- 1. Answr the questions first in each home work.
- 2. Then read the related keywords of the given title in SM.
- 3. Do the questions again as home work.
S101. Indefinte equation : One hundred people divide one hundred cakes
Definition
- Two unknown with one equation
- Three unknown with two equations
- One hundred people include men, women and children
- Give 3 cakes for each men
- Give 2 cakes for each women
- For each 3 children gives one cake
- Find the number of men, women and children
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Study subjects :
Solution : AL 19 02
Go to Begin
S102. Divergent series : 0 + 0 + 0 + 0 + ..... = 1
Convergent and divergent
- The series is convergent if the sum goes to a definite value
- The seris is diverent if the sum goes to infinite or to indefinite value
-
Study subjects :
Solution : AN 18 03
Go to Begin
S103. Harmonic series Sum[1/n] is divergent
Solution
-
Study subjects :
Solution : AN 18 04
Go to Begin
S104. Study the curve of y = 1/(2*x)
Questions
- Prove that the curve is symmetrical to line y = x
-
Study subjects :
Solution : TR 27 01
Go to Begin
S105. Twin patterns of R = sin(p*A/q)^M and R = cos(p*A/q)^M
Question
- 1. What are twin patterns ?
- 2. Find the conditions of the twin patterns
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Study subjects :
Solution : AN 10 08
Go to Begin
S106. Circle inscribed an equilateral triangle
Question
- Find the ratio of the area of triangle to area of circle
-
Study subjects :
Solution : GE 27 06
Go to Begin
S107. Square inscribed an equilateral triangle
Question
- Find the ratio of the area of triangle to area of square
-
Study subjects :
Solution : GE 27 07
Go to Begin
S108. Triangle : Medians are concurrent
Solution
-
Study subjects :
Solution : Q06 in GE 03 03
- What is one third rule of the median of triangle ?
- What is two third rule of the median of triangle ?
Go to Begin
S109. Triangle : Area of triangle formed by medians fo triangle ABC
Diagram
-
Study subjects :
Solution : GE 27 08
- 1. Draw a triangle ABC, find its area
- 2. Find the length of the medians
- 3. Use the medians making a triangle PQR
- 4. Find the area of triangle PQR
- 5. Find ratio of area of triangle ABC to area of triangle PQR
Go to Begin
S110. Triangle : Heights of triangle are concurrent
Solution
-
Study subjects :
Solution : Q07 in GE 03 03
- What is pedal triangle ?
Go to Begin
S111. Triangle : Ortho-center, centroid, circum-center colinear
Diagram
- Study subjects : GE 27 15 GE 27 15
Go to Begin
S112. Equilateral triangle : Distance of inside point to sides equals height
Diagram
- Study subjects : GE 27 18
Go to Begin
S113. Equilateral triangle : Divide side into 3 equal parts
Method Proof
- Study subjects : GE 27 17
Go to Begin
S114 : y = (x^3)/(x^2 - 1)
Diagram
- 1. Domain if y' = (-)
- 2. Domain if y" = (-)
- 3. Find maximum and minimum points
- 4. Find point of inflection
- CA 27 17
Go to Begin
S115 : y = (x^4)/(x^2 - 1)
Diagram
- 1. Domain if y' = (+)
- 2. Domain if y" = (+)
- 3. Find maximum and minimum points
- 4. Find point of inflection
- CA 27 18
Go to Begin
S116 :
Questions
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S117 :
Go to Begin
S118 :
Go to Begin
S119 :
Study transformation of circle (x-h)^2 + (y-k)^2 = r^2
Go to Begin
S120 :
Go to Begin