Mathematics – Class 10 – CBSE Syllabus

Unit-wise and chapter-wise breakdown with sections, competencies, and learning outcomes.

1.REAL NUMBERS
Fundamental Theorem of Arithmetic – statements after reviewing work done earlier and after illustrating and motivating through examples.
Proofs of irrationality of \(\sqrt{2}\), \(\sqrt{3}\), \(\sqrt{5}\).
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 / Learning Outcomes:
  • Describes Fundamental Theorem of Arithmetic with examples.
  • Proves algebraically the irrationality of numbers like \(\sqrt{2}\), \(\sqrt{3}\), \(\sqrt{5}\), \(3 + 2\sqrt{5}\) etc.

1POLYNOMIALS
Zeros of a polynomial.
Relationship between zeros and coefficients of quadratic polynomials.
Competencies:
  • Develops a relationship between algebraic and graphical methods of finding the zeroes of a polynomial.
Explanation / Learning Outcomes:
  • Finds the zeros of polynomial graphically and algebraically and verifies the relation between zeros and coefficients of quadratic polynomials.
2PAIR 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.
Solution of a pair of linear equations in two variables algebraically – by substitution and elimination. Simple situational problems.
Competencies:
  • Describes plotting a pair of linear equations and graphically finding the solution.
  • Models and solves contextualised problems using equations (e.g., simultaneous linear equations in two variables).
Explanation / Learning Outcomes:
  • Finds the solution of pair of linear equations in two variables graphically and algebraically (substitution and elimination method).
3QUADRATIC EQUATIONS
Standard form of a quadratic equation \(ax^2 + bx + c = 0, (a \neq 0)\).
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 / Learning Outcomes:
  • Solves quadratic equations using factorization and quadratic formula.
  • Determines the nature of roots using discriminant.
  • Formulates and solves problems based on real-life context.
4ARITHMETIC 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 A.P. to daily life situations.
Explanation / Learning Outcomes:
  • Applies concepts of AP to find the nth term and sum of n terms.
  • Applies AP in real-life problems.

1COORDINATE 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 and determining the coordinates of a point between any two given points.
Explanation / Learning Outcomes:
  • Solves problems using distance formula and section formula.

1TRIANGLES
Definitions, examples, counterexamples of similar triangles.
(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.
State (without proof) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side.
State (without proof) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar.
State (without proof) If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar.
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 / Learning Outcomes:
  • Proves Basic Proportionality Theorem and applies the theorem and its converse in solving questions.
  • Proves similarity of triangles using different similarity criteria.
2CIRCLES
Tangent to a circle at point of contact.
(Prove) The tangent at any point of a circle is perpendicular to the radius through the point of contact.
(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 / Learning Outcomes:
  • Proves the theorems based on the tangent to a circle.
  • Applies the concept of tangents of a circle to solve various problems.

1INTRODUCTION TO TRIGONOMETRY
Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined).
Motivate the ratios which are defined at 0° and 90°. Values of the trigonometric ratios of 30°, 45° and 60°.
Relationships between the trigonometric ratios.
Competencies:
  • Understands the definitions of the basic trigonometric functions, including the introduction of the sine and cosine functions.
Explanation / Learning Outcomes:
  • Evaluates trigonometric ratios.
  • Describes trigonometric ratios of standard angles and solves related expressions.
2TRIGONOMETRIC IDENTITIES
Proof and applications of the identity \(\sin^2A + \cos^2A = 1\).
Only simple identities to be given.
Competencies:
  • Uses trigonometric identities to solve problems.
Explanation / Learning Outcomes:
  • Proves trigonometric identities using \(\sin^2A + \cos^2A = 1\) and other related identities.
3HEIGHTS AND DISTANCES: Angle of Elevation and 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 distances from them.
Explanation / Learning Outcomes:
  • Finds heights and distances in real-life word problems using trigonometric ratios.

1AREAS 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 angles of 60°, 90°, and 120° only.)
Competencies:
  • Derives and uses formulae to calculate areas of plane figures.
Explanation / Learning Outcomes:
  • Visualises and evaluates areas of sector and segment of a circle.
2SURFACE 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 / Learning Outcomes:
  • Evaluates the surface areas and volumes of combinations of solids by visualisation.

1STATISTICS
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 / Learning Outcomes:
  • 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.
2PROBABILITY
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 / Learning Outcomes:
  • Determines the probabilities in simple real-life problems.