# Math

## Area of Triangles

Area of  Triangles An Area of  triangle PQR with vertices  P(x₁ , y₁), Q(x₂ , y₂) , and R(x₃ , y₃). An Area of triangle PQR is denoted by ▲and is given as : Note : a) if an area of a triangle is given then use  ±  sign. b) if points P, Q & …

## Distance Formula

Distance  Formula In X-Y Plane , The distance formula between two points P(x₁ , y₁) & Q(x₂ , y₂)– let extends both points and create lines  meet at intersection point R. so, here PQR form a right angled triangle. using Pythagoras theorem in right angled triangle PQR Note :  If Distance is given then use …

## geometric mean

Geometric mean: If a, b, c are in G.P . Then middle term of this G.P is known as geometric mean of a G.P. let b be geometric mean in a, b, c .      b2 =  a.c 1. Single geometric mean of n positive numbers : Let G be the geometric mean of …

## Arithmetic Mean

Arithmetic Mean If a, b, c are in A.P . Then middle term of this A.P is known as arithmetic mean of an A.P. let b be arithmetic mean in a, b, c .      b =  (a + c)/2 Single arithmetic mean of  ’n’ positive numbers : Let us assume ’n’ positive numbers …

## harmonic progression

A Harmonic Progression is defined as that in which reciprocal of its terms are in Arithmetic Progression. If a1 , a2 , a3 , ….are in H.P , then 1/a1 , 1 / a2 , 1 / a3 ,…. are in A.P. Note: 1.Generalized formula is not available to find sum of n terms of …

## geometric progression

Geometric Progression A geometric progression defined as that in which the ratio between two terms ( any term & its just preceding term)  is always constant. this constant term is known as the common ratio. so , we can say that Geometric Progression (G.P) is increased or decreased with multiple of a fixed number ( …

## arithmetic progression

Arithmetic progression (A.P) An  Arithmetic  progression  is  defined  as  that  in  which the difference between any two terms is always constant (fixed).                      Or Any quantity is increase or decrease by the same constant then such quantities form a series which is known as an Arithmetic …

## sequence & series

Sequence : It is a function of a natural numbers . Sequence may be finite or infinite depends on number of terms. A Sequence is defined as some objects are arranged in a particular fashion. Example :      1, 2,3,4, ……..      2 , 4 , 6 , 8 ,  …….      …

## Maximum & Minimum Value

Maximum and Minimum Value of Quadratic function f(x) : Vertex of parabola : ( y+D/4a) = a (x +b/2a)2   ….(1) let  y + D/4a = Y & x + b/2a = X    ∴             Y = aX2 Y=0                      …

## Location of Roots

Location of roots : Roots are lies in a particular interval. f(x) = ax2 + bx + c   ; a , b , c ∈ R & a≠0 and a ,β are roots of ax2 + bx + c =0 . Assume  k , k1 , k2 ∈ R & k1 < k2. Case 1. For a number k.             …

error: Content is protected !!