NCERT Book for Class 11 Maths

Mathematics is an essential subject that students are taught right from their early school days. It is important to be very clear about the basics of the subject as success at the advanced levels is built on the foundational concepts.

The syllabus in Class 11th Maths book PDF is fairly exhaustive and discusses all the topics that are included in the CBSE exam. If you are looking for convenient study material, you can download the NCERT book of Maths Class 11 from our website. You can also solve the questions provided in these NCERT books for Class 11 Maths at the end of each chapter.

Chapter 1: Sets 

The first chapter of NCERT book for Class 11 Maths includes – (1) Sets and their Representation, (2) Empty Set, (3) Finite and Infinite Sets, (4) Equal Sets, (5) Subsets, (6) Power Set, (7) Universal Set, (8) Venn Diagrams, (9) Operations on Sets and (10) Complement of a Set.

As explained in the Class 11 NCERT Maths book, a null or an empty set refers to such a set that contains no members. The notation symbol ∅ represents an empty set. In the case of a finite and infinite set, these terms are self-explanatory. A set will be considered to be finite when there is a starting and endpoint that is having a limited number of elements. 

On the other hand, when the number of elements is unlimited, it represents an infinite set. Furthermore, you can see in the Class 11 MMathsNCERT book PDF that a subset is essentially a part of another set. For instance, set Y will be a subset of set X if all elements of set Y comprise the elements of set X.

Chapter 2: Relations and Functions

The chapter includes – (1) Cartesian Product of Sets, (2) Relations, and (3) Functions. 

The Cartesian product of sets, as discussed in NCERT Maths Class 11 book PDF, is the cross product of two sets, say, X and Y noted as XxY is the set of all ordered pairs. It implies that XxY ≠ YxX. If either X or Y is a null set, the XxY will also be an empty set, that is, X x Y= φ.

Relations and Functions are essentially an ordered pair containing a set of inputs and outputs representing a relationship between two values. A relation is a given set of inputs and outputs, wherein the relation of one output with each input amounts to function.

Chapter 3: Trigonometric Functions

This chapter of the NCERT book for Class 11 Maths includes – (1) Angles, (2) Trigonometric Functions, (3) Trigonometric Functions of Sum and Difference of Two Angles, and (4) Trigonometric Equations.

The explanation of angles, degree measure, radian measure, the relation between radian and real numbers, the relation between degree and radian etc., are found in Chapter 3 of the NCERT book of Maths Class 11. The real functions relating to an angle of a right-angled triangle with that of the ratio of side lengths are known as trigonometric functions.

The basic trigonometric functions are sine, cosine and tangent. Other derived trigonometric functions include cosecant, secant and cotangent. The chapter shows trigonometric equations as equations of trigonometric functions of a variable.

Chapter 4: Principle of Mathematical Induction

The chapter includes – (1) Motivation, and (2) The Principle of Mathematical Induction.

Chapter 4 of the NCERT Class 11 Maths explains the principle of mathematical induction as the method of proving various mathematical statements noted in terms of n, which is a positive integer. It mainly includes deductive reasoning where the veracity of a given statement will have to be found out. Motivation, in this context, relates to mathematical induction.

Chapter 5: Complex Numbers and Quadratic Equations

The Chapter 5 of NCERT book for Class 11 Maths includes – (1) Complex Numbers, (2) Algebra of Complex Numbers, (3) The Modulus and the Conjugate of a Complex Number, (4) Argand Plane and Polar Representation, and (5) Quadratic Equations.

As discussed in the Class 11 Maths textbook PDF, the number which is expressed in the form of (a+bi) a and b=real numbers and the value of i is the solution of x₂=-1. Real numbers cannot satisfy this equation. Hence, it is termed as an imaginary number. However, a complex number can be purely real if its imaginary component is 0. The standard form of the quadratic equation ithe the NPRNCR+ bx + c = 0. The graph of the quadratic function formula is a parabola, and a, b, c in the quadratic equation which are not equal to zero.

Chapter 6: Linear Inequalities

The chapter includes – (1) Inequalities, (2) Algebraic Solutions of Linear Inequalities in One Variable and their Graphical Representation, (3) Graphical Solution of Linear Inequalities in Two Variables, and (4) Solution of System of Linear Inequalities in Two Variables.

Chapter 6 in the NCERT Mathematics Class 11 PDF shows that linear inequality essentially represents an equation, but in the place of equal signs, it has an inequality symbol. The solution of a linear inequality is not a specific value but involves a range of values. As for algebraic solutions of linear inequalities with one variable, the different values of the variable that make the inequality to be a true statement is a solution set.

Chapter 7: Permutations and Combinations

The 7th chapter in the NCERT book for Class 11 Maths includes - (1) Fundamental Principle of Counting, (2) Permutations, and (3) Combinations.

