# Mathematics (M 1208) - Grade 12

Unit Area Covered Marks
Unit 1 Relations and Functions 10 Read more
Unit 2 Inverse trigonometric functions 10 Read more
Unit 3 Matrices and Determinants 05 Read more
Unit 4 Determinant of a square matrix (up to 3 × 3 matrices) 05 Read more
Unit 6 Calculus 05 Read more
Unit 7 Applications of Derivatives 05 Read more
Unit 8 Indefinite Integrals 05 Read more
Unit 9 Definite integrals 05 Read more
Unit 10 Application of the integrals 10 Read more
Unit 11 Differential Equations 05 Read more
Unit 12 Vectors and Three Dimensional Geometry 10 Read more
Unit 13 Three-dimensional Geometry 05 Read more
Unit 14 Probability 10 Read more
Total Marks 100

# Unit 1

Relations and Functions

• Types of relations : reflexive, symmetric, transitive and equivalence relations
• One to one and on to functions
• Composite functions
• Inverse of a function and binary operations
• Concept of exponential and logarithmic function to the base e, logarithmic function as inverse of exponential function and their graphs

# Unit 2

Inverse trigonometric functions

• Definition of inverse trigonometric function in a unit circle
• Range, domain, principal value branches
• Graphs of inverse trigonometric functions
• Elementary properties of inverse trigonometric functions
• Problems based on properties

# Unit 3

Matrices and Determinants

• Matrices
• Equality of matrices
• Operation on matrices
• Multiplication of matrices
• Transpose of matrix
• Symmetric and skew-symmetric matrices
• Concept of elementary row and column transformations

# Unit 4

Determinants

• Determinant of a square matrix (up to 3 × 3 matrices)
• Application of determinant
• Properties of determinants
• Cramer's Rule

# Unit 5

Adjoint and Inverse of a matrix

• Singular and Non singular matrix
• Invertible matrices
• Solving a system of linear equations by Matrix method

# Unit 6

Calculus

• Differentia-bility
• Product Rule
• Quotient Rule
• Derivatives of implicit functions
• Derivative of logarithmic and exponential functions
• Derivative of Infinite Series
• Logarithmic differentiation
• Differentiation of one function with respect to another.
• Derivatives of functions expressed in parametric form
• Second order derivative

# Unit 7

Applications of Derivatives

• Rate of change
• Increasing/decreasing functions
• Rolle's theorem, Lagrange's mean value theorem (without proof) and their geometrical interpretation and simple application
• Tangents and normals
• Approximations
• Maxima and minima (local maxima/local minima and absolute maxima/absolute minima), first derivative test, second derivative test, simple problems (that illustrate basic principles and understanding of the subject as well as real life situations)

# Unit 8

Indefinite Integrals

• Integration as an inverse process of differentiation
• Increasing/decreasing functions
• Integration of a variety of functions by substitution
• Integration by parts
• Some special integrals
• Integration by partial fraction

# Unit 9

Definite integrals

• Fundamental theorem of calculus (without proof)
• Definite integral by substitution
• Basic properties of definite integrals and evaluation of definite integrals
• Definite integrals as a limit of sum

# Unit 10

Application of the integrals

• Finding the areas of circles/parabolas/ ellipses (in standard form only)
• Area bounded by a curve and a line
• Area bounded between two curves

# Unit 11

Differential Equations

• Definition, order and degree
• General particular solutions a differential equation
• Formation of differential equation
• Homogenous differential equation of first order and first degree
• Linear equation of first order
• Applications of differential equation

# Unit 12

Vectors and Three Dimensional Geometry

• Vectors and Scalars
• Magnitude and direction of a vector
• Position vector of a point
• Components of a vector
• Properties of addition of vectors
• Multiplication of a vector by a scalar
• Position vector of a point dividing a line segment in a given ratio
• Direction cosines and direction ratios of vector
• Scalar (dot product) of vectors
• Projection of a vector on a number line
• Vector product
• Scalar triple product

# Unit 13

Three-dimensional Geometry

• Brief recall of direction cosines and direction ratios of a line
• Cartesian and vector equation of a straight line
• Angle between two lines
• Shortest distance between two lines
• Distance between parallel lines
• Equation of a plane in normal form
• Equation of a plane passing through a given point
• Equation of plane in intercept form
• Equation of plane in general form
• Equation of plane through the intersection of two planes
• Angle between two planes
• Distance of a point from a plane
• Image of a point in plane
• Coplanar lines

# Unit 14

Probability

• Conditional Probability
• Multiplication theorem on probability
• Independent Events
• Total Probability
• Baye's theorem
• Random variable and it's probability distribution
• Mean and variance of random variable
• Repeated independent (Bernoulli) trials and Binomial distribution