Uttarakhand Board Class 10 Syllabus 2027 Mathematics

FOR UTTARAKHAND CLASS 10 PREPARATION

Uttarakhand Board
Class 10 Syllabus 2027
Mathematics
EXAM YEAR TYPE SUBJECT

Uttarakhand Class 10 2027 Syllabus Maths

Notes · Sample Papers · Previous Year Papers · Mock Tests

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Class – X
TOTAL MARKS- 100 ¿ 80 (Theory) + 20 (Internal Assessment)À
THEORY: 80 Marks Time: 3:00 Hrs.
Units Unit Name Marks
I NUMBER SYSTEMS 06 m
II
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VI MENSURATION 10
VII STATISTICS & PROBABILTY 11
Total 80

UNIT I: NUMBER SYSTEMS
REAL NUMBER
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Fundamental Theorem of Arithmetic- statements after reviewing work done earlier and after
illustrating and motivating through examples
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Proofs of irrationality of
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Competencies  Develops understanding of numbers, including the set of real numbers and its
properties.
 Extends the understanding of powers (radical powers) and exponents.
 Applies Fundamental Theorem of Arithmetic to solve problems related to real life
contexts.
Explanation  Describes Fundamental Theorem of Arithmetic with examples
 Prove algebraically the Irrationality of numbers like √2, √3, √5, 3 + 2√5 etc.

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UNIT II: ALGEBRA
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1. POLYNOMIALS
Zeros of a polynomial.
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Relationship between zeros and coefficients of quadratic polynomials.

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Competencies Develops a relationship between algebraic and graphical
ag zeroes of a polynomial.
Explanation Find the zeros of polynomial graphically and algebraically and verifying the relation
between zeros and coefficients of quadratic polynomials.

2. PAIR OF LINEAR EQUATIONS IN TWO VARIABLES
Pair of linear equations in two variables and graphical method of their solution,
consistency/inconsistency.
Algebraic conditions for number of solutions.
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Solution of a pair of linear equations in two variables algebraically- by substitution, by elimination.
Simple situational problems.
Competencies  Describes plotting a pair of linear equations and graphically finding the solution.
 Models and solves contextualized problems using equations (e.g., simultaneous
linear equations in two variables).
Explanation Find the solution of pair of linear equations in two variables graphically and
algebraically (substitution and elimination method)

3. QUADRATIC EQUATIONS
Standard form of a quadratic equation ax2 + bx + c = 0, (a ≠ 0).
Solutions of quadratic equations (only real roots) by factorization, and by using quadratic formula.
Relationship between discriminant and nature of roots.
Situational problems based on quadratic equations related to day-to-day activities to be
incorporated.
Competencies Demonstrates strategies of finding roots and determining the nature of roots of a
quadratic equation.
Explanation  Solves quadratic equations using factorization and quadratic formula
 Determines the nature of roots using discriminant
 Formulates and solves problems based on real life context

4. ARITHMETIC PROGRESSIONS
Motivation for studying Arithmetic Progression
Derivation of the nth term and sum of the first n terms of AP and their application in solving daily
life problems.
Competencies Develops strategies to apply the concept of AP to daily life situations.
Explanation  Applies concepts of AP to find the nth term and sum of n terms.
 Application of AP in real life problems

UNIT III: COORDINATE GEOMETRY
Coordinate Geometry
Review: Concepts of coordinate geometry. Distance formula. Section formula (internal division).
Competencies Derives formulae to establish relations for geometrical shapes in the context of a
coordinate plane, such as, finding the distance between two given points, to
determine the coordinates of a point between any two given points.
Explanation Solves problems using distance formula and section formula.

