CBSE Class 10 Board — Complete Syllabus

Statement and application of the Fundamental Theorem of Arithmetic, which states that every integer greater than 1 is either a prime number itself or can be represented as the product of prime numbers.

Algebraic proofs demonstrating the irrationality of specific square roots like √2, √3, and √5.

Understanding and finding the zeros (roots) of a polynomial.

Establishing and using the relationship between the zeros and the coefficients of a quadratic polynomial.

Solving pairs of linear equations in two variables using the graphical method, including understanding consistency and inconsistency.

Solving pairs of linear equations in two variables algebraically using substitution and elimination methods, including simple situational problems.

Solving quadratic equations (with real roots) by factorization and using the quadratic formula.

Determining the nature of the roots of a quadratic equation using the discriminant.

Derivation and application of the formulas for the nth term and the sum of the first n terms of an Arithmetic Progression.

Calculating the distance between two points in a coordinate plane using the distance formula.

Finding the coordinates of a point that divides a line segment internally in a given ratio.

Understanding and proving the Basic Proportionality Theorem and its converse, and applying them to solve problems involving similar triangles.

Proving similarity of triangles using different criteria (AAA, SAS, SSS) and applying these to solve geometric problems.

Proving that the tangent at any point of a circle is perpendicular to the radius through the point of contact.

Proving that the lengths of tangents drawn from an external point to a circle are equal.

Understanding trigonometric ratios (sine, cosine, tangent, etc.) for acute angles in a right-angled triangle.

Evaluating trigonometric ratios for standard angles (0°, 30°, 45°, 60°, 90°).

Understanding and proving basic trigonometric identities, primarily focusing on sin²A + cos²A = 1.

Solving simple problems involving heights and distances using angles of elevation and depression (limited to 30°, 45°, 60°).

Calculating the areas of sectors and segments of a circle, with restrictions on central angles.

Calculating surface areas and volumes of combinations of basic solids like cubes, cuboids, spheres, hemispheres, cylinders, and cones.

Computing the mean, median, and mode for grouped frequency distributions using various methods.

Understanding the classical definition of probability and solving simple problems related to the likelihood of events.