Try to Understand Math trough Video
NOTATION FOR DERIVATIVE
Before
we learn about the notation for derivative, there is a question, what is
derivative? Derivative can be told as the slope of tangent at point. Then, when
we take a look at the formula derivative
can be said as the change of y
over the change of x . Then,
derivative can be symbolize as fI(x) or yI or dy/dx.
We
can symbolize the formula: fI(x)= yI= dy/dx= change in
y’s/change in x’s
Then,
when we want to find the slope of two
points we can use this formula:
fI(x) =change in y’s/change in x’s
=y2-y1/x2-x1
=rise/run
Another
way to get derivative, we can use limit function. For looking for fI(x),
we take limit h approach to 0 for
f(x+h)-f(x)/h. in this case, h is the
amount interval.
Example:
1. Given
f(x)=4x2-8x+3. Find f1(2)!
Solution:
To
find fI(x), first we substitute x=2 in 4x2-8x+3, then we
substitute x=(2+h) in 4x2-8x+3.
F(2)=3
F(2+h)=4h2+8h+3
Then:
fI(x)=
lim h->0 f(x+h)-f(x)/h
= lim h->0 3/4h2+8h+3
=8
ANGLE
Angle
is constructed by two ray and one vertex. One ray is called initial side, then
another side is called terminal side. Angle can be divided into three kinds.
There
are:
1. Acute
angle. Acute angle is angle that the measure less then 90 degrees.
2. Right
angle. Right angle is the angle that the measure is 90 degrees.
3. Obtuse
angle. Obtuse angle is angle that the measure is more than 90 degrees.
TRIGONOMETRY
Before
we learn about trigonometry, of course about the basic of trigonometry, do you
know what is trigonometry? Trigonometry comes from two words. There are triangle and measure. In the basic of trigonometry, it is possible for us to
find sin, cos, tan, etc. How can we find the value of sin, cos, tan, quickly
and easily? There are some alternate way to find the value of sin, cos, tan,
quickly and easily.
Let:
S=side opposite
hypotenuse
O=over
H=hypotenuse
C=adjustion
T=segment front of
angle
Then using a right
triangle,
Sin = SOH
Cos = CAH
Tan = TOA
INTEGER
What is integer? Integer is whole numbers but not
fraction number.
Integers are included :
1. Positive
numbers, for example 1 2 3 4 5. . .n
2. Negative
numbers, for example -1 -2 -3 -4 -5. . .-n
3. Zero
number
Then, how about the name of each number on each
position in any integer?
For example if we have number 5431, so how to
grouped each number?
In this case:
1 = unit place
3 = tens place
4 = hundreds place
5 = thousand place
FACTORING POLYNOMIAL
One way how to get the
factor of polynomial is divide the polynomial with the factor given.
For more understand this topic, it is better for us
to take one example.
1. If
we have polynomial x3-7x-6, then one factor of that polynomial is 3,
so what are the other factors?
Solution:
Because
one of the factors of x3-7x-6 is 3, we can divide x3-7x-6 with x-3, since 3 is the factor of x3-7x-6.
From that operation we will get result x2+3x+2. Then from x2+3x+2,
we can change that form into x+2 and x+1. For x+2, it means x=-2, then from x+1
it means that x=-1.
Finally
we can conclude that the factors of x3-7x-6 are 3,-2, and -1.
SOLVING WORD PROBLEMS
Sometimes,
so hard for solving Mathematics in word problems. It is because for solving
word problems need more understanding. Without more understanding, so hard for
getting the solution. However, we must know how to solve word problem because
of in our life, problems are always represented by words. So, it is very
necessary for us to understand word problems.
In this case, we have a key how to
solve word problem easily. Well, let call it BUCK key. What is BUCK? Let check it out:
B=
Box the question. It means that you have to know what the question is first.
U=
Underline the info. It means that you must underline every info given in the
question.
C=
Circle the vocab. Sometimes there is a key word that we have to understand.
K=
Knock out information you don’t need. It means that better for you to knock out
information that you don’t need for solving the problem.
