April 3, 2023

The syllabus allows students to understand the objectives of the course and to help them learn efficiently and plan the assessment effectively. Read the complete post to know about the detailed Class 11 Commerce Maths Syllabus 2020-21.

This year, the CBSE and ICSE boards have reduced nearly 30% of the syllabus from all subjects for 2020-21. Go through the revised Class 11 Maths Syllabus PDF and also know which topics or units have been deleted from the curriculum.

The Maths theory exam holds a weightage of 80 marks and 20 marks are allotted to internal assessment. These two sum up the final calculations for the Board exam.

The unit wise weightage as per the updated 11th Class Maths syllabus is listed below:

Unit Name |
Unit/Chapter |
Marks |

I. Sets and Functions | Sets | 23 |

Relations & Functions | ||

Trigonometric Functions | ||

II. Algebra | Complex Numbers and Quadratic Equations | 30 |

Linear Inequalities | ||

Permutations and Combinations | ||

Sequence and Series | ||

III. Coordinate Geometry | Straight Lines | 10 |

Conic Sections | ||

Introduction to Three-dimensional Geometry | ||

IV. Calculus | Limits and Derivatives | 07 |

V. Statistics and Probability |
Statistics | 10 |

Probability | ||

Total | 80 | |

Internal Assessment | 20 |

Below mentioned is the detailed syllabus of 11th commerce maths:

**1. Sets**

Sets and their representations. Empty set. Finite and Infinite sets. Equal sets. Subsets. Subsets of a set of real numbers especially intervals (with notations). Power set. Universal set. Venn diagrams. Union and Intersection of sets.

**2. Relations & Functions**

Ordered pairs. Cartesian product of sets. The number of elements in the Cartesian product of two finite sets. Cartesian product of the set of reals with itself ( R x 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, co-domain and range of a function. Real valued functions, domain and range of these functions, constant, identity, polynomial, rational, modulus, signum, exponential, logarithmic and greatest integer functions, with their graphs.

**3. 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 the unit circle. Truth of the identity sin2x + cos2x = 1, for all x. Signs of trigonometric functions. Domain and range of trigonometric functions and their graphs. Expressing sin (x±y) and cos (x±y) in terms of sinx, siny, cosx & cosy and their simple applications.

Deducing identities like the following:

Identities related to sin2x, cos2x, tan2x, sin3x, cos3x and tan3x. General solution of trigonometric equations of the type siny = sina, cosy = cosa and tany = tana.

**1. Complex Numbers and Quadratic Equations**

Need for complex numbers, especially√−1, to be motivated by the inability to solve some of the quadratic equations. Algebraic properties of complex numbers. Argand plane. Statement of Fundamental Theorem of Algebra, solution of quadratic equations (with real coefficients) in the complex number system.

**2. Linear Inequalities**

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 to a system of linear inequalities in two variables.

**3. Permutations and Combinations**

The fundamental principle of counting. Factorial n. (n!) Permutations and combinations, the formula for nPr and nCr, simple applications.

**4. Sequence and Series**

Sequence and Series. Arithmetic Progression (A. P.). Arithmetic Mean (A.M.) Geometric Progression (G.P.), general term of a G.P., the sum of n terms of a G.P., infinite G.P. and its sum, geometric mean (G.M.), the relation between A.M. and G.M.

**1. Straight Lines**

Brief recall of two-dimensional geometry from earlier classes. The slope of a line and angle between two lines. Various forms of equations of a line: parallel to the axis, point-slope form, slope-intercept form, two-point form, intercept form and normal form. General equation of a line. The distance of a point from a line.

**2. Conic Sections**

Sections of a cone: circles, ellipse, parabola, hyperbola. Standard equations and simple properties of parabola, ellipse and hyperbola. Standard equation of a circle.

**3. Introduction to Three-dimensional Geometry**

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

**1. Limits and Derivatives**

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

**1. Statistics**

Measures of Dispersion: Range, Mean deviation, variance and standard deviation of ungrouped/grouped data.

