Math meeting 7-28-2011

Hi,

We have reviewed (07-28-2011)

Multiple Choice Practice - Parallels and Quadrilaterals 

Next math meeting;

08-02-2011 Am 10:00-12:00

We will discuss problem solving strategies

Fraction, direct and inverse fraction

Direct and Inverse Proportion

Two types of proportions
Direct proportion;
Y=f(x)=kx  k is a constant
or Y/X=k
Y and X are direct proportion
The more X is, the more Y is
ex: buy one book costs $2, two books costs $4, 3 books costs $6.......
(given k=2, when x=1then y-=2,x=2then y=4 ,x=3 then y=6.............)
the more  x is, the more y is
the more the books, the more  the cos is
x and y are direct proportion (books and cost are direct proportion)

Inverse proportion:
Y=f(x)=k /X             k is a constant
or XY=k
X and Y are inverse proportion
The more X is, The less Y is
ex: D=RT
if D is a constant.
The faster the rate is , the less  the time it will take
EX1: k=xy (D=RT)                                                                      k=xy (D=RT)
 Given 120 miles, rate at 30 mph, it takes 4hours(given k=120   120=30x4)
                           rate at 60 mph, it takes 2 hours(given k=120, 120=60x2)
                          rate ate 120 mph, it takes 1hour(given k=120  120=120x1)
                       
The more x is, the less y is (k=xy)
The more R is, the less T is (D=RT)
x and y are inverse proportion (R and T are inverse proportion)

Ex2: It takes 10 workers and works 100 hours to finish a project(Given k=1000=10x100 )
        It takes 20 workers and works  50 hours to finish a project (k=1000, 1000=20x50)
        It takes 40 workers and work 25 hours to finish a project   (k=1000, 1000=40x25)

Problem Solving Strategy:
Step1: to recognize if it is direct or inverse proportion
Step2: If it is direct proportion: y=f(x)=kx
          If It is inverse proportion: y=f(x)=k/x
Step3: find k=? and put the value in the known variable, and solve the unknown variable.

Q1, For the function f , y=f(x) is inversely proportional to x, when x>0.  If f(3) =6, what is the value of f(2)?

Since it is  inversely proportional- xy=k, y=k/x
 y=f(x)=f(3) =k/3=6, so k=18
f(2)=k/x=18/2=9


Q2, If y is directly proportional to x square and y=1/8 when x=1/2 what is the positive value of x when y=9/2
Since it is directly proportional , y=k(x)(x)
1/8=k(1/4), so k=1/2
9/2=k(x)(x)=1/2(x)(x)
so x=3


Q3, If 5 chickens lay 5 eggs in 5 days. How many eggs will 25 chickens lay in 25 days?
The more chicken, the more eggs, and the less days
Chicken(C) and eggs (E)are direct proportional, and chicken(C) and days(D) are inverse 
proportional ,
Therefore, k=CD/E , k=(5x5)/5=5
k=5=(25x25)/D
D= 125


More Study:

Math Word Problem of the Day

Quadrilaterals

More Study:
Quadrlaterals

Math meeting 07-26-2011-circle-review

Hi,

We have review properties of a circle we have learned.

I, Vocabularies and definition
http://lin-mathclub.blogspot.com/2011/07/circle-some-definition.html

II, Chords and Circles
http://lin-mathclub.blogspot.com/2011/07/circle-arc-and-chord.html

III, Tangent line
http://lin-mathclub.blogspot.com/2011/07/circle-tangent-line.html

IV, Circle and angles: Central angles and Inscribed angles
http://lin-mathclub.blogspot.com/2011/07/circle-arc-and-chord.html

V, The Alternate Segment Theorem
http://lin-mathclub.blogspot.com/2011/07/alternate-segment-theorem.html

VI, Angles and Circles
http://lin-mathclub.blogspot.com/2011/07/circle-circle-and-angles.html

VII, Chords, Secants, Tangents in Circles-Power of a point
http://lin-mathclub.blogspot.com/2011/07/circle-power-of-point.html


More Study:


Multiple Choice Practice - Circles 
Next meeting :

07-28-2011 Am10:00-12:00

We will discuss Geometry-Quadrilateral Family

Math meeting 07-25-2011

Hi,

We discussed circle-power of a point


http://lin-mathclub.blogspot.com/2011/07/circle-power-of-point.html.

