Syllabus Of Grade IX - Mathematics (ME904)

The Mathematics syllabus for Grade IX is organised into ten core units. Each unit builds conceptual understanding, logical reasoning and problem-solving skills. Separate marks are given with each unit and together they form a 3-hour examination of 100 marks.

Total Marks: 100Time: 3 HoursSeparate marks are given with each unit.

Across all units, learners engage with: number systems, algebra, coordinate geometry, geometry, mensuration, trigonometry, statistics and probability through structured concepts and real-life applications.

Unit-wise Summary

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Unit	Area Covered	Marks	Read More
Unit 1	Number System and Number Sense	5	Read more
Unit 2	Algebra (core)	10	Read more
Unit 3	Coordinate Geometry (core)	15	Read more
Unit 4	Lines, Angles and Triangles (core)	20	Read more
Unit 5	Quadrilaterals and Area of Parallelograms & Triangles (core)	5	Read more
Unit 6	Circle (core)	15	Read more
Unit 7	Area of Plane Figures and Solid Shapes (core)	10	Read more
Unit 8	Volume of Solids (core)	5	Read more
Unit 9	Introduction to Trigonometry (core)	10	Read more
Unit 10	Introduction to Statistics and Probability (core)	5	Read more
Time: 3 Hours		Total Marks	100

Grade IX · Mathematics · Unit 1

Number System and Number Sense (5 Marks)

5 Marks

Review and recall

Natural, whole numbers and integers and their representation on the number line.
Basic laws of exponents.

Rational and irrational numbers

Definition of rational numbers as p/q where p, q are integers and q ≠ 0.
Difference between rational numbers and fractions.
Number line representation and symbol Q for the rational number system.
Idea of irrational numbers and symbol used for them.
Decimal representation of rational (terminating / recurring) and irrational (non-terminating, non-recurring) numbers.

Real numbers

Real numbers as the set containing both rational and irrational numbers.
Use of symbol R for the real number system.
Representation of real numbers on the number line.
Understanding that both rational and irrational numbers are infinite in number.

Algebra of real numbers

Operations on rational numbers - sum, difference, product and quotient.
Sum, difference, product and quotient of irrational numbers (where defined).
Properties of rational numbers under addition and multiplication.
Properties of real numbers under addition and multiplication.

Grade IX · Mathematics · Unit 2

Algebra (core) (10 Marks)

10 Marks

Review & recall

Idea of variables, constants, algebraic expressions and equations.

Polynomials

Definition and degree of a polynomial in one variable.
Classification by number of terms - monomial, binomial, trinomial etc.
Classification by degree - linear, quadratic and higher degree polynomials.

Algebra of polynomials

Addition, subtraction, multiplication and division of polynomials.
Division algorithm for polynomials.
Factor and remainder theorems and simple applications.

Algebraic identities and factorisation

Difference between a polynomial, an equation and an identity.
Use and verification of standard identities such as (a + b + c)², a⁴ − b⁴, a³ − b³, a³ + b³ etc.
Factorisation by common factors and by splitting the middle term.
Factorisation using the above identities.

Linear & quadratic forms

Linear equations in one variable, solution and representation on the number line.
Translating word problems into linear equations.
Simple linear inequalities in one variable and their representation on the number line.
Idea of a quadratic equation in one variable and checking a given solution.

Patterns

Recognition and extension of number patterns and simple geometric patterns.

Grade IX · Mathematics · Unit 3

Coordinate Geometry (core) (15 Marks)

15 Marks

Cartesian system

Axes, origin, quadrants, abscissa, ordinate and ordered pairs.
Cartesians coordinates and the idea of independent and dependent variables.

Points in a plane

Writing coordinates of a point in the plane.
Plotting points for a given ordered pair.

Linear graphs

Graphs of x = constant, y = constant and y = mx + c.
Gradient (slope) of a line as ‘rise over run’.
Relationship between gradients of parallel straight lines.

Simultaneous linear equations

Graphical representation of two linear equations in the same plane.
Point of intersection as the solution of the simultaneous equations (when it exists).

Interpretation of graphs

Reading and interpreting graphs from real-life contexts such as travel and conversion graphs.
Graphs of quantities that change with time.

Scatter diagrams

Plotting pairs of values on a scatter diagram.
Visual recognition of positive or negative correlation.

Grade IX · Mathematics · Unit 4

Lines, Angles and Triangles (core) (20 Marks)

20 Marks

Basic geometrical ideas

Point, line, line segment, collinear and non-collinear points.
Angles - right, acute, obtuse, straight, reflex; complementary and supplementary angles.
Parallel and perpendicular lines, transversal.
Types of triangles - scalene, isosceles, equilateral, acute, right and obtuse angled.
Median, altitude, angle bisector and perpendicular bisector.