**2. Probability**

Random experiments; outcomes, sample spaces (set representation). Events; the occurrence of events, ‘not’, ‘and’ and ‘or’ events, exhaustive events, mutually exclusive events, Probability of an event, probability of ‘not’, ‘and’ and ‘or’ events.

CBSE Class 11th Maths syllabus question-wise distribution according to paper design is tabulated below

Typology of Questions | Total Marks | Weightage (%) |

Remembering: Exhibit memory of previously learned material by recalling facts, terms, basic concepts, and answers.Understanding: Demonstrate understanding of facts and ideas by organizing, comparing, translating, interpreting, giving descriptions, and stating main ideas |
44 | 55 |

Applying: Solve problems to new situations by applying acquired knowledge, facts, techniques, and rules in a different way. |
20 | 25 |

Analyzing: Examine and break information into parts by identifying motives or causes. Make inferences and find evidence to support generalizationsEvaluating: Present and defend opinions by making judgments about information, validity of ideas, or quality of work based on a set of criteria.Creating: Compile information together in a different way by combining elements in a new pattern or proposing alternative solutions |
16 | 20 |

Total | 80 | 100 |

The Maths theory exam holds a weightage of 80 marks and 20 marks are allotted to Project Work. These two sums up the final calculations for the Board exam. ICSE class 11th Maths syllabus is divided into three sections A, B, and C.

- Section A is compulsory for all candidates. Section A (65 marks) will consist of six questions. Candidates will be required to attempt all questions. The internal choice will be provided in two questions of two marks, two questions of four marks and two questions of six marks each.
- Candidates will have a choice of attempting questions from either Section B or Section C. Section B / C (15 marks), Candidates will be required to attempt all questions EITHER from Section B or Section C. Internal, the choice will be provided in one question of two marks and one question of four marks.

The unit wise weightage as per the updated Class 11th Maths syllabus is listed below:

S.No | Unit/Chapter | Marks |

Section A: 65 Marks |
||

1 | Sets and Functions | 20 Marks |

2 | Algebra | 24 Marks |

3 | Coordinate Geometry | 8 Marks |

4 | Calculus | 6 Marks |

5 | Statistics & Probability | 7 Marks |

Section B: 15 Marks |
||

6 | Conic Section | 7 Marks |

7 | Introduction to Three Dimensional Geometry | 5 Marks |

8 | Mathematical Reasoning | 3 Marks |

Section C: 15 Marks |
||

9 | Statistics | 5 Marks |

10 | Correlation Analysis | 4 Marks |

11 | Index Numbers & Moving Averages | 6 Marks |

Total | 80 | |

Project work | 20 |

**(i) Sets**

Sets and their representations.Empty set. Finite and Infinite sets. Equal sets. Subsets. Subsets of a set of real numbers especially intervals (with notations). Power set. Universal set. Venn diagrams. Union and Intersection of sets. Practical problems on union and intersection of two and three sets. A difference of sets. A complement of a set. Properties of Complement of Sets.

Ordered pairs, Cartesian product of sets. A number of elements in the cartesian product of two finite sets. Cartesian product of the set of reals with itself (upto R x R x R). Definition of relation, pictorial diagrams, domain, co-domain and range of a relation. Function as a special type of relation. Function as a type of mapping, types of functions (one to one, many to one, onto, into) domain, co-domain and range of a function.

Basic concepts of Relations and Functions -

- Ordered pairs, sets of ordered pairs.
- Cartesian Product (Cross) of two sets, cardinal number of a cross product.
- Relations as: - an association between two sets.
- a subset of a Cross Product. - Domain, Range and Codomain of a Relation.
- Functions: - As special relations, the concept of writing “y is a function of x” as y = f(x).
- Introduction of Types: one to one, many to one, into, onto. - Domain and range of a function.

Signs of trigonometric functions. Expressing sin (x±y) and cos (x±y) in terms of sinx, siny, cosx & cosy and their simple applications.

