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# Class 11 Maths

Class 11 maths is considered the basic level for advanced-level math studies. It introduces students to a wide variety of abstract concepts that forms the core of various scientific studies including physics and engineering. Thus, studying each and every topic covered under Class 11 maths is highly important for students.

## Class 11 Maths Syllabus

Class 11 maths syllabus comprises topics related to sets, functions, trigonometry, derivatives, statistics, coordinate geometry and more. It covers various concepts in detail to help students acquire them with ease. Here is the complete syllabus of class 11 Maths.

**Sets and Functions**

**Sets**- Sets and their representations
- Types of sets: empty set, finite and Infinite sets, equal sets, universal set
- Subsets: subsets of a set of real numbers in interval notation
- Power set
- Venn diagrams
- Operations on sets: union and intersection of sets

**Relations & Functions**- Ordered pairs
- Cartesian product of sets: number of elements in the cartesian product of two finite sets; the cartesian product of the set of reals with itself ( R × R only)
- Definition of relation, pictorial diagrams
- domain, co-domain and range of a relation
- Function as a special type of relation
- Pictorial representation of a function, domain, range, and codomain of a function.
- Real valued functions: constant, identity, polynomial, rational, modulus, signum, exponential, logarithmic and greatest integer functions, with their graphs, and domain and range of these functions

**Trigonometric Functions**- Angles in radians and in degrees; conversion of one measure to the other
- Trigonometric functions by unit circle
- Trigonometric identities
- Graphs of trigonometric functions and their domain and range
- Periods of trigonometric functions, positive and negative angles
- Sum and difference formulas: sin(x + y), sin(x - y), cos(x + y), cos(x - y)

**Algebra**

**Principle of Mathematical Induction**: Process of the proof by induction**Complex Numbers and Quadratic Equations**- Definition of complex numbers using the definition of √−1 = i
- Operations on complex numbers: Adding, subtracting, multiplying, dividing
- Argand plane
- Solving quadratic equations
- Statement of the fundamental theorem of algebra
- Quadratic equations with complex solutions

**Sequence and Series**- Sequence and series
- Arithmetic Progression (A. P.)
- Arithmetic Mean (A.M.)
- Geometric Progression (G.P.): general term, sum of n terms., infinite G.P. and its sum, geometric mean (G.M.)
- relationship between A.M. and G.M.

**Binomial Theorem**- Pascal's triangle
- Expansion of (a + b)
^{n}by the binomial theorem - Finding the general term of the expansion
- Finding the middle term(s) in the expansion

**Linear Inequalities**- Solving linear inequalities in one variable and their representation on the number line
- Solving of linear inequalities in two variables graphically

**Permutations and Combinations**- Fundamental principle of counting
- Factorial of n (n!)
- Permutations and combinations: nPr and nCr formulas and applications.

**Mathematical Reasoning:**

- Mathematical statement
- Compound statements using "and", "or", "there exists" and "for every"
- Conditional statements
- Converse and contrapositive
- Method to determine the validity of statements: direct method, contrapositive method, method of contradiction, using a counter-example

**Coordinate Geometry**

**Straight Lines**- Slope of a line
- Different forms of equations of a line: point-slope form, slope-intercept form, two-point form, intercept form and normal form
- General equation of a line
- Angle between two lines
- Distance of a point from a line

**Conic Sections**- Conic Sections: circles, ellipse, parabola, hyperbola
- Equation of a circle
- Standard equations and simple properties of parabola, ellipse and hyperbola

**Introduction to Three-dimensional Geometry**- Three-dimensional coordinate plane: Coordinates of a point in 3D plane
- Distance between two points and section formula

**Calculus**

**Limits & Derivatives**- Definition of limits
- Limits of different types of functions
- Definition of derivatives
- Derivative rules

**Statistics and Probability**

**Statistics**: Measures of dispersion: range, mean deviation, variance and standard deviation of ungrouped/grouped data.**Probability:**- Random experiments: Representing outcomes, sample spaces as sets
- Types of events; ‘not’ events, ‘and’ and ‘or’ events, exhaustive events, mutually exclusive events
- Probability of different types of events

## Develop 11th Maths Skills

11th maths focuses on developing various real-life skills in students. At this stage, students progress on advanced concepts like functions, calculus, probability, etc. A thorough understanding of mathematics class 11 concepts can be implemented through various interactive activities and visualization.

**Algebra:** In class 11 maths students are pretty comfortable with working on equations and developing their basic skills to work on linear inequalities. They also learn to find the algebraic solutions of linear inequalities in one variable and two variables and their representation on the number line.

**Functions:** Students must be able to understand, construct and describe functions in various ways, including a graph, an algebraic expression, a recursive rule or the Fibonacci sequence.

