Class 9 - Mathematics

Syllabus:

1. REAL NUMBERS

Representation of natural numbers, integers and rational numbers on the number line – Terminating and recurring decimals – non-terminating and non-recurring decimals – Irrational numbers – Representation of irrational numbers on the number line – Surds and square roots – Rationalization of surds – Logarithms and their laws – Applications of logarithms.

2. SETS

Concept of sets – Empty sets, finite and infinite sets – Equal sets and subsets – Universal set – Cardinality of sets – Intervals of real numbers – Venn diagrams – Union, intersection and difference of sets – Applications of set theory.

3. POLYNOMIALS

Definition and types of polynomials – Monomials, binomials and trinomials – Zeroes of polynomials – Polynomial division – Remainder theorem – Factor theorem – Algebraic identities – Factorization of polynomials – Applications in algebra.

4. LINEAR EQUATIONS IN TWO VARIABLES

Introduction to equations in two variables – Graphical representation – Solutions by substitution and graphical methods – Graphs of straight lines – Lines parallel to axes – Word problems involving linear equations.

5. EUCLID’S GEOMETRY

History of Euclid and geometry – Definitions, axioms, postulates and theorems – Euclid’s five postulates – Relationship between axioms and theorems – Logical development of geometry.

6. GEOMETRY

Lines and angles – Parallel lines and transversals – Triangles and congruence criteria (SAS, ASA, SSS, RHS) – Properties of triangles – Quadrilaterals and parallelograms – Mid-point theorem – Area of parallelograms and triangles – Circles and their properties – Chords, arcs and angles – Cyclic quadrilaterals – Geometrical proofs and constructions.

7. COORDINATE GEOMETRY

Cartesian coordinate system – Coordinates of points – Plotting points on a plane – Understanding quadrants – Applications in graphing and geometry.

8. MENSURATION

Surface area and volume of cubes and cuboids – Surface area and volume of cylinders, cones, spheres and hemispheres – Relationship between surface area and volume – Word problems involving solid figures.

9. STATISTICS AND PROBABILITY

Frequency distributions – Mean, median and mode – Experimental probability – Random experiments – Tossing coins and dice – Notion of chance and randomness – Visualization of frequency distributions – Applications of probability in daily life.