Basic Math Formulas

Mathematics is divided into various branches according to the way of calculation involved and the topics covered by them. All the branches have various formulas that are used for solving various mathematical problems. The branches include geometry, algebra, arithmetic, percentage, exponential, etc.

This article will provide you with all the basic formulas for different branches of mathematics, including trigonometry, geometry, algebra, probability, coordinate geometry, etc.

List of Basic Algebra Formulas

• a² – b² = (a – b)(a + b)
• (a + b)² = a² + 2ab + b²
• a² + b² = (a + b)² – 2ab
• (a – b)² = a² – 2ab + b²
• (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca
• (a – b – c)² = a² + b² + c² – 2ab + 2bc – 2ca
• (a + b)³ = a³ + 3a²b + 3ab² + b³
• (a – b)³ = a³ – 3a²b + 3ab² – b³
• a³ – b³ = (a – b)(a² + ab + b²)
• a³ + b³ = (a + b)(a² – ab + b²)
• (a + b)⁴ = a⁴ + 4a³b + 6a²b² + 4ab³ + b⁴
• (a – b)⁴ = a⁴ – 4a³b + 6a²b² – 4ab³ + b⁴
• a⁴– b⁴ = (a – b)(a + b)(a² + b²)
• (a^m)(aⁿ) = a^{m + n}
• (ab)^m = a^mb^m
• (a^m)ⁿ = a^mn

Various algebraic formulas that are widely used are given in the image below.

Basic Geometry Formulas

We study Geometry formulas under two headings, that is,

• 2-D Formulas
• 3-D Formulas

2D Formulas

• Rectangle

• Perimeter of Rectangle = 2(l + b)
• Area of Rectangle  = l × b

Where 
‘l’ is Length
‘b’ is Breadth

• Square

• Area of Square = a²
• Perimeter of Square = 4a

Where 
‘a’ is the length of sides of a Square

• Triangle

• Area of Triangle= 1/2 × b × h

Where 
‘b’ is the base of the triangle and 
‘h’ is the height of the triangle

• Trapezoid

• Area of Trapezoid = 1/2 × (b₁ + b₂) × h

Where 
b₁ and b₂ are the bases of Trapezoid
h is height of Trapezoid

• Circle

• Area of Circle = π × r²
• Circumference of Circle = 2πr

Where 
‘r’ is radius of a Circle

Various formulas used for 2-D objects are,

3D Formulas

• Cube

• Surface Area of Cube = 6a²
• Volume of Cube = a³

Where 
‘a’ is the length of sides of Cube

• Cylinder

• Curved Surface Area of Cylinder = 2πrh
• Total Surface Area of Cylinder = 2πr(r + h)
• Volume of Cylinder = V = πr²h

Where 
‘r’ is the radius of base of Cylinder
‘h’ is the height of Cylinder

• Cone

• Curved Surface Area of Cone = πrl
• Total Surface Area of Cone = πr(r + l) = πr[r + √(h² + r²)]
• Volume of Cone = V = 1/3× πr²h

where, 
‘r’ is the Radius of base of Cone
h is the Height of the Cone

• Sphere

1. Surface Area of a Sphere = S = 4πr²
2. Volume of a Sphere = V = 4/3 × πr³

Where, 
r is the Radius of Sphere

Various formulas used for 3-D objects are,

Basic Probability Formulas

Probability can simply be defined as the possibility of the occurrence of an event. It is expressed on a linear scale from 0 to 1. There are three types of probability: theoretical probability, experimental probability, and subjective probability.

P(A) = n(A)/n(S)

Where,
P(A) is the Probability of an Event.
n(A) is the Number of Favourable Outcomes
n(S) is the Total Number of Events

Basic Fraction Formulas

A fraction is a number expressed with integers in which the numerator is divided by the denominator. A fraction is basically the quotient of a division. 

• Addition of a whole number and a fraction:
  \left( a + \frac{b}{c} \right) = \frac{(a \times c) + b}{c}
• Addition of fractions with the same denominator:
  \frac{a}{b} + \frac{d}{b} = \frac{a + d}{b}
• Addition of fractions with different denominators:
  \frac{a}{b} + \frac{c}{d} = \frac{a \times d + b \times c}{b \times d}
• Multiplication of fractions:
  \frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}
• Division of fractions:
  \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

Basic Percentage Formula

A percentage is a numerical value or ratio expressed as a fraction of 100. It is generally symbolized by the sign %.

Percentage = (Given Value/Total Value) × 100

Distance Formula

If the coordinates of points A are (x₁, y₁) and B are (x₂, y₂), the formula used to calculate the distance between these two points is discussed in the image below.

Trigonometry Formulas

The six basic functions of Trigonometry are,

• Sin Function
• Cos Function
• Tan Function
• Cosec function
• Sec Function
• Cot Function

The three basic trigonometric functions formulas are,

Basic Math Formulas Chart

All the general formulas in Maths are discussed below.

Math Formulas List

Here is the list of the most commonly used maths formulas :

Solved Question on Basic Math Formulas

Question 1: Determine the probability of drawing an ace from a standard deck of cards.

Solution:

Given:

• Total number of outcomes n(S) = 52
• Number of favorable outcomes​ n(A) = 4 aces

Now,
P(A) = n(A)/n(S)
= 4/52
= 1/13

Hence, The probability of drawing an ace is 1/13

Question 2: Simplify 3/(x - 1) + 1/(x - 1) = 2/x

Solution:

3/(x-1) + 1/(x - 1) = 2/x
4/(x - 1) = 2/x
2x = x - 1
x = -1

Question 3: If x + 1/x = 3. Find the value of x² + 1/x².

Solution:

Given,
x + 1/x = 3

Squaring both side
x + 1/x)² = (3)²
x² + 2 × x × 1/x + (1/x)² = 9
x² + 1/x² + 2 = 9
x² + 1/x² = 7

Question 4: If the radius of a circle is 21cm. Find the area of the given circle.

Solution:

Given:
Radius of Circle = 21cm

We have,
Area of the circle (A) = πr²
A = 22/7 × 21 × 21
A = 1386cm²

Hence, the area of the given circle is 1386cm²

Question 5: Find the area of a triangle having a base of 100cm and a height of 20cm.

Solution:

Given:

• Base of the triangle = 100cm
• Height of the triangle = 20cm

We have,
Area(A) = 1/2 × b × h
= 1/2 × 100 × 20
= 1000cm²

Question 6: Punam has 4/5 parts of the field, among which she uses 2/5 parts for farming. How many parts of the farm are left for other purposes?

Solution:

Given,

• Total Fraction of Land = 4/5
• Total Fraction used for Farming = 2/5.

Now,
Land  Left = 4/5 - 2/5
= 2/5

Hence, 2/5 part of the field is left for other purposes.

Question 7: What will be 20% of 240 kg?

Solution:

Given,

= 20% of 240kg
= 20/100 × 240
= 48 kg

Hence, 20% of 240 kg will be 48 kg.