Deducing the identities like the following:

Identities related to sin 2x, cos2x, tan 2x, sin3x, cos3x and tan3x. •

**Trigonometric Functions -**

- Relationship between trigonometric functions.
- Proving simple identities.
- Signs of trigonometric functions.
- Domain and range of the trigonometric functions.
- Trigonometric functions of all angles.
- Periods of trigonometric functions

**Compound and multiple angles -**

- Addition and subtraction formula: sin(A ± B); cos(A ± B); tan(A ± B); tan(A + B + C) etc., Double angle, triple angle, half angle and one third angle formula as special cases.
- Sum and differences as products

SinC+ SinD =2SinC+D2CosC-D2 , etc.

- Product to sum or difference i.e. 2sinAcosB = sin (A + B) + sin (A – B) etc.

Process of the proof by induction, motivating the application of the method by looking at natural numbers as the least 3 inductive subsets of real numbers. The principle of mathematical induction and simple applications. Using induction to prove various summations, divisibility.

Introduction of complex numbers and their representation, Algebraic properties of complex numbers. Argand plane and polar representation of complex numbers. Square root of a complex number. Cube root of unity.

Conjugate, modulus and argument of complex numbers and their properties.

- Sum, difference, product and quotient of two complex numbers additive and multiplicative inverse of a complex number.
- Square root of a complex number.
- Cube roots of unity and their properties.

Equations Statement of Fundamental Theorem of Algebra, solution of quadratic equations (with real coefficients)

Use of the formula:

In solving quadratic equations.

**Nature of roots**

- Product and sum of roots
- Roots are rational, irrational, equal, reciprocal, one square of the other.
- Complex roots
- Framing quadratic equations with given roots.

NOTE: Questions on equations having common roots are to be covered. •

**Quadratic Functions**

Givenα, β as roots then find the equation whose roots are of the form α3 ,β3 , etc.

- Case I: a > 0 Real roots, Complex roots, Equal roots
- Case II: a < 0 Real roots, Complex roots, Equal roots

Where ‘a’ is the coefficient of x2 in the equations of the form ax^2 + bx + c = 0. Understanding the fact that a quadratic expression (when plotted on a graph) is a parabola.

**Sign of quadratic**

Sign when the roots are real and when they are complex.

**Inequalities**

Quadratic Inequalities Using method of intervals for solving problems of the type:

A perfect square e.g. x^2-6x+90

The fundamental principle of counting. Factorial n. (n!) Permutations and combinations, derivation of formulae for Pn r and Cn r and their connections, simple application.

- Factorial notation n! , n! =n (n-1)!
- Fundamental principle of counting.

Permutations - n Pr.

- Restricted permutation.
- Certain things always occur together.
- Certain things never occur.
- Formation of numbers with digits.
- Word building -repeated letters No letters repeated.
- Permutation of alike things.
- Permutation of Repeated things.

Combinations -

History, statement and proof of the binomial theorem for positive integral indices.

Pascal's triangle, General and middle term in binomial expansion, simple applications.

i.e.

Questions based on the above

Sequence and Series. Arithmetic Progression (A. P.). Arithmetic Mean (A.M.) Geometric Progression (G.P.), general term of a G.P., sum of first 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 n,n2,n3**Arithmetic Progression (A.P.) -**

**Geometric Progression (G.P.) -**

Brief recall of two-dimensional geometry from earlier classes. Shifting of origin. Angle between two lines. Various forms of equations of a line: intercept form and normal form. General equation of a line. Distance of a point from a line.

Basic concepts of Points and their coordinates.

Equations of a circle in:

Given the equation of a circle, to find the centre and the radius.

Finding the equation of a circle.

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 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.

**Limits**

**Differentiation**

Measures of dispersion: range, mean deviation, variance and standard deviation of ungrouped/grouped data.

NOTE: Mean of grouped and ungrouped data are required to be covered.

