Tuesday, April 26, 2016

Logarithms–Important Laws & Formulas

Q) Why log 1=0?
The important thing to remember is the log represents the exponent.  In the case of common logs, the base is always base 10.  Now lets see some examples which clears your doubt:
1) log 100 = 2 because 102 = 100.
2) log 1000 = 3 because 103 = 1000.
3) log 1 = 0 because 100 = 1.
4)  log .1 = -1 because 10-1 = .1
5)  log .01 = -2 because 10-2 = .01logarithms important formulaes for SSC
Q) How to change base in logarithms?
We can change any base to a different base any time we want. The most used bases are obviously base 10 and base e.
Change of base formula:  Logb x = Loga x/Loga b

Sunday, April 24, 2016

Quadratic Equations–Important Formulas

Given the General Equation - ax2 + bx + c = 0, will have 2 roots, as the highest power in the equation is 2.
Those 2 roots are given by the equation  x = -b ± √(b2 -4ac) / 2a

Further, the questions in SSC wont ask you directly to find the roots. Instead he may ask:
a)  Sum of Roots of a quadratic equation = -b/a
b) Product of the roots of a quadratic equation= c/a

Important Concept about the roots:
While finding roots if following conditions are satisfied, then the nature of the roots is as follows:

Wednesday, April 20, 2016

Cyclic Quadrilateral

Q) All triangles have a circum-circle, but not all quadrilaterals do.
Q) Another necessary and sufficient condition for a convex quadrilateral ABCD to be cyclic is that an angle between a side and a diagonal is equal to the angle between the opposite side and the other diagonal. That is, for example,
Q) Ptolemy's theorem expresses the product of the lengths of the two diagonals e and f of a cyclic quadrilateral as equal to the sum of the products of opposite sides:
Q) Ptolemy's Theorem Extension: In a cyclic quadrilateral the ratio of the diagonals equals the ratio of the sums of products of the sides that share the diagonals' end points. In other words, the ratio of the diagonals of any cyclic quadrilateral equals the ratio of the sums of the rectangles contained by the sides that share the diagonals' end points.