Mind map : learning made simple Chapter-1
Term Rationalising
factor
1
r
r
−3−2−1 0 1 2 3
1 Rationa
r+s liza
r−s Transform
tion er line Every point on the line Successive
mb
1 denominator into Nu represents real numbers magnificati
on
r−s a rational number
r+s
Number
1
r+ s ers System
r− s Pow Real
gral nu
e
m
I
nt
be
r
ith
1 Rational numb
r− s r er (
Oswaal CBSE Chapterwise Mind Maps, MATHEMATICS, Class-IX
r+ s mbe
ts w
nu
Q) gers (Z)
n
. −3,−2,−1,0
l Ir Inte −∞..
e
ea ,1,
ra
2,
ti
fr
3.
o
to
p
n Form
..∞
q
roo
Expon
al n
n th
q≠0, (p,q) ∈ z W
h ole n u m b ers ( W ) 0,1,2,3...∞
Product law aman = am+n
N atu
(Q
umber )
a = (b)1/n
r al
Quotient law am ÷ an = am−n
n
a,b − real numbers Cannot be written um
Power law (am)n = amn n − +ve integer in p/q form be
rs
(Z) 1,2,3...∞
a −m b m
Reciprocal law = a
b
Exam
r o ot
C ube
root
Square
3
x = x1/2 x = (x)1/3
ples 2,
Example 5, 7 Example 3 7, 3 4
3
[1
,
2]
Mind map : learning made simple Chapter-2
(x+y)2 x2 + 2xy+y2
(x−y)2 x2 − 2xy+y2
x2−y2 (x − y) (x + y)
(x+a) (x+b) x2 + (a + b)x + ab
(x + y + z)2 x2+y2+z2+2xy+2yz+2zx
= x2+y2+z2+2 (xy+yz+zx)
(x + y)3 x3 + y3+ 3xy (x + y)
(x − y)3 x3 − y3 − 3xy (x − y)
x3+y3+z3−3xyz (x+y+z) (x2+y2+z2−xy−yz−zx)
(i) x3+y3+z3 = 3xyz An algebraic expression of the Polynomial in one
If x + y + z = 0 form: variable:
(ii) x2 + y2 + z2 = 3 ial 1
m
yz xz xy f(x) = anxn + an−1 xn–1 + ... a1x + a0x0 ax3 − bx2 − cx + d
no
Alge
x3 + y3 (x+y)(x2−xy+y2) bra
Poly
Iden ic
x3 − y3 (x-y)(x2+xy+y2) titi
es
Factor Theorem
(i) if (x−a) is a if p(x) is a
polynomial
Theorem Polynomial Example
factor of p(x), s Polynomials Types
Terms
then p(a) = 0 of degree n>1, Constant
a: any real number l 4, − 7/5
mia e (or independent)
no
m
gre
(ii) if p(a) = 0, then ly
o re
De
po Degree not defined
f
Zero
he
(x−a) is a factor
so
(constant polynomial 0)
of p(x). rT
oe
de
er
if p(x) polynomial ai n Polynomial Example Degree Monomial 4x
Z
Re m
Divident = (Divisor of degree n>1, is Binomial 2x + 3
Linear 3x + 2 1
× Quotient) divided by x−a, Number that satisfies
+ Remainder p(a) is the remainder the equation Quadratic 2x2 + 3x + 1 2 Trinomial 3x2 + 7x + 2
Cubic 3
ple
7y3 + 6y2 + 2y+ 2
Exam
P(x) = 2x + 1
find zeroes of the polynomial
P(x) = 0
2x + 1 = 0
x = −1/2
−1/2 is the zeros of
the polynomial
Oswaal CBSE Chapterwise Mind Maps, MATHEMATICS, Class-IX
Term Rationalising
factor
1
r
r
−3−2−1 0 1 2 3
1 Rationa
r+s liza
r−s Transform
tion er line Every point on the line Successive
mb
1 denominator into Nu represents real numbers magnificati
on
r−s a rational number
r+s
Number
1
r+ s ers System
r− s Pow Real
gral nu
e
m
I
nt
be
r
ith
1 Rational numb
r− s r er (
Oswaal CBSE Chapterwise Mind Maps, MATHEMATICS, Class-IX
r+ s mbe
ts w
nu
Q) gers (Z)
n
. −3,−2,−1,0
l Ir Inte −∞..
e
ea ,1,
ra
2,
ti
fr
3.
o
to
p
n Form
..∞
q
roo
Expon
al n
n th
q≠0, (p,q) ∈ z W
h ole n u m b ers ( W ) 0,1,2,3...∞
Product law aman = am+n
N atu
(Q
umber )
a = (b)1/n
r al
Quotient law am ÷ an = am−n
n
a,b − real numbers Cannot be written um
Power law (am)n = amn n − +ve integer in p/q form be
rs
(Z) 1,2,3...∞
a −m b m
Reciprocal law = a
b
Exam
r o ot
C ube
root
Square
3
x = x1/2 x = (x)1/3
ples 2,
Example 5, 7 Example 3 7, 3 4
3
[1
,
2]
Mind map : learning made simple Chapter-2
(x+y)2 x2 + 2xy+y2
(x−y)2 x2 − 2xy+y2
x2−y2 (x − y) (x + y)
(x+a) (x+b) x2 + (a + b)x + ab
(x + y + z)2 x2+y2+z2+2xy+2yz+2zx
= x2+y2+z2+2 (xy+yz+zx)
(x + y)3 x3 + y3+ 3xy (x + y)
(x − y)3 x3 − y3 − 3xy (x − y)
x3+y3+z3−3xyz (x+y+z) (x2+y2+z2−xy−yz−zx)
(i) x3+y3+z3 = 3xyz An algebraic expression of the Polynomial in one
If x + y + z = 0 form: variable:
(ii) x2 + y2 + z2 = 3 ial 1
m
yz xz xy f(x) = anxn + an−1 xn–1 + ... a1x + a0x0 ax3 − bx2 − cx + d
no
Alge
x3 + y3 (x+y)(x2−xy+y2) bra
Poly
Iden ic
x3 − y3 (x-y)(x2+xy+y2) titi
es
Factor Theorem
(i) if (x−a) is a if p(x) is a
polynomial
Theorem Polynomial Example
factor of p(x), s Polynomials Types
Terms
then p(a) = 0 of degree n>1, Constant
a: any real number l 4, − 7/5
mia e (or independent)
no
m
gre
(ii) if p(a) = 0, then ly
o re
De
po Degree not defined
f
Zero
he
(x−a) is a factor
so
(constant polynomial 0)
of p(x). rT
oe
de
er
if p(x) polynomial ai n Polynomial Example Degree Monomial 4x
Z
Re m
Divident = (Divisor of degree n>1, is Binomial 2x + 3
Linear 3x + 2 1
× Quotient) divided by x−a, Number that satisfies
+ Remainder p(a) is the remainder the equation Quadratic 2x2 + 3x + 1 2 Trinomial 3x2 + 7x + 2
Cubic 3
ple
7y3 + 6y2 + 2y+ 2
Exam
P(x) = 2x + 1
find zeroes of the polynomial
P(x) = 0
2x + 1 = 0
x = −1/2
−1/2 is the zeros of
the polynomial
Oswaal CBSE Chapterwise Mind Maps, MATHEMATICS, Class-IX
