This comprehensive online Mathematics course by Shubham Goel is designed for students of CBSE Class X and XII. The program covers the complete CBSE syllabus with a strong conceptual foundation, step-by-step problem-solving techniques, and exam-focused preparation.

The course emphasizes clarity in core topics such as Algebra, Calculus, Geometry, Trigonometry, Probability, and Linear Programming. Each unit is taught in a structured format with conceptual explanations, solved examples, practice questions, and exam-oriented strategies to help students perform confidently in board examinations.

Whether students aim for strong board results or preparation for competitive exams, this course builds mathematical reasoning, logical thinking, and problem-solving efficiency.

What Student Will Learn

CBSE Class 12 Mathematics: Course Syllabus

Unit 1: 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, and principal value branch. Graphs of inverse trigonometric functions.

Unit 2: Algebra

• Matrices: Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew-symmetric matrices. Operation on matrices (Addition, multiplication, and scalar multiplication).

• Determinants: Determinant of a square matrix (up to 3 \times 3), properties of determinants, minors, co-factors, and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. Solving systems of linear equations using the matrix inverse method.

Unit 3: Calculus

Continuity and Differentiability: Continuity, differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, and implicit functions. Logarithmic differentiation.

Applications of Derivatives: Rate of change of bodies, increasing/decreasing functions, maxima and minima (first and second derivative tests).

Integrals: Integration as the inverse of differentiation. Integration by substitution, partial fractions, and by parts. Evaluation of definite integrals and their properties.

Applications of the Integrals: Applications in finding the area under simple curves, especially lines, circles/parabolas/ellipses (standard forms 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 and homogeneous differential equations of first order and first degree.

Unit 4: Vectors and Three-Dimensional Geometry

• Vectors: Vectors and scalars, magnitude and direction of a vector. Direction cosines and direction ratios of a vector. Types of vectors, position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar. Dot product and 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, skewed lines, shortest distance between two lines. Angle between two lines.

Unit 5: Linear Programming

• Linear Programming: Introduction, related terminology such as constraints, objective function, optimization, different types of linear programming (L.P.) problems. Graphical method of solution for problems in two variables, feasible and infeasible regions, feasible and infeasible solutions, optimal feasible solutions.

Unit 6: Probability

• Probability: Conditional probability, multiplication rule of probability, independent events, total probability, Bayes' theorem, Random variable and its probability distribution.

CBSE Class 10 Mathematics: Course Syllabus

Unit 1: Number Systems

• Real Numbers: Fundamental Theorem of Arithmetic (Prime Factorization), proving the irrationality of numbers like \sqrt{2}, \sqrt{3}, \sqrt{5}.

Unit 2: Algebra

• Polynomials: Zeros of a polynomial, relationship between zeros and coefficients of quadratic polynomials.

• Pair of Linear Equations in Two Variables: Graphical method of solution, consistency/inconsistency, Algebraic methods (Substitution and Elimination).

• Quadratic Equations: Standard form ax^2 + bx + c = 0, solution by factorization and Quadratic Formula, nature of roots based on the Discriminant (D = b^2 - 4ac).

• Arithmetic Progressions (AP): Derivation of the n^{th} term (a_n = a + (n-1)d) and Sum of first n terms (S_n = \frac{n}{2}[2a + (n-1)d]).

Unit 3: Coordinate Geometry

• Lines (In two-dimensions): Review of coordinate geometry, Distance Formula, and Section Formula (internal division).

Unit 4: Geometry

• Triangles: Definitions, examples, and counter-examples of similar triangles.

• Core Theorem: Proof and application of the Basic Proportionality Theorem (Thales Theorem).

• Criteria for Similarity: SAS, SSS, and AA.

• Circles: Tangent to a circle at the point of contact.

• Theorems: (1) The tangent at any point is perpendicular to the radius through the point of contact. (2) The lengths of tangents drawn from an external point to a circle are equal.

Unit 5: Trigonometry

Introduction to Trigonometry: Trigonometric ratios of an acute angle of a right-angled triangle. Values of ratios for 0^\circ, 30^\circ, 45^\circ, 60^\circ, 90^\circ.

Trigonometric Identities: Proof and applications of \sin^2 A + \cos^2 A = 1.

Heights and Distances: Simple problems on heights and distances using angles of elevation and depression (not exceeding two right triangles).

Unit 6: Mensuration

• Areas Related to Circles: Area of sectors and segments of a circle (central angles of 60^\circ, 90^\circ, 120^\circ).

• Surface Areas and Volumes: Surface areas and volumes of combinations of any two: cubes, cuboids, spheres, hemispheres, and right circular cylinders/cones.

Unit 7: Statistics and Probability

• Statistics: Mean, median, and mode of grouped data (including bimodal situations).

• Probability: Classical definition, simple problems on finding the probability of an event.

Teaching Methodology

• Concept clarity with real-life examples
• Step-by-step problem-solving approach
• Board exam pattern practice
• Important questions and previous year questions
• Doubt-clearing sessions
• Regular assessments and revision tests
• Personalized attention in online sessions

Who Can Join

• CBSE Class 10 students preparing for board exams
• CBSE Class 12 students preparing for boards and competitive exams
• Students needing strong foundation in Algebra and Calculus
• Learners aiming for higher studies in Mathematics

Learning Outcomes

• Strong conceptual understanding
• Improved speed and accuracy in problem solving
• Confidence in tackling board exam questions
• Clear understanding of calculus and algebraic applications
• Better analytical and logical reasoning skills