1.1 Sets and their representation

1.2 Union

1.3 Intersection and complement of sets and their algebraic properties

1.4 Power set

1.5 Relation

1.6 Types of relations

1.7 Equivalence relations

1.8 Functions

1.9 one-one, into and onto functions

1.10 Composition of functions

VideosMCQ Notes

2.1 Complex numbers as ordered pairs of reals

2.2 Representation of complex numbers in the form a+ib and their representation in a plane

2.3 Argand diagram

2.4 algebra of complex numbers

modulus and argument (or amplitude) of a complex number

2.5 square root of a complex number

2.6 triangle inequality

2.7 Quadratic equations in real and complex number system and their solutions

2.8 Relation between roots and co-efficients

2.9 nature of roots

2.10 formation of quadratic equations with given roots

VideosMCQ Notes

3.1 Matrices

3.2 Algebra of matrices, types of matrices, determinants and matrices of order two and three

3.3 Properties of determinants, evaluation of determinants, area of triangles using determinants

3.4 Adjoint and evaluation of inverse of a square matrix using determinants and elementary transformations, Test of consistency and solution of simultaneous linear equations in two or three variables using determinants and matrices

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4.1 Fundamental principle of counting

4.2 permutation as an arrangement and combination as selection

4.3 Meaning of P (n,r) and C (n,r)

4.4 simple applications

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5.1 Principle of Mathematical Induction and its simple applications

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6.1 Binomial theorem for a positive integral index

6.2 general term and middle term

6.3 properties of Binomial coefficients and simple applications

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7.1 Arithmetic and Geometric progressions

7.2 insertion of arithmetic

7.3 Geometric means between two given numbers

7.4 Relation between A.M. and G.M. Sum upto n terms of special series: S n, S n2, Sn3

7.5 Arithmetico-Geometric progression

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8.1 Real - valued functions

8.2 algebra of functions, polynomials, rational, trigonometric, logarithmic and exponential functions, inverse functions

8.3 Graphs of simple functions

8.4 Limits, continuity and differentiability

8.5 Differentiation of the sum, difference, product and quotient of two functions

8.6 Differentiation of trigonometric

8.7 inverse trigonometric

8.8 logarithmic, exponential, composite and implicit functions

8.9 derivatives of order upto two

8.10 Rolle's and Lagrange's Mean Value Theorems

8.11 Applications of derivatives: Rate of change of quantities

8.12 monotonic - increasing and decreasing functions

8.13 Maxima and minima of functions of one variable

8.14 tangents and normals

VideosMCQ Notes

9.1Integral as an anti - derivative

9.2 Fundamental integrals involving algebraic

9.3 trigonometric, exponential and logarithmic functions

9.4 Integration by substitution

9.5 by parts and by partial fractions

9.6 Integration using trigonometric identities

9.7 Integral as limit of a sum

9.8 Fundamental Theorem of Calculus

9.9 Properties of definite integrals

9.10 Evaluation of definite integrals

9.11 determining areas of the regions bounded by simple curves in standard form

VideosMCQ Notes

10.1 Ordinary differential equations

10.2 their order and degree

10.3 Formation of differential equations

10.4 Solution of differential equations by the method of separation of variables

10.5 solution of homogeneous and linear differential equations

VideosMCQ Notes

11.1 Cartesian system of rectangular co-ordinates 10 in a plane

11.2 distance formula

11.3 section formula

11.4 locus and its equation

11.5 Translation of axes

11.6 Slope of a line

11.7 parallel and perpendicular lines

11.8 intercepts of a line on the coordinate axes

11.9 Straight lines

11.10 Various forms of equations of a line

11.11 intersection of lines

11.12 angles between two lines

11.13 conditions for concurrence of three lines

11.14 distance of a point from a line

11.15 equations of internal and external bisectors of angles between two lines

11.16 coordinates of centroid

11.17 orthocentre and circumcentre of a triangle

11.18 equation of family of lines passing through the point of intersection of two lines

11.19 Circles, conic sections

11.20 Standard form of equation of a circle

11.21 general form of the equation of a circle

11.22 its radius and centre

11.23 equation of a circle when the end points of a diameter are given

11.24 points of intersection of a line and a circle with the centre at the origin and condition for a line to be tangent to a circle

11.25 equation of the tangent

11.26 Sections of cones

11.27 Equations of conic sections (parabola, ellipse and hyperbola) in standard forms

11.28 condition for y = mx + c to be a tangent and point (s) of tangency

VideosMCQ Notes

12.1Coordinates of a point in space

12.2 distance between two points

12.3 section formula

12.4 direction ratios and direction cosines

12.5 angle between two intersecting lines

12.6 Skew lines

12.7 the shortest distance between them and its equation

12.8 Equations of a line and a plane in different forms

12.9 intersection of a line and a plane

12.10 coplanar lines

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13.1Vectors and scalars

13.2 addition of vectors

13.3 components of a vector in two dimensions and three dimensional space

13.4 scalar and vector products

13.5 scalar and vector triple product

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14.1 Measures of Dispersion: Calculation of mean

14.2 Median

14.3 Mode of grouped and ungrouped data calculation of standard deviation

14.4 variance and mean deviation for grouped and ungrouped data

14.5 Probability: Probability of an event

14.6 addition and multiplication theorems of probability

14.7 Baye's theorem

14.8 probability distribution of a random variate

14.9 Bernoulli trials and Binomial distribution

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15.1 Trigonometrical identities and equations

15.2 Trigonometrical functions

15.3 Inverse trigonometrical functions and their properties

15.4 Heights and Distances

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16.1 Statements

16.2 logical operations and, or, implies, implied by, if and only if

16.3 Understanding of tautology, contradiction, converse and contrapositive

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