Entering Class 9 is a big academic change, especially in the case of Mathematics. From algebra and geometry to intricate data handling, the CBSE Class 9 Maths syllabus introduces a new host of ideas, setting the foundation for higher-end mathematics. Achieving top scores, preparing for Olympiads or simply creating a solid foundation of these new ideas - whichever your goal, knowing the syllabus is where you start.
In this study guide, we dissect the complete CBSE Class IX Maths syllabus with tips, weightage of marks, and all you need to not only pass but score high in the finals. So, let's solve the maths mystery and make your path smooth to score high!
The CBSE syllabus of class 9 mathematics is framed in a manner that it develops and challenges the logical reasoning, problem-solving ability and application-based knowledge of students. The syllabus comprises 6 broad mathematical units, which are:
All class 9 maths topics are distributed in equal amounts to achieve the final exam criteria of 80 marks, along with an internal assessment of 20 marks. Here is a chapter-wise explanation of all these topics included under the Class 9 syllabus:
Unit I: Number Systems
1. Real Numbers
1. Review of representation of natural numbers, integers, and rational numbers on the number line. Rational numbers as recurring/ terminating decimals. Operations on real numbers.
2. Examples of non-recurring/non-terminating decimals. Existence of non-rational numbers (irrational numbers) such as , and their representation on the number line. Explaining that every real number is represented by a unique point on the number line and conversely, viz. every point on the number line represents a unique real number.
3. Definition of nth root of a real number.
4. Rationalization (with precise meaning) of real numbers of the type (and their combinations) where x and y are natural number and a and b are integers.
5. Recall of laws of exponents with integral powers. Rational exponents with positive real bases (to be done by particular cases, allowing learners to arrive at the general laws.)
Unit II: Algebra
1. Polynomials
Definition of a polynomial in one variable, with examples and counter examples. Coefficients of a polynomial, terms of a polynomial and zero polynomial. Degree of a polynomial. Constant, linear, quadratic and cubic polynomials. Monomials, binomials, trinomials. Factors and multiples. Zeros of a polynomial. Motivate and State the Remainder Theorem with examples. Statement and proof of the Factor Theorem. Factorization of where a, b and c are real numbers, and of cubic polynomials using the Factor Theorem. Recall of algebraic expressions and identities. Verification of identities:
and their use in factorization of polynomials.
2. Linear Equations In Two Variables
Recall of linear equations in one variable. Introduction to the equation in two variables. Focus on linear equations of the type ax + by + c=0.Explain that a linear equation in two variables has infinitely many solutions and justify their being written as ordered pairs of real numbers, plotting them and showing that they lie on a line.
Unit III: Coordinate Geometry
Coordinate Geometry
The Cartesian plane, coordinates of a point, names and terms associated with the coordinate plane, notations.
Unit IV: Geometry
1. Introduction To Euclid's Geometry
History - Geometry in India and Euclid's geometry. Euclid's method of formalizing observed phenomenon into rigorous Mathematics with definitions, common/obvious notions, axioms/postulates and theorems. The five postulates of Euclid. Showing the relationship between axiom and theorem, for example:
(Axiom) 1. Given two distinct points, there exists one and only one line through them.
(Theorem) 2. (Prove) Two distinct lines cannot have more than one point in common.
2. Lines And Angles
1. (Motivate) If a ray stands on a line, then the sum of the two adjacent angles so formed is 180O and the converse.
2. (Prove) If two lines intersect, vertically opposite angles are equal.
3. (Motivate) Lines which are parallel to a given line are parallel.
3. Triangles
1. (Motivate) Two triangles are congruent if any two sides and the included angle of one triangle is equal to any two sides and the included angle of the other triangle (SAS Congruence).
2. (Prove) Two triangles are congruent if any two angles and the included side of one triangle is equal to any two angles and the included side of the other triangle (ASA Congruence).
3. (Motivate) Two triangles are congruent if the three sides of one triangle are equal to three sides of the other triangle (SSS Congruence).
4. (Motivate) Two right triangles are congruent if the hypotenuse and a side of one triangle are equal (respectively) to the hypotenuse and a side of the other triangle. (RHS Congruence)
5. (Prove) The angles opposite to equal sides of a triangle are equal.
6. (Motivate) The sides opposite to equal angles of a triangle are equal.
4. Quadrilaterals
1. (Prove) The diagonal divides a parallelogram into two congruent triangles.
2. (Motivate) In a parallelogram opposite sides are equal, and conversely.
3. (Motivate) In a parallelogram opposite angles are equal, and conversely.
4. (Motivate) A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and equal.
5. (Motivate) In a parallelogram, the diagonals bisect each other and conversely.
6. (Motivate) In a triangle, the line segment joining the mid points of any two sides is parallel to the third side and in half of it and (motivate) its converse.
5. Circles
1.(Prove) Equal chords of a circle subtend equal angles at the center and (motivate) its converse.
2.(Motivate) The perpendicular from the center of a circle to a chord bisects the chord and conversely, the line drawn through the center of a circle to bisect a chord is perpendicular to the chord.
3. (Motivate) Equal chords of a circle (or of congruent circles) are equidistant from the center (or their respective centers) and conversely.
4.(Prove) The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.
5.(Motivate) Angles in the same segment of a circle are equal.
6.(Motivate) If a line segment joining two points subtends equal angle at two other points lying on the same side of the line containing the segment, the four points lie on a circle.
7.(Motivate) The sum of either pair of the opposite angles of a cyclic quadrilateral is 180° and its converse.
Unit V: Mensuration
1. Areas
Area of a triangle using Heron's formula (without proof)
2. Surface Areas And Volumes (17) Periods
Surface areas and volumes of spheres (including hemispheres) and right circular cones.
Unit VI: Statistics
Statistics
Bar graphs, histograms (with varying base lengths), and frequency polygons.
The internal assessment system makes learning math not merely a matter of memorising formulas. It is an excellent means of testing the performance of the student in terms of consistency, comprehension, and applicability of concepts during the entire academic year instead of one final examination. This is a detailed insight into how 20 marks of internal assessments are allocated:
The 9th class brings a fundamental shift in the way we learn maths, from elementary arithmetic to more systematic, concept-based learning by introducing new subjects. Keeping up with these changes is not possible with textbooks alone; this is where intelligent study and its tools can help. Let's see these intelligent tools to transcend textbooks:
NCERT Exemplar: NCERT Exemplar is tailor-made for students looking to solve tough, application-based problems, which are ideal for solving the critical thinking part of the CBSE maths exam.
Support Material: Authored by government schools, these books carry additional questions, a synopsis, sample papers, and CBSE class 9 maths exam previous year question papers. Students also have the option to download the e-books from online sites.
RD Sharma's Mathematics Class 9,
RS Aggarwal's Math series, and
Arihant's All-in-One Mathematics Class 9th
Looking for a high score in the 9th class maths exam? The first step is always to understand the new syllabus — master it, plan according to it, and create your ideal study plan.
(Session 2025 - 26)