# (NIOS Syllabus) Class 12 NIOS Syllabus | Mathematics 2012

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**Senior Secondary Course (Syllabus) Mathematics**

**RATIONALE**

The curriculum in Mathematics has been designed to cater to the specific needs of NIOS learners. The thrust is on the applicational aspects of mathematics and relating learning to the daily life and work situation of the learners. The course is modular in nature with – eight compulsory modules forming the core curriculum and four optional modules out of which the learner is to choose one optional module. An attempt has been made to reduce rigour and abstractness.

**OBJECTIVES**

The course aims at enabling learners to :

• become precise, exact and logical.

• acquire knowledge of mathematical terms, symbols, facts and formulae.

• develop an understanding of mathematical concepts.

• develop problem solving ability.

• acquire skills in applying the learning to situation including reading charts, tables, graphs etc.

• apply the above skills in solving problems related to Science, Commerce and daily life.

• develop a positive attitude towards Mathematics and its application.

**COURSE STRUCTURE**

The compulsory modules are :

1. Complex Numbers and Quadratic Equations

2. Determinants and Matrices

3. Permutations and Combinations

4. Sequences and Series

5. Trigonometry

6. Coordinate Geometry

7. Differential Calculus

8. Integral Calculus

The optional modules are :

9. Statistics and Probability

10. Vectors and Analytical Solid Geometry

11. Linear Programming

**MODULE WISE DISTRIBUTION OF STUDY HOURS AND MARKS**

S.No. | Compulsory Modules | Minimum Study Hours | Marks |

1 | Complex Numbers & Quadratic Equations | 15 | 10 |

2 | Determinants & Matrices | 15 | 10 |

3 | Permutations & Combinations | 20 | 08 |

4 | Sequences & Series | 20 | 08 |

5 | Trigonometry | 30 | 10 |

6 | Coordinate Geometry | 30 | 10 |

7 | Differential Calculus | 45 | 17 |

8 | Integral Calculus | 45 | 17 |

Optional Modules(The learner have to choose any one module) | |||

9 | Statistics & Probability OR | 20 each | 10 each |

10 | Vectors & Analytical Solid Geometry OR | ||

11 | Linear Programming | ||

Total | 240 | 100 |

**CURRICULUM OF SENIOR SECONDARY MATHEMATICS**

**COMPULSORY MODULES**

**Module 1: Complex Numbers and Quadratic Equations**

**Study Time: 15 hrs. Max. Marks: 10**

**Pre-requisites: Real numbers and quadratic equations with real coefficients.**

**Content and Extent of Coverage**

**Complex Numbers**

– Definition in the form x + iy

– Real and imaginary parts of a complex number.

– Modulus and argument of a complex number

– Conjugate of a complex number**Algebra of Complex number**

– Equality of complex numbers

– Operations on complex numbers (addition, subtraction, multiplication and division)

– Properties of operations (closure, commutativity, associativity, identity, inverse, distributivity)

– Elementary properties of modulus namely

(i) | z | = 0 z = 0 and z1 = z2 | z1| = | z2 |

(ii) | z1 + z2 | ≤ | z2 | + | z2 |

(iii) | z1/z2 | = | z1 | / | z2 | (z2≠0)**Argand Diagram**

– Representation of a complex number by a point in a plane.**Quadratic Equations**

– Solution of quadratic equation with real coefficients using the quadratic formula

– Square root of a complex number

– Cube roots of unity

**Extended Learning**

- Polar representation of a complex number
- Quadratic equations with complex coefficients

**NOTE :**

– “Division by zero is not allowed in complex numbers” to be stressed.

– Lack of order in complex numbers to be highlighted.

– The fact that complex roots of a quadratic equation with real coefficients occur in conjugate pairs but the same may not be true if the coefficients are complex numbers is to be verified using different examples.

**Module 2: Determinants and Matrices**

**Study Time: **15 hrs. Max. Marks: 10

**Pre-requisites :** Knowledge of number systems; solution of system of linear equations.

**Content and Extent of Coverage**

**Determinants and their Properties**

– Minors and Cofactors

– Expansion of a determinant

– Properties of determinants**Matrices**

– Introduction as a rectangular array of numbers

– Matrices upto order 3×4**Types of matrices**

– Square and rectangular matrices

– Unit matrix, zero matrix, diagonal, row and column matrices

– Symmetric and skew symmetric matrices**Algebra of matrices**

– Multiplication of a matrix by a number

– Sum and difference of matrices

– Multiplication of matrices**Inverse of a square matrix**

– Minor and cofactors of a matrix

– Adjoint of a matrix

– Inverse of a matrix**Solution of a system of linear equations**

– Solution by Cramer’s Rule

– Solution by matrix method

**NOTE:**

– The properties of determinants to include the following:

1. If any two rows or columns of a determinant are interchanged, then the sign of the determinant is changed.

2. If each element of a row (or column) of a determinant is multiplied by a constant, the value of the determinant gets multiplied by.

