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Class 12

Mathematics

62 lessons in 13 chapters, explained in plain words.

Relations and Functions

  1. Kinds of relations
  2. Equivalence relations
  3. One-one and onto functions
  4. Bijections and counting functions
  5. Composition and inverses

Inverse Trigonometric Functions

  1. Principal value branches
  2. Values of inverse trig expressions
  3. Simplest form and identities
  4. Inverse trig equations

Matrices

  1. What is a matrix?
  2. Adding matrices and scaling them
  3. Multiplying matrices
  4. Transpose, symmetric and skew symmetric
  5. Inverses and matrix problems

Determinants

  1. What is a determinant?
  2. Area of a triangle
  3. Minors and cofactors
  4. Adjoint and inverse
  5. Solving linear equations with matrices

Continuity and Differentiability

  1. Continuity at a point
  2. Building continuous functions
  3. Differentiability, chain rule and implicit functions
  4. Exponential, log and logarithmic differentiation
  5. Parametric forms and second derivatives
  6. Mixed problems

Application of Derivatives

  1. Rates of change
  2. Increasing and decreasing functions
  3. Local maxima and minima
  4. Absolute maximum and minimum
  5. Optimisation problems

Integrals

  1. Integration as anti-differentiation
  2. Substitution and trig identities
  3. Special forms and partial fractions
  4. Integration by parts
  5. Definite integrals
  6. Properties of definite integrals

Application of Integrals

  1. Area under a curve
  2. Curves that cross the axis

Differential Equations

  1. What is a differential equation?
  2. Solutions of a differential equation
  3. Variables separable
  4. Particular solutions and growth
  5. Homogeneous equations
  6. Linear equations

Vector Algebra

  1. What is a vector?
  2. Components and unit vectors
  3. Points, ratios and lines
  4. Dot product: angles
  5. Dot product: properties
  6. Cross product

Three Dimensional Geometry

  1. Direction of a line in space
  2. Equation of a line
  3. Angle between two lines
  4. Shortest distance between lines

Linear Programming

  1. Linear programming: the corner point method
  2. Unbounded and empty regions

Probability

  1. Conditional probability
  2. Conditional probability by counting
  3. Multiplication rule and independence
  4. Working with independent events
  5. Total probability and Bayes' theorem
  6. Bayes' theorem in real life