Next meeting:

We will review all  properties of a circle we have learned

Please print out the attachments  and bring to the meeting.

Meeting time:
07-26-2011 Am 10:00-12:00

Circle:Chords, Secants, Tangents in circles -Power of a point

Power of a point:



More Study:
Rules for Dealing with Chords, Secants, and Tangents in Circles:
Working with Chords, Secants, and Tangents in Circles:
(Circles: Chords, Secants and Tangents)

Math meeting 07-21-2011

Hi, We have discussed  1,Circle-angles formed by intersecting chords,secants-tangents-arcs-angle 2, Problem solving : word problems Homework Angles in a circle http://www.regentsprep.org/Regents/math/geometry/GP15/PcirclesN2.htm Angles outside a circle http://www.regentsprep.org/Regents/math/geometry/GP15/PcirclesN3.htm Practice with circle proofs http://www.regentsprep.org/Regents/math/geometry/GP15/pracProofs.htm Next Meeting 07-25-2011 10:00-12:00AM Please print the attachments and bring to the meeting

Math meeting 07-19-2011

Hi,

We have discussed the attachment 3-Circle-other angles and circle

Please print out the first two attachments (if you did not print last time)

Next meeting

07-21-2011

10:00am- 12:00

Math meeting 7-18-2011

We have discussed the alternate segment theorem

Homework: please finish the practice part The intersection of a tangent and chord ( The alternate segment theorem) http://www.mathwarehouse.com/geometry/circle/angle-tangent-and-chord.php Next Meeting: 07-19-2011 AM10:00-12:00 We are going to discuss 1,Review: Circle,    2,angles in a circle

Math meeting 7-13-2011

Hi,

Today we have reviewed central and inscribed angles  in a circle.

Homework: do the following practice

http://www.mathwarehouse.com/geometry/circle/tangent-to-circle.php

http://www.mathwarehouse.com/geometry/circle/arc-of-circle.php

http://www.mathwarehouse.com/geometry/circle/inscribed-angle.html

http://www.mathwarehouse.com/geometry/circle/central-angle-of-circle.php

http://www.mathwarehouse.com/geometry/circle/chord-of-circle.php

Ya-Chi

The Alternate Segment Theorem

More Study:
Alternate segment theorem
Proof: http://www.absorblearning.com/media/attachment.action?quick=l9&att=1522

Math meeting 7-12-2011

Hi,

We have discussed
1,angles in a circle-central , inscribed angles
2,triangle exterior angle theorem and proportion theorem

Homework:

http://www.regentsprep.org/Regents/math/geometry/GP15/PcirclesN.htm

Next meeting:

AM 10:00-12:00 07-13-2011

1, Review:Circle, similar triangle

2, The Alternate Segment Theorem

Meeting time: 7-11-2011

Homework: Tangents and Circles http://www.regentsprep.org/Regents/math/geometry/GP14/PracCircleTangents.htm Meeting: 7-12-2011 AM10:00-12:00

Circle-Circle and Angles

Practice Questions




Central angle= 1/2Inscribed angle

More study:
Circles and angles-(Circles:  Angles and Arcs )

Circle-Tangent Line

More Study:
Tangents and Circles（ Circles: Chords, Secants and Tangents）  

Math Meeting : 07-07-2011

Hi,

Today we discuss some vocabularies , chords and arcs about circles
We also review the congruent  triangles

Homework:

http://www.regentsprep.org/Regents/math/geometry/GP14/PracCircleChords.htm

Math meeting 7-5-2011-Triangle Properties

Properties of Triangles:

1Pythagorean Theorem 2,Isosceles Triangle Theorem 3,Congruent Triangles  4, Similar Triangles 5, Triangle Proportionality Theorem 6,Triangle Inequality theorem 7, Exterior Angles of Triangles

Multiple Choice Practice - Triangles