3. If k times a row (or column) is added to another row (or column) the value of the determinant remains unchanged.

– The number of equations and variables to be restricted to three only.

**Extended Learning**

- Cramer’s Rule for four or more equations
- Determi

nant as a function - Matrix as a function
- Matrices over complex numbers
- Hermitian and Skew Hermitian
- Rank of a Matrix
- Inverse by elementary row transformations
- Solution of 4 or more than 4 linear equations in 4 more than 4 variables

**Module 3: Permutations, Combinations and Binomial Theorem**

**Study Time: **20 hrs. Max. Marks: 8

**Pre-requisites : **Number Systems

**Content and Extent of coverage**

**Mathematical Induction**

– Principle of mathematical induction

– Application of the principle in solving problems**Permutations**

– Fundamental Principle of Counting

– Meaning of nPr

– Expression for nPr**Combinations**

– Meaning of nCr

– Expression for nCr

– Properties of nCr namely

(i) nCr = nPr/n!

(ii) n Cr=nCn-r

(iii) nCr-1+nCr=n+1Cr**Binomial Theorem**

– Binomial theorem for a positive index with proof.

Extended Learning**Circular permutations****Pascal’s triangle****Binomial theorem for negative index and rational indices (without proof)**

**Module 4: Sequences and Series**

**Study Time: **20 hrs. Max. Marks: 8

**Pre-requisites : **Permutation, Combination and concept of a function, Exponential functions, Logarithmic functions and their properties, and graphs.

**Content and Extent of coverage**

**Arithmetic Progression**

– Concept of a sequence

– A.P as a sequence

– General term of an A.P

– Sum upto ‘n’ terms of an A.P.**Geometric Progression**

– G.P as a sequence

– General term of a G.P

– Sum upto ‘n’ terms of a G.P.

– Sum upto infinite terms of a G.P.

**Series**

– Concept of a series

– Some important series, etc. using method of differences and mathematical induction**Exponential and Logarithmic Series**

– Representation of x e and log(1+ x) as series.

– Properties of x e and log(1+ x)

**Extended Learning**

- Arithmetic Mean, Geometric Mean
- Harmonic Progression, Arithmetico- Geometric Progression and their relationships
- Logarithms on any base

**Module 5 : Trigonometry**

**Study Time: **30 hrs. Max. Marks: 10

**Pre-requisites : **Trigonometric ratios of an acute angle.

**Content and Extent of coverage**

**Functions**

– Concept of a function

– Domain, codomain and range of a function

– Graphs of functions

– Odd and even functions

– Some important functions**Composition of Functions**

– Composition of two or more functions

– Inverse of a Function**Trigonometric Ratios**

– Radian measure of angles

– Trigonometric ratios as functions

– Graphs of T-ratios

– Periodicity

– T-ratios of allied angles

– Inverse Trigonometric ratios**Addition and Multiplication formulae**

– Addition and subtraction formulae for trigonometric functions

– Sines, Cosines and Tangents of multiples and submultiples

– Solution of simple trigonometric equations

**Extended Learning**

- Properties of triangles
- Solution of triangles
- Properties of inverse functions
- Trigonometric equations and their solutions
- General solution of Trigonometric equations

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is there a choice between limit and differentiation

is there a choice between tangents and differentition

tamannachawla on 02 Mar 2013INSURANCE & SHARE/ DEBENTURES CHAPTER ARE INCLUDED IN MATHS SYLLABUS OR NOT ?

AMANAT on 01 Feb 2013i want the new syllubus of 2012/2013.bcoz i’m not sure if it is the new or old syllubus

rose on 24 Jan 2013i want detail of all chapter for maths (12 class),,,,,plzzz tel me ,,,,

yusuf ishtiyaque on 12 Jan 2013give details of all the chapters that are to be studied for exams.give details of the topics of each chapter

puneet on 04 May 2012Pleas give details of the all chapters for mathematics.kindly let me know the details of all the chapters ,that are to be studied.

puneet on 04 May 2012in book there are many places where sum is miss print

and rear examples…

abdul aziz on 06 Apr 2012I am madan kumar, 12th class student. I am exam october

(Mai mdan kumar, 12th class me admission liya hu, jo mera final paper april me hoga ab mai october me mai math ka paper dena chah raha hu,to math me mera kam number aaya or mai math me pass hu, to mai percentage(%)bdhane ke liye april me exam de sakta hu. please send massage.

Thank you

madan kumar

Roll no. 27000613550

madan kumar on 14 Jul 2011is question asked in board exam coming from the same maths book.text book . Which we get from nios?

akash purty on 25 Jun 2011my self MD ASIF RAZA,

i wanna know about CYLLABUS of NIOS

subject of MATHMATICS(311) AND CHEMISTRY(312),

PLESE TELL ME ABOUT THIS,

my examination going on APRIL.

MD ASIF RAZA on 01 Mar 2011