The representation of a collection of objects within a set and a subset or different manner of arranging data relates to permutation and combination. To be specific, a permutation is the selection of data from a cluster. Combination, on the other hand, is the order in which such data is represented. The chapter in NCERT Class 11 Maths textbook PDF indicates the notations of permutation and combination. nPr is the permutation of r elements from a group of n elements. nr is the combination of r elements taken from n.

Chapter 8: Binomial Theorem

The chapter includes – (1) Binomial Theorem for Positive Integral Indices, and (2) General and Middle Terms.

Binomial theorem propounds that in the case of any positive integer (n), the nth power of a sum of two numbers, x and y, is expressed as a sum of n + 1. Chapter 8 in the 11th NCERT Maths book PDF includes Pascal’s Triangle for elucidation of the binomial theorem. The general term of expansion of (a + b)n is Tr + 1 = nCran– r. br. Binomial factors include such polynomial factors that have only two terms and the square of binomial is a sum of the squares of the first term, the square of the last term and twice the product of two terms.

Chapter 9: Sequence and Series

The chapter includes – (1) Sequences, (2) Series, (3) Arithmetic Progression, (4) Geometric Progression, (5) Relationship between Arithmetic and Geometric Progression, and (6) Sum to n terms of Special Series. 

As elaborated in Chapter 9 of Class 11 Maths book PDF, arithmetic progression amounts to such a sequence of numbers wherein the consecutive terms are established with the addition of a constant quantity with preceding terms. Geometric progression, on the other hand, is such a sequence of numbers where each number is formed from the previous one by multiplying the same with a constant. Here, the ratio of two consecutive terms will always be equal.

Chapter 10: Straight Lines

This chapter in the NCERT book for Class 11 Maths includes – (1) the Slope of a line, (2) Various Forms of the Equation of a Line, (3) the General Equation of a Line, and (4) the Distance of a Point from a Line.

The definition of line and other related concepts is provided in Chapter 10 of the NCERT book for Class 11 Maths. The slope of a line is a measurement of its steepness. It also characterises the direction of a line. 

A slope of a line is determined through a division of the difference of y-coordinates of two points on the C line by a difference of x-coordinates of two same points. There are different forms of equations of a straight line – (i) equation of horizontal and vertical lines, (ii) point-slope form equation of a line, (iii) two-point form equation of a line, (iv) slope-intercept form equation of a line and (v) intercept form. 

Chapter 11: Conic Sections

The chapter includes – (1) Sections of Cone, (2) Circle, (3) Parabola, (4) Ellipse, and (5) Hyperbola.

The definition of a circle in Class 11th Maths book PDF is a congregation of all points in a plane that remains equidistant from a point fixed on the plane. The fixed point is held to be the centre of the circle, and the radius is the distance from the centre to a point in the circle. 

Parabola is a set of all points on a plane that is equally distant from both, a fixed-line as well a point on the plane that is fixed. This point, however, is not located on the line. When the sum of all points on a plane have the sum, where the latter is constant between two fixed points, is an Ellipse.

Chapter 12: Introduction to the Three Dimensional Geometry 

The chapter includes – (1) Coordinate Axes and Coordinate Planes in Three Dimensional Space, (2) Coordinates of a Point in Space, (3) Distance between Two Points, and (4) Section Formula.

It is defined in Chapter 12 of the NCERT book of Maths Class 11 in three-dimensional geometry, coordinate axes of rectangular Cartesian coordinate system are essentially three mutually perpendicular lines. The axes are x, y and z, respectively. The planes determined by a pair of axes are the XY, YZ and ZX planes. These coordinate planes divide the space into eight distinct parts called octants. The notations of a point are – (x,0,0), (0,y,0), (0,0,z) for x-axis, y-axis and z-axis respectively.

Chapter 13: Limits and Derivatives

The chapter includes – (1) Intuitive Idea of Derivatives, (2) Limits, (3) Limits of Trigonometric Functions, and (4) Derivatives.

Chapter 13 of Class 11th Maths book PDF introduces calculus through limits and derivatives. Limit is the value that is approached by a function consistent with the approach of input towards a value. A derivative is understood as the instantaneous rate of change of a particular quantity to another quantity. 

It determines the change in every moment of the amount. There is an inherent distinction between limits and derivatives. While a limit is a value of function near to the input, a derivative is an example of a limit.

Chapter 14: Mathematical Reasoning

The chapter includes – (1) Statements, (2) New Statements from Old, (3) Special Words/Phrases, (4) Implications, and (5) Validating Statements.

Mathematical reasoning in Class 11th Maths book PDF involves the determination of the acceptability of mathematical statements. Compound statements are obtained by the combination of one or more statements with the help of connecting words such as "or", "and", etc. Statements constituting a compound statement is called a component statement. A mathematically acceptable statement will comprise only such statements that can be either true or false.