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 studied in earlier classes. Probability of an event, probability of 'not', 'and' and 'or' events.

Sections of a cone, ellipse, parabola, hyperbola, a point, a straight line and a pair of intersecting lines as a degenerate case of a conic section. Standard equations and simple properties of parabola, ellipse and hyperbola.

Conics as a section of a cone.

e=1, y=4ax, x2=4ay, y2=-4ax, x2=-4ay

x2a2+y2b2=1,e<1,b2=a2,a2=(1-e2)

x2a2-y2b2=1,e>1,b2=a2,a2=(e2-1)

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

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 the Mathematics and real life. Difference between contradiction, converse and contrapositive.

Definition and meaning of covariance.

Coefficient of Correlation by Karl Pearson.

If If x- x’ y -y’ are small non fractional numbers we use

r=(x-x)(y-y)(x-x)2 (y-y)2

If x and y are small numbers, we use

r=xy-xyN x2-(x)2N y2-(y)2N

Otherwise, we use assumed means A and B, where u = x-A, v = y-B r=uv-(u)(v)Nu2-(u2N v2-(v)2N

*(i) Index Numbers** -*

*(ii) Moving Averages** -*

The table below shows the best Preparation Books for Class 11th Maths Syllabus prescribed by CBSE Board.

Publisher Name | 11th Maths book CBSE | 11th Maths books price |

NCERT | Mathematics Textbook for Class 11 | Rs. 210/- |

NCERT | NCERT Mathematics Exemplar Problems For Class XI | Rs. 165/- |

NCERT | Mathematics Lab Manual class XI | |

Oswaal | Oswaal NCERT Exemplar (Problems - solutions) Class 11 Mathematics | Rs. 253/- |

Arihant | NCERT Solutions Mathematics Class 11th | Rs. 185/- |

CBSE 11th std new syllabus maths guide Books: | ||

R.D Sharma | Mathematics for Class 11 by R D Sharma (set of 2 volumes) | Rs. 580/ |

R.S. Aggarwal | Senior Secondary School Mathematics for Class 11 Examination | Rs. 500/ |

Oswaal | Oswaal CBSE Sample Question Paper Class 11 Mathematics | Rs. 199/ |

The table below shows the best Preparation Books for Class 11th Maths Syllabus prescribed by the ICSE Board.

Author | 11th Maths books | 11th Maths books price |

O.P. Malhotra, S.K. Gupta, | ISC Mathematics Book I for Class XI Paperback | Rs. 369/- |

M.L. Aggarwal | Understanding I.S.C. Mathematics (Vol. I & II) Class- XI Paperback – 1 January 2019 | Rs. 895/- |

C.B. Gupta | S. Chand's ISC Commerce for Class XI Paperback – 1 January 2016 | Rs. 630/- |

Arihant Experts | All In One ISC Mathematics Class 11 Paperback – 16 June 2019 | Rs.375/- |

R.D Sharma | Mathematics for Class 11 by R D Sharma (set of 2 volumes) | Rs. 580/ |

R.S. Aggarwal | Senior Secondary School Mathematics for Class 11 Examination | Rs. 500/ |

Oswaal | Oswaal Sample Question Paper Class 11 Mathematics | Rs. 199/ |

Here are a few crucial tips and tricks that will help you prepare for your

- When all things are different.
- When all things are not different
- Significance of Pascal’s triangle.
- Binomial theorem (proof using induction) for positive integral powers,

- Tn = a + (n - 1)d
- Sn = n/2{2a+(n-1)d};
- Arithmetic mean: 2b = a + c
- Inserting two or more arithmetic means between any two numbers.
- Three terms in A.P. : a - d, a, a + d - Four terms in A.P.: a - 3d, a - d, a + d, a + 3d

- Tn = ar^(n-1) ,
- Sn=a(r^n-1)/(r-1),
- S∞=a/1-r;|r|<1;
- Geometric Mean, b =ac
- Inserting two or more Geometric Means between any two numbers. -
- Three terms are in G.P. ar, a, ar-1 -
- Four terms are in GP ar3, a, ar , ar-1
- Special sums n,n2,n3

- Angle between two lines.
- Intercept form.
- Perpendicular /normal form.
- General equation of a line.
- Distance of a point from a line.
- Distance between parallel lines.
- Equation of lines bisecting the angle between two lines.
- Definition of a locus.

