Mathematics Syllabus for Class 9 2021-2022

                                                      Algebra

Sets

• Introduction

• Methods of writing sets

• Types of sets

• Subset - Proper, Improper subset

• Super set · Universal set

• Venn diagrams

• Operations on sets

• Relations between various operations

• Number of elements in the set and related results.

Real Numbers 

• Revision of natural numbers, integers, rational numbers and irrational numbers

•  Existence of irrational numbers and their representations on the number line

•  Every real number is represented by a unique point on the number line and conversely, every point on the number line represents a unique real number 

• Properties of real numbers

• Definition of nth root of a real number

•  Surds - Definition

• Forms of surds

•  Operations and Laws of surds

• Rationalization of Surds

• Absolute value of real numbers

•  Euclid's division Lemma

• Fundamental theorem of Arithmetic

Algebraic Expressions

• Introduction to algebraic expression ?

• Operations on algebraic expressions

• Methods of factorization of algebraic expression ?

• Introduction to polynomials

• Operations on polynomials

• Value of polynomials

• Zeros/roots of polynomial

• Relation between zeros and coefficient of polynomials?

• Remainder theorem

• Factor theorem

Graphs

• Cartesian coordinate system

• Understanding of graphs of lines parallel to axes

•  Graph of line ax + by + c = o

Linear equations in two variables

• System of linear equations

• Solution of system of linear equations in two variables(Algebraic methods)

Ratio, proportion and variation

• Introduction to ratio

•  Properties of ratio

•  Properties of equal ratios

• Theorem on equal ratios

•  Percentage as a ratio

•  Introduction to proportion

•  Introduction to variation

•  Revision of concepts based on Direct variation, Inverse variation

•  Mixed variation

•  Real life problems based on ratio, proportion and variation

Statistics 

• Collection of data

• Classification and tabulation of data

• Diagramatic representation of data

• Graphical representation of data

• Mean, median, mode of ungrouped data

                                                                   Geometry 

Lines and Angles

• Introductions to line

• Basic terms and definitions related to line

• Introduction to Euclid's Geometry

•  Plane seperation axiom

•  Introduction to angles in terms of rotation

•  Directed angles, Sexagesimal system

• Types of angles

• zero angle, straight angle,coterminal angle

•  Relation between angles

•  Introduction to mathematical proofs

•  Parallel lines

•  Results on parallel lines and transversal

•  Tests of parallel lines

•  Results on perpendicular lines

•  Distance of a point from a line

Triangles

• Types of triangles

• Terms related to triangle

•  Properties of triangle

•  Exterior angles and corresponding interior opposite angles

•  Results involving exterior angle and corresponding interior opposite angles

•  Similar triangles

Congruence of triangles

• Criteria of congruent triangles

•  Theorem of an isosceles triangle and its converse

•  Perpendicular bisector theorem

•  Angle bisector theorem

•  Properties of triangles based on inequalities

•  Property of perpendicular drawn from a point outside the line.

Circle

• Introduction to circle and related terms

•  Circle passing through the given points

• One and only one circle passes through the three non collinear points.

•  Congruence of circles

•  Properties of chords of the circle

Quadrilateral 

• Properties of quadrilateral

•  Properties of parallelogram

• Properties of rectangle

•  Properties of a trapezium

•  Properties of a rhombus

•  Properties of a square

• Kite

• Tests for particular quadrilateral

•  Theorem on midpoints of two sides of a triangle and its converse

Coordinate Geometry 

• Distance formula

•  Section formula

•  Area of a triangle

Geometric constructions 

• Basic construction - perpendicular bisector of given segment.

• Construction of a triangle - Sum/difference of two sides and base angles is given - Perimeter and base angles are given

Trigonometry

• Introduction to trigonometric ratios

•  Trigonometric Ratios of angles 0o, 30 o, 45 o, 60 o, 90 o

• Trigonometric identities for complementary angles

Mensuration

• Area of triangle

• Area of regular hexagon, polygon

•  Area of quadrilaterals

•  If two parallelograms lie between two parallel lines and have the same base then they have thesame area.

•  If a triangle and a parallelogram have the same base and lie between the same parallel lines, then the area of the triangle is half the area of the parallelogram.

• Perimeter of triangle and quadrilateral

• Area of circle

                                                  General Mathematics

PART-1

Unit I - Arithmetic

1 Variation 

• Introduction

• Types of variation

• Time, work and speed

2 Sequences

• Introduction

• Patterns of numbers

• Progressions

• Arithmetic Progressions

Unit II - Commercial Mathematics

3 Modern marketing techniques

• Discount

• Rebate

• Commission

• Brokerage

• Instalments

4 Taxes and Investments

a. Introduction

b. Sales tax

c. VAT

d. Income Tax

e. Investments

i. Bank investment

ii. Post investment

iii. Life insurance

iv. Shares and Mutual funds

Unit III – Algebra

5 Linear equations in two variables

• Introduction

• Solution of equations in two variables

• Methods of solving linear equations in two variables

6 Quadratic equations

• Introduction

• Solution of quadratic equations

• Methods of solving quadratic equations

PART-2

Unit IV - Geometry

1. Similarity

• Introduction

• Test of similarity

• Properties of similar triangles

• Basic proportionality theorem

• Similarity in right angled triangle.

• Pythagoras theorem statement

• Pythagorian Triplets

• Application of Pythagoras theorem

• Appolloneous theorem

2. Circle

• Introduction

• Terms related to circle

• Properties of chords

• Properties of tangents

• Arc of circle

3. Trigonometry

• Basic concepts in Trigonometry

• Problems related to height and distance

Unit V - Constructions

4. Geometric Constructions

• Construction of incircle of triangle

• Construction of circumcircle of triangle

• Tangents to the circle

• Construction related to design

Unit VI- Mensuration

5. Surface area and volume

• Parallelopiped

• Rectangular parallelopiped

• Cube

• Cylinder Cone

• Sphere and hemisphere

Unit VII - Statistics

6. Statistics 

• Representation of data

• Histogram

• Frequency polygon

• Pie Diagram

• Measures of central tendency for grouped data

• Probability