Mathematical Formulas

Maths formula

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]

Linear Equation in Two Variables

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 Circle=πr²
Circumference of a circle=2πr
Ares of the sector if angle θ=Ares of the sector if angle θ
Length of an arc of a sector of an 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

Area of a Segment of a Circle
Circle with segment

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

Mensuration Formulas

Name of the SolidFigureVolumeLateral/ Curved/ Surface AreaTotal Surface Area
Cube 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 )+ ( 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:

A30°45°60°90°
sin A01/21/√2√3/21
cos A1√3/21/√21/20
tan A01/√31√3Undefined
cosec AUndefined√3√22/√30
sec A12/√3√2√3Undefined
cot AUndefined√311/√30
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