- Standard form.
- Diameter form.
- General form.
- Parametric form.

- Given three non collinear points.
- Given other sufficient data for example centre is (h, k) and it lies on a line and two points on the circle are given, etc

- Notion and meaning of limits.
- Fundamental theorems on limits (statement only).
- Limits of algebraic and trigonometric functions.

- Meaning and geometrical interpretation of derivatives.
- Derivatives of simple algebraic and trigonometric functions and their formulae.
- Differentiation using first principles.
- Derivatives of sum/difference.
- Derivatives of product of functions
- Derivatives of quotients of functions.

- Mean deviation about mean.
- Standard deviation - by direct method, short cut method and step deviation method.

- Random experiments and their outcomes.
- Events: sure events, impossible events, mutually exclusive and exhaustive events.
- Definition of probability of an event
- Laws of probability addition theorem.

- Definition of Foci, Directrix, Latus Rectum.
- PS = ePL where P is a point on the conics, S is the focus, PL is the perpendicular distance of the point from the directrix.

- Rough sketch of the above.
- The latus rectum; quadrants they lie in; coordinates of focus and vertex; and equations of directrix and the axis.
- Finding the equation of Parabola when Foci and directrix are given, etc.
- Application questions based on the above.

- Cases when a > b and a < b.
- Rough sketch of the above.
- Major axis, minor axis; latus rectum; coordinates of vertices, focus and centre; and equations of directrices and the axes.
- Finding the equation of ellipse when focus and directrix are given.
- Simple and direct questions based on the above.
- Focal property i.e. SP + SP′ = 2a.

- Cases when coefficient of y2 is negative and the coefficient of x2 is negative.
- Rough sketch of the above.
- Focal property i.e. SP - S’P = 2a.
- Transverse and Conjugate axes; Latus rectum; coordinates of vertices, foci and centre; and equations of the directrices and the axes.
- General second-degree equation
**ax****2****+2hxy+b****y****2****+2gx+2fy=0** - Case 1: pair of straight line if abc+2fgh-af2-bg2-ch2=0
- Case 2: abc+2fgh-af2-bg2-ch20, then represents a parabola if h2 = ab, ellipse if h2 < ab, and hyperbola if h2 > ab.

- As an extension of 2-D
- Distance formula.
- Section and midpoint form

- Combined mean and standard deviation.
- The Median and Quartiles.

- Price index or price relative.
- Simple aggregate method.
- Weighted aggregate method.
- Simple average of price relatives.
- Weighted average of price relatives (cost of living index, consumer price index)

- Meaning and purpose of the moving averages.
- Calculation of moving averages with the given periodicity and plotting them on a graph.

- First of all, take a thorough look at the detailed class 11th Maths Syllabus and exam pattern. Study each topic of the Ncert book thoroughly for CBSE Boards and from books recommended by school for ICSE Board.
- Make sure you make notes which include important points during your study. Those notes will help during the revision period.
- Strategize and than prepare, the long-form questions (5-6 marks), which are the most feared, usually come from the calculus or differential equation section, so try to gain perfection in them by practicing them regularly.
- Try as many mock tests as you can. Practice until you have perfected that part.
- After completing each section, attempt the section-wise tests to evaluate your preparation.
- Make a list of your mistakes and try to improvise on the same thing.
- Make sure you follow up on your study plan regularly, consistency and perseverance are of the utmost importance to excel in boards.

Frequently Asked Questions

What is the difference between the subjects ' Mathematics ' and ' Applied Mathematics ' ?

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What would be more difficult, CBSE Maths Examination or ICSE Maths Examination?

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