Summary - Mathematics

Class – X
MATHEMATICS

IMPORTANT CONCEPTS AND FORMULAE
1. Relation between HCF and LCM
HCF x LCM = Product of two numbers
2. If denominator has factors as 2 & 5 only, then the fraction is terminating.
If denominator has at least one factor other than 2 & 5, then the fraction is non-
terminating.
3. For , p  x   ax 2  bx  c
b
Sum of zeros =    
a
c
Product of zeros =  
a
The relation to form the quadratic formula:
k  x 2  Sx  P  ; k  any integer
S  Sum of zeroes
P  Product of zeroes
4.
 2   2       2
2



     4
2
  
 3   3       2   2   


 3   3       2   2   
5.




6.

, Quadratic formula to find x
ax 2  bx  c  0
D  b2  4ac
b  D
x
2a
7.




8. If the quadratic equation ax 2  bx  c  0 has equal and real roots/zeros
D0
b2  4ac  0
9. nth term of A.P.
an  a   n  1  d d  a2  a1
Sum of n terms of A.P.
n
Sn  2a   n  1  d 
2
n
Sn   a  l 
2
10. If three numbers are in A.P
a, b, c are in A.P.
Then, 2b = a + c
11. If three numbers are to be assumed in A.P.
a – d, a, a + d
12. Distance formula,

 x2  x1    y2  y1    z2  z1 
2 2 2
d
13. Section formula,
 mx2  nx1 my2  ny1 
 mn , mn 
 
14. If points are collinear
Area of triangle = 0.
1
ar      x1  y2  y3   x2  y3  y1   x3  y1  y2 
2
15.


16.