AP SSC Math Syllabus 2025-26 - AP Board Class 10 Math Syllabus Download PDF

Unit-I

Number System

(i).

Real Numbers

More about rational and irrational numbers.

• Fundamental Theorem of Arithmetic – statements.

• Proofs of results, irrationality of 2, 3 etc. and decimal expansions of rational numbers in terms of terminating, non-terminating, recurring, and vice versa.

• Properties of real numbers

• Introduction of logarithms

• Conversion of a number in exponential form to a logarithmic form

• Properties of logarithms loga a =1; loga 1=0

• Laws of logarithms

log xy = logx + logy;

log x/y = logx – logy

log xn = n log x

• Standard base of logarithms and usage

(ii).

Sets - Sets and their representations: Empty set, Finite and infinite sets. Equal sets. Subsets, subsets of the set of real numbers (especially intervals with notations). Universal set and cardinality of sets.

• Venn diagrams: Union and intersection of sets. Difference of sets. Complement of a set. Disjoint sets.

Unit-II

Algebra

(i).

Polynomials

• Zeros of a polynomial.

• The graph-based geometric interpretation of the zeros of cubic and quadratic polynomials.

• The relationship between a polynomial's zeros and coefficients, with an emphasis on quadratic polynomials.

• Statement and simple problems on division algorithm for polynomials with integral coefficients.

(ii).

Pair of Linear Equations in Two Variables.

• Pair of linear equations in two variables. Geometric representation of different possibilities of  solutions / inconsistency.

• Algebraic conditions for number of solutions.

• Using cross multiplication, substitution, and elimination to solve a pair of linear equations in two variables.

• Simple equation-related problems that can be reduced to linear equations.

(iii)

Quadratic Equations

• The quadratic equation ax2 + bx + c=0, (a 0), in standard form.

• Solving quadratic equations using the quadratic formula by factorization and completing the square (only for real roots).

• The association between the roots' nature and the discriminant.

(iv)

Progression

• Sequence and series

• Motivation for studying AP. Derivation of standard results of finding the nth term and sum of first n terms.

• Motivation for studying G.P.

• nth termof G.P.

Unit-III

Trigonometry

(i) Trigonometry Introduction

• Trigonometric ratios of an acute angle of a right-angled triangle i.e. sine, cosine, tangent, cosecant, cotangent.

• Motivate the ratios, whichever are defined at 00 and 900

• Values (with proofs) of the trigonometric ratios of 300, 450 and 600. Relationships between the ratios.

• Trigonometric Identities: Proof and applications of the identity sin2A+cos2A=1.

1+tan2A=sec2A

cot2+1=cosec2

(ii).

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 of elevation/ depression.

Unit-IV

Co-ordinate Geometry

(i).

Lines (In two-dimensions)
• Review the concepts of coordinate geometry done by the graphs of linear equations.
• Distance between two points i.e. p (x1, y1) and q (x2, y2)
• Section formula internal division of a line segment in the m:n.
• Area of a triangle on the coordinate axis.
• Slope of a line joining two points.

Unit-V

Geometry

(i)

Similar triangles

Examples, definitions, and characteristics of similar triangles.

• The distinction between triangle congruency and triangle similarity.

• (Prove) The other two sides of a triangle are divided in the same ratio if a line drawn parallel to one side of a triangle intersects the other two sides in clearly defined points.

• (Motivate) A line is parallel to the third side of a triangle if it divides the first two sides of the triangle in the same ratio.

• (Motivate) If the corresponding sides of two triangles are proportionate, the corresponding angles are equal, and the triangles are comparable (AAA).

• (Motivate) If two triangles' corresponding sides are proportionate, their corresponding angles are equal, and the two triangles are similar (SSS), then the two triangles are similar.

• (Motivate) Two triangles are comparable if one of their angles is equal to another triangle's angle and the sides that include these angles are proportionate.

• (Prove) The ratio of the squares on the corresponding sides of two comparable triangles equals the ratio of the areas of the triangles.

(ii)

Construction

• Dividing a line segment utilizing the fundamental proportionality theorem.

• A triangle that, using the scale factor given, is comparable to the given triangle.

(iii)

(iii) 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.

Unit-VI

Mensuration

(i).

• Problems involving calculating the surface areas and volumes of mixtures of any two of the following: cubes, cuboids, spheres, hemispheres, and right circular cylinders/cones.

• Conversion-related difficulties, as well as other mixed challenges, including different types of metallic solids. (Problems with mixing more than two different substances at once should be taken.)

Unit-VII

Data Handling

(i).

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.

• The meaning and purpose of Arithmetic Mean, the Median and the Mode

• Simple problems on finding Mean, Median and Mode for grouped / ungrouped data.

• Usage and different values and central tendencies through Ogives.

(ii).

Probability

• Concept and definition of Probability.

• Simple problems (day-to-day life situation) on single events, simple using set notation.

• Concept of complementary events.