# ISC Class 11 Syllabus for Maths

ISC Syllabus for Class 11 Maths is provided here for students to prepare well for the exam. The ISC Class 11 Maths is an important subject, as it helps to get thorough with the concepts that are asked in competitive and entrance examinations. Students see the crucial concepts in the ISC Class 11 Syllabus for Maths. Thus, it is crucial for them to have an idea about it. Getting acquainted with the syllabus of Class 11 Maths will help them know the topics to be studied. Also, the ISC Class 11 Maths Syllabus help students to know the topics, marks weightage, evaluation scheme, project work, activities, etc.

We, at BYJUâ€™S, provide students with the Class 11 Maths Syllabus that would help them in getting an in-depth idea about the pattern of examination, as well as the mark-wise weightage of each chapter, which is as follows:

### Marks Weightage of ISC Class 11 Maths Syllabus

 S.No. Unit Total Weightage Section A: 65 Marks 1. Sets and Functions 20 Marks 2. Algebra 24 Marks 3. Coordinate Geometry 08 Marks 4. Calculus 06 Marks 5. Statistics & Probability 07 Marks Section B: 15 Marks 6. Conic Section Â 07 Marks 7. Introduction to Three-dimensional Geometry 05 Marks 8. Mathematical Reasoning 03 Marks OR Section C: 15 Marks 9. Statistics 05 Marks 10. Correlation Analysis 04 Marks 11. Index Numbers and Moving Averages 06 Marks Total 80 Marks

## ISC Syllabus for Class 11 Maths

### Section A

1. Sets and Functions

(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. Difference of sets. Complement of a set. Properties of Complement of Sets.

(ii) Relations & Functions

Ordered pairs, Cartesian product of sets. 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. Real valued functions, domain and range of these functions, constant, identity, polynomial, rational, modulus, signum, exponential, logarithmic and greatest integer functions, with their graphs. Sum, difference, product and quotient of functions.

(iii) Trigonometry

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. Truth of the identity sin2x+cos2x=1, for all x. Signs of trigonometric functions. Domain and range of trignometric functions and their graphs. Expressing sin (xÂ±y) and cos (xÂ±y) in terms of sinx, siny, cosx & cosy and their simple applications. Deducing the identities like the following:

$$\begin{array}{l}tan (x\pm y) = \frac{tan x\pm tan y}{1\mp tanxtay}\end{array}$$
$$\begin{array}{l}cot(x\pm y) = \frac{cotxcoty\mp 1}{coty\mp cotx}\end{array}$$
$$\begin{array}{l}sin \alpha \pm sin\beta = 2sin\frac{1}{2}(\alpha \pm \beta)cos\frac{1}{2}(\alpha \mp \beta)\end{array}$$
$$\begin{array}{l}cos\alpha + cos\beta = 2 cos\frac{1}{2}(\alpha +\beta)cos\frac{1}{2}(\alpha – \beta)\end{array}$$
$$\begin{array}{l}cos\alpha – cos\beta = -2sin \frac{1}{2} (\alpha =\beta)sin \frac{1}{2}(\alpha -\beta)\end{array}$$

Identities related to sin 2x, cos2x, tan 2x, sin3x, cos3x and tan3x. General solution of trigonometric equations of the type siny = sina, cosy = cosa and tany = tana. Properties of triangles (proof and simple applications of sine rule cosine rule and area of triangle).

1. Algebra

(i) Principle of Mathematical Induction

Process of the proof by 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.

(ii) Complex Numbers

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.

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

(iv) Permutations & Combinations

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

(v) Binomial Theorem

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

(vi) Sequence and Series

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 sumsÂ âˆ‘ n,âˆ‘ n , âˆ‘ n .

1. Coordinate Geometry

(i) Straight Lines

Brief recall of two-dimensional geometry from earlier classes. 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, slopeintercept form, two-point form, intercept form and normal form. General equation of a line. Equation of family of lines passing through the point of intersection of two lines. Distance of a point from a line

(ii) Circles

1. Calculus

(i) Limits & Derivatives

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 relate it to scope of tangent of the curve, Derivative of sum, difference, product and quotient of functions. Derivatives of polynomial and trigonometric functions.

1. Statistics & Probability

(i) Statistics

Measures of dispersion: range, mean deviation, variance and standard deviation of ungrouped/grouped data. Analysis of frequency distributions with equal means but different variances.

(ii) Probability

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.

### Section B

1. Conic Section

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

1. 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. Mathematical Reasoning

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. Validating the statements involving the connecting words, difference between contradiction, converse and contrapositive.

Section C

1. Statistics
1. Correlation Analysis
1. Index Numbers and Moving Averages

(i) Index Numbers

(ii) Moving Averages

We hope students have found this information on the ISC Class 11 Maths Syllabus useful for their studies. To get the syllabus for all the subjects of Classes 11 and 12, visit the ISC Syllabus page. Stay tuned for the latest update on ICSE/ISC/CBSE/State Board and competitive exams.