Other Math Notes

1) Integers

I= { .., -3,-2,-1,0,1,2,3,..}

2) 6.25% of 80 in which No. 80 is called the BASE of the exponent.

3) If quantity increase from 600 to 750, then % increase would be:

150
-----X 100 = 25%
600

If quantity decrease from 500 to 400, then % decrease would be:

100
-----X 100 = 20%
500

4) For any 2 positive numbers x,y; where x

y is

( y-x)100
--------- % greater than x
x

x is

(y-x)100
---------- % less than y
y

5) o(Zero) to the power o(zero) is undefined.

6) Inequalities reversed if the constant is negative and is multiplied on both sides of the equation.

7) A straight line is a graph of a linear equation of the form y=mx+b
where m-> slope of the line passing through points P(x1,y1) & Q(x2,y2) and 'b' is called the y-intercept, m=
y1-y2
-------- (x1 != x2)
x1-x2

8) i) An even number times any integer yield an even Number.
ii) An odd number times an odd number yield an odd number.
iii) Two even Nos. or 2 odd Nos. added together yield an even No.
iv) An odd No. added to an even No. will yield an odd No.

9) Convex Polygon:
----------------- Measure of each interior angle of the polygon is less than 180 deg.

10) The sum of the measures of the interior angles of an n-sided polygon is (n-2) 180 deg.

11) The length of the sides of an isosceles triangle are in the ratio 1 to 1 to Sq.Root(2).

12) The lengths of the sides of 30-60-90 right triangle are in the ratio 1 to Sq.Root(3) to 2.

13) Area of a trapezoid (Only one pair of opp. sides parallel) =
(b1 + b2) h
------------
2
where b1 and b2 are the parallel sides.

14) Length of an arc( in a circle) Arc Measure ( in degrees)
----------------------------- = ----------------------------
Circumference 360


15) Also, Area of sector Arc Measure (in degrees)
---------------------= ---------------------------
Area of entire circle 360

16) Cube
------ Surface Area = 2(lb+bh+lh)

17) Cylinder
--------- Surface Area = 2 pi. r (r + h)

18) Mean- Average
Median - Mid Value
Mode- Most frequently occuring value
Range -Simplest measure of dispersion= (greatest -least) measurement.

19) Standard Deviation : i) Find Mean.
ii) Difference between mean and each measure.
iii) Square each of them.
iv) Sum squared values.
v) Divide the sum by 'n'.
vi) Take the non (-ve) sq. root of quotient.

20) The No. of different committees of 3 people that can be selected from 5 people is
5 !
--------
(5-3)! 3!

5!
=------
2! 3!

120
=-------
2X6

=10

21) In any "staircase", the perimeter is just twice the sum of the height and the length.

22) If the side of a square is 'a', it's diagonal is a X Sq. Root(2).

23) Area of an equilateral triangle is
2
Sq. Root (3) X a
-----------------------
4

24) The sum of the first 'n' positive integers is n(n+1)
--------.
2


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25) + & - Even Odd
-----------------------------------
Even Even Odd
-----------------------------------
Odd Odd Even
-----------------------------------

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X Even Odd
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Even Even Even
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Odd Even Odd
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