English_What
you know about math?
First,
we saw the video with the title how you know about math? This is the lyrics of
the song.
Part
1 : What you know about math?
What you know about math?
What you know about math?
Part 2 : Hey, don’t you know I
represent Math League
When I add shorty
subtract
Freshmen backpack
where I’m holding all my work at
Back
to Part 1
I
know all about math
Answers
44
It’s
real easy cuz of sig figs
You got 45 you rounded high
Your answers too big
Back to Part 1
I know all about math
TI-84
Solar Edition you know I’m shining dawn
Extra memory, I look back to do my natural
log
You know we multiply
While memorizing pi
Take limits to the sky
be sure to simplify
Graphing utility that’s trigonometry
One hundred I’m math b don’t you cheat off me
the sine graph ain’t a line exponential decline
but your score can’t beat mine
We’re memorizing grades for our mathly states
against the mathly greats not getting many
dates
I got to find a mate but girls just play hate
and always make me wait (can’t even
integrate)
Back to Part 2
Back to Part 1
I know all about math (heh)
English_Degree
Degree is measured by one full counterclockwise
rotation of terminal side of angle back to its starting point measures (3600)
three hundred sixty degrees. Three hundred sixty degrees (3600) angle
is one move minute hand in counter clockwise way around clock back to original
position to make a circle. Then, three hundred sixty degrees degree (3600)
is equal to a circle then 1 degree is equal one over three hundred sixty
degrees(3600) of full revolution and 11 degrees is equal to eleven
over three hundred sixty degrees of full revolution. Ninetydegrees (900)
is equal to one fourth of full revolution and it is called right angle. If we
move the terminal side of the angle in counterclockwise direction in the
additional ninety degrees (900), the angle measure is one hundreds
and eighty (1800). It is called straight angle.
Beside degree, the other unit that we can used to
measure angle is radian. The radian uses radius of the circle to figure out
measurement of an angle. Radians and degrees have a measurement relationship.
As we know that 3600is single counterclockwise revolution and one
full revolution is equal to 2π. Then, we know that 3600 is equal to
2π radians. To convert radians to degrees or vice versa, we must simplify the
equation. First.3600 is equals 2π radians then we simplify it until
we get that 1 degree is equal to π/180 radians and one radian is equal to 1800/π.
For example, we want to convert 1200 into radians in to degrees. If
we have 1 degree is equal to π/180 radians, remember for algebra, to do it we
must multiply both sides of equation by 120, so any time you alter one side of
equation you have to do it to the other side too. Therefore, 1200 is
equal to 2 π/3 radians. The other example is if we want to convert 11π/12
radians to degree. Same with above, we have 1 radians is equal to 1800/π
then remember we can doing something to one side without doing something on the
other side, so multiply it with 11π/12 radians. Thus we get that 11π/12 is
equal to 1650
English_Limit by
Inspections
To determine limit by inspection, we must know two
conditions. First, this matter only can apply if x goes to positive or negative
infinity and second is if limit involves a polynomial is divided by a
polynomial. For example,
,
this problem fits the 2 condition because it is polynomial that divided by a
polynomial and x approaches infinity. The key to determining limits by
inspection is in looking at powers of x in the numerator and the denominator.
This is the shortcut to determine limit by
inspection. First shortcut rule, if the highest power of x is greater in
numerator then the limit is positive or negative infinity. For example,
,
you can see that x approach to infinity. Then, the highest power of x in
numerator is 3is greater than the highest power of x in denominator is 2, so
the limit of this expression can be positive or negative infinity. Since all
the numbers are positive and x going to positive infinity, the limit must be
positive infinity. If you can’t tell if the answer is positive or negative
infinity, you can substitute a large number of x and see you end up with a
positive or negative number. Whatever sign you get is the sign of infinity for
the limit. Second shortcut rule, if the highest power of x is in the
denominator then the limit is zero. For example,
,
since the highest power of x in numerator is 2 is less than the highest power
of x in denominator is 3, so the limit of this expression can be positive or
negative infinity. Thus the limit of the inspection is zero. Now, the last
shortcut rule is little bit trickier. The trick is used iwhen the hghest power
of x in numerator is same as the highest power of x in denominator. If this is
a case, so
is equal to the quotient of the coefficients
of the two highest powers. Remember that the coefficient is the number that
goes with a variable, for example 2 is the coefficient of
.
This is the example of the last shortcut,
.
You can see that the highest power in denominator and numerator is 3. According
to this rule, let’s mean that lim is equal to coefficient of
’s
over each other. The coefficientof
’s
in the numerator is 4 and the coefficient of
’s
in the denominator is 3 so the limit is equal to 4/3.
English_The Golden X
The first equation look like this is ax=b, where x is variable,
and a, b is constant, because of a and b isn’t number so we don’t need to solve
it. Let’s take a equation when the value of a is 4 and b is 12, that means we
got an equation 4x = 12. Remember we try to figure out the value of x,
therefore we can get variable x on side by itself. Thus, we must simplify each
side by 4, then in the left side 4 divide by 4 is equal 1, so they cancel out
and 12 divide 4 is equal 3. So the answer is 3, we always can check it by
substitute the answer to the original question, then we get 4(3) is equal 12.
