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Free math tutoring topics


We offer help in almost all topics in math.  A few are mentioned below.
 
  1. Pre Algebra
  2. Algebra
  3. Number Sense
  4. Calculus
  5. Trigonometry
  6. Geometry
  7. Probability
  8. Statistics
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Free Online Tutoring for Math

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Following are few examples of solved problems.
Example 1: -
If the letters of the word " FATHER" are arranged alphabetically as in a dictionary, show that it will occur as the 261 word.
Solution: -
There are six letters in the word "FATHER".  Since the words are arranged alphabetically, first comes the words starting with A.  Then starting with E and then  comes the words starting with F. To find the number of words beginning with A, keep A fixed at the first letter and arrange the remaining 5 letters.  This can be done in 5! = 120 ways.  Similarly the number of words starting with E is 120.  Therefore the total number of words beginning with A and E is 240. Now the words begin with F.  To find the words beginning with FA, arrange the remaining 4 letters which can be done in 4! = 24 ways.  The 241th word is" FAEHRT" and 240+24 = 264 th word is "FATRHE".  THE 263RD WORD IS :fatreh" and the 262nd word is "FATHRE". Therefore, the 261th word is "FATHER".

Example 2: -
If the roots of the equation x2 - 2x + 7 = 0 are α and β, find the equation whose roots are α2+ β and β2+ α
Solution: -
Since α and β are the roots of the equation x2 - 2x + 7 = 0, α + β = 2 and αβ = 7.
Now sum of the roots α2+ β + β2+ α = α2+ β2 + α + β
                                                        =(α + β)2- 2αβ + α + β
                                                        = 22 - 2 x 7+ 2
                                                        = 4 -14 + 2 = -8
Product of the roots = (α2+ β)( β2+ α) = α2β2 + α3 + β3+ αβ
                                                           = α2β2 + (α + β)3- 3αβ(α + β) + αβ
                                                           = 72 + 23 - 3 x 7 x 2 + 7
                                                           = 49 + 8 - 42 + 7
                                                           = 22
Therefore the equation whose roots are α2+ β and β2+ α is
x2 - (sum of the roots)x + product of the roots = 0
That is x2 + 8x + 22 = 0

Example 3: -
The sum of three numbers in Arithmetic Progression is 42 and their product is 2618.  Find the numbers.
Solution: -
Let the numbers be a - d, a, a + d
Given that the sum of the number is 42.
That is a - d + a + a + d = 42
               3a  = 42
That is a = 42/3 =14.
Also given product of the numbers is 2618
That is (a - d) a(a + d) = 2618
a(a2 - d2) = 2618
14(142 -d2)  = 2618
Dividing both sides by 14, we get
142 -d2 = 187
subtracting 142 from both sides, we get
-d2 = -9
That is d =  ± 3
When d = 3 and a = 14, the numbers are 11, 14, 17.
When d = -3 and a =  14, the numbers are 17, 14, 11.