**NCERT Class 11 Mathematics Solutions**: Mathematics is one of the core disciplines that function on figures and calculations. It is an objective subject that adds up to the emerging with all other important subjects for the students of the 12^{th} standard, respectively. For professional courses like Engineering, Computer Applications, Physical and Bioscience, and others require the expertise of calculations that is rightly derived from Mathematics. The current syllabus for the subjects has been designed after revision in accordance to the National Curriculum Framework 2005 and also as per the guidelines given in the Focus Group on Teaching of Mathematics 2005, as well. Every year the students across the country appear for the 10+2 examinations to secure the best scores at the end of the academic year. The students have always been navigated to use the NCERT books as they relate them to the basic concepts of all the subjects that is included in the curriculum. The course or syllabus of the subjects are clearly carried and covered in a student-friendly manner by the NCERT books which give the students precise ideas about the scores, the typology of the questions and also the marking scheme according to which they are expected to prepare the answers in the examinations. Mathematics is always fun for the students as it has a large scoring scope if practiced really well with the involvement of the calm mind and focus relying upon the guidelines of the same. The **NCERT Class 11 Mathematics Solutions **is helpful for all the students as it allows the academic applicants to prepare well with a well cohesive idea of marks, ways and curriculum as well.

## NCERT Class 11 Mathematics Solutions

Mathematics is a subject of practice and without the same one cannot gain confidence. NCERT solutions are not only essential for regular school studies but also help in solving the competitive questions referring to the examinations. Mostly, all the schools rely on the NCERT books as it is considered as the student friendly reference for all standards and all subjects, in particular. The books are designed in a manner to cover the whole syllabus altogether by providing questions as well as answers for the same. Each of the mathematics sums is framed in step wise structure created completely by the subject experts comprehensively. All the solutions are framed keeping the guidelines of CBSE in mind in the PDF format, free of cost and with no effort of time consumption.

## NCERT Class 11 Mathematics Syllabus Rationale:

*Unit-I: Sets and Functions*

- Sets
- Relations & Functions
- Trigonometric Functions

**Course of objectives:**

**SETS**

- Sets and their representatives
- Empty Set
- Finite and Infinite Sets
- Equal Sets
- Subsets
- Subsets of the real numbers
- Power Sets
- Universal Sets
- Union and Intersection of Sets

**Relations and Functions**

- Ordered Pairs
- Cartesian product of Sets
- Number of Sets in the Cartesian product
- Cartesian product of the set of itself
- Definition of relations
- Pictorial Diagrams
- Co-domain and range of relations
- Domain and co-domain
- Real valued functions
- Signum
- Exponential
- Polynomial
- Logarithmic
- Greatest Integer functions and graphs

**Trigonometric Functions:**

- Positive and Negative Angles
- Measuring angles in radians and in degrees and conversion from one measure to another
- Definition of trigonometric functions with the help of unit circle
- sin2x + cos2x = 1, for all x
- Signs of trigonometric functions
- trigonometric functions and their graphs
- Expressing sin (x±y) and cos (x±y) in terms of sinx, siny, cosx & cosy and their simple applications

*Unit-II: Algebra*

- Principle of Mathematical Induction
- Complex Numbers and Quadratic Equations
- Linear Inequalities
- Permutations and Combinations
- Binomial Theorem
- Sequence and Series

**Principle of Mathematical Induction (10) Periods**

- Process of the induction motivating the application of the method by looking at natural numbers as the least inductive subset of real numbers.
- The principle of mathematical induction and simple applications.

**Complex Numbers and Quadratic Equations (15) Periods**

- Need for complex numbers
- quadratic equations
- Algebraic properties of complex numbers
- Argand plane and polar representation of complex numbers
- Statement of Fundamental Theorem of Algebra
- Solution of quadratic equations (with real coefficients) in the complex number system
- Square root of a complex number.

**Linear Inequalities (15) Periods**

- Linear inequalities
- Algebraic solutions of linear inequalities in one variable and their representation on the number line
- Graphical solution of linear inequalities in two variables
- Graphical method of finding a solution of system of linear inequalities in two variables

**Permutations and Combinations (10) Periods**

- Fundamental principle of counting
- Factorial n. (n!) Permutations and combinations
- Derivation of formulae for and their connections
- Simple applications

**Binomial Theorem (10) Periods**

- History, statement and proof of the binomial theorem for positive integral indices
- Pascal’s triangle
- General and middle term in binomial expansion
- Simple applications

**Sequence and Series (10) Periods**

- Sequence and Series
- Arithmetic Progression (A. P.)
- Arithmetic Mean (A.M.)
- Geometric Progression (G.P.)
- General term of a G.P.
- Sum of n terms of a G.P.
- Infinite G.P. and its sum
- Geometric mean (G.M.)
- Relation between A.M. and G.M
- Formulae for the following special sums.

