Chapter 14
MATHEMATICAL REASONING
Type-I
Concept: statements: A sentence which is either true or false, but not
both
(1) N.C.E.R.T text book page 324
Question no.1(*) , 2(*),4(*),9(*),10(*)
Type-II
Negation of a statement: Denial of a statement is called
Chapter 5
COMPLEX NUMBERS AND QUADRATIC EQUATIONS
INTRODUCTION
,
etc do not have values in the system of real numbers.
So we need to extend the real numbers system to a larger system.
Let us denote
by the symbol i.
2
ie i = -1
A number of the form a+ib w
Chapter 16
Probability
For important terms and definitions refer NCERT text book.
Type- I
Concept : sample space
(1)NCERT text book page 386 question no. 1 (*)
(2) NCERT text book page 386 question no. 2 (*)
(3) NCERT text book page 386 question no. 3 (*)
Chapter 4
PRINCIPLE OF MATHEMATICAL INDUCTION
INTRODUCTION
To prove certain results or statements in Algebra, that are formulated in terms of
n, where n is a natural number, we use a specific technique called principle of
mathematical induction (P.M.I)
St
Chapter 10
STRAIGHT LINES
SLOPE OF A LINE :
m = tan if is the angle of inclination.
if (
m =
,
)
and
(
,
) are two points on the line.
SLOPE of a horizontal line is 0 and vertical line is not defined.
If m1 and m2 are slopes of L1 and L2 respectively.
L1
CHAPTER 7
PERMUTATIONS (Arrangements) AND COMBINATIONS (selections)
In permutation order is important, since 27 & 72 are different
numbers(arrangements). In combination order is not important.
Fundamental principle of counting (FPC)
Station A
Station C
S
Chapter 1
Sets
Concept: Representation of a set
Concepts:- Different types of sets Subsets- Power sets Universal set
Operations on sets Compliment of a set Practical Problems.
Text book questions
Ex: 1
Questions 3, 4,5
Ex: 2
Questions 1, 2
Ex: 3
Question
Chapter 12
THREE DIMENSIONAL GEOMETRY
Any point on x axis - > ( x, 0, 0)
Any point on y axis - > ( 0, y, 0)
Any point
on z axis - > ( 0, 0, z)
Any point on XY - plane
( x, y, 0)
Any point on YZ - plane
( 0, y, z)
Any point on ZX - plane
( x, 0,z)
Distance
Chapter 3: Trigonometric functions
Concept:
Radian measure- relation between degree and radian- trigonometric
functions- sign of trigonometric functions- trigonometric functions of
sum and difference of two angles- trigonometric equations- sine
formula- c
Chapter 11
CONIC SECTION
CIRCLE:
The equation of a circle with centre at (h, k) and radius r is (
(
)
)
Equation of a circle with centre at origin and radius r is
PARABOLA( Symmetric about its axis)
Equation
Axis
Figure
Right
Left
Upward
Downward
y=0
y= 0
Chapter 9
SEQUENCES AND SERIES
Arithmetic progression (A.P)
Standard AP
a, a+d, a+2da+(n-1)d
An = a+ (n-1) d
Sn = (
(
) )
)
= (
Arithmetic mean A between the two numbers a and b is
A =
If A1,A2,.An are n A.M between the two numbers a and b,
Then
d=
A1 =
CHAPTER 6
LINEAR INEQUALITIES
Rules for solving inequalities
The following rules can be applied to any inequality
Add or subtract the same number or expressions to both sides.
Multiply or divide both sides by the same positive number.
By multiplying or
Chapter 13
LIMITS AND DERIVATIVES
Some standard results on limits
( )
1)
( )
iff
2)
( )
where k is a fixed real number.
( )
3)
( )
where f(x) is a real polynomial in x.
for all n N
4)
5)
x
c
Algebra of limits
Refer : NCERT Textbook page no: 292.
Evaluatio