Thus, we get the right value of x. why we divide it with 4? It is because the
term 4x means that 4 and x are multiplied together. To get the value of x, we
must do the opposite of multiplication that is division. The other example is
,
it is means that 7 times x. to get x, we can divide both side by 7, so we get
x=9. We can check it to original equation that is 7(9) is equal to 63, so 9 is
the right value of x. the other equation form is
,
where a, b, and c are constant. For example,
.
In this case, we need to move 3 first because 3 in the left side so we need to subtract
both side with 3. Therefore, we get
,
then we can divide it by 5, so we get x = 3.
English_Integers
Integers are the whole number and their negatives.
Whole numbers are not fractions or decimals. If we take number 1, then we keep
to add 1 to it, all of the number that we get is whole number. Therefore,
2.000.000, 134, and 5 are whole numbers. Back to the definition of integer,
integer can be positive, negative, or zero. The easy ways to visualize integer
is number line. Number line is vertical or horizontal line that is marked at
event intervals or units similar with thermometer. It is the number line works.
When moving to right or up of the number line, the numbers become greater. When
moving to left or down of the number line, the numbers become smaller. Any
number above or to right of zero is positive or greater than zero but any
number below or to left of zero is negative or less than zero. The number is
negative if it has a minus sign in front like -5. The number line will be
useful to world to we get the operation of negative number. The end of the
number line goes on forever because there is no end or the numbers go on
infinity. Integers are made from digits. Digits are simply the numbers 0 to 9.
Every digit goes in a certain place. The first number in whole number is unit
place. The tens place is just next on left. One place over from the ten place
is hundreds place. To the left of the hundreds place, thousands, ten thousands,
hundred thousands, millions, ten millions, and soon. Just like we saw the
integer in the number line, the digit go on forever because the number go on to
infinity. Let’s take a look at the number 1492. For this number, 2 is the
unitplace, moving to the left is 9 in ten place and the 4 is hundreds place.
Finally, the
1 is the thousand place.
English_MultiplyingEksponent
The first rule is multipying exponents, we can use
it when the exponents are same for both base number that we are multiplied,
then multiply the bases and keep same exponent. The algebra form is a n-th power
times b to n-th power is equal to a times b to the n-th power.For example, 35x45,
we just multiply the base that 3.4 that is 12, and keep same exponent, so the
result is 125. If we see something raise to the second power, it is
called square. When we see something raise with the third power, it is called
cubed.
The second rule is just like the first rule, only
this time it is only divide instead of multiply. We use the second rule when
dividing two numbers with same exponents. The algebra form islikea n-th power
is divided by b to n-th power is equal to a over b to the n-th power. For example,
, we just
divide the base numbers, six is divided by 2 is equal to 3 and use the
common exponent so the result is 33.
The third rule is little
different with the other. If we have base number raised to a power and completely
exponential term raised to another power, then we can multiply the two
exponents. The algebra form is like a to the n-th power to the m-th power is equal
to a to the n-th times m-th power. For example,
,
we can multiply the exponent that is 3 times 2 is equal to 6, and keep base the
same, so the result is 26.
The fourth rule is multiplying integers
with different exponents and the same base number with add the exponents and
use the common base. The algebra form is like a to the n-th power times a to
the m-thpower is equal to a to the (n+m)-th power. For example, 23 x
25, first keep the base 2 and then add the exponents 3+5 =8, so the
result is 23 x 25=28.
The last rule is same in the fourth rule,
the difference is in dividing and subtracting. The rule is dividing integers
with different exponents and the same base number with subtract the exponents
and use the common base. The algebra form is like a to the n-th power is
divided by a to the m-thpower is equal
to a to the (n-m)-th power. For example,
,
first keep the base 2 and then add the exponents 5subtract3 is equal 2, so the
result is
is equal 42.
English_Function
Terminology
The basic of building algebra is
function. Function is an algebraic statement that provides a link between 2 or
more variables. It is used to find the value of 1 variable if you know the
values of the others. For example,
,
if you know x, you can find y. Let
the
, so y is equal to 10. This situation occur if
one variable apperas by itself on one side of the equation. For example,
,
y is the function of x, because y appears by itself. It is important that y is
underdone by the other symbol like
is just y. Whenever you compute the right side, you will find the value of
y. So a function is
a codependent relationship between x’s and y’s without get x, you can’t get y.
The official meaning of function is very
specific kind of relation in which each element of one set is paired with one
and only one, element of the second set. The relation is any numerical
expression relating one number, or set of numbers, to another. There are two
kind of relations, that is, equations and inequalities. Relation can be simple
thing by equation
and the inequality
when
the specific numbers are being related to each other. Algebra explore relation
between the nonspecific number or variable like x and y that represent the
whole set of possible numbers. Variable relations is the expressions that
contain variables like
.
The kind that can be used to determine just one value for one of the variables
that exactly like
,
when you substitute a value for x, you can calculate just 1 value for y. An
equation with one variable by itself on 1 side and we say that one variable is
a function of whatever variables appear on the other side.
Function of x or f(x) or f of x is equal
to y. For example,
,
so y is express the function of x because
so
.
is
the standard form to express a function.
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