Unit 1: Relations and Functions
- Chapter 1: Relations and Functions Explore the higher-level types of relations (Reflexive, Symmetric, Transitive) and functions (One-to-One, Onto). Learn how to determine if a function is Bijective.
- Chapter 2: Inverse Trigonometric Functions Understand the restricted domains and ranges required to define inverse functions for $sin$, $cos$, and $tan$. Master the Principal Value Branch calculations.
Unit 2: Algebra
- Chapter 3: Matrices Learn about the arrangement of numbers into rows and columns. Study Matrix operations, Transpose, and Symmetric/Skew-symmetric matrices.
- Chapter 4: Determinants A vital tool for solving linear equations. Learn about Minors, Cofactors, and how to find the Adjoint and Inverse of a square matrix.
- Key Formula: $A^{-1} = \frac{1}{|A|} adj(A)$
Unit 3: Calculus (The 35-Mark Unit)
- Chapter 5: Continuity and Differentiability Study the smoothness of functions. Master the Chain Rule, Logarithmic differentiation, and the differentiation of infinite series.
- Chapter 6: Application of Derivatives Learn how math tracks change. Focuses on Tangents and Normals, Increasing/Decreasing functions, and finding the Maxima and Minima of a function.
- Chapter 7: Integrals The inverse of differentiation. Learn Integration by Parts, Substitution, and Partial Fractions. This chapter is essential for both Physics and Engineering.
- Key Identity: $\int udv = uv – \int vdu$
- Chapter 8: Application of Integrals Use integration to calculate the area under simple curves, circles, parabolas, and ellipses.
- Chapter 9: Differential Equations Learn to solve equations involving derivatives. Covers Order and Degree, Variable Separable method, and Homogeneous equations.
Unit 4: Vectors and Three-Dimensional Geometry
- Chapter 10: Vector Algebra Understand magnitude and direction. Learn about Scalar (Dot) and Vector (Cross) products and their geometric significance.
- Chapter 11: Three Dimensional Geometry Move from lines on a page to lines in space. Study Direction Cosines, Direction Ratios, and the equations of lines and planes in 3D space.
Unit 5: Linear Programming & Probability
- Chapter 12: Linear Programming A chapter that relates directly to business. Learn to optimize (Maximize/Minimize) resources like profit or cost based on specific constraints.
- Chapter 13: Probability Move beyond basic chance to Conditional Probability, Bayes’ Theorem, and Random Variables. Essential for understanding risk in the banking and insurance sectors.
💡 Pro-Tip for Maths Students
Calculus is 60% of your Class 12 board paper. Don’t start Integrals until your Derivatives are perfect. At Mobotes, we suggest making a “Formula Wall” in your study room. Seeing the integration identities every day makes them second nature during the pressure of an exam!