Concept: statements: A sentence which is either true or false, but not
(1) N.C.E.R.T text book page 324
Question no.1(*) , 2(*),4(*),9(*),10(*)
Negation of a statement: Denial of a statement is called
COMPLEX NUMBERS AND QUADRATIC EQUATIONS
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.
ie i = -1
A number of the form a+ib w
For important terms and definitions refer NCERT text book.
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 (*)
PRINCIPLE OF MATHEMATICAL INDUCTION
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)
SLOPE OF A LINE :
m = tan if is the angle of inclination.
) 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.
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)
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
Questions 3, 4,5
Questions 1, 2
THREE DIMENSIONAL GEOMETRY
Any point on x axis - > ( x, 0, 0)
Any point on y axis - > ( 0, y, 0)
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)
Chapter 3: Trigonometric functions
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
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)
SEQUENCES AND SERIES
Arithmetic progression (A.P)
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
If A1,A2,.An are n A.M between the two numbers a and b,
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
LIMITS AND DERIVATIVES
Some standard results on limits
where k is a fixed real number.
where f(x) is a real polynomial in x.
for all n N
Algebra of limits
Refer : NCERT Textbook page no: 292.