Lines and angles

Adjacent angles, linear pairs and vertically opposite angles.
Linear pair axiom.
Exterior, interior, corresponding and alternate interior angles for a transversal.
Properties of parallel lines with a transversal and their converses.
Sum of interior angles of a triangle and exterior angle property (with proofs).

Triangles and congruence

Congruence criteria - SSS, SAS, ASA, RHS.
Properties of isosceles triangles and their converses.
Angles of an equilateral triangle.

Grade IX · Mathematics · Unit 5

Quadrilaterals and Area of Parallelograms & Triangles (core) (5 Marks)

5 Marks

Basic terms and types

Polygons, convex and concave polygons; quadrilaterals and their parts.
Types of quadrilaterals - square, rectangle, parallelogram, rhombus, trapezium, isosceles trapezium and kite.
Base and altitude of a parallelogram.

Properties of parallelograms

Opposite sides equal and parallel, diagonals bisecting each other - and converses.
Special parallelograms - rectangle, rhombus and square - and their diagonal properties.
Simple problems based on these properties.

Mid-point theorem

Line joining midpoints of two sides of a triangle is parallel to the third side and half of it.
Corollary about a line through the midpoint parallel to another side bisecting the third side.

Area of parallelograms & triangles

Diagonal of a parallelogram divides it into two triangles of equal area.
Parallelograms on the same base and between the same parallels have equal area.
Relationship of areas of a triangle and a parallelogram on the same base and parallels.
Area of a parallelogram as base × corresponding height.
Area of a triangle as ½ × base × corresponding height.

Grade IX · Mathematics · Unit 6

Circle (core) (15 Marks)

15 Marks

Basic circle concepts

Circle, centre, radius, diameter and circular region.
Interior, exterior and boundary points.
Chord, arc, segments, sectors and semicircular region.
Circumference and angles subtended at the centre or on the circle.
Concentric, intersecting and congruent circles; concyclic points.

Angles & chords

Equal chords subtend equal angles at the centre.
Equal angles at the centre correspond to equal chords.

Perpendicular from centre

Perpendicular from the centre to a chord bisects the chord.
Line through the centre bisecting a chord is perpendicular to the chord.

Grade IX · Mathematics · Unit 7

Area of Plane Figures and Solid Shapes (core) (10 Marks)

10 Marks

Basic ideas

Perimeter and area of plane figures.
Curved surface area and total surface area of solid shapes.

Area of plane figures

Area of right, isosceles and equilateral triangles.
Area of rectangle, square, parallelogram, rhombus and trapezium.

Heron’s formula

Using Heron’s formula to find area of a triangle.
Application to find area of a quadrilateral by splitting into triangles.

Surface area of solids

Surface area of cube and cuboid.
Curved surface area and total surface area of cylinder, cone, sphere and hemisphere.

Applications

Using area concepts in everyday contexts like fields and land.

Grade IX · Mathematics · Unit 8

Volume of Solids (core) (5 Marks)

5 Marks

Idea of volume

Volume as area of base × height for right solids.

Basic solids

Volume of cubes and cuboids.
Simple applications to given dimensions.

Cylinders and cones

Volume of a right circular cylinder including hollow cylinders.
Metal volume required for casting and pipes.
Volume of a right circular cone and relation with cylinder of same base and height.

Spheres

Volume of sphere and hemisphere for a given radius.

Grade IX · Mathematics · Unit 9

Introduction to Trigonometry (core) (10 Marks)

10 Marks

What is trigonometry?

Study of right-angled triangles using relations between sides and angles.

Trigonometric ratios

Right-angled triangle terms - hypotenuse, adjacent and opposite sides.
Definition of sine, cosine and tangent as ratios of sides.
Standard values of trigonometric ratios for 30°, 45° and 60°.

Angles of elevation & depression

Idea of viewing angles from horizontal line of sight.
Drawing simple figures involving one right-angled triangle for such situations.

Grade IX · Mathematics · Unit 10

Introduction to Statistics and Probability (core) (5 Marks)

5 Marks

Introduction to statistics

Why we collect, organise and interpret data.
Meaning of statistics in everyday context.

Types and classification of data

Primary and secondary data.
Ungrouped and grouped data, class interval, class mark, upper and lower limits, range and cumulative frequency.
Discrete vs continuous data.

Analysis of data

Measures of central tendency - mean, median and mode (for ungrouped data).
Reading bar graphs, histograms of equal width and frequency polygons.

Introduction to probability

Chance of occurrence of events in simple experiments.
Basic terms - experiment, sample space, event, favourable outcomes, sure and impossible events.
Classical definition of probability as P(E) = n/N.