**Probability:** Students must develop their skills in gathering, summarizing, representing, and interpreting data.

## Mathematics Class 11 Tips and Tricks

The following tips would be very helpful for the students who are studying 11th maths to attain good marks and better grades.

**Study Regularly:** Studying regularly will benefit in completing the class 11 maths syllabus properly without much stress. Students must properly complete their assignments and practice every day to get a hold of complex topics. Students must begin with easier topics first and then gradually proceed to complex ones. It will help them develop important mathematical concepts with ease.

**Solve Sample Question Papers: **Solving question papers will not only enhance speed and accuracy but will also help in decreasing the possibility of making small mistakes in calculations.

## Class 11 Maths Formulas

Class 11 maths students should keep the booklet of all formulas handy and keep referring to it whenever possible. Here is the list of important formulas of mathematics class 11.

- sin
^{2}θ + cos^{2}θ = 1; cosec^{2}θ - cot^{2}θ = 1; sec^{2}θ - tan^{2}θ = 1 - sin(x + y) = sin(x) cos(y) + cos(x) sin(y)
- sin(x - y) = sin(x) cos(y) - cos(x) sin(y)
- cos(x + y) = cos(x) cos(y) - sin(x) sin(y)
- cos(x - y) = cos(x) cos(y) + sin(x) sin(y)
- lim
_{x → a }(x^{n}- a^{n}) / (x - a) = na^{n - 1} - lim
_{x → a}sin x / x = 1 - d/dx [f(x) ± g (x)] = d/dx [f(x)] ± d/dx [g(x)]
- d/dx (f(x)·g(x)) = g(x) × f'(x) + f(x) × g'(x)
- [f(x)/g(x)]' = [g(x) × f'(x) - f(x) × g'(x)]/[g(x)]
^{2}

For the complete list of class 11 maths formulas, click here.

## Solved Examples on 11th Maths

**Example 1:** Are the following sets equal? A = {1, 3}, B = {x: x is the solution of x^{2}- 4x + 3 = 0}.

**Solution:**

Set B is given in the set-builder notation. We will find its elements which are solutions of the following equation.

x^{2}- 4x + 3 = 0

(x - 1) (x - 3) = 0

x - 1 = 0; x - 3 = 0

x = 1; x = 3

Therefore, B = {1, 3}. It is given that the set A is also equal to {1, 3}. Hence, A = B.

**Answer:** Yes, the given two are equal sets.

**Example 2:** What is the derivative of the function f(x) = x sin x?

**Solution:**

The given function is a product of two functions. So we will find the derivative using the product rule. Assume that u = x, and v = sin x. Then by product rule:

f'(x) = uv' + v u'

= x (cos x) + sin x (1)

= x cos x + sin x

**Answer:** The derivative of the given function is x cos x + sin x.

## FAQs on Class 11 Maths

### What are Class 11 Maths Chapters?

The following is a brief list of **class 11 maths **chapters. The complete detailed list along with subtopics is mentioned in this page.

- Sets
- Relations & Functions
- Trigonometric Functions
- Principle of Mathematical Induction
- Complex Numbers and Quadratic Equations
- Sequence and Series
- Linear Inequalities
- Permutations and Combinations
- Binomial Theorem
- Mathematical Reasoning
- Straight Lines
- Conic Sections
- Introduction to Three-dimensional Geometry
- Limits & Derivatives
- Statistics
- Probability

### How are Class 11 Maths Solutions Helpful?

Class 11 maths solutions contain step-by-step solutions for the problems of all the chapters. Keeping them handy is very useful whenever the students feel trouble in solving the questions.

### How to Get 100% in Mathematics Class 11?

To get 100% in class 11 maths, one should follow all teaching lessons without missing, maintain full-fledged notes, understand the concept before working on the problems, work on class 11 maths worksheets to make sure that the concept is learned properly, keep revising formulas, make sure that all weaker areas are keep revised, etc. Also, practising the previous year's question papers is a great benefit to attain 100% in 11th maths.

### Is Class 11 Maths Hard?

It is harder compared to the 10th maths in terms of the number of chapters and complexity as well. But it is not too hard as long as the student is trying to focus on understanding the concepts.

### Is 11th Maths Difficult or 12th Maths?

11th maths and 12th maths have almost the same chapters. But 12th maths has more depth and also has extra concepts and hence 12th maths is more difficult.

### Is 80% in Class 11 Maths Good?

Class 11 maths has many concepts as compared to class 10. Also, it has many new concepts like graphing trigonometric functions, calculus, and more. Hence, getting 80% in 11th maths is considered good.

### What is the Most Difficult Chapter in 11th Maths?

11th maths has some difficult chapters like trigonometric functions, conic sections, derivatives, etc. Among these, the most difficult is conic sections.

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