1. Sets
Content: Introduction to sets, types of sets, operations on sets,
and Venn diagrams.
Objective: Understand the concept of sets and their applications in
mathematics, particularly in solving problems involving collection of objects.
2. Relations and Functions
Content: Definition of relations, types of relations, functions,
and types of functions (oneone, onto).
Objective: Learn to define and work with relations and functions,
and their graphical representations.
3. Trigonometric Functions
Content: Study of angles, trigonometric ratios, and identities,
along with graphs of trigonometric functions.
Objective: Develop understanding of trigonometric concepts, their
applications, and how they relate to angles in various geometrical settings.
4. Principle of Mathematical Induction
Content: Introduction to the principle of mathematical induction
and its application in proving mathematical statements.
Objective: Learn how to prove various mathematical propositions
using the method of induction.
5. Complex Numbers and Quadratic Equations
Content: Definition of complex numbers, their algebraic properties,
and the solution of quadratic equations using complex numbers.
Objective: Understand the concept of complex numbers and their
application in solving quadratic equations with no real solutions.
6. Linear Inequalities
Content: Representation of linear inequalities in one and two
variables, and graphical solutions of linear inequalities.
Objective: Develop skills in solving and graphically representing
inequalities involving one or two variables.
7. Permutations and Combinations
Content: Basics of counting techniques, permutations, combinations,
and the fundamental principles of counting.
Objective: Learn to calculate possible arrangements and selections
in various scenarios.
8. Binomial Theorem
Content: Expansion of binomial expressions using binomial theorem
for positive integral indices.
Objective: Master the binomial theorem and its use in expanding
algebraic expressions efficiently.
9. Sequence and Series
Content: Study of sequences, arithmetic progression (AP), geometric
progression (GP), and the formulas for their nth term and sum.
Objective: Understand the behavior of sequences and series, and
apply formulas to find terms and sums.
10. Conic Sections
Content: Definitions and equations of circles, parabolas, ellipses,
and hyperbolas, along with their graphical representations.
Objective: Learn the standard forms and properties of various conic
sections and their applications in geometry.
11. Introduction to ThreeDimensional Geometry
Content: Coordinates of points in threedimensional space, distance
between two points, and section formula in 3D geometry.
Objective: Understand basic concepts of 3D geometry and their use
in calculating distances and midpoints.
12. Limits and Derivatives
Content: Introduction to the concept of limits, continuity, and
derivatives of functions.
Objective: Develop a basic understanding of limits and derivatives,
laying the groundwork for calculus.
13. Mathematical Reasoning
Content: Statements, logical connectives, and basic reasoning
methods such as tautology, contradiction, and implications.
Objective: Enhance logical thinking and problem solving skills
through formal reasoning techniques.
14. Statistics and Probability
Content: Measures of central tendency (mean, median, mode),
dispersion, and probability theory.
Objective: Learn to analyze data using statistical methods and
understand the basic concepts of probability.