There
are some example for solving word problems:
1. How
much money should Maria bring to buy a pair of shoes, if the original price is
$80.00 and there is a discount 20%. This sale will last one week.
Solution:
First step we must box
the question, and the question is how much money should Maria bring to buy a
pair of shoes.
Then, the next step is
underline the info given. In this question, the info are the original price is
$80.00 and discount 20%.
The third step is
circle the vocab. On question above, the vocab is original and discount.
Then the fourth step is
knock out information you don’t need. In this problem, we knock out sentence
‘This sale will last one week’.
>original price $80.00
>discount 20% = 20% x 80.00 = 16.00
>new price = 80.00-16.00 = 64.00
So, we can conclude that Maria should
pay $64.00.
2. A
college student plan to spend $420 on books for one semester. He also plans to
spend $20 per week on pizza. The fall semester in 18 week long. How much will
he need for books and pizza?
Solution:
First step we must box the question, and
the question is how much will he need for books and pizza?
The second step is underline the info
given. In this question, the info are :
>$420
for books in one semester.
>$20
for pizza in 18 weeks (one semester)
The third step is circle the vocab. On
question above, the vocab is spend.
Then the fourth step is knock out
information you don’t need. In this problem, there is no sentence that have to
knock out.
Calculating
:
>books:
$420
>pizza:
$20 x 18 = $360
>books+pizza
= 420+360= 780
So,
from that calculation we can conclude that he need $780.00 for books and pizza.
3. A
first number plus twice a second number is 23. Twice the first number plus the
second number is 31. Find for each number!
Solution:
From the problem above, let :
The first number=x
The second number=y
Then, we translate the information above
into symbol in Mathematics.
>x+2y=23…(i)
>2x+y=31…(ii)
Then
we multiply equation (i) by 2, and
equation (ii) by 1.
Then
we get :
>2x+4y=46…(i)
>2x+y=31…(ii)
After
that, we subtract equation (i) to
equation (ii).
We
get 3y=15 so y=5
If
y=5 so we can get x=13
From
that, we get y=5 and x=13.
4. The
sum of two numbers is 16. The first number plus 2 more than times the second number equals to 18. Find
each number!
Solution:
From the problem above, let :
The first number=x
The second number=y
Then, we translate the information above
into symbol in Mathematics.
>x+y=16…(i)
>x+(3y+2)=18…(ii)
On second equation we can simplify into
x+3y=16…(iii)
Then we subtract equation (i) and (iii).
So
we get that y=0 and x=16.
PROPERTIES OF LOG
In
the properties of log, there is a basic formula that we have to know and
understand.
If we have logbx=y
it means that by=x.
For more understand let
go to the example.
1. Log10100=x,
determine the value of x.
Solution:
Let
see on the basic formula above, so we will get:
10x=100
X=2
So,
the value of x is 2.
2. Log2x=3,
determine the value of x.
Solution:
Let
see on the basic formula above, so we will get:
23=x
X=8
So,
the value of x is 8.
3. Log7(1/49)=x,
determine the value of x.
Solution:
Let
see on the basic formula above, so we will get:
7x=1/49
7x=1/72
7x=7-2
X=-2
So
we can conclude that the value of x is -2.
Then,we also have the formulas:
Logb(M.N) = logb
M+logb N (i)
Logb(M/N) = logb
M-logb N (ii)
Logb(Xn) = n.logbX (iii)
For more understand that formulas,
let go to the example:
1. Log3[x2(y+1)/z3],
simplify using formulas above!
Solution:
=Log3
[x2(y+1)]-log3 z3, using (ii)
=
Log3 x2+ Log3(y+1)- log3 z3,
using (i)
=2
Log3 x+ Log3(y+1)-3 log3 z, using (iii)
TERMINOLOGI
Function is an algebra
statement
For example:
1. Y=2x
To
find the value of y, we must know the value of x first. If the value of x is 5,
so y is 10. It can be said that without x,
you can’t get y.
Function
can be grouped into two, there are:
1. Equation
Example:
1+3=4
2. Inequalities
Example:
8>5
Function
can be notate f(x) or y. f(x) means that that is the function of x.
For
example: f(x)=y=3x+4 (standart form)
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