*Unit-III: Coordinate Geometry*

- Straight Lines
- Conic Sections
- Introduction to Three-dimensional Geometry

**Straight Lines (10) Periods**

- Brief recall of two dimensional geometry
- Shifting of origin
- Slope of a line and angle between two lines
- Various forms of equations of a line: parallel to axis, point-slope form, slope- intercept form, two-point form, intercept form and normal form
- General equation of a line

**Conic Sections (20) Periods**

- Sections of a cone: circles, ellipse, parabola, hyperbola, a point, a straight line and a pair of intersecting
- Lines as degenerated case of conic section
- Standard equations and simple properties of parabola, ellipse and hyperbola
- Standard equation of a circle

**Introduction to Three-dimensional Geometry (10) Periods**

- Coordinate axes and coordinate planes in three dimensions
- Coordinates of a point
- Distance between two points and section formula

*Unit-IV: Calculus*

- Limits and Derivatives

**Limits and Derivatives (30) Periods**

- Derivative introduced as rate of change both as that of distance function and geometrically.
- Intuitive idea of limit
- Limits of polynomials and rational functions trigonometric, exponential and logarithmic functions
- Definition of derivative relates it to scope of tangent of the curve, derivative of sum, difference, product and quotient of functions
- Derivatives of polynomial and trigonometric functions

*Unit-V: Mathematical Reasoning*

- Mathematical Reasoning

**Mathematical Reasoning (10) Periods**

Mathematically acceptable statements

- Connecting words/ phrases – consolidating the understanding of “if and only if (necessary and sufficient) condition”, “implies”, “and/or”, “implied by”, “and”, “or”, “there exists” and their use through variety of examples related to real life and Mathematics.
- Validating the statements involving the connecting words, difference among contradiction, converse and contra positive

*Unit-VI: Statistics and Probability*

- Statistics
- Probability

**Statistics (15) Periods**

- Measures of Dispersion: Range, Mean deviation, variance and standard deviation ungrouped/grouped data.
- Analysis of frequency distributions with equal means but different variances.

**Probability (15) Periods**

- Random experiments; outcomes, sample spaces (set representation)
- Events; occurrence of events, ‘not’, ‘and’ and ‘or’ events, exhaustive events, mutually exclusive events, Axiomatic (set theoretic) probability, connections with other theories of earlier classes
- Probability of an event, probability of ‘not’, ‘and’ and ‘or’ events

#### NCERT Class 11 Mathematics Syllabus

Number of Chapters |
Names of Chapter |
Download Link |

1 | Sets | |

2. | Relations and Functions | |

3. | Trigonometric Functions | |

4. | Principle of Mathematical Induction | |

5. | Complex Numbers and Quadratic Equations | |

6. | Linear Inequalities | |

7. | Permutations and Combinations | |

8. | Binomial Theorem | |

9. | Sequences and Series | |

10. | Straight Lines | |

11. | Conic Sections | |

12. | Introduction to Three Dimensional Geometry | |

13. | Limits and Derivatives | |

14. | Mathematical Reasoning | |

15. | Statistics | |

16. | Probability |

### Best Preparation Strategies for Mathematics class 11

All the students who have mathematics as their subject in the 10+2 must make sure that they carefully deal with subject so as not to mess with the same. Mathematics can be dealt only with lots of practice paving its way. The more one practices mathematics, the more one gains more knowledge about each and every concept.

**Allocation of Adequate Time:**Manage time for all the topics separately. Once you are introduced to each and every concept of the subject, you get the urge of practicing them to get your concepts clarified about all the tough as well as easy sums.**Relevance of a Study Plan:**All the students appearing in the science or commerce stream are expected to prepare a study plan or chart after referring the date sheet and curriculum. After the same they can make notes according to their own convenience and choice so that their studying and revising becomes way easier at the end of the examination preparation tenure.**Building of Patience:**Mathematics is completely based upon patient practice. The students must carry on their continuous practice regarding the subject so that they do not fail to skip off understanding of any of the concepts at any cost that was taught in school.**Confidence is the Key:**The students who are going to appear in the class 12 board examinations must make sure that they have faith in themselves. Confidence and determination makes things easier and one begins to challenge oneself regarding the completion of the same.**Dedicate Study Time:**The board applicants are required to dedicate at least 2-3 hours every day to the practicing purpose of the subject. Mathematics expects attention and thus, the same works the best in solving easy to the most miscellaneous sums in all the chapters.**Refer to the Answer Key/ Solution:**It is not possible for the school teachers to solve each and every sum at once, contained in all the chapters present in the book. This is the time when the solutions of the same published make sense.**Practice Sample Question Papers of Previous Years:**Solving more and more previous year sample question papers for the several subjects occurring by the board authorities for 10+2 assists the students largely. Practicing the sums from the previous five to ten years question papers of the subjects targeted helps the students to grab idea on the typology of the questions occurring, Not only this, but the students also get an idea of the pattern of the questions and also the marking scheme designed for both short and long answered questions.**Refer to the Best Publications in Consultation with Experts:**Good references are a must for good guidance of the board applicants. If one chooses the best publication books, then it is possible that they get an access to the best guidance for the lessons that they are approaching.**Take Advices from Qualified:**The boards applicants are expected to take advices form their seniors who have already passed or qualified the exams, their parents, their peers as well as subject teachers who can explain them the whole process of studying. Not only will they suggest books that would help them but also ways to prepare for the examinations.

#### About the NCERT Class 11 Mathematics Solutions

NCERT stands for National Council for Educational Research and Training. It is a prominent resource dedicated towards the imparting of education with prominent publications of question papers and solution or answer keys to the questions posed against the students. It has been successful in maintaining the academic balance among all the students across the country studying in different schools (both private and public). NCERT has been supporting and enhancing the educational agenda for all the standards since its inception and will continue the same. The solutions of all the subjects that are declared by the NCERT help the students to get parallel with the answers to all their queries concerning the questions that they face in the books, and also in the sample question books as well and get fluent with practice.