Uttarakhand Board Class 11 Maths Syllabus
Uttarakhand Board Class 11 Maths Syllabus

Uttarakhand Board of School Education (UKBSE) designs the detailed syllabus of Class 11 Mathematics subject. The board conducts an annual exam for this subject consisting of a theory paper and a practical exam or viva. Class 11 is considered as an important and crucial academic year for students as it prepares them for their higher studies.


A student must invest a lot of time and energy to learn many new things and revise the old concepts learnt in their previous classes to prepare for the journey ahead. In fact, all the subjects are important in the class 11. However, some subjects are a little more important as you will need them throughout your life. Maths is one such subject.


The concepts studied and thoroughly practiced in Maths are bound to help students in their career ahead. Moreover, those students who have decided to give the nаtiоnаl level entrаnсe exаms suсh аs the IIT-JEE and NEET will benefit frоm the revisiоn оf the Uttarakhand Board Class 11 Maths syllabus and the concepts therein.


The entire Maths syllabus consists of a total of 16 chapters. These chapters have been provided below:


Unit Name


Sets and Functions

  • Sets


  • Relations & Functions


  • Trigonometric Functions

















  • Principle of Mathematical Induction


  • Complex Numbers and Quadratic Equations


  • Linear Inequalities


  • Permutations and Combinations


  • Binomial Theorem


  • Sequence and Series


Coordinate Geometry

  • Straight Lines


  • Conic Sections


  • Introduction to Three-dimensional Geometry


  • Limits and Derivatives





Mathematical Reasoning

  • Mathematical Reasoning

Statistics and Probability

  • Statistics


  • Probability



Theory Syllabus of Uttarakhand Board Class 11 Maths


Below we are providing a detailed summary of each unit and chapter:

Unit-I: Sets and Functions

Chapter 1. Sets – Sets and their representation; 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



Chapter 2. 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 real numbers with itself (up to R x R only); Definition of a 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.


Chapter 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 unit circle; Truth of the identity sin2 x + cos2 x = 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 sin x, sin y, cos x & cos y and their simple applications; Deducing identities like the following: 6 Identities related to sin2x, cos2x, tan2 x, sin3x, cos3x, and tan3x.



Unit-II: Algebra

Chapter 4. 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.


Chapter 5. 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 the fundamental theorem of Algebra; Solution of quadratic equations (with real coefficients) in the complex number system

Chapter 6. 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 of the system of linear inequalities in two variables

Chapter 7. Permutations and Combinations – Fundamental principle of counting; Factorial n. (n!) Permutations and combinations; derivation for the formula for nPr and nCr and their connections, with simple applications


Chapter 8. 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

Chapter 9. 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 n terms of a G.P., infinite G.P. and its sum, geometric mean (G.M.); Relation between A.M. and G.M.



Unit-III: Coordinate Geometry

Chapter 10. 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 the axis, point-slope form, slope-intercept 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


Chapter 11. Conic Sections – Sections of a cone: circles, 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; Standard equation of a circle

Chapter 12. Introduction to Three-dimensional Geometry – Coordinate axes and coordinate planes in three dimensions; Coordinates of a point; Distance between two points and section formula


Unit-IV: Calculus

Chapter 13. Limits and 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 functions, exponential functions, and logarithmic functions; Definition of derivative relate it to the slope of the tangent of the curve, derivative of the sum, difference, product and quotient of functions; Derivatives of polynomial and trigonometric functions 


Unit-V: Mathematical Reasoning


Chapter 14. 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 a variety of examples related to real life and mathematics. Validating the statements involving the connecting words; Difference between contradiction, converse, and contrapositive.


Unit VI: Statistics and Probability


Chapter 15. Statistics – Measures of Dispersion: Range, mean deviation, variance, and standard deviation of ungrouped/grouped data


Chapter 16. 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 of earlier classes; Probability of an event; Probability of “not,” “and,” and “or” events.



Frequently Asked Questions of Uttarakhand Board Class 11 Maths

Q1. What are some tips for the Uttarakhand Board Class 11 Maths Exam?

Answer: Students must be familiar with the exam syllabus, question paper pattern, and should focus on crucial areas (refer to important questions, sample papers to get an idea), and stick to a study schedule to prepare for the exam. They must also devote a significant amount of time to revising and practicing numerical problems.



Q2. How should students prepare for the UKBSE Board Class 11 Maths Exam?

Answer: Students should create organized timetables for a subject like Maths. They need to study the basic concepts of Maths, which their teachers teach. After completing each topic, they should practice the questions given at the end of each chapter. After the completion of the entire Maths syllabus, they need to attempt the full-length mock tests properly. These will help students revise the concepts for their final examinations.


Q3. When do I have to submit my practical file?

Answer: Your school will give you dates to submit your practical files/notebooks. Please contact your school and confirm. Typically, the deadline is in the last half of January.



Q4. From where should students prepare for Uttarakhand Board Class 11 Maths Exam?

Answer: Students can solve the Class 11 questions from their UKBSE Board state text books. They can also go through the last ten years’ question papers to familiarize themselves with the entire coursework.



Q5. Will the examination be held online?

Answer: No, as of now, the examination is set to be held offline. Please be aware of any further notifications issued by your school. As the pandemic recedes, the schools are planning to start operating as usual. However, new plans may be undertaken as the situation develops.


Q6. Will the syllabus be reduced for the academic session 2021-22 as well?

Answer: Keeping in mind the Covid-19 restrictions, the Uttarakhand Board had reduced the syllabus for all the subjects by 25% for the year 2020-21 for the convenience of students. However, no such announcement has been made for the academic session 2021-22. Students are advised to keep visiting the official website of the UKBSE – https://ubse.uk.gov.in/ to stay updated.