# 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 5 |
Adjoint of a matrix | 10 | 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**

- Adjoint 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
- Addition of vectors
- 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