UNIT IV: GEOMETRY
1. TRIANGLES
Definitions, examples, counter examples of similar triangles.
a. (Prove) If a line is drawn parallel to one side of a triangle to intersect the other two sides in
distinct points, the other two sides are divided in the same ratio.
b. State (without proof) If a line divides two sides of a triangle in the same ratio, the line is parallel
to the third side.
c. State (without proof) If in two triangles, the corresponding angles are equal, their
correspondingsides are proportional and the triangles are similar.
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a d. State (without proof) If the corresponding sides of two
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corresponding angles are equal and the two triangles are similar.
e. State (without proof) If one angle of a triangle is equal to one angle of another triangle and the
sides including these angles are proportional, the two triangles are similar.
Competencies  Works out ways to differentiate between congruent and similar figures.
 Establishes properties for similarity of two triangles logically using different
geometric criteria established earlier such as, Basic Proportionality Theorem, etc.
Explanation  Prove Basic Proportionality theorem and applying the theorem and its converse
in solving questions.
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 Prove similarity of triangles using different similarity criteria.
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2. CIRCLES
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Tangent to a circle at, point of contact
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a. (Prove) The tangent at any point of a circle is perpendicular to the radius through the point of
contact.
b. (Prove) The lengths of tangents drawn from an external point to a circle are equal.
Competencies Derives proofs of theorems related to the tangents of circles.
Explanation  Prove the theorems based on the tangent to a circle.
 Applies the concept of tangents of circle to solve various problems

UNIT V: TRIGONOMETRY
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1. INTRODUCTION TO TRIGONOMETRY
Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well
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Motivate the ratios whichever are defined at 0o and 90o. Values of the trigonometric ratios of 300,
450 and 600.
Relationships between the ratios.
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Competencies Understands the definitions of the basic trigonometric functions (including the
introduction of the sine and cosine functions).
Explanation  Evaluates trigonometric ratios
 Describes trigonometric ratios of standard angles and solving related expressions

2. TRIGONOMETRIC IDENTITIES
Proof and applications of the identity sin2A + cos2A = 1. m
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c. oCompetencies Uses Trigonometric identities to solve problems. m .co
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Proves trigonometric identities using sin2A + cos2A = 1 and other identities
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a 3. HEIGHTS AND DISTANCES: Angle of Elevation, Angle of Depression.
Simple 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°.
Competencies Applies Trigonometric ratios in solving problems in daily life contexts like finding
heights of different structures or distance from them.
Explanation Find heights and distances in real life word problems using trigonometric ratios

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UNIT VI: MENSURATION
1. AREAS RELATED TO CIRCLES
Area of sectors and segments of a circle.
Problems based on areas and perimeter/circumference of the above said plane figures. (In
calculating area of segment of a circle, problems should be restricted to central angle of 60°, 90°
and 120° only.
Competencies Derives and uses formulae to calculate areas of plane figures.
Explanation Visualises and evaluates areas of sector and segment of a circle.

2. SURFACE AREAS AND VOLUMES
Surface areas and volumes of combinations of any two of the following: cubes, cuboids, spheres,
hemispheres and right circular cylinders/cones.
Competencies Visualises and uses mathematical thinking to discover formulae to calculate
surface areas and volumes of solid objects (cubes, cuboids, spheres, hemispheres,
right circular cylinders/cones, and their combinations).
Explanation Evaluates the surface areas and volumes of combinations of solids by visualization.

UNIT VII: STATISTICS AND PROBABILITY
1. STATISTICS
Mean, median and mode of grouped data (bimodal situation to be avoided).
Competencies Calculates mean, median and mode for different sets of data related with real life
contexts.
Explanation  Computes the mean, of a grouped frequency distribution using direct, assumed
mean and step deviation method.
 Computes the median and mode of grouped frequency distribution by algebraic
method

2. PROBABILITY
Classical definition of probability.
Simple problems on finding the probability of an event.
Competencies Applies concepts from probability to solve problems on the likelihood of everyday
events.
Explanation Determines the probabilities in simple real-life problems

INTERNAL ASSESSMENT Max. Marks: 20
(i) Activities (02)- 2X5 10 Marks
(ii) Project Work (01) 05 Marks
(iii) Continuous Assessment (Unit Test) 05 Marks
(There will be total 3 Unit Tests (two Unit Tests before half yearly examination and one after half yearly
examination) and a pre-board examination. At the time of half yearly result preparation best of two Unit
Tests (I & II) marks will be taken and converted to the weightage of 05 marks. In annual board
examination, marks of the best out of 3 Unit Tests will be taken and converted to the weightage of 05
marks for the board result preparation.)
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PRESCRIBED BOOKS:

1. Xkf.kr (Mathematics) - Textbook for class IX - NCERT Publication

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2. Xkf.kr (Mathematics) - Textbook for class X - NCERT Publication
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3. Laboratory Manual - Mathematics, secondary stage - NCERT Publication
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4. Mathematics
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5. Mathematics exemplar problems for class X, NCERT publication.

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