Board | CBSE |

Class | 9 |

Session | 2023-24 |

Subject | Mathematics (041) |

Type | Syllabus |

Official Website | https://cbseacademic.nic.in |

**MATHEMATICS (Code No. 041)**

**CLASS – IX (2023-24)**

- Theory - 80 Marks
- Internal Assessment - 20 Marks

COURSE STRUCTURE CLASS –IX

Units | Unit Name | Marks |

I | Number Systems | 10 |

II | Algebra | 20 |

III | Coordinate Geometry | 04 |

IV | Geometry | 27 |

V | Mensuration | 13 |

VI | Statistics & Probability | 06 |

Total | 80 |

**UNIT I: NUMBER SYSTEMS**

**REAL NUMBERS**

- Review of representation of natural numbers, integers, and rational numbers on the number line. Rational numbers as recurring/ terminating decimals. Operations on real numbers.
- Examples of non-recurring/non-terminating decimals. Existence of non-rational numbers (irrational numbers) such as √2, √3 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.
- Definition of nth root of a real number.
- Rationalization (with precise meaning) of real numbers of the type
^{1}/_{a+b√x }and^{1}/_{√x + √y }(and their combinations) where x and y are natural numbers and a and b are integers. - Recall of laws of exponents with integral powers. Rational exponents with positive real bases (to be done by particular cases, allowing the learner to arrive at the general laws.)

**UNIT II: ALGEBRA **

**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 *ax*^{2 }*+ bx + c, a ≠ 0 *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 the factorization of polynomials.

**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, and notations.

**UNIT IV: GEOMETRY**

**INTRODUCTION TO EUCLID'S GEOMETRY**

History - Geometry in India and Euclid's geometry. Euclid's method of formalizing observed phenomena 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.

**LINES AND ANGLES**

- (Motivate) If a ray stands on a line, then the sum of the two adjacent angles so formed is 180° and the converse.
- (Prove) If two lines intersect, vertically opposite angles are equal.
- (Motivate) Lines which are parallel to a given line are parallel.

**TRIANGLES **

- (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).
- (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).
- (Motivate) Two triangles are congruent if the three sides of one triangle are equal to the three sides of the other triangle (SSS Congruence).
- (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)
- (Prove) The angles opposite to equal sides of a triangle are equal.
- (Motivate) The sides opposite to equal angles of a triangle are equal.

**QUADRILATERALS**

- (Prove) The diagonal divides a parallelogram into two congruent triangles.
- (Motivate) In a parallelogram opposite sides are equal, and conversely.
- (Motivate) In a parallelogram opposite angles are equal, and conversely.
- (Motivate) A quadrilateral is a parallelogram if a pair of opposite sides are parallel and equal.
- (Motivate) In a parallelogram, the diagonals bisect each other conversely.
- (Motivate) In a triangle, the line segment joining the midpoints of any two sides is parallel to the third side and in half of it and (motivate) its converse.

**CIRCLES**

- (Prove) Equal chords of a circle subtend equal angles at the center and (motivate) its converse.
- (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.
- (Motivate) Equal chords of a circle (or of congruent circles) are equidistant from the center (or their respective centers) and conversely.
- (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.
- (Motivate) Angles in the same segment of a circle are equal.
- (Motivate) If a line segment joining two points subtends equal angles at two other points lying on the same side of the line containing the segment, the four points lie on a circle.
- (Motivate) The sum of either of the pair of opposite angles of a cyclic quadrilateral is 180° and its converse.

**UNIT V: MENSURATION **

**AREAS**

Area of a triangle using Heron's formula (without proof)

**SURFACE AREAS AND VOLUMES**

Surface areas and volumes of spheres (including hemispheres) and right circular cones.

**UNIT VI: STATISTICS & PROBABILITY **

** STATISTICS**

Bar graphs, histograms (with varying base lengths), and frequency polygons.

Download Class 9 Mathematics Syllabus for 2023-24 [PDF]

**Deleted Topics from Class 9 NCERT Maths:**

Chapter | Page No. | Dropped Topics/Chapter |

Chapter 1: Number Systems | 15-18 27 |
1.4 Representing real numbers on the number line |

Chapter 2: Polynomials | 35-40 50 |
2.4 Remainder theorem |

Chapter 3: Coordinate Geometry | 61-65 | 3.3 Plotting a point in the plane if its coordinates are given |

Chapter 4: Linear Equations in Two Variables | 70-75 75-77 |
4.4 Graph of linear equations in two variables 4.5 Equations of lines parallel–x-axis and y-axis |

Chapter 5: Introduction– Euclidean Geometry | 86-88 | 5.3 Equivalent versions of Euclid’s fifth postulate |

Chapter 6: Lines and Angles | 98-100 103 105-108 |
6.5 Parallel lines and a transversal 6.7 Angle sum property of a triangle |

Chapter 7: Triangles | 129-134 | 7.6 Inequalities in triangles |

Chapter 8: Quadrilaterals | 135-138 145-147 151 |
8.1 Introduction 8.2 Angle sum property of a quadrilateral 8.3 Types of quadrilaterals 8.5 Another condition for a Quadrilateral–be a parallelogram |

Chapter 9: Areas of Parallelogram and Triangles | 152-167 | Full chapter |

Chapter 10: Circles | 168 169-171 174-176 186-187 |
10.1 Introduction 10.2 Circles and its related terms: Review Circle through three points |

Chapter 11: Construction | 188-196 | Full chapter |

Chapter 12: Heron