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)