Providing Class 9th Maths formulas list chapter-wise that makes your work easy.

### Number Systems

⇒ Pythagoras Theorem:- H² = P² + B²

⇒ (a+b)²=a²+2ab+b²

⇒ (a-b)²=a²-2ab+b²

⇒ (a+b)(a-b)=a²-b²

⇒ a-ᵐ = 1/aᵐ

⇒ aᵐ×aⁿ=aᵐ⁺ⁿ

⇒ aᵐ÷aⁿ=aᵐ⁻ⁿ

⇒ (aᵐ)ⁿ=aᵐⁿ

⇒ aᵐ×bᵐ=(ab)ᵐ

⇒ aᵐ÷bᵐ=(a÷b)ᵐ

⇒ a° = 1

### Polynomials

⇒ (x+y)²=x²+2xy+y²

⇒ (x-y)²=x²-2xy+y²

⇒ (x+y)(x-y)=x²-y²

⇒ (x+a)(x+b)=x²+(a+b)x+ab

⇒ (x+a)(x-b)=x²+(a-b)x-ab

⇒ (x-a)(x+b)=x²+(-a+b)x-ab

⇒ (x-a)(x-b)=x²+(-a-b)x+ab

⇒ (x+y+z)²=x²+y²+z²+2xy+2yz+2zx

⇒ (-x+y+z)²=x²+y²+z²-2xy+2yz-2zx

⇒ (x-y+z)²=x²+y²+z²-2xy-2yz+2zx

⇒ (x+y-z)²=x²+y²+z²+2xy-2yz-2zx

⇒ (x+y)³=x³+y³+3x²y+3xy²

⇒ (x-y)³=x³-y³-3x²y+3xy²

⇒ x³+y³=(x+y)(x²-xy+y²)

⇒ x³-y³=(x-y)(x²+xy+y²)

⇒ x³+y³+z³=3xyz

⇒ x³+y³+z³-3xyz=(x+y+z)(x²+y²+z²-xy-yz-zx)

⇒ Area of Rectangle = Length×Breadth

⇒ Volume of Cuboid = Length×Breadth×Height

### Linear Equations in Two Variables

⇒ General form of linear equation in two variables:- ax+by+c=0

### Lines and Angles

⇒ Zero Angle is 0°.

⇒ The right Angle is 90°.

⇒ Acute Angles are between 0° to 90°.

⇒ Obtuse Angles are between 90° to 180°.

⇒ Straight Angle is 180°.

⇒ Reflex angles are between 180° to 360°.

⇒ Complete Angle is 360°.

⇒ Sum of two complementary angles = 90°.

⇒ Sum of two supplementary angles = 180°.

⇒ When the sum of adjacent angles is 180° they are known as Linear pairs.

⇒ Vertically opposite angles are equal.

⇒ Straight line make 180° angle.

⇒ Exterior angle of triangle = Sum of its opposite interior angles.

⇒ Alternate interior angles are equal.

⇒ Sum of all interior angles in triangle = 180°

### Triangles

⇒ Angles opposite to equal sides of an isosceles triangle are equal.

⇒ The side opposite to equal angles of a triangle are equal.

⇒ Sum of all interior angles in triangle = 180°

⇒ Each angle of equilateral triangle = 60°

### Quadrilateral

**Theorem 8.1:** A diagonal of a parallelogram divides it into congruent triangles.

**Theorem 8.2: **In a parallelogram, opposite sides are equal.

**Theorem 8.3: **If each pair of opposite sides of a quadrilateral is equal, then it is a parallelogram.

**Theorem 8.4: **In a parallelogram, opposite angles are equal.

**Theorem 8.5: **If in a quadrilateral, each pair of opposite angles is equal, then it is a parallelogram.

**Theorem 8.6: **The diagonals of a parallelogram bisect each other.

**Theorem 8.7: **If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.

**Theorem 8.8: **The line segment joining the mid-points of two sides of a triangle is parallel to the third side.

**Theorem 8.9: **The line drawn through the mid-point of one side of a triangle, parallel to another side bisects the third side.

### Circles

**Theorem 9.1: **Equal chords of a circle subtend equal angles at the center.

**Theorem 9.2: **If the angles subtended by the chords of a circle at the center are equal, then the chords are equal.

**Theorem 9.3: **The perpendicular from the centre of a circle to a chord bisects the chord.

**Theorem 9.4: **The line drawn through the centre of a circle to bisect a chord is perpendicular to the chord.

**Theorem 9.5: **Equal chords of a circle are equidistant from the centre.

**Theorem 9.6: **Chords equidistant from the centre of a circle are equal in length.

**Theorem 9.7: **The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.

**Theorem 9.8: **Angles in the same segment of a circle are equal.

**Theorem 9.9: **If a line segment joining two points subtends equal angles at two other points lying on the same side of the line containing the line segment, the four points lie on a circle.

**Theorem 9.10: **The sum of either pair of opposite angles of a cyclic quadrilateral is 180°.

**Theorem 9.11: **If the sum of a pair of opposite angles of a quadrilateral is 180°, the quadrilateral is cyclic.

⇒ Pythagoras theorem:- H² = P² + B²

⇒ Sum of all interior angles in triangle = 180°

### Heron's Formulas

⇒ The perimeter of the triangle= Sum of all sides

⇒ The perimeter Equilateral triangle= 3×Side

⇒ Area of Right-angled triangle=1/2×Base×Height

⇒ Area of triangle by Heron's formula=√[s(s-a)(s-b)(s-c)]

where s=semi-perimeter, & a,b,c=sides of the triangle.

⇒ Semiperimeter s=(a+b+c)/2

### Surface Area and Volume

⇒ Diameter = 2×Radius

⇒ Radius = Diameter/2

⇒ Slant Height of cone l=√(r²+h²)

⇒ Radius of cone r=√(l²-h²)

⇒ Height of Cone h=√(l²-r²)

⇒ (CSA) Curved Surface Area of cone = 𝞹rl

⇒ (TSA) Total Surface Area of cone = 𝞹r(l+r)

⇒ Radius of Cone = CSA of Cone/𝞹l

⇒ Area of Rectangle = Length×Breadth

⇒ Surface Area of Sphere = 4𝞹r²

⇒ (CSA) Curved Surface Area of Hemisphere = 2𝞹r²

⇒ (TSA) Total Surface Area of Hemisphere = 3𝞹r²

⇒ Radius of Sphere = √(Surface Area/4𝞹)

⇒ (CSA) Curved Surface Area of Cylinder = 2𝞹rh

⇒ Volume of Cone = 1/3𝞹r²h

⇒ 1 litre = 1000cm³

⇒ Radius of Cone = √(3×Volume/𝞹h)

⇒ The volume of Sphere = 4/3𝞹r³

⇒ Volume of Hemisphere = 2/3𝞹r³

⇒ 1000 litre = 1m³

### Statistics

⇒ Class-mark = (Upper Limit + Lower Limit)/2