Important formulas of mathematics.

Algebraic formulas

The following formulas are very important to solve any problem of Algebra from 7th to 10th class.

A formula is written in several ways, but it is better to memorize each formula.

If you know these important formulas, you can understand how to solve any number by looking at any number.

1. (a + b) ² = a² + 2ab + b²

2. (a + b) ² = (ab) ² + 4ab

3. (ab) ² = a²-2ab + b²

4. (ab) ² = (a + b) ²-4ab

5. a² + b² = (a + b) ²-2ab.

6. a² + b² = (ab) ² + 2ab.

7. a²-b² = (a + b) (a-b)

8. 2 (a² + b²) = (a + b) ² + (ab)

9. 4ab = (a + b) ²- (ab)

10. ab = {(a + b) / 2} ² - {(ab) / 2}

11. (a + b + c) ² = a² + b² + c² + 2 (ab + bc + ca)

12. (a + b) ³ = a³ + 3a²b + 3ab² + b³

13. (a + b) ³ = a³ + b³ + 3ab (a + b)

14. ab) ³ = a³-3a²b + 3ab²-b³

15. (ab) ³ = a³-b³-3ab (ab)

16. a³ + b³ = (a + b) (a²-ab + b²)

17. a³ + b³ = (a + b) ³-3ab (a + b)

18. a³-b³ = (ab) (a² + ab + b²)

19. a³-b³ = (ab) ³ + 3ab (ab)

20. (a² + b² + c²) = (a + b + c) ² - 2 (ab + bc + ca)

21. 2 (ab + bc + ca) = (a + b + c) ² - (a² + b² + c²)

22. (a + b + c) ³ = a³ + b³ + c³ + 3 (a + b) (b + c) (c + a)

23. a³ + b³ + c³ - 3abc = (a + b + c) (a² + b² + c² – ab – bc– ca)

24. a3 + b3 + c3 - 3abc = ½ (a + b + c) (a – b) ² + (b – c) ² + (c – a) ²

25. (x + a) (x + b) = x² + (a + b) x + ab

26. (x + a) (x - b) = x² + (a - b) x - ab

27. (x - a) (x + b) = x² + (b - a) x - ab

28. (x - a) (x - b) = x² - (a + b) x + ab

29. (x + p) (x + q) (x + r) = x³ + (p + q + r) x² + (pq + qr + rp) x + pqr

Necessary formula of the parameter chapter

You must memorize the following formulas to do the arithmetic chapter. Moreover, you can solve the mathematical problems of Satyam VIII through this figure.

All the formulas of the rectangle are given below:

1. Area of ​​rectangle = (length * width) square unit

2. Perimeter of rectangle = 2 (length + width) unit

3. The angle of the rectangle = √ (length: + width:) unit

4. Length of rectangle = area ÷ width unit

5. Width of rectangle = area / Length unit

Square

1. Area of ​​a square = (length of any one arm) ² square unit

2. The perimeter of a square = 4 *  the length of one arm

3. The angle of the square = √2  * the length of one arm

4. Arm of a square = Area or range ÷ 4 units

Triangle

1. Area of ​​an equilateral triangle = √¾ × (arm)

2. Height of equilateral triangle = √3 / 2 × (arm)

Area of ​​equilateral triangle = √s (sa) (sb) (sc)

Here a, b, c is the length of three sides of the triangle, s = semicircle

Range 2s = (a + b + c)

4 Area of ​​a common triangle =

(Land × height) square unit

5. Area of ​​a right triangle = ½ (a × b)

Here the right sides of the triangle are adjacent sides a and b.

6. Area of ​​an isosceles triangle = 2√4b²-a² / 4 Here, a = land; b = the other arm.

7. Height of triangle = 2 (area / land)

8. The hypotenuse of a right triangle = √ perpendicular + ground

9. Perpendicular = hopecreole²-land²

10.Land = Ataribhujah-vertical

11. Height of isosceles triangle = √b² - a² / 4

Here a = land; b = equal length of two arms.

12.  Perimeter of a triangle = sum of three sides

The following formulas should be used to solve all the problems related to rhombuses.

1. Area of ​​rhombus = ½ × (product of two ears)

2. Range of rhombs = 4 × length of one arm

The following are the formulas for determining the area of ​​a parallelogram:

1. Area of ​​parallelogram = land × height =

2. Parallelogram = 2 × (sum of adjacent arms)

If there is only one formula for trapezium then the area is given below:

1. Area of ​​trapezium = ½ × (sum of two parallel arms) height

 Cube

1. The cube of a cube = (any arm) ³ cube unit

2. The total surface area of ​​a cube = 6 × arm: square unit

3. Corner of the cube = √3 × arm unit

Rectangular

1. The volume of a rectangle = (length × width × height) cubic unit

2. The total area of ​​a rectangle = 2 (ab + bc + ca) square unit

[Where a = length b = width c = height]

3. The angle of a rectangle = √a² + b² + c² unit

4. Area of ​​four walls = 2 (length + width) × height

Circle

1. Area of ​​the circle = πr² = 22 / 7r² {Here π = constant 22/7, radius of the circle = r.

2. Circumference of the circle = 2πr

3. The surface area of ​​the sphere = 4πr² square unit

4. Volume of the sphere = 4πr³ ÷ 3 cubic units

5. The radius of the circle formed at the bottom at h height = √r²-h² unit

6. Length of arc s = πrθ / 180 °,

Here θ = angle

Isosceles cylinder / roller

If the ground radius r and height h of the isosceles cylinder and the height of the inclined surface l,

1. Volume of cylinder = πr²h

2. Area of ​​curvature of the cylinder (CSA) = 2πrh.

3. Cylinder surface area (TSA) = 2πr (h + r)

Equilateral angles

If the radius r and height h of the isosceles ground and the height of the sloping surface are l,

1. Area of ​​curve of angle = πrl square unit

2. Area of ​​angle plane = πr (r + l) square unit

3. Volume of angle = ⅓πr²h cubic unit

Number of angles of a polygon = n (n-3) / 2

The sum of the angles of a polygon = (2 n-4) right angles

Here n = number of arms

Perimeter of quadrilateral = sum of four sides

Trigonometry formulas:

1. sinθ = ल म्ब / अतिभुज

2. cosθ = land / hypotenuse

3. taneθ = l mb / land

4. cotθ = land / perpendicular

5. secθ = overlap / land

6. cosecθ = hypotenuse / perpendicular

7. sinθ = 1 / cosecθ, cosecθ = 1 / sinθ

8. cosθ = 1 / secθ, secθ = 1 / cosθ

9. tanθ = 1 / cotθ, cotθ = 1 / tanθ

10. sin²θ + cos²θ = 1

11. sin²θ = 1 - cos²θ

12. cos²θ = 1- sin²θ

13. sec²θ - tan²θ = 1

14. sec²θ = 1+ tan²θ

15. tan²θ = sec²θ - 1

16, cosec²θ - cot²θ = 1

17. cosec²θ = cot²θ + 1

18. cot²θ = cosec²θ - 1