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Mathematics Dictionary
Dr. K. G. Shih
Question and Answer
Questions



  • Keyword | Absolute Operation in linear equations
      * Example 1 : Solve abs(x+1)+abs(x+2) = 4
      * Example 2 : Solve abs(x-1)+abs(x+2) = 4
  • Keyword | Absolute operation
    • How many real roots in abs(x^2 - 6*abs(x) + 8) = 0.5
    • How many real roots in abs(x^2 - 6*abs(x) + 8) = 1
    • How many real roots in abs(x^2 - 6*abs(x) + 8) = 8
    • How many real roots in abs(x^2 - 6*abs(x) + 8) = 9
    • If |x^2 - 6*|x| + 8 | = d has 8 real roots, find d.
  • Keyword | Abundant numbers
    • There 22 abundant numbers from 1 to 100
    • Prove that 945 is an abundant number
  • Keyword | Algebra : Graphs of y = F(x)
  • Keyword | Algebra Index
  • Keyword | Algebra Subjects
  • Keyword | Amicable number pairs
      * Example 1 : What are amicable number pairs ?
      * Example 2 : Who discoved amicable number pairs.
  • Keyword | Amicable number pairs
      * Example 1 : 220 and 284 are amicable number pairs
      * Example 2 : 1184 and 1210 are amicable number pairs
      * Example 3 : 2620 and 2924 are amicable number pairs
  • Keyword | Amicable number pairs discovered by Euler
  • Keyword | Amicable number pairs
    • 1. Prove that 220 and 284 are amicable pairs
    • 2. Prove that 1184 and 1210 are amicable pairs
    • 3. Prove that 2620 and 2924 are amicable pairs
    • 4. Prove that 5052 and 5564 are amicable pairs
    • 5. Prove that 6232 and 6368 are amicable pairs
  • Keyword | Analytic Geometry : Diagrams
  • Keyword | Analytic Geometry Index
  • Keyword | Analytic Geometry Subjects
  • Keyword | Angle 30 degrees and 45 degrees
    • 1. Find sin(30) without calculator
    • 2. Find sin(45) without calculator
    • 3. Find sin(60) without calculator
  • Keyword | Angle (A+B) and (A-B)
    • sin(A+B) = sin(A)*cos(B) + cos(A)*sin(B)
    • sin(A-B) = sin(A)*cos(B) - cos(A)*sin(B)
    • cos(A+B) = cos(A)*cos(B) - sin(A)*sin(B)
    • cos(A-B) = cos(A)*cos(B) + sin(A)*sin(B)
  • Keyword | Arcsin(x) : Properties and derivative
  • Keyword | Arcsin(x)
    • 1. First derivative y' = 1/Sqr(1 - x^2)
    • 2. Series of arcsin(x)
  • Keyword | Arctan(x)
    • 1. Area under curve y = 1/(1 + x^2)
    • 2. Series of arctan(x)
  • Keyword | Area of triangle ABC
    • 1. Area of triangle = a*b*sin(C)/2
    • 2. Area of triangle = Sqr(s*(s-a)*9s-b)*(s-c))
    • 3. Area of triangle = abc/(4*R)
    • 4. Area of triangle = 2*(R^2)*sin(A)*sin(B)*sin(C)
    • 5. Area of triangle = r*s
    • 6. Area of triangle = 0.5*(x1*y2 + x3*y1 + x2*y3 - x3*y2 - x2*y1 - x1*y3)
  • Keyword | Area of triange ABC : F on BC, E on CA and T on AB
    • Keyword | Find area EFT if BF = BC/2, CE = CA/2, AT = AB/2
    • Keyword | Find area EFT if BF = BC/3, CE = CA/3, AT = AB/3
    • Keyword | Find area EFT if BF = BC/4, CE = CA/4, AT = AB/4
    • Keyword | Find area EFT if BF = BC/n, CE = CA/n, AT = AB/n
    • Keyword | Find area EFT if BF = BC/2, CE = CA/3, AT = AB/4
  • Keyword | Area of triangle ABC : BF = BC/2, CE = 2*CA/3
    • Find BT : AT if (BTF)^2 = (CEF)*(AET)
  • Keyword | Arithmetic series
  • Keyword | Arrangement of integer n as 3 positive integers
    • Find arrangements to express 7 interms of 3 integers
  • Keyword | Arrangement of integer n as 4 positive integers
  • Keyword | Arrangement of integer n as 5 positive integers
  • Keyword | Arrangement of three digit number from 1, 2, 3, 4
  • Keyword | Arrangement of two digit number from 1, 2, 3
  • Keyword | Asymptote : Definition and rational functions
    • 1. y = ((x - 1)^3)/(2*x), find asymptote
    • 2. y = ((x - 1)^4)/(2*x), find asymptote
  • Keyword | Axioms and Law

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    Copyright © Dr. K. G. Shih, Nova Scotia, Canada.
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