Mathematical Formulas Algebra Formulas

1. (a+b =a²+2ab+b²
2. (ab)² =a²2ab+b²
3. (a+b)(ab) =a²b²
4. (x+a)(x+b) =x²+(a+b)x+ab
5. (x+a)(xb) =x²+(ab)xab
6. (xa)(x+b) =x²+(ba)xab
7. (xa)(xb) =x²(a+b)x+ab
8. (a+b =a³+b³+3ab(a+b)
9. (ab)³ =a³b³3ab(ab)
10. (x+y+z)² =x²+y²+z²+2xy+2yz+2xz
11. (x+yz)² =x²+y²+z²+2xy2yz2xz
12. (xy+z)² =x²+y²+z²2xy2yz+2xz
13. (xyz)² =x²+y²+z²2xy+2yz2xz
14. x³+y³+z³3xyz =(x+y+z)(x²+y²+z²xyyzxz)
15. x²+y² =12[(x+y)²+(xy)²]
16. (x+a)(x+b)(x+c) =x³+(a+b+c)x²+(ab+bc+ca)x+abc
17. x³+y³ =(x+y)(x²xy+y²)
18. x³y³ =(xy)(x2+xy+y2)
19. x²+y²+z²xyyzzx =12[(xy)²+(yz)²+(zx)²]

Coordinate Geometry

• Distance Formulae: Consider a line having two points A(x1, y1) and B(x2, y2), then the distance of these points is given as:
• Section Formula: If a point p divides a line AB with coordinates A(x1, y1) and B(x2, y2), 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(x1, y1) and B(x2, y2), are given as:
• Area of a Triangle: Consider the triangle formed by the points A(x1, y1) and B(x2, y2) and C(x3, y3) 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 180o.

Important formulas related to circles:

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

Trigonometry Formulas

In a right-angled triangle, the Pythagoras theorem states
(perpendicular )+ ( 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:

• sin2A + cos2A=1
• tan2A +1 = sec2A
• cot2A + 1= cosec2A

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: