Goa SSC Syllabus 2024-25 Released : Download Latest and Revised GBSHSE Class 10th Syllabus PDF with Subject-wise

1) Real Numbers

a) Concept of Real numbers.

b) To find the H.C.F of two numbers by Euclid’s Division Algorithm

c) To find HCF/LCM by prime factorization method.

d) Revisiting Rational Numbers and Their Decimal Expansions.

2) Polynomials

a) Concept of a Polynomial, degree & types.

b) Zero(es) of a Linear Polynomial, Quadratic Polynomial, geometric meaning of the zeroes of a Polynomial, relationship between zeroes and coefficients.

c) Finding a Quadratic Polynomial given sum and product of zeroes/zeroes.

d) To find the Quotient and remainder when a Cubic Polynomial is divided by a Linear polynomial and to express in the form: Dividend = Divisor x Quotient + Remainder

3) Pair of Linear equations in Two variables

a) General form of a pair of linear equations in two variables

b) Conditions for a pair of Linear equations in two variables to have a unique solution, no solution, infinitely many solutions, (Consistent/Inconsistent), finding the value of the unknown

c) Find the solution of a pair of linear equations in two variables by

(I) Elimination method

(II) Substitution method (one equation should have a coefficient of x or y as one)

(III) Graphical method (both equations should have one coefficient of x or y as one)

4) Quadratic Equations

a) Concept of a Quadratic equation - standard form

b) Finding the Roots of a Quadratic equation by

(I) Factorisation method

(II) Quadratic formula

c) Nature of Roots based on discriminant

5) Arithmetic Progressions

a) Concept of an AP - first term, common difference

b) Questions based on the nth term, the sum of n terms of an AP

6) Triangles

a) Concept of Similarity of Triangles - Tests for similarity of Triangles

b) Concept of theorem on Areas of Similar Triangles (Proof not for evaluation)

c) B.P.T., Pythagoras theorem and Converse of Pythagoras theorem (Proofs for evaluation)

d) Numerical applications of the above 4 theorems

7) Coordinate Geometry

a) Concepts/Applications of

(I) Distance Formula

(II) Section Formula

(III) Area of Triangle Formula

8) Introduction to Trigonometry

a) Concept of Trigonometry

b) Trigonometric ratios and their relationships, k method

c) Proving the Basic Trigonometric identities with the help of a figure.

(I) Sin²θ + Cos²θ = 1

(II) 1 + Tan²θ = Sec²θ

(III) 1 + Cot²θ = Cosec²θ

d) To evaluate expressions involving Trigonometric ratios of some specific angles: 0⁰, 30⁰, 45⁰, 60⁰, 90⁰

e) Trigonometric ratios of complementary angles

9) Some Applications of Trigonometry

a) Heights and Distances: Angle of Elevation and Angle of Depression

b) Problems with heights and Distances. Problems should have only one right triangle with either angle of elevation or depression

10) Circles

a) Concept of Tangent, Thm.10.1 (proof not for Evaluation) Thm.10.2 (with Proof)

b) Numerical applications

11) Constructions

a) Construction of Tangents to a Circle from a point outside the circle.

b) Construction of Similar Triangles as per the given scale factor. Note: Angles can also be drawn using a protractor

12) Areas Related to Circles

a) Perimeter and Area of a Circle

b) Areas of Segment, Sector, Quadrant of a Circle and Semicircle

c) Applications to find areas of shaded region

13) Surface Areas and Volumes

The whole topic is included for evaluation

14) Statistics

a) Concept of Mean, Median, Mode, and the empirical relationship between them

b) To find the Mean of grouped data by Direct method

c) To find Mode of grouped data

15) Probability

a) Concept of Theoretical Probability

b) Probability of a Sure event and an Impossible event, 0 ≤ P(E) ≤ 1, P(not E)

c) Problems based on coins, Dice (only 1), playing cards, numbered cards, items in a box

Logarithms Part 2 (Std X)

a) Laws of Logarithms

b) Logarithm method and its applications

1

H1. Early Trade Activities

5

2

H2. The Age of Industrialisation Age

5

3

H3. Post Industrialisation Age

4

4

H4. The American War of Independence

6

5

H5. The French Revolution

6

6

H8. Emergence of Nationalism in India

6

7

H9. Goa Struggle for Freedom

6

8

PS10. Union Legislature

5

9

PS11. Union Executive

5

10

PS12. Judiciary

6

11

PS13. State Legislature

6

12

PS14. State Executive

4

13

PS15. Urban Local Government

4

14

PS16. Panchayati Raj System in India

2

Total

70