In-Depth Mathematics 


ScienceGenic introduces the Senior Philosophy Classroom Program, a premier educational offering for students in grade 12. This program is designed to prepare students for the challenges of higher education and beyond, offering comprehensive support and advanced learning experiences. Here’s what sets our program apart:

Specialized Subject Teachers: Our program features highly qualified and specialized teachers for each core subject—Physics, Chemistry, Biology, and Mathematics. These expert educators bring a deep understanding of their subjects and a passion for teaching, offering personalized instruction to every student.

Supervised and Supported Teaching: The Senior Philosophy Classroom Program ensures quality teaching through careful supervision and support for educators. Teachers receive guidance from the syllabus manager and psychologist to create an engaging and holistic learning environment.

Integrated Communication Channels: Seamless communication between the syllabus manager, psychologist, and teachers enables a collaborative approach to education. This teamwork fosters a comprehensive understanding of each student’s academic and emotional needs.

Deep Understanding of Subject Knowledge: Our curriculum focuses on in-depth exploration of advanced concepts in each subject. Students are encouraged to think critically, analyze complex topics, and apply their knowledge in real-world contexts.

Personalized Guidance and Support: We recognize that every student is unique, and we tailor our approach to meet their individual needs. Our collaborative team works closely with students to provide personalized guidance and support throughout their educational journey.

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Syllabus 12th CBSE Mathematics

Unit-I: Relations and Functions

Relations and Functions

Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions.

Inverse Trigonometric Functions

Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions. Unit-II: Algebra


Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew symmetric matrices. Operations on matrices: Addition and multiplication and multiplication with a scalar. Simple properties of addition, multiplication and scalar multiplication. Non- commutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2). Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).


Determinant of a square matrix (up to 3 x 3 matrices), minors, co-factors and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix.

Unit-III: Calculus

Continuity and Differentiability

Continuity and differentiability, chain rule, derivative of inverse trigonometric functions, 𝑙𝑖𝑘𝑒 sin−1 𝑥 , cos−1 𝑥 and tan−1 𝑥, derivative of implicit functions. Concept of exponential and logarithmic functions. Derivatives of logarithmic and exponential functions. Logarithmic differentiation, derivative of functions expressed in parametric forms. Second order derivatives.

Applications of Derivatives

Applications of derivatives: rate of change of quantities, increasing/decreasing functions, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as real- life situations).


Integration as inverse process of differentiation. Integration of a variety of functions by substitution, by partial fractions and by parts, Evaluation of simple integrals of the following types and problems based on them.

Applications of the Integrals

Applications in finding the area under simple curves, especially lines, circles/ parabolas/ellipses (in standard form only)

Differential Equations

Definition, order and degree, general and particular solutions of a differential equation. Solution of differential equations by method of separation of variables, solutions of homogeneous differential equations of first order and first degree.

Unit-IV: Vectors and Three-Dimensional Geometry


Vectors and scalars, magnitude and direction of a vector. Direction cosines and direction ratios of a vector. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Definition, Geometrical Interpretation, properties and application of scalar (dot) product of vectors, vector (cross) product of vectors.

Three - dimensional Geometry

Direction cosines and direction ratios of a line joining two points. Cartesian equation and vector equation of a line, skew lines, shortest distance between two lines. Angle between two lines.

Unit-V: Linear Programming

Linear Programming

Introduction, related terminology such as constraints, objective function, optimization, graphical method of solution for problems in two variables, feasible and infeasible regions (bounded or unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).

Unit-VI: Probability


Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, Random variable and its probability distribution, mean of random variable.