Sunday, March 25, 2012

MARCH 20,2012
AIM: HOW DO WE FIND THE AREA OF A CIRCLE ?
To find the area of the circle we need to use the formula: 
A= πr2
In the circle 
to find the area we need to know the radius 
at times the radius might not be given to us but since the diameter is twice of the radius we divide the diameter by 2.


For example:
           FIND THE AREA !

To find the area we need to know the radius but it isnt given to us. in that case like i said before divide the diameter by 2 to get the radius,
10/2 = 5 
the radius turns out to be 5.
when you have the radius then plug it in the formula: A= πr2
Next plug it in :
A=π(5)2
Do the exponent :
A=π (25)
final answer:
A=π25


Leave the answer in the pi form because with pi the answer is accurate. If you are to to round to the nearest tenth then round otherwise leave it as in form of pi.

you try:

 
Jessica is making a circular table cloth for an art project.  She wants half of the cloth to be a plain colored fabric and half to be a print fabric.  How many square yards of each fabric (to the nearest hundredthof a yard) will she actually be using if the diameter of the cloth is 6 feet?
Choose:
 1.57 sq. yds
 1.58 sq. yds
 14.13 sq. yds
 14.14 sq. yds
Sources:
regents prep.org for the you try and the little circle above.

Posted by at No comments:
march 19,2012

Aim: How do we find the area of regular polygons ?

STEP 1:
when finding the area of a regular polygon we first need to notice what kind of polygon we are working with.




in the image oin the right is a hexagon.
in the hexangon if a teacher or a person were to say what is the area of the hexagon then look its a hexagon.














STEP 2 : KNOW WHAT AN APOTHEM IS :)


LEts ssay this is a regents problem and thety tell you to find the area of the polygon.First know the formula.
The formula :
NAS
   2
N: number of sides
A: apothem
S: the base
and divide that by 2.





many might not know what an aopothem is :)
so ill tell you :)
an apothem is the distance between the sides of the polygon to the center.
in this case the apothem is 2.

STEP 3:COUNT THE SIDES ! FOR N  :):D
 Like i said before
N is the number of sides
in this case since its a hexagon  there is six sides

like in the image shown in the left ------>















STEP 4: THE S IS NEXT :)
                     
 So from step 2 and step 3 we know that  N ISTHE NUMBER OF SIDES
A IS THE LENGTH BETWEEN THE SIDES AND THE CENTER

THE S :
the s is the base and dont get confuse just because its the base it doesnt mean that its in the bottom the base is anywhere that the number is next to a side.
in this case the s would be 6.

STEP 5: PLUG IT IN !!! YAY ^O^

now that we know what an apothem , n, and s is we can plug the numbers in the formula for area.
SO...... now we apply the new knwodleg we now know and solve the problem :)
ALSO DONT FORGET TO
 SHOW WORK !

FORMULA :
NAS
  2
PLUG IN :
 6*2*6 
    2
multiply first :
6*6= 36*2 =72
THEN DIVIDE:
72 
2
Final answer is
36 because 72/2  is 36
so the final area would be 36.


YOU SHOULD KNOW :
what an apothem is now :)
how to calculate the area of any polygon because the formula:
NAS
  2
works for every polygon


there might be a case where the area was already given to you: in that case plug in the area and dop it like a equation 


for example:
A= 72 
a=6
n=6
find the S


then we plug in the equation 


72= 6*6*s
          2
To get rid of the two in the other side of the equation you multiply 72*2 which equals 144. then also multiply 6*6 which are the other side of the equation. once that's done divide 144/36 which gives us 4 and that would be the S= the base :).


NOW YOU TRY:D

If we have an area of 20 and the apothem of 2 and there are 2 sides what is the S ?



Posted by at No comments:

Sunday, March 18, 2012

March 15,2012


AIM: How do we find the area of parallelograms, kite and trapezoids ?

PARALLELOGRAM:
To find the area of a parallelogram
is like finding the are of a rectangle .


For the parallelogram we need to first cut a line in the parallelogram where it forms a triangle. in the image to the left parallelogram ABED we cut a line from A to C with that forming triangle we place the triangle to the other side forming a rectangle ACFD.

