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# Basic Math Formula Sheet

Math Formula Sheet:

The Basic Math formula sheet covers the topic under number system, algebra, Trigonometry and Geometry part of the subject. The easy understanding and memorizing of the given formulas helps students to score well in their exam. Based on the requirement of student learning purposes a list of basic math formula  are given below.

Rule of Proportion Formula:

1. Addition: $\frac{a}{b}$ + $\frac{c}{d}$ = $\frac{ad+bc}{bd}$

2. Subtraction:  $\frac{a}{b}$ - $\frac{c}{d}$ = $\frac{ad-bc}{bd}$

3. Multiplication:  $\frac{a}{b}$  = $\frac{c}{d}$,then a*d = c*b

4. Division:  $\frac{\frac{a}{b}}{\frac{c}{d}}$ = $\frac{ad}{bc}$

Consumer Math Formulas:

When rate of discount is given  Discount = $\frac{MP*Rate of Discount}{100}$

Simple Interest = $\frac{PTR}{100}$ where P = Principal , T = Time in years R = Rate of interest per annum

Principal = $\frac{100*S.I}{R*T}$

Rate = $\frac{100*S.I}{P*T}$

Time = $\frac{100*S.I}{P*R}$

Principal = Amount - Simple Interest
Discount = MP - SP

Commutative and Associative properties of sets:

Commutative  property:

1.  A∩B = B∩A
2.  A∪B = B∪A

Associative   property:

1. (A∩B)∩C = A∩(B∩c)
2. (A∪B)∪C = A∪(B∪c)

Expansion of Algebraic Expression:

1. (x + a) (x + b) = x+ x(a+b) + (ab)
2. (a + b)2 = a+ 2ab + b2
3. (a - b)2  = a- 2ab + b2
4. (a- b2) = (a + b) (a - b)

Properties of multiplication of algebraic terms:

Commutative law : a*b = b*a
Associative law :   a*(b*c) = (b*c)*a = (c*a)*b
Distributive law :    a(b + c) = ab + ac

Speed and Time:

Speed = $\frac{distance\ travelled}{Time\ taken}$

Number of Revolution = $\frac{Distance\ travelled}{Circumference\ of\ the\ wheel}$

BODMAS Rule:

Brackets Of
Division
Multiplication
Subtraction

Permutation and  Combination:

The number of permutation of n different things taken r at a time is nPr = $\frac{n!}{(n-r)!}$

The number of combination of n different things taken r at a time is nCr = $\frac{n!}{r!(n-r)!}$

Geometric Formula:

Diameter of a circle d = 2r  , where r is radius
Circumference of  a circle C = 2πr  , when radius is given
Relation between circumference and diameter is C = πd

Area:

Area of a circle = πr2, where r is the radius
Area of rectangle = l*b  ,where l is length and b is breadth
Total surface area of cube = 6a2 sq.units
Total surface area of cuboid = 2[lb+bh+hl] sq.units

Volume:

Volume of cube = l3
Volume of Sphere = ($\frac{4}{3}$) × π × r3
π: 3.14, r: radius of sphere
Volume of a cylinder: π × r2 × h
π: 3.14, r: radius of the circle of the base, h: height of the cylinder

Perimeter:

Perimeter of square : 4s  , s is sides of square
Perimeter of Rectangle : 2(l + w),  l is length and w is width of rectangle

Capacity and Volume:

Metric:
1 liter = 1000 milliliters
Customary:
1 gallon  = 4 quarts
1 gallon = 128 fluid ounces
1 quart = 2 pints
1 pint = 2 cups
1 cup = 8 fluid ounces

Distance Formula:  d = $\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

Slope of a line  m = $\frac{y_{2}-y_{1}}{x_{2}-x_1}$

Midpoint formula : $\left ( \frac{x_1+x_2}{2},\frac{y_1+y_2}{2} \right )$

Slope of an Equation y = mx+b