TS SSC Math Syllabus 2025-26: Check Telangana Board Class 10th Math Unit-Wise Syllabus

Chapter 1

Real Numbers

• Euclid division lemma

– Introduction, HCF

– Some number generalisations

• Rational and irrational numbers.
• Fundamental Theorem of Arithmetic – statements.
• LCM, HCF
• Properties of real numbers in terms of rationality and irrationality
• Proofs of results irrationality of 2, 3etc. and decimal expansions of rational numbers in terms of terminating, non-terminating, recurring decimals and vice versa.
• Introduction of logarithms
• Conversion of a number in exponential form to a logarithm tic form
• Properties of logarithms loglogaa=1; loga 1 = 0
• Laws of logarithms

Chapter 2

Sets

• Sets and their representations: Empty set, Finite and infinite sets.

Equal sets. Subsets, subsets of the set of real numbers.

Universal set and cardinality of sets.

• Venn diagrams

– Sets, subsets

– Disjoint sets.

• Basic operations on sets

– Union, intersection, difference of sets

Chapter 3

Polynomials

• zeros of a polynomial (cubic polynomials, linear and quadratic).
• Graphs that illustrate the geometric meaning of the zeroes in cubic and quadratic polynomials.
• The connection between a polynomial's zeroes and coefficients, specifically with quadratic polynomials.
• Proposition and elementary problems about the division procedure for polynomials containing integral coefficients.
• A biquadratic polynomial's zeroes.

Chapter 4

Pair of Linear Equations in Two Variables

• Two variable linear equations in pair form. Geometric depiction of several possible solutions and inconsistencies.
• Number of solutions: algebraic conditions (consistent, inconsistent).
• Algebraic solution of a pair of linear equations in two variables: substitution and elimination techniques straightforward situational problems
• Simple equations that can be reduced to two-variable linear equations.

Chapter 5

Quadratic Equations

• Standard form of a quadratic equation ax2+bx+c=0, (a ≠ 0).
• Solutions of quadratic equations by factorization and by completing the square, i.e., by using formula to find roots of quadratic equation.
• Relationship between discriminant and nature of roots.
• Problems related to day-to-day life situations.

Chapter 6

Progressions

• Sequence and series
• Progressions –introduction
• Derivation of standard results of finding the nth term and sum of first n terms of A.P.
• Motivation for studying G.P
• nth term of G.P.

Chapter 7

Coordinate Geometry

• Examine the coordinate geometry concepts shown by the linear equation graphs.
• Distance between two points i.e. P (x1 , y1) and Q (x2 , y2)
• Section formula (internal division of a line segment in the ratio m:n).
• Area of a triangle on a coordinate plane.
• Slope of a line joining two points.

Chapter 8

Similar Triangles

Similar triangles

Definition, illustrations, and characteristics of related triangles.

• Distinction between triangle congruence and similarity.
• (Prove) The other two sides of a triangle are divided in the same ratio if a line is drawn parallel to one side and intersects the other two sides at different positions.
• (Motivate) A line is parallel to the third side of a triangle if it divides the first two sides in the same ratio.
• (Motivate) If the matching sides of two triangles are proportionate, the corresponding angles are equal, and the triangles are comparable (AAA).
• (Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar (SSS).
• (Motivate) A triangle is similar to another if its angle is equal to that of another triangle and the sides that include these angles are proportionate.
• (Prove) The ratio of the squares on the matching sides of two similar triangles equals the ratio of their areas.
• (Motivate) The triangles on each side of the perpendicular are identical to the triangle as a whole and one another if the perpendicular is drawn from the right angle's vertex to the hypotenuse.
• (Prove) The square on the hypotenuse of a right triangle equals the sum of the squares on the other two sides.

Chapter 9

Tangents and Secants to a Circle

• Tangents to a circle motivated by chords drawn from points coming closer and closer to the point.
• (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.
• Segment of a circle made by the secant.
• Finding the area of the minor/ major segment of a circle.

Chapter 10

Mensuration

• Problems in finding surface areas and volumes of combinations of any of the following: cubes, cuboids, spheres, hemispheres, and right circular cylinders/cones.
• Problems involving converting one type of metallic solid into another and other mixed problems. (Problems with a combination of not more than two different solids be taken.)

Chapter 11

Trigonometry

• Trigonometric ratios of an acute angle by using right angled triangle i.e. sine, cosine, tangent, cosecant and cotangent.
• Values (with proof) of the trigonometric ratios of 30°, 45°& 60°
• Relationship between the ratios.
• Trigonometric Identities:

Proof and applications of the identities

sin2A + cos2 A =1

1 + tan2A = sec2A

cot2A + 1 = cosec2A

Chapter 12

Applications of Trigonometry

• Angle of elevation, angle of depression
• Simple and daily life problems on heights and distances. Problems should not involve more than two right triangles and angles elevation/depression should be only 30°, 45°& 60°

Chapter 13

Probability

• Concept and definition of Probability.
• Simple problems (day to day life situation) on single events simple using set notation.
• Concept of complementary events.

Chapter 14

Statistics

• Revision of Mean, median and mode of ungrouped (frequency distribution) data.
• Understanding, the concept of Arithmetic Mean, Median and Mode for grouped (classified) data.
• Why and what the arithmetic Mean, Median, and Mode mean
• Fundamental problems with determining the Mode, Median, and Mean for both grouped and ungrouped data.
• Utilization, as well as various values and core tendencies, are provided by O.