FORMULA: B x H
-----------------------------------------------------------
[IMAGE] EXAMPLE:
Find the are of a parallelogram with a base of 12 centimeters
and a height of 5 centimeters.
First : Apply the formula
A=B*H
Then : plug in the base and height:
A=12*5
solve the equation:
A= 60cm2
------------------------------------------------------------------------------
TRAPEZOID :
[IMAGE] 
   Formula :   A= (B1+B2)H
                                2
B stands for base
H for height
A for area
-----------------------------------------------------------------------------
Example:
[IMAGE]         
First:
 write the formula :
A= ( B1+B2)H
            2
Plug in numbers:
A= (10+14)5
          2
Solve :
A=( 24)5 
        2
A= 120
       2
A= 60 in2
------------------------------------------------------------------------------
Kite:


WHAT THE PICTURE SHOWS:
  • it shows the formula for the are of a kite
  •  D1 and D2 of the kite are shown.
-------------------------------------------------------------------------------

EXAMPLE:

First:
 rewrite the formula : A= D1*D2
                                          2
SECOND: PLUG IT IN
A= D1+D2 
          2  
A= 10*2
       2  
 Solve the equation :
A= 20 = 10
      2
Answer
A=10
------------------------------------------------------------------------------
TRY IT:

Find the area of the kite. Measurements shown are in cm. [Given x = 12 and y = 16.]

Sources used :
Try it : http://www.icoachmath.com/math_dictionary/Kite.html
 kite: http://www.k6-geometric-shapes.com/image-files/formula-area-kite.jpg 
Trapezoid: 
http://www.mathgoodies.com/lessons/vol1/area_trapezoid.html
Parallelogram:

Posted by at 1 comment:
March12,2012
Aim: How do we calculate the area of rectangles and triangle?


To find the area we first  need to know what area is .
AREA is the amount of surface that a shape contains.


RECTANGLE:

 Area (rectangle)
or
 Area (rectangle) = (length)•(width)

B:base     
H: height 


The rectangle has two formulas of a triangle and either formulas can give the correct area of a rectangle.


For example :  
In the image to the left the rectangle has a base of 5cm and a height of 10 cm.
To find the are we first 
multiply : 5 x 10 
which gives us 50 and since its in centimeter, our final answer is 50cm2




TRIANGLE:
Formula for the area of the triangle :

B: BASE 
H: Height

For Example :

                 
In the image above we have a base of  5 cm and a height of 6cm. First :
Multiply 6and 5 to give us 30.
THEN :
Divide 30 by 2 giving us an answer of 15.
FINALLY:
Use 15 and have the proper units.
The answer for the triangle would be 
15CM2

NOW TRY THIS :D


 FIND THE AREA OF THE RECTANGLE BELOW.


SOURCES:
For the image of the rectangle and more areas go to : http://www.regentsprep.org/Regents/math/ALGEBRA/AS1/RefARea.htm 

The picture of the "now try this " was taken by:
 http://www.google.com/imgres?hl=en&biw=1440&bih=742&gbv=2&tbm=isch&tbnid=hTTL5Vh5Ah4VtM:&imgrefurl=http://ed101.bu.edu/StudentDoc/current/ED101fa10/alliero/content%25203.html&docid=-nMWyZZgSX4ypM&imgurl=http://ed101.bu.edu/StudentDoc/current/ED101fa10/alliero/Images/rectangle%252520area.jpg&w=330&h=257&ei=MStmT8mMB4fX0QGLq7C3CA&zoom=1&iact=hc&vpx=215&vpy=239&dur=2935&hovh=198&hovw=254&tx=147&ty=81&sig=107129537430957669125&page=1&tbnh=162&tbnw=208&start=0&ndsp=16&ved=1t:429,r:11,s:0 
My brain :D
Posted by at 1 comment:

Sunday, March 11, 2012

March 7,2012
Aim: How do we find compound loci ?

A compound loci is a problem that involves finding the locus but it also involves the words "AND" and "And ALSO".

Exercise :
Try figure out, if the statements below are compound loci or only locus problems.

1) What is the locus of points 3 inches from point B?

2) Graph the locus of points equidistant from x=7 and y=3?

3) Im hungry ....
---------------------------------------------------------
In compound loci problems there are certain steps to take:

Problem 1:
Parallel lines r and s are 8 meters apart, and A is a point on line s.  How many points are equidistant from r and s and also 4 meters from A? 



