Andhra Pradesh SSC Board (BSEAP) Class 10 Maths Syllabus – Latest 2022-2023

Mathematics Syllabus – Academic Standards – Elementary Secondary Level

Number System

(i) Real numbers (15 periods) :

• More about rational and irrational
• Fundamental Theorem of Arithmetic –
• Proofs of results, irrationality of  2 , 3 and decimal expansions of rational numbers in terms of terminating, non terminating, recurring of decimals and vice versa.
• Properties of real numbers
• Introduction of logarithms
• Conversion of a number in exponential form to a logarithm tic form
• Properties of logarithms log_a a =1; log_a 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 (8 periods):
  • Sets and their representations : Empty set, Finite and infinite sets. Equal 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.

Algebra

(i) Polynomials (8 periods)

• Zeros of a
• Geometrical meaning of zeros of quadratic and cubic polynomials using
• Relationship between zeros and coefficients of a polynomial with particular reference to quadratic
• Statement and simple problems on division algorithm for polynomials with integral

(ii) Pair of Linear Equations in Two Variables (15 periods)

Pair of linear equations in two variables. Geometric representation of different

possibilities of solutions / inconsistency.

• Algebraic conditions for number of
• Solution of pair of linear equations in two variables algebraically – by substitution, by elimination and by cross Simple situational problems.
• Simple problems on equations reducible to linear

(iii) Quadratic Equations (12 periods)

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

(iv) Progressions (11 periods)

• Sequence and series
• Motivation for studying AP. Derivation of standard results of finding the n^th term and sum of first n terms.
• Motivation for studying G.P
• n^th term of G.P.

Trigonometry

(i) Introduction (15 periods)

• Trigonometric ratios of an acute angle of a right- angled triangle i.e. sine, cosine, tangent, cosecant,
• 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
• Trigonometric Identities: Proof and applications of the identity sin²A+cos²A=1. 1+tan²A=sec²A cot²+1=cosec²A only simple identities
• Trigonometric ratios of complementary

(ii) Applications of trigonometry (8 periods)

• 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 30⁰, 45⁰, 60⁰.

Coordinate geometry Lines (In two-dimensions) (15 periods)

• Review the concepts of coordinate geometry done by the graphs of linear
• 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 coordinate
• Slope of a line joining two points.

Geometry

(i) Similar triangles (18 periods)

Definitions, examples, properties of similar triangles.

• Difference between congruency and similarity of
• (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
• (Motivate) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side.

(Motivate) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar (AAA).

• (Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar (SSS).
• (Motivate) 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.
• (Prove) The ratio of the areas of two similar triangles is equal to the ratio of the squares on their corresponding
• (Motivate) If a perpendicular is drawn from the vertex of the right angle to the hypotenuse, the triangles on each side of the perpendicular are similar to the whole triangle and to each
• (Prove) In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.
• (Prove) In a triangle, if the square on one side is equal to sum of the squares on the other two sides, the angles opposite to the first side is a right triangle.

(ii) Construction:

• Division of a line segment using basic proportionality
• A triangle similar to given triangle as per the given scale

(iii) Tangents and secants to a circle (15 periods)

• 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
• (Prove) The lengths of tangents drawn from an external point to a circle are
• Segment of a circle made by the secant.
• Finding the area of the minor/ major segment of a

(iv) Constructions

A tangent to a circle through point given on it.

• Tangent to a circle from a point outside it.

Mensuration

1. Surface Areas and Volumes (10 periods)

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

Data handling        (15 hrs)

(i) Statistics (15 periods)

• Revision of Mean, median and mode of ungrouped (frequency distribution)
• Understanding, the concept of Arithmetic Mean, Median and Mode for grouped (classified)
• The meaning and purpose of arithmetic Mean, Median and Mode
• Simple problems on finding Mean, Median and Mode for grouped / ungrouped
• Usage and different values and central tendencies through

 (ii) Probability (10 periods)

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

Mathematical Modeling (8 periods)

• Concept of Mathematical modeling

Discussing the broad stages of modeling – real life, situations (ration, proportion, percentage, probability, fair installments, payments etc.)