Uttarakhand Board Class 10 Maths Syllabus
Uttarakhand Board Class 10 Maths Syllabus

Uttarakhand Board of School Education (UKBSE) has been proactive in designing the syllabus of Class 10 Mathematics subject each year to make sure the students get a better understanding of the subject and are benefited in their higher studies. Mathematics has become an important field of study and finds it’s applications across banks, pharmaceutical sector, space exploration, engineering, insurance, etc. Therefore, students are advised to study Mathematics in detail to build a strong foundation in the subject and prepare themselves for their higher studies.


The Uttarakhand Board has structured the Class 10 Mathematics syllabus really well. It will help the students in planning their study time, break down the parts of the syllabus, and prepare well for the exams. Mathematics is a highly scoring subject and can increase the overall marks of a student.


The total marks for the subject are 100, divided into two parts: theory paper and internal assessment. The theory paper is of 80 marks and the internal assessment carries the remaining 20 marks. To score well in the Uttarakhand Board Class 10 exam, a student should be well-aware of the syllabus and prepare the subject thoroughly.


Theory Syllabus of Uttarakhand Board Class 10 Maths


Around 14 chapters have been spread across 7 units mentioned. The chapters listed in the syllabus are mentioned below in detail:





Number Systems

Real Numbers

4 Marks




20 Marks

Pair of Linear Equations in Two Variables

Quadratic Equations

Arithmetic Progressions




Introduction to Trigonometry


12 Marks

Trigonometric Identities

Heights and Distances


Coordinate Geometry


Lines (In Two Dimensions)

8 Marks




16 Marks






Areas Related to Circles

10 Marks

Surface Areas and Volumes


 Statistics and Probability



10 Marks





Unit I: Number System

Chapter 1-Real Numbers: Euclid’s division lemma, Fundamental Theorem of Arithmetic – statements after reviewing work done earlier and after illustrating and motivating through examples. Proofs of results – irrationality of √2 , √3, √5 , decimal expansions of rational numbers in terms of terminating/non-terminating recurring decimals.


Unit II: Algebra

Chapter 2- Polynomials: Zeros of a polynomial. Relationship between zeros and coefficients of a polynomial with particular reference to quadratic polynomials. Statement and simple problems on division algorithms for polynomials with real coefficients.


Chapter 3 -. Pair of Linear Equations in Two Variables. Geometric representation of different possibilities of solutions/inconsistency. Algebraic conditions for number of solutions. Solution of pair of linear equations in two variables algebraically – by substitution, by elimination and by cross multiplication. Simple situational problems must be included. Simple problems on equations reducible to linear equations may be included.


Chapter 4-Quadratic Equations: Standard form of a quadratic equation ax2 + bx + c = 0, (a ≠ 0). Solution of quadratic equations (only real roots) by factorization and by completing the square, i.e., by using quadratic formula. Relationship between discriminant and nature of roots. Problems related to day-to-day activities to be incorporated.


Chapter 5- Arithmetic Progressions (AP) : Motivation for studying AP. Derivation of standard results of finding the nth term and sum of first n terms.



Unit III:  Trigonometry

Chapter 6- Introduction to Trigonometry : Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined); motivate the ratios, whichever are defined at 0° and 90°. Values (with proofs) of the trigonometric ratios of 30°, 45° and 60°. Relationships between the ratios. Trigonometric Identities: Proof and applications of the identity sin2A + cos2 A = 1. Only simple identities to be given. Trigonometric ratios of complementary angles.


Chapter 7-Heights and Distances:Simple and believable problems on heights and distances. Problems should not involve more than two right triangles. Angles of elevation/depression should be only 30°, 45° and 60°.


Unit IV: Coordinate Geometry


Chapter 8-Lines (In two-dimensions):Review the concepts of coordinate geometry done earlier including graphs of linear equations. Awareness of geometrical representation of quadratic polynomials. Distance between two points and section formula (internal). Area of a triangle.


Unit V: Geometry

Chapter 9-Triangles: Definitions, examples, counter examples of similar triangles.


Chapter 10- Circles: Tangents to a circle motivated by chords drawn from points coming closer and closer to the point.


Chapter 11- Constructions


Division of a line segment in a given ratio (internally).

Tangent to a circle from a point outside it.

Construction of a triangle similar to a given triangle.

Unit VI: Mensuration

Chapter 12- Areas Related to Circles : Motivate the area of a circle; area of sectors and segments of a circle. Problems based on areas and perimeter/circumference of the above said plane figures. (In calculating the area of the segment of a circle, problems should be restricted to the central angle of 60°, 90° and 120° only. Plane figures involving triangles, simple quadrilaterals and circles should be taken.)


Chapter 12-Surface Areas and Volumes

Problems on finding surface areas and volumes of combinations of any two of the following: cubes, cuboids, spheres, hemispheres and right circular cylinders/cones. Frustum of a cone.

Problems involving converting one type of metallic solid into another and other mixed problems. (Problems with combinations of not more than two different solids can be taken.)


Unit VII: Statistics and Probability


Chapter 13-Statistics: Mean, median and mode of grouped data (bimodal situation to be avoided). Cumulative frequency graph.


Chapter 14- Probability:  Classical definition of probability. Connection with probability as given in Class IX. Simple problems on single events, not using set notation.


Uttarakhand Board Class 10 Maths Practical /Internal Assessment Exam


The internal assessment exam for Class 10 Maths is of 20 marks. Generally, the marks for internal assessment are distributed as follows:

       –>  5 Marks for Attendance (for 90% Attendance)

       –>  5 Marks for Extra-Curricular Activities

       –>  10 Marks for Mock Test / Assignment

The assignment or the project work performed for the internal assessment is evaluated by an internal subject teacher and an external examiner. Both the internal and the external examiner give marks to the students.



Frequently Asked Questions for Uttarakhand Board Class 10 Maths Exam:


Q1. How are the marks for the Uttarakhand Board Class 10 Maths divided?

Ans.  The total marks allotted for the UKBSE board class 10 maths are 100 marks. These marks are divided between theory paper (80 marks) and internal assessment (20 marks) exams.


Q2. What is the weightage for the units of the class 10 maths syllabus?

Ans.  The following shows the unit-wise weightage of the marks for the class 10 maths syllabus:

  1. Number system– 6 marks
  2. Algebra – 20 marks
  3. Coordinate Geometry – 6 marks
  4. Geometry – 15 marks
  5. Trigonometry – 12 marks
  6. Mensuration – 10 marks
  7. Statistics & Probability — 11 marks


Q3. Which unit has the highest weightage for the class 10 maths syllabus?

Ans: For the class 10 maths syllabus, the unit with the highest weightage is “Algebra.” 



Q4. When will the practical/internal assessment exams be held?

Ans:  The dates for internal assessment exams will be declared by your school authorities. Students are advised to contact their school exam department for further information.


Q5. Will the syllabus be reduced for the academic session 2021-22 as well?

Ans:  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 Board – https://ubse.uk.gov.in/ to stay updated.


Q6. Is Uttarakhand Board Class 10 Maths a difficult subject to study?

Ans: The difficulty of a unit in maths depends on the ability of a student. Some may find it easy, while others may be struggling to understand the same topic. But most of the time, students find “geometry” difficult. However, a student can improve with diligent practice and study.