Maths formulas

Maths formulas and Maths formulas sheets are the most usefully content for all most every student. We have created a detailed Maths sheet of all important formulas used while solving Maths problems. Our academic team consist of more than six thousand maths teachers who are involved in Home tuitions across the county having experience in teaching students of different boards like CBSE, ICSE, state board and different competitive entrance exams like JEE, NTSE, SSC, and UPSC. Such experienced teachers understand the role and use of Maths formulas and know-how to prepare the Maths formulas sheet. Based on our teacher's vast experience we have selected the most used Maths formulas and prepared a list of Maths formulas to help students in final revisions.

Key features of Maths formulas

We have prepared one sheet for each Maths formula having the following key features

1. All maths formulas are convers in the following sheet starting from class 1 Maths formulas to graduation level Maths formulas.
2. For each math formula, we have prepared a different sheet and page to give you all details required.
3. Each Maths formulas sheet not only covers the formula details but also added all the details required to understand the application of the formulas in the numerical.
4. All formulas are explained with the help of solved examples so that students can not only learn the important formulas but also understand the application of formulas through the use of solved examples
5. Few Maths formulas required a bit more explanation, for such formulas we have added proper theory and images to explain such concepts.

10 Most Important Maths formulas class wise

List of Important Maths formulas for class 1

Class 1 is the start of your academics and students learn mainly numbers in this class so the use of maths formulas is limited still few of the maths formulas use in this class are.

1. Counting tricks and Formula for Class 1 Maths

2. Additive identity formula for class 1

If we add or subtract zero from any number we will get the same number.

a + 0 = a ; 0 + a = a

If we subtract zero from any number we will not get the same number.

2 – 0 = 2, 0 – 2 = -2
3 – 0 = 3, 0 – 3 = -3
0 – a is not equal to a – 0

3. Similar shape used in class 1 Maths

Two shapes are called similar shapes if they have looks the same but size may be different.

5. a + b = b + a is always true.

a – b ≠ b – a is true if a and b are different.

a – b = b – a is true if a and b are the same.

List of Important Maths formulas for class 2

1. Sequence formulas and trick

The sequence is a collection of objects. Which follows a pattern

2. Week

There are seven days a week

Yesterday → 1 day before

Tomorrow → 1 day after.

DAYS OF THE WEEK

Yesterday and Tomorrow

YEAR – In a year, there are 12 months and 365 or 366 days.

January – 31 days. February – 28/29 days. December – 31 days. 4 months have 30 days. 7 months have 31 days. February is the shortest month

3. Knuckles Method and formula used in it

List of Important Maths formulas for class 3

1. Even Number formulas: All numbers that end with 0, 2, 4, 6 or 8 are called even numbers.

Even number example for apples:

If we add or subtract zero from any number we will get the same number.

a + 0 = a ; 0 + a = a

2. Odd Numbers formulas

All numbers that end with 1, 3, 5, 7 or 9 are called odd numbers.

Odd number example for mangoes:

3. Shapes :

Q.1. How many CHIPS have a triangle shape?

Ans. 6 chips are having a triangle shape.

Q.2. How many T.V have rectangle shapes?

Ans. There is 5 TV  having rectangle shapes.

Q.3. How many biscuits have a square shape?

Ans. 4 biscuits are having a square shape.

Q.4. How many coins have a circular shape?

Ans. 7 coins are having circular shapes.

4. Measurement of length
For lengths: we use, Kilometres, Meters, Centimetres, and Multi-Metre.
1 Km = 1000 m

1 m = 100 cm

1 cm = 10 mm

Measuring Length

5. Measurement of weight

For weight: we use, kilogram (kg), Gram(gm), Multi-gram (m)

1 Kg = 100 gm

weighting 1kg of potato

1 gm = 1000 mg Paperclip weighing 1 gram

6. General measurement

1 litre = 1000 ml

7.1 Rupee = 100 paisa

= 100 times of

8. Face Value formula and application

The face value of any digit is the numerical value of the digit itself.

Place value and Face value in an Abacus

9. Place value

Place value is the value represented by a digit in the number on the bonds of its position.

Place value of digit formula= (face value) × (numerical value of place)

Face value = 6

26749

Place Value = 6 x 1000 = 6000

Difference between place value and face value

10. Table:

9 Times Table

8 Times Table

7 Times Table

6 Times Table

6 x 1 = 6

6 x 2 = 12

6 x 3 = 18

6 x 4 = 24

6 x 5 = 30

6 x 6 = 36

6 x 7 = 42

6 x 8 = 48

6 x 9 = 54

6 x 10 = 60

5 Times Table

4 Times Table

3 Times Table

2 Times Table

List of Important Maths formulas for class 4

1. Multiplication and Division (Formula and tricks)

(a) a × b = b × a

(b) a × 0 = 0 × a = 0

0 × 1 = 0

0 × 4 = 0

0 × 7 = 0

0 × 9 = 0

0 × 13 = 0

0 × 18 = 0

(c) a × 1 = 1 × a = a

Identity property of multiplication

A number × 1 = the number

1 × a number = the number

0 × 3 = 3

0 × 6 = 6

0 × 8 = 9

0 × 17 = 17

0 × 74 = 74

0 × 99 = 99

2. Division

3.

