Unit 2, Day 8: Objective: Volume of prism, pyramid, cylinder, cone, sphere

Define: -Prism: area of base x 3D height
            -Pyramid: 1/3 x area of the base (AofB) x 3D height (3DH)
           - Cylinder: area of the base x 3D height
            -Cone: 1/3 x area of base x 3D height
            -Sphere: 4/3 x pie x r^3




Quiz:
     1) what is the formula to find the volume of a sphere?
     2) what is the formula to find the volume of a pyramid?
     3) what is the formula to find the volume of a prism?



Key:
1) 4/3 x pie x r^3
2) 1/3 x area of the base (AofB) x 3D height (3DH)
3) area of base x 3D height

make sure to watch these video: http://www.youtube.com/watch?v=Cx4XDe8TUHM  http://www.youtube.com/watch?v=Ov1ZlAquHRU 
http://www.youtube.com/watch?v=zPd21soIZw0
http://www.youtube.com/watch?v=l_KW_pRkEzg
http://www.youtube.com/watch?v=6KrZVsnynpU

Unit 2, Day 2: Review Pythagorean theorem. Definitions of angles. triangle angle sum; triangle classifications, distance formula.

Pythagorean theorem: A theorem attributed to Pythagoras that the square of the hypotenuse of a right triangle is equal to the sum f the squares of the other.

Triangle Angle Sum: The sum of the interior angles of any triangle is equal to 180 degrees. Triangle classifications: The basic elements of any triangle are its sides and angles. triangles are classified depending on relative sizes of their elements.

Triangle Classification: The basic elements of any triangle are its sides and angles. Triangles are classified depending on relative sizes of their elements.

make sure to watch these videos:http://www.youtube.com/watch?v=D_y_owf1WsI and http://www.youtube.com/watch?v=QNl_yb8doRk

Tips from the pros Video: http://www.youtube.com/watch?v=ZdpvX7GqAr4

Unit 2, Day 4: Objective: Vertical angles: multiplication of radicals


     Define: We multiply binomial expressions involving radicals by using the FOIL (First, Outer, Inner, Last) method.

make sure to watch this video:http://www.youtube.com/watch?v=lIBMq2yDgbQ














Quiz:
     1)
     2)
    

Unit 2, Day 6: Objective: Special right traingles

Define: A special triangle is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist.


Quiz:

1) Find the exact value of

           sin 45º + cot 45º. 


2) Find the exact value of
           (cos 45º)(cos 45º).    




     3)What three mathematic strategies do you use in solving triangles?





 Key:
     1)

      2) 1
      3) Sin, Cos, Tan


make sure to watch this video: http://www.youtube.com/watch?v=VWhg5qm92JA

Unit 2, Day 5: Objective: Addition and subtraction of radicals

 Definition: When adding or subtracting radicals, you must use the same concept as that of adding or subtracting "like" variables. 

adding:
 


subtracting:







Quiz: ( /= the radical sign )              
     1) add 5/3+2/75
     2) 5/8-3/18+/3 
     3) 2/12 +/27



Key:
     1) 15/3
     2) /2+/3
     3) 7/3

make sure to watch this video: http://www.youtube.com/watch?v=MKwxPbITcXQ

Unit 2, Day 3: Objective: Simplify radicals; distance formula can be introduced


Distance Formula: The formula, which is used to find the distance between two points (X1,Y1) and (X2,Y2) is called the distance formula.






or...

Quiz:
     1) What is the distance between the points A (4, 6) B (-2, -2)?
     2) Find the distance between the points. (2, 5) (1,3 ).
     3) Define Distance formula

Key
     1) you have to use the distance formula so, AB = square root of (-2, -4)^2 + (-2, -6)^2 = 10 units
     2) Square root of (2 - 1)^2 + (5 - 3)62 = square root of 1^2 + 2^2 = square root of 1 + 4 equals square root of 5
     3) The formula, which is used to find the distance between two points (X1,Y1) and (X2,Y2) is called the distance formula.

make sure to watch these video: http://www.youtube.com/watch?v=HhQLwjHxUIM and http://www.youtube.com/watch?v=h5XXu1tijXo

Unit 2, Day 1: review of slopes of lines; slopes of parallel and perpendicular lines.


Defininition: The slope or gradient of a line describes its steepness, incline, or grade. Parallel lines have slopes that are negative reciprocals of each other. Perpendicular if and only if their slopes are negative reciprocals of each other.


                                                                       parallel:





Quiz:

1. Define slope
a)                           b)
 
2. Which one is a perpendicular line?
3. Which one is a parallel line?


Answer Key:

1. The slope or gradient of a line describes its steepness, incline, or grade.
2. B is a perpendicular line.
3. A is a perpendicular line.










               
                                                        perpendicular:



make sure to watch these videos: http://www.youtube.com/watch?v=H0jDRFlrHhM
and http://www.youtube.com/watch?v=Lc3dPkoCOHc

Linear Equation

A linear equation is an equation between two variables that gives a straight line when plotted on a graph. So basicaly its an equation that makes a straight line. This equation is in y=mx+b form. this equation can be configured into different forms but it will always be straight.

 now its time for tips for the pros...
         
http://www.youtube.com/watch?v=ba7OhZyYUUc




Quiz:  1) what is a linear equation?
          2) can this equation be reconfigured?
          3)  is the line always straight?



Key:  1) A linear equation is an equation between two variables that gives a straight line when plotted on a graph.
         2) yes
         3)  yes

 

Y-Intercept

          The Y-Intercept is the y-coordinate of a point where a line, curve, or surface intersects the y-axis. So basically, its when your line crosses the Y-Axis and the X-Axis is at zero. In a linear equation (y=mx+b), the Y-Intercept is B. No matter what configuration the equation is in the Y-Intercept will always be B.

  or more simply put...

 

Quiz: 1) what is the Y-Intercept?

         2) what is the value of X at the Y-Intercept?

         3)  where does the Y-Intercept go in your equation? 

Key:  1) The Y-Intercept is the y-coordinate of a point where a line, curve, or surface intersects the y-axis

         2) 0

         3) B

Unit 5.Day 2.Students will write the linear equation of a line using data from a a line of best fit,or given 2 points.

Definition: An equation between two variables that gives a straight line when plotted on a graph.  A linear line is basicullay a straight line that is connected by 2 points, which never ends.

 Y=Mx+B is the root equation of a linear line. this picture clearly explains it. 




Quiz: 1) What is a linear line?
          2) What does y=mx+b mean?
          3) Does a linear line curve?

Key:  1) a straight line that is connected by 2 points, which never ends.
          2) Y=Mx+B is the root equation of a linear line, all you have to do is "plug and play" in the   numbers that are in your problem.
          3)  NO