First step :
Break down the first line of the problem and sketch it 

Parallel lines R and S are 8 meters apart, and A is a point on line S.

Second step :
re-read the second sentence before the AND.
 How many points are equidistant from R and S. 
According to the Locus theorem if we need to find locus of two parallel lines like R and S then the locus would form a line.
Then sketch it 

Third step :
re-read the end of the sentence.
Also four meters from point A. 
Then sketch it.

Finally in the compound loci you see where both the equidistant line and the circle of point A touches. In this case its one time so the answer is 1.

Try it :D
Two points A and B are 7 units apart.  How many points are there that are 12 units from A and also 4 inches from B?



Choose:
 0  1 2 3



Sources used :
for both problems: regentsprep.org
the picture with the question mark :http://www.brainbasedbusiness.com
the rest is in my notes and head :P

Posted by at 3 comments:
March 5,2012
Aim: How do we find the locus of points?


First : What is LOCUS ??
LOCUS is the set points that stratifies certain conditions.
P.s Locus in plural from is LOCI


One point locus:
 In a one point locus question, the regents or your teacher might ask you to find the loci. 
        When finding the locus of one point, like point T 
the distance has to remain the same. 
In the picture below, T is the point and the distance is 5 as you can see from point T the distance remains same forming a circle.
             

Two points locus :
The two point locus,is a  line segment that is in between the two points .
The locus of the two points is an line segment because no matter where the points are if they keep the same distance then the locus will always be a line.

For example:
The picture above shows the locus between those two points. 
In this case the distance between these two points is 5 so the line segment would be in the middle of the two points.
One line locus:

The locus of one line are two parallel lines that are equidistant from  the one line .

For example:
find the locus of points from the original line with a distance of 5.
Like in the image on the top the original line is shown, to find the locus with a distance of 5 the original line has to be an equidistant from the original line which forms two parallel lines.

TWO PARALLEL LINES:
With the two parallel lines the locus of points will form a line because the two parallel lines will always remain the same distance.

For example ,in the image below the two parallel lines have a distant of 5, the distance of 5 from both lines will  forming one line.
              
Two intersecting points:
when having two intersecting lines the locus is much more different than the one point locus or like the two parallel line loci. The two intersecting line from two diagonal lines because because the distance of both intersecting lines from a diagonal line.


In the image below the two intersecting are the red dotted line the lines L1 and L2 are the locus of points. 



 
TRY IT NOW 

 How many point are equidistant from two parallel lines and also equidistant from two points on one of the lines?
      [1]  1            [2]  2                   [3]  3                [4]  4
-------------------------------------------------------------------------------------------
Sources used :
The penguin ,two intersecting line picture, and the try it problem are from regentsprep.org
The rest is from my notes and brain :D
Posted by at 1 comment:


Q:How do we solve logical problems using conditionals?
A :
we solve logical problems with conditionals by adding if and then
to solve with a conditional first we need a hypothesis and a conclusion.
we can have a logical sentence like :
Tomorrow is my birthday so i will eat cake 


Tomorrow is my birthday is the hypothesis
I will eat cake is the conclusion
Combing them together would give us a conditional like :
If tomorrow is my birthday then i will eat cake.

try it :D
I can eat a box of donuts (hypothesis )

Im a healthy person (conclusion)

TURN IT TO A CONDITIONAL !!!!

sources used 

THE DONUTS:

and my brain :)
Posted by at No comments:

Sunday, March 4, 2012

Q:What is a mathematical  statement?
A: a mathematical statement is a statement that can be judged by truth or false.


For example :
 1) Is a square a triangle?
this is a false mathematical statement because it is a question .


2) 2 is more than 1
this is a true mathematical statement because 2 is bigger than one.

Read more »
Posted by at No comments:
Q: What is logic?


A: Logic is a tool used to decide whether a statement is true or false.


Logic is everywhere around you 
Its when you decided what to eat or whether you want to take a shower. 

Logic Problems:
         Logic problems often tell the reader or player to determine the age of people or to figure out which is which.All of the logic problems  give clues so then with our own logic we use the clues and determine whether its true or false.


example:D
below there is a fun logic game try it and have a fun time :D 
bye-bye ^O^


 


Sources used: 
The kidz page.com
My notebook 
Posted by at No comments:
Subscribe to: Posts (Atom)