I've covered the majority of the math topics for practice.

• SETS

• RELATION AND FUNCTION

• TRIGONOMETRY

• COMPLEX NUMBER

• QUADRATIC EQUATION

• PERMUTATION AND COMBINATION

• SEQUENCE AND SERIES

• STRAIGHT LINE

• CONIC SECTION

• LIMIT AND DERIVTIVES

• PROBABILITY

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  Chapter 1: Sets

  • Sets and their representations

  • Empty set

  • Finite and infinite sets

  • Equal sets. Subsets

  • Subsets of a set of real numbers, especially intervals (with notations)

  • Power set

  • Universal Set

  • Venn diagrams

  • Sets: Union and Intersection of Sets

  • Difference of sets

  • Complement of a set

  • Properties of Compound Sets

  • Practical Problems based on Sets

  Chapter 2: Relations and Functions

  • Ordered pairs

    • The Cartesian product of sets

  • The number of elements in the cartesian product of two finite sets

  • The Cartesian product of the sets of real (up to R R)

  • The definition of

    • Relation

    • Pictorial diagrams

    • Domain

    • co-domain

    • range of a relation

  • Function as a special kind of relation from one set to another

  • Pictorial representation of a function, domain, co-domain, and range of a function

  • Real-valued functions, the domain and range of these functions

    • Constant

    • Identity

    • polynomial

    • Rational

    • Modulus

    • Signum

    • Exponential

    • Logarithmic

    • The greatest integer functions (with their graphs)

  • sum, difference, product, quotients of functions.

  Chapter 3: Trigonometric Functions

  • Positive and negative angles

  • Measuring angles in radians and in degrees and conversion of one into the other

  • Definition of trigonometric functions with the help of the unit circle

  • Truth of the sin2x + cos2x = 1, for all x

  • Signs of trigonometric functions

  • The domain and range of trigonometric functions and their graphs

  • Expressing sin (xy) and cos (xy) in terms of sinx, siny, cosx, and cosy and their simple application

  • Identities related to sin 2x, cos2x, tan 2x, sin3x, cos3x, tan3x,

  • general solution of trigonometric equations of the type sin y = sin a, cos y = cos a, and tan y = tan a.

  Unit-II: Algebra

  Chapter 1: The Principle of Mathematical Induction

  • Process of the proof by induction

    • Motivating the application of the method by looking at natural numbers as the least inductive subset of real numbers

  • The principle of mathematical induction and its simple applications

  Chapter 2: Complex Numbers and Quadratic Equations

  • The need for complex numbers, especially 1, to be motivated by the inability to solve some of the quadratic equations

  • Algebraic properties of complex numbers

  • The Argand plane and polar representation of complex numbers

  • Statement of the Fundamental Theorem of Algebra

  • Solution of quadratic equations in the complex number system

  • The square root of a complex number

  Chapter 3: Linear Inequalities

  • Linear inequalities

  • Algebraic solutions of linear inequalities in one variable and their representation on the number line

  • Graphical solution of linear inequalities in two variables

  • Graphical solution of a system of linear inequalities in two variables

  Chapter 4: Permutations and Combinations

  • The fundamental principle of counting

  • Factorial

  • Permutations and combinations

  • The derivation of formulae and their connections

  • Simple applications

  Chapter 5: Binomial Theorem

  • History

  • Statement and proof of the binomial theorem for positive integral indices

  • Pascal's triangle

  • General and middle terms in binomial expansion

  • Simple applications

  Chapter 6: Sequence and Series

  • A Sequence and Series

  • Arithmetic Progression (A.P.)

  • Arithmetic Mean (A.M.)

  • Geometric Progression (G.P.)

  • general term of a G.P.

  • sum of n terms of a G.P.

  • The arithmetic and geometric series G.P. and its sum

  • Geometric mean (G.M.)

  • Relationship between A.M. and G.M.

  Unit-III: Coordinate Geometry

  Chapter 1: "Straight Lines"

  • Brief recall of two-dimensional geometries from earlier classes

  • Shifting of origin

  • The slope of a line and the angle between two lines

  • Various forms of equations for a line

    • Parallel to the axis

    • Point-slope form

    • Slope-intercept form

    • Two-point form

    • Intercept form

    • Normal form

  • A general equation of a line

  • equation of a family of lines passing through the point of intersection of two lines

  • The distance of a point from a line

  Chapter 2: Conic Sections

  • Sections of a cone

    • Circles

    • Ellipse

    • Parabola

    • a point, a straight line, and a pair of intersecting lines as a degenerated case of a conic section.

  • Standard equations and simple properties of −

    • Parabola

    • Ellipse

    • Hyperbola

  • The standard equation of a circle

  Chapter 3. Introduction to Three-dimensional Geometry

  • Coordinate axes and coordinate planes in three dimensions.

  • The coordinates of a point

  • Distance between two points and section formula

  Unit-IV: Calculus

  Chapter 1: Limits and Derivatives

  • Derivative introduced as rate of change both as that of distance function and geometrically

  • Intuitive idea of limit

  • Limits of −

    • Polynomials and rational functions

    • Trigonometric, exponential and logarithmic functions

  • Definition of derivative, relate it to slope of tangent of a curve, derivative of sum, difference, product and quotient of functions

  • The derivative of polynomial and trigonometric functions