Chapter 15: Statistics

The chapter includes – (1) Measures of Dispersion, (2) Range, (3) Mean Deviation, (4) Variance and Standard Deviation, and (5) Analysis of Frequency Distributions.

Chapter 15 of NCERT Mathematics Class 11 PDF discusses the measures of dispersion of scattered data based on observation and central tendency. The different measures of dispersion include – range, quartile deviation, standard deviation, and mean deviation. Range is understood as maximum value – minimum value.

Chapter 16: Probability

The chapter includes – (1) Random Experiments, (2) Event, and (3) Axiomatic Approach to Probability.

As discussed in the NCERT book of Maths Class 11, random experiments include such instances where the outcome cannot be predicted before the result. Outcome refers to all possible results of a particular experiment. A set of such outcomes comprises the sample space. An event is thus a subset of sample space.

Why are NCERT books preferred by Students and Teachers alike?

The textbooks published by NCERT are favoured by teachers and students alike. While these books are essentially prescribed as texts by schools, like NCERT books for Class 11 Maths, they also enjoy popularity among students for their lucid explanations and illustrations. There are a few aspects that make NCERT books a preferred option.

• Format: The format of NCERT textbooks is simple and precise. The presentation is simple enough to retain students’ attention. At the same time, it makes it easy for them to understand the content but does in no way compromise the content in that regard. 

• Lucid Explanation: The topics are explained simply with appropriate illustrations in places. Not only does it make for an easy read, but students also have greater clarity about the topic through pictorial representations.

• Easy Problem-solving Exercises: Each chapter comes with a set of questions at the end. Practising them enables students to revise what they have studied in a chapter, and at the same time, gain an understanding of any doubts or confusions that they might have.

• Strict Adherence to the Syllabus: NCERT books are also compiled strictly as per the syllabus prescribed by CBSE. The topics thus covered offer a clear insight into what a student shall learn in his/her curricular exam preparation.

• Students should master the concepts thoroughly so that they can respond whenever the topic of sustainability arises in any area of the chapter. CBSE ensures that questions are based on the chapters' main themes. You won't be afraid of exams if your notions are clear.

• Each chapter's concepts should be explained to students in a way that they can grasp. Teachers should make a concerted effort to use the NCERT texts in their classrooms. Instead of focusing on the chapter's solutions and activities, students should learn the chapter's concepts and fundamentals.

Advice from experts to top in Class 11 maths:

Math in CBSE Class 11 is very different from what we learn in secondary school. The level of mathematics changes dramatically, but there's no need to be concerned. The following pointers may assist you in passing CBSE Class 11 maths.

• Have a devoted mindset to study and work consistently throughout the year, which includes doing something small every day. Many online lectures, such as Vedantu, clarify all concepts and answer intext questions. Many teachers have offered their services to pupils on YouTube for free.

• Choosing the appropriate teacher/mentor is crucial; choose someone who always creates a spark in you whenever you engage, because learning requires students to be enthusiastic. Young minds are incredibly energetic and, if properly developed, have enormous potential. Vedantu has a number of teaching professionals on staff, as well as interactive and unique workshops.

• Instead of the question itself, it is critical that you understand how to solve every question of that type. Try once, twice, three times, but don't dismiss the concepts; instead, ask your teacher to clarify them until you understand them.

• Because of their importance in mathematics, there are several chapters that you simply cannot overlook. They will follow you through to Class 12th and are frequently asked in competitive examinations:1)SETS, 2)Trigonometry(This one is really very important), 3)Permutations and Combinations., 4)Binomial Theorem.

• There are no shortcuts to learning mathematics; you will have to put in a lot of effort if you want to do well in this subject. There are several Math books on the market, however, NCERT is regarded as a fundamental textbook that is highly recommended for academics. As a result, before referring to any other books, one must complete the NCERT of Mathematics.

Achieve Success with Vedantu!

While there is no substitute for hard work, a little smart work is also required to attain your goals. Guidance is important for exam preparation, and Vedantu strives to extend you just that! We bring experienced subject experts who provide all help that you may need for optimum preparations and high scores. In recent years, e-learning has become a buzzword in the field of education. Vedantu has simply taken the entire social structure involving a student and teacher online and integrated it into their platform. The government's attempt to mainstream e-learning and digital education is a positive and sensible move forward.

Vedantu is rising from strength to strength, with more than 80k students using its services. It will come as no surprise if Vedantu becomes one of the most valuable assets in digital education. Traditional teaching methods, such as coaching centresyou must understandand private tuition groups, could be severely impacted. The availability of 1-on-1 study sessions on such a big scale reflects students' and parents' growing confidence in their educational model.

Our live classes also allow you to clarify all your doubts. You will also find various other resources such as NCERT books for class 11 Maths on the online platform along with study notes, question solutions, etc. across classes and subjects.

Download our Vedantu app today to experience the best e-learning!

Other Free CBSE Class 11 Maths Study Material

Other Free Study CBSE Material for Class 11