**Algebra Formulas**

- (a+b)² =a²+2ab+b²
- (a−b)² =a²−2ab+b²
- (a+b)(a–b) =a²–b²
- (x+a)(x+b) =x²+(a+b)x+ab
- (x+a)(x–b) =x²+(a–b)x–ab
- (x–a)(x+b) =x²+(b–a)x–ab
- (x–a)(x–b) =x²–(a+b)x+ab
- (a+b)³ =a³+b³+3ab(a+b)
- (a–b)³ =a³–b³–3ab(a–b)
- (x+y+z)² =x²+y²+z²+2xy+2yz+2xz
- (x+y–z)² =x²+y²+z²+2xy–2yz–2xz
- (x–y+z)² =x²+y²+z²–2xy–2yz+2xz
- (x–y–z)² =x²+y²+z²–2xy+2yz–2xz
- x³+y³+z³–3xyz =(x+y+z)(x²+y²+z²–xy–yz−xz)
- x²+y² =12[(x+y)²+(x–y)²]
- (x+a)(x+b)(x+c) =x³+(a+b+c)x²+(ab+bc+ca)x+abc
- x³+y³ =(x+y)(x²–xy+y²)
- x³–y³ =(x–y)(x2+xy+y2)
- x²+y²+z²−xy–yz–zx =12[(x−y)²+(y−z)²+(z−x)²]

**Linear Equation in Two Variables**

**Linear Equation in Two Variables**

### Coordinate Geometry

**Distance Formulae:**Consider a line having two points A(x_{1}, y_{1}) and B(x_{2}, y_{2}), then the distance of these points is given as:

**Section Formula:**If a point p divides a line AB with coordinates A(x_{1}, y_{1}) and B(x_{2}, y_{2}), in ratio m:n, then the coordinates of the point p are given as:

**Mid Point Formula:**The coordinates of the mid-point of a line AB with coordinates A(x_{1}, y_{1}) and B(x_{2}, y_{2}), are given as:

**Area of a Triangle:**Consider the triangle formed by the points A(x_{1}, y_{1}) and B(x_{2}, y_{2}) and C(x_{3}, y_{3}) then the area of a triangle is given as-

### Circles

**Important properties related to circles:**

- Equal chord of a circle are equidistant from the centre.
- The perpendicular drawn from the centre of a circle, bisects the chord of the circle.
- The angle subtended at the centre by an arc = Double the angle at any part of the circumference of the circle.
- Angles subtended by the same arc in the same segment are equal.
- To a circle, if a tangent is drawn and a chord is drawn from the point of contact, then the angle made between the chord and the tangent is equal to the angle made in the alternate segment.

- The sum of opposite angles of a cyclic quadrilateral is always 180
^{o}.

**Important formulas related to circles:**

Area of a Circle= | πr² |

Circumference of a circle= | 2πr |

Ares of the sector if angle θ= | |

Length of an arc of a sector of an angle θ= |

Area of a Segment of a Circle: If AB is a chord which divides the circle into two parts, then the bigger part is known as major segment and smaller one is called minor segment

Here, Area of the segment APB = Area of the sector OAPB – Area of ∆ OAB

### Mensuration Formulas

Name of the Solid | Figure | Volume | Lateral/ Curved/ Surface Area | Total Surface Area |

Cube | a³ | 4a² | 4a²+2a² or 6a² | |

Cuboid | lbh | 2lh+2lb or 2l(h+b) | 2lh+2lb+2bh or 2(lh+lb+bh) | |

Right Circular Cylinder | πr²h | 2πrh | 2πrh+2πr² or 2πr(h+r) | |

Right Circular Cone | 1/3πr²h | πrl | πrl+πr² or πr(l+r) | |

Sphere | 4/3πr³ | 4πr² | 4πr² | |

Hemisphere | 2/3πr³ | 2πr² | 2πr²+πr² or 3πr² |

### Trigonometry Formulas

In a right-angled triangle, the Pythagoras theorem states

(perpendicular )^{2 }+ ( base )^{2} = ( hypotenuse )^{2}

**Important trigonometric properties:** (with P = perpendicular, B = base and H = hypotenuse)

- SinA = P / H
- CosA = B / H
- TanA = P / B
- CotA = B / P
- CosecA = H / P
- SecA = H/B

**Trigonometric Identities:**

- sin
^{2}A + cos^{2}A=1 - tan
^{2}A +1 = sec^{2}A - cot
^{2}A + 1= cosec^{2}A

**Relations between trigonometric identities are given below:**

**Trigonometric Ratios of Complementary Angles are given as follows:**

- sin (90° – A) = cos A
- cos (90° – A) = sin A
- tan (90° – A) = cot A
- cot (90° – A) = tan A
- sec (90° – A) = cosec A
- cosec (90° – A) = sec A

**Values of Trigonometric Ratios of 0° and 90° are tabulated below:**

∠ A | 0° | 30° | 45° | 60° | 90° |

sin A | 0 | 1/2 | 1/√2 | √3/2 | 1 |

cos A | 1 | √3/2 | 1/√2 | 1/2 | 0 |

tan A | 0 | 1/√3 | 1 | √3 | Undefined |

cosec A | Undefined | √3 | √2 | 2/√3 | 0 |

sec A | 1 | 2/√3 | √2 | √3 | Undefined |

cot A | Undefined | √3 | 1 | 1/√3 | 0 |