HENDRA LISTYA KURNIAWAN
08305144014
MATEMATIKA SWADANA
MATHEMATIC IS MY LIFE
I.Properties of Logarithms
Just as you have been knew, logb x = y equal by = x. To search of “x”, we can use formula it.
Example 1 :
log10 x = log x
We are assumption 10 equal b, log x equal y. And then, we are substitute of 10 and log x in the formula by = x.
10x = 100
102 = 100
x = 2
So, we are come into possession of x = 2 from log10 x = log x. In the natural logarithms, we can also use formula log ex = ln x.
Example 2 :
log 2 x = 3
Just as example 1, we are assumption with 2 equal b and 3 equal y.
log2 x = 3
23 = x
8 = x
From log2 x = 3 and use formula logb x = y equal by = x, with that x = 8.
Example 3 :
log7 () = x
We are assumption 7 equal b, x equal y.
log7 () = x
7x =
7x = 7-2
x = -2
From example 1 up to 3, we can nature of logarithms, such as :
logb (M.N) = logb M + logb N
logb () = logb M – logb N
logb (xn) = n logb x
Expand !!!
log3 ()
From nature of logarithms, we can calculate :
log3 () = log3 (x2(y+1)) – log3(z3)
= log3 (x2) + log3 (y+1) – log3 (z3)
= 2 log3 x + log3 (y+1) – 3 log3 2
II.Common Factors and Grouping
Onetime, we have been introduced “FPB” by teacher. In English, “FPB” is Common Factors and Grouping (GCF). It’s consist of product and factors. Example :
15 = 3 x 5
15 is product and (3 or 5) are factors.
Finding The Greatest Common Factors (GCF) of Numbers
a)The GCF of a list of integers in the largest common factor of integers in the list.
Example :
Find of the Greatest Common factors from 45 and 60 !
45 = 3.3.5 = 32.5
60 = 2.2.2.3.5 = 23.3.5
To search GCF, we must search same number in the number of the Greatest Common with the smallest power. So, the GCF of 45 and 60 are 3.5 = 15.
b)The Finding the GCF, choose prime factors with the smallest exponents and find their product.
Example :
Find the GCF from 36, 60, 108.
Firstly, we must search factors 36 = 22.32 ; 60 = 22.3.5 ; 108 = 22.33
After we are find factors, just example 1 we are search number with smallest power. With that, we are find 22.3 = 12.
To fast formula, we can use share of joint.
236 60 108
218 30 54
3 9 15 27
3 5 9
III.Trigonometri Function
Ratios of different sides of a triangle with respect to an angle. You only need to know valves of sides to find measure of all parts of atriangle.
Rigonometri function consist of sine, cosine, tangent, cosecant, secant, and cotangent. The six basic trigonometri function defined by :
1.Side of atriangle.
2.Angle being measured.
HYP
OPP
ⱷ
ADJ
Information:
OPP : side opposite theta
ADJ : side adjacent to theta
HYP : hypotenuse
To calculate sine, cosine, tangent, cosecant, secant, and cotangent we can use formula :
sin ⱷ = csc ⱷ =
cos ⱷ = sec ⱷ =
tan ⱷ = cot ⱷ =
Astudent usally use quick formula. To facilitate commit to memory, we can memorize with :
S O H C A H T O A
i p y o d y a p d
n p p s j p n p j
e o o i a o g o a
s t n c t e s c
i e e e e n i n
t n n n t t n
e u t u e t
s s
e e
IV.Factoring Polynomials
Algebraic long division
Example is x-3 a factor of x3-7x-6
equal



- 3
3 -
3 - 9x
2x – 6
2x – 6
0
is no remainder, x -3 is a factor x3-7x-6
= x2+3x+2
x2+3x+2 also a factor of x3-7x-6. If we are write to mathematics.
x3-7x-6 = (x-3) (x2+3x+2) = (x-3) (x+1) (x+2)
roots = 3,-1,-2
3 roots for this 3rd degree equation quadratic (2nd degree) equastion always have at most 2 roots. A 4 th degree equation would have 4 or fewer roots. The degree of a polynomial equation always limits the number of roots.
Long division for a 3rd order polynomial :
1.Find a partial qouetient of x2, by dividing x into x3 to get x2.
2.Multiply x2 by the divisor and sustract the product from the dividend.
3.Repeat the process until you either “clear it out” or reach a remainder.

V.Function Terminology
Definition of function :
1.An algebraic statement that provides a link betweentwo or more variables.
2.Used to find the value of one variable if you know the values of the others.
Example :
y = 2x. If you know x = 5 with that y = 2.5 =10
One variable appears by itself on one side of the equation.
Example : y = 3x + 4, y equal by it self.
A function is a codependent relationship between x’s and y’s without x, you can’t get y.
Definition of function from Master of Mathematics :
1.Any numerical expression relating one number, or set of numbers, to another.
2.Two kind of relations are equations and inequalities. Equation is 1+3 = 4, inequality is 8 > 5.
Spesific numbers are being related to each other.
Equations and inequalities the kind that can be used to determine just one value for one of the variables y=3x+4. When you substitute a value for y. An equation with one variable is a function of whatever variables appear on the other side.
Function of x, f(x)=y, f of x
y = 3x+4function of x
f(x) = 3x+4 (standard form).
Put function that are not in standard form into standardform.
Example :
g(x) = x3-3x+2
x = 5g(5) = x3-3x+2
= 52-3.5+2
= 25-25+2
= 12
VI.Parallelogram
If a quadrilateral is a parallelogram, then opposite sides of parallel.

A B


D C
A quadrilateral consist of 4 side; , , If ABCD is a parallelogram, with that :
\\
\\
If a side is not abreast, with that quadrilateral is not parallelogram.