Mathematics Dictionary
Dr. K. G. Shih
Mathematics Examples
Symbol Defintion
...... Example : x^2 = square of x
Keywords
.............. Find given keyword by numbers
A
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B
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C
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D
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E
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F
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G
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H
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I
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J
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K
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L
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M
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N
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O
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P
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Q
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R
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S
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T
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U
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V
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W
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X
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Y
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Z
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Topics by Keywords
Q01. A
Example |
Absolute - Solve abs(x - 2) + Abs(x + 3) = 6
Example |
Absolute - Solve abs(x^2 - 6*Abs(x) + 8) = 0.5
Example |
Amicable number - Find factors of amicable number
Example |
Amicable number
1. Prove 220 and 284 are amicable pairs
2. Prove 1184 and 1210 are amicable pairs
Topic |
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Q02. B
Example |
Binomial expansion : 5^(2*n) - 24*n - 1 is divisible by 576
Topic |
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Q03. C
Example |
Chords : 11 points on circle, how many chords can be drawn
Example |
Cosine Function - Spectial value of cos(60)
Example |
Cos(18) = Sqr(2*Sqr(5) + 10)/4 in TR 14 02
Topic |
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Q04. D
Example |
Demovire's Theory : Solve x^4 + x^3 + x^2 + x + 1 = 0 by construction
Example |
Demovire's Theory : Solve x^4 - x^3 + x^2 - x + 1 = 0 by construction
Example |
Determinant : Two rows are same or two columin are same (AL 13 11)
Topic |
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Q05. E
Example |
Equation : Solve x^5 + 1 = 0 by construction
Example |
Equation : Solve x^5 - 1 = 0 by construction
Example |
Equation : Solve x^5 +3*x^4 - 5*x^3 - 15*x^2 + 4*x + 12 = 0
Example |
Equation : Solve x^7 + 1 = 0 by construction
Example |
Equation : Solve x^7 - 1 = 0 by construction
Example |
Equation : Solve x^7+ 2*x^6- 5*x^5- 13*x^4- 13*x^3- 5*x^2+ 2*x+ 1 = 0
Topic |
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Q06. F
Example |
Fibonacci's sequence in Pascal triangle
Topic |
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Q07. G
Topic |
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Q08. H
Topic |
Hyperbola : 9*x^2 - 25*y^2 + 18*x + 50*y - 191 =0
1. Find focal length
2. Find coresponding polar form
Topic |
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Q09. I
Keyword |
Intersection of quadratic function with its inverse
1. Find intersections of y = x^2 - 2*x + 4 with its inverse
2. Find intersections of y = x^2 - 3*x + 4 with its inverse
Keyword |
Intersection of quadratic function with its inverse
1. How many intersections of quadratic function with its inverse ?
2. Find intersections of y = x^2 - 5*x + 8 with its inverse
Keyword |
Intersection of quadratic function with its inverse
1. (b - 1)^2 - 4*a*c = 0 has one point of intersection
2. Find intersections of y = x^2 - 6*x + 8 with its inverse
Topic |
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Q10. J
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Q11. K
Topic |
Keywords of the system
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Q12. L
Example |
Lim[sin(a*x)/x] = a and application
Example |
Lim[(1+a*x)^(1/x)] = e^a and application
Example |
Lim[(1+1/x)^(a*x) = e^a and application
Topic |
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Q13. M
Topic |
Magic circles of number 1 to 33
Topic |
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Q14. N
Topic |
Number : Arrangement of number 7 as n1 + n2 + n3
Topic |
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Q15. O
Topic |
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Q16. P
Example |
Pascal triangle : Find Fibonacci's sequence in Pascal triangle
Example |
Perfect numbers - Find factors of 1st 7 perfect numbers
Example |
Perfect numbers - Prove that 496 is a perfect number
Example |
Probability - Six color balls A, A, B, B, C, C each two puts into 3 boxes
Example |
Probability - Eight color balls A,A,B,B,C,C,D,D each two puts into 4 boxes
Topic |
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Q17. Q
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Q18. R
Topic |
R = cos(2*A) and R = sin(2*A) : Comparison
Topic |
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Q19. S
Example |
Sine function - Spectial value of sin(30)
Example |
Sin(18) = Sqr(Sqr(5) - 1)/4 in TR 14 02
Example |
Series : Sum[n^2] = n*(n+1)*(2*n+1)/6
Example |
Series : Sum[n^3] = (n*(n+1)/2)^2
Keyword |
Series : Sum[n^2] = n*(n+1)*(2*n+1)/6
1. Prove by observation
2. prove by using sum[C(n+1,2)] = C(n+2,3)
3. Prove by induction
4. Prove by Sum[(x+1)^3 - x^3] = (x + 1)^3 - 1
Keyword |
Series : Sum[n^2] = (n*(n+1)/20^2
1. Prove by observation
2. prove by using sum[C(n+2,3)] = C(n+3,4)
3. Prove by induction
4. Prove by Sum[(x+1)^4 - x^4] = (x + 1)^4 - 1
Topic |
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Q20. T
Example |
Tangent function - Spectial value of tan(45)
Topic |
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Q21. U
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Q22. V
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Q23. W
Example |
Weekday Index - Find day of week
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Q24. X
Example |
x^5 + 3*x^4 - 5*x^3 - 15*x^2 + 4*x + 12 = 0
Example |
x^7 + 2*x^6 - 5*x^5 - 13*x^4 - 13*x^3 - 5*x^2 + 2*x + 1 = 0
Topic |
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Q25. Y
Example |
y = x^5 + 3*x^4 - 5*x^3 - 15*x^2 + 4*x + 12
Example |
y = x^7 + 2*x^6 - 5*x^5 - 13*x^4 - 13*x^3 - 5*x^2 + 2*x + 1
Topic |
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Q26. Z
Example |
z = cos(Sqr(x^2 + y^2))
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Copyright © Dr. K. G. Shih, Nova Scotia, Canada.
