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



  • Keyword | S87 - Parabola Asymptote : Sketch y = x^2 + 1/x
  • Keyword | S33 - Parabola : Properties of y = (x^2)/2 - 1
  • Keyword | S36 - Parabola : Construct using locus definition
  • Keyword | S22 - Parabola : Find equation of directrix
  • Keyword | F306- Parabola : Locus y = (x^2)/(2*D) - D/2
  • Keyword | F312- Parabola : Sketch
    • Convert R = D/(1 - sin(A)) to rectangular form
  • Keyword | F313- Parabola : Polar form
    • 1. Compare R = D/(1 - sin(A)) with R = D/(1 - cos(A))
    • 2. Compare R = D/(1 - sin(A)) with y = (x^2)/(2*D) - D/2
    • 3. Compare R = D/(1 - sin(A)) with y = a*(x^2) + B*x + c
  • Keyword | F314- Parabola : Quadratic function
    • 1. Properties of y = a*x^2 + b*x + c
    • 2. Parabola of y = a*x^2 + b*x + c
  • Keyword | S20 - Parametric : Comparison
    • x = sec(t) and y = tan(t) with x = tan(t) and y = sec(t)
  • Keyword | P001- Parametric equation : x = tan(t) and y = sec(t)
    • 1. Find coordinate of foci
    • 2. Find equation of asymptotes
  • Keyword | Z005 - Pascal triangle and sequence
    • Find sequence from Pascal triangle
    • Prove that Sum[n*(n + 1)/2] = n*(n + 1)*(n + 2)/6
    • Prove that Sum[C(n + 1, 2)] = C(n + 2, 3)
  • Keyword | Pascal triangle and symmetrical matrix order 5
    • 1. Find element row 1 and column 5 for power 3 of the matrix
    • 2. Find element row 1 and column 5 for power 4 of the matrix
    • 3. Find element row 1 and column 5 for power 5 of the matrix
  • Keyword | S11 - Pedal triangle : Definition and construction
  • Keyword | S24 - Pentagon : Change it to an equal area triangle
  • Keyword | S77 - Petals of R = sin(2*A)
  • Keyword | F426- Petals of R = sin(p*A)
    • 1. Prove that graph of R = sin(A) is a circle
    • 2. Prove that graph of R = sin(p*A) has p petals if p is odd
    • 3. Prove that graph of R = sin(p*A) has 2*p petals if p is even
  • Keyword | F425- Petals of R = sin(p*A/2)
    • 1. Prove that graph of R = sin(p*A/2) has 2*p petals if p is odd
    • 2. Prove that graph of R = cos(p*A/2) has 2*p petals if p is odd
    • 3. Twin patterns of R = sin(p*A/2) and R = cos(p*A/2) if p is odd
  • Keyword | S78 - Petals of R = sin(3*A)
  • Keyword | S79 - Petals of R = sin(3*A/2)
  • Keyword | S04 - Perfect number
    • 1. What is perfect number
    • 2. How to find 3rd perfect number ?
    • Keyword | P005- Perfect number
      • 1. prove that 496 is a perfect number
      • 2. prove that 8128 is a perfect number
    • Keyword | P006- Pi = 3.14159....
      • 1. Value of pi to 1000 decimal place
      • 2. Story of pi
    • Keyword | P003 - Probability
      • Four pairs color balls. Put each 2 balls into 4 boxes
      • Find probability all boxes having different color
    • Keyword | P004 - Probability
      • Hypergeommetric
      • Find probability with no spade in a hand of bridge
    • Keyword | P004 - Probability
      • Hypergeometric
      • 24 electric bulbs with 12.5% defective. Take 3 bulbs and all bad
    • Keyword | S49 - Product formula
      • Example : Angles of triangle in GP terms and common ratio = 3
    • Keyword | S54 - Product formula
      • S(n) = cos(x) + cos(3*x) + ... + cos((2*n-1)*x)
    • Keyword | S55 - Product formula
      • S(n) = sin(x)^2 + sin(2*x)^2 + ... + sin(2*x)^n
    • Keyword | S60 - Product formula
      • Find cos(20)*cos(40)*cos(60)*cos(80) without calculator
    • Keyword | S59 - Product formula
      • Find cos(20)*cos(40)*cos(60)*cos(80) without calculator
    • Keyword | S09 - Properties of numbers
      • Abundunt number, perfect number and deficient number
    • Keyword | S00 - Pythagorean Law
      • 1. Pythagorean relations
      • 2. Pythagorean triples


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