I will keep adding formulas to this formula sheet. You are welcome to add more onto these.

Algebra

(a+b)^2 = a^2 + b^2 + 2*ab

a^2 - b^2 = (a+b)(a-b)

(a+b)^3 = a^3 + b^3 + 3ab*(a+b)

a^3 + b^3 = (a+b)(a^2+b^2-ab)

a^3 - b^3 = (a-b)(a^2+b^2+ab)

Notes:

(a+b) is always a factor of [a^n + b^n] IFF n is positive odd integer

(a-b) is always a factor [a^n - b^n] IFF n is a positive integer

Sets

AUB = A + B - AnB

AUBUC = A + B + C - AnB - AnC - BnC + AnBnC

Permutation and Combination

Permutations are taken when arrangements are important (the order in which the quanitites occur is important) 

Arrange m out of n things: nPm = n!/[n-m]!

Combinations are taken when selections are important and the order in which people are arranged in the selection doesnt matter for example a,b,c and c,b,a are the same selections or combinations BUT different permutations.

Select m out of n things: ⁿC_m = n!/[ (n-m)! * m! ]

One interesting property:  ⁿC_m = ⁿC_(n-m) 

Probability

P(AUB) = P(A) + P(B) - P(AnB) .... Always Holds for two events A and B

Independent Events: P(AnB) = P(A)*P(B)

Two events A and B are considered independent when occurance of A doesnt affect occurance of B. For example tossing of two coins, the event A that one coin has heads and event B that other coin has tails ... will be two independent events, because neither is connected with each other [both can occur at the same time].

Mutually Exclusive Events: P(AUB) = P(A) + P(B) and P(AnB)=0

Two events A and B are considered Mutually Exclusive, then the occurance of A automatically implies that B CANNOT occur and vice versa. Basically, if one occurs, other cannot.

Coordinate Geometry

Distance:

Distance between two points (x1, y1) and (x2, y2) = sqrt [ (y2-y1)^2 + (x2-x1)^2 ] (this is similar to pythagoras theorem)

Equation of a line:

If two points on the line are (x1, y1) and (x2,y2): [y2 - y1]/[x2 - x1] = [y2-y]/[x2-x]

If the slope m and a point (x1, y1) is given: m = [y-y1]/[x-x1]

If the slope m and Y-intercept c is given: y=mx+c [remember c can be negative]

Geometry

Area of a triangle: 0.5 * base * height

Pythagoras theorem for right angled triangles: hypotenuse^2 = perpendicular^2 + base^2

Important: I am putting forth this sheet for ScoreChase members only! Please seek my permission before distributing this formula list anywhere on the internet.