n
If three numbers form a line arithmetic, to facilitate calculation of the number-eg the number that is a - b, a, a + b
2. Geometry

Line geometry
U 1, U 2, U 3, U ......., n-1, U n is called the line geometry, if
U 1 / U 2 = U 3 / U 2 = .... = U n / U n-1 = constant
This constant is called a comparison / ratio (r)
Ratio r = U n / U n-1
Tribe to n-line geometry
a, ar, ar ², ....... ar n-1
U 1, U 2, U 3 ,......, U n
Tribe to n U n = ar n-1 ® exponential function (in n)
Array geometry
a + ar ² + ....... + Ar n-1 called array geometry
a = beginning of the race
r = ratio
n = many tribes
N the number of tribes
Sn = a (r n -1) / r-1, if r> 1
= A (1-r n) / 1-r, if r <1 ® exponential function (in n)
Description:
The ratio between the two tribes that sequence is still
Line geometry will be increased, if applicable for each n
U n> U n-1
Line geometry will be down, if applicable for each n
U n
Alternately up and down, if r <0
Valid relations U n = S n - S n-1
If the number of odd tribe, the tribe of the
Ut = 1 Xu Ö U Ö U n = 2 n-1 Xu ff.
If three numbers form a line geometry, to facilitate the calculation, eg the number-number is the a / r, a, ar
Array geometry BERHINGGA TAK
Array geometry is not berhingga's Answer
U 1 + U 2 + U 3 + ..............................
¥
å Un = a + ar + ar ² .........................
n = 1
where n ® ¥ and -1 <1 so that r n ® 0
By using the formula the number of array geometry obtained:
Amount not berhingga ¥ S = a / (1-r)
Array geometry is not convergent berhingga will (have any number of) for -1 <1
Note:
a + ar + ar 2 + ar 3 + ar 4 + ....... ..........
The number of tribes in the odd position
a + ar 2 + ar 4 + ....... odd S = a / (1-r ²)
The number of tribes in the whole
a + ar 3 + ar + 5 ...... even S = ar / 1-r ²
Obtained the relationship: S even / odd S = r
USE
Calculation TUNGGAL INTEREST (Interest is calculated based on the initial capital)
M 0, M 1, M 2, M n .............,
M 1 = M 0 + P/100 (1) M 0 = (1 + P/100 (1)) M 0
M 2 = M 0 + P/100 (2) M 0 = (1 + P/100 (2)) M 0
M n = M 0 + P/100 (n) ® M 0 M n = (1 + P/100 (n)) M 0
Calculation BUNGA compound (Interest is calculated based on the capital last)
M 0, M 1, M 2, M n ..........,
M 1 = M 0 + P/100. M 0 = (1 + P/100) M 0
M 2 = (1 + P/100) M 0 + P/100 (1 + P/100) M 0 = (1 + P/100) (1 + P/100) M 0
= (1 + P/100) 0 M ²
Mn = (1 + P/100) n M 0
Description:
M 0 = initial capital
M n = n the period after the Capital
p = Percent per period or interest rate
n = Number of
Note:
Compound interest formula can also be used for plant growth, the development of bacteria (p> 0) and also for shortening the engine, radio active material shedding (p <0).