0 ÷ a = 0 , a ÷ 0 ≠ 0

a ÷ 1 = 0

a ÷ b ≠ b ÷ a

4. Factor

Factors – Factors are numbers that are multiplied together to get the given number.

5. Prime Number

Prime numbers are numbers that are not divisible by any number other than 1 and the number itself

6. Composite Number

These numbers have more than two factor

Examples of Composite Numbers

4,6,8,9,10,12,14,15

Special Note:

Every Whole Number from 2 on is

either composite or prime.

Whole Numbers and Natural Numbers

Divisibility Rule and formula

1. A number is divisible by 2 if the digits at the unit place are 0, 2, 4, 6 or 8.
2. A number is divisible by 3 if the sum of its digits is divisible by 3.
3. A number is divisible by 5 if the digit at one place is 0 or 5
4. A number is divisible by 6 if it is divisible by 2 and 3 both.
5. A number is divisible by 10 if the digit at one place is 0.

8. Diameter of circle formula = 2 × radii of the circle.

9. Perimeter of square formula = 4 × (length of a side)

Perimeter of rectangle formula = 2 × (length + breadth)

The perimeter of the triangle = the sum of the length of the sides

P = a + b + c

Perimeter of triangle

10. Area of rectangle formula = length × breadth

Area of Rectangle

Area of square = side × side

List of Important Maths formulas for class 5

1. Volume of Cuboid formula

The volume of cuboid = length × breadth × height

2. Volume of the cube formula

The volume of the cube = side × side × side.

The volume of the cube formula

the volume of a cube with side length s
V = s x s x s = s³

3. Speed

Speed = distance travelled in 1 hours/min/sec.

4. Regular polygon –

Any polygon which has all sides equal is called a Regular polygon. Eg. Square, pentagon, hexagon.

5. Right angle and formula of right angle

when the angle is 90^°

6. Acute angle formula

when the angle is 90^°

7. Obtuse angle formula

when the angle is 90^°

8. Sum and difference of two odd numbers are even.

9. Sum and difference of two even numbers are even.

10. If one angle of a triangle is 90° then the triangle is called a right-angled triangle

List of Important Maths formulas for class 6

1. Natural Number - All positive integers are called natural numbers.
2. Whole Number
   Natural numbers along with zero form the collection of whole numbers.
3. Every prime number except 2 is odd and 2 is the smallest prime number which is even.
4. A number is divisible by.
   1. 4 if the number formed by its last two digits is divisible by 4.
   2. 8 if the number formed by the last three digits is divisible by 8
   3. a9 if the sum of digits of numbers is divisible by 9.
   4. 11 if the difference between the sum of digits at odd places and the sum of digits at even places (from right) of the numbers is either 0 or multiple of 11.
5. Equilateral Triangle: A triangle in which all sides are equal


6. Rhombus: A quadrilateral in which all sides are equal and opposite sides are parallel.


7. 1. a + b = b + a
   2. (a + b) + c = a + (b +c)
8. 1. a × b = b × a
   2. a × (b + c) = a × b + a × c
9. Isosceles Triangle: A triangle in which two sides are equal


10. Scalene Triangle: A triangle in which all three sides are of different lengths, and all three angles are of different measures.

List of Important Maths formulas for class 7

Mean

The mean is the average of the norm.

Add up all the values to find the total.

Divide the total by the number of values you added together.

2 + 2 + 5 + 6 + 7 + 8 = 30

30 ÷ 6 = 5

The mean number is 5.???????

???????

Median

Order the set of numbers, the median is the middle number

9 , 3 , 1 , 8 , 3 , 6

1 , 3 , 3 , 6 , 8 , 9

(3 + 6) ÷ 2

The median is 4.5.???????

Mode

The most common number

9 , 3 , 1 , 8 , 3 , 6

The mode is 3.

Range

The difference between the highest and lowest number

9 , 3 , 1 , 8 , 3 , 6

9 - 1 = 8.

The Renge is 8.

The angle sum property of a triangle states that the angles of a triangle always add up to 180°

∠A + ∠B + ∠C = 180°

∠D + ∠E + ∠F = 180°

∠P + ∠Q + ∠R = 180°

Triangle Inequality Theorem The sum of lengths of any two sides of a triangle is greater than the third side. a + b > c a + c > b b + c > a They have to be able to reach!! Note that there is only one situation in which you can have a triangle; when the sum of two sides of the triangle is greater than the third. Where, P is Principal r is % rate of interest per year T is the number of years. Mean = sum of all observations/number of all observations Mode – mode of a set of observations is the observation that occurs most often Median – After arranging data in ascending or descending order, the middle term is median. Sum of the angle of a triangle = 180° Sum of lengths of any two sides of a triangle is greater than the third side. In a right-angled triangle C2 = a2 + b2 (PYTHAGORAS PROPERTY) BC2= AB2+AC2 Simple Interest = PRT/100 Area of parallelogram = base × height Triangle = 1/2 × base × height. List of Important Maths formulas for class 8 Probability of an event formula (where a is positive) Amount after n years when interest is compounded annually Where, P is Principal r is the % rate of interest per year. Identity – An identity is an equality which is true for all values of the variable in the equality (a + b)2 = a2 + 2ab + b2 (a - b)2 = a2 - 2ab + b2 (a + b) (a - b) = a2 - b2 (a - b)2  = (a + b)2- 4ab  For any polyhedron = [F + V - E = 2] where, F is the number of faces V is the number of vertices E is the number of edges Area of trapezium = 1/2 × (sum of the length of parallel sides) × (perpendicular distance between them) Area of rhombus = 1/2 × (product of diagonals) Formula of Surface area (i) Cuboid = 2 (lb × bh + LH) (ii) Cube = 6l2 (iii)Cylinder = 2ρr (r + h) Formula Volume  (i) Cuboid = lbh (ii)Cube = l3 (iii)Cylinder = ρr2h General approach to numbers If ab is a two-digit number then ab = 10a + b List of Important Maths formulas for class 9 Factor theorem If f(x) is a polynomial of degree n ≥ 1 and ‘a’ is any real number, then, (x-a) is a factor of f(x), if f(a) = 0. Remainder theorem If a polynomial f(x) is divided by the binomial x-a, the remainder obtained is f(a). General formula (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx (x + y)3 = x3 + y3 + 3xy (x + y) (x – y)3 = x3 – y3 – 3xy (x – y) x3 + y3 + z3 – 3xyz = (x + y + z) (x2 + y2 + z2 – xy – yz – zx) x2 + y2 + z2 – xy – yz – zx = 1/2 [(x – y)2 + (y – z)2 + (z – x)] x3 + y3 + z3 – 3xyz = 0 and x + y + z = 0 OR x = y = z Relation between the area of a triangle and the median of the triangle A median of a triangle divides it into two triangles of equal areas. Cyclic quadrilateral If the sum of opposite angles of a quadrilateral is 180° the hen quadrilateral is cyclic. ∠A + ∠C = 180° ∠B + ∠D = 180° Properties of the triangle in a circle. Angles in the same segment of the circle are equal. Angle in a semicircle at the right angle. (here AB is diameter). HERON's FORMULA Area of triangle = and a,b, and c are the length of the sides Area-related terms The curved surface area of the cylinder = 2ρrh The curved surface area of the cone = ρrl The surface area of the sphere = 4ρr2 Volume-related terms Volume of cone = 1/3ρr2h The volume of the sphere = 4/3ρr2 List of Important Maths formulas for class 10 If α, β are roots of ax2 + bx + c = 0 (where a ≠ 0) Then a + b = -b/a and ab = c/a If x1, x2, x3 are root of ax3 + bx2 + cx + d = 0 (where a ≠ 0) Then, Sum of roots = x1, x2, x3 = -b/a Product of roots taken two at a time = x1x2 + x2x3 + x3x1 = c/a Product of roots = x1, x2, x3 = -d/a Remainder Theorem If a polynomial p(x) is divided by any non-zero polynomial g(x) then p(x) = g(x) × q(x) + r(x), Where r(x) = 0 or degree of r(x) < degree of g(x) Roots of quadratic equation ax2 + bx + c = 0 where and (where D = b2 – 4ac & D > 0 (i)If D > 0, root are real and distinct. (ii) If D = 0, root are real and equal. (iii) If D < 0, root are non-real or imaginary. Arithmetic Progression nth term of A.P. is Tn = a + (n – 1)d Sum of n term of A.P. is Sn = n/2 [2a + (n – 1)d], (where a → first term, d → common difference) Distance between two points A(x1, y1) & B(x2, y2) is Section formula : If a point p(x, y) divides the line joining A(x1, y1) & B(x2, y2)in the ratio of m : n. (i) internally then Section Formula (ii)Externally then, When vertex coordinates of a triangle are given, When vertex coordinates of a triangle are given, A(x1, y1) & B(x2, y2) is Area = 1/2 |x1(y2 – y3) + x2(y3 – y1) + x3(y1 – y2)| Circle-related terms Length of the arc of a circle which subtend angle q (in degree) at centre and Area of sector Frustum-Related Term The volume of a frustum of cone = The curved surface area of a frustum of a cone = The total surface area of a frustum of a cone = List of Important Maths formulas for class 11 De morgan's Law If A and B are two sets. Then, (i) (ii) Binomial The general term in the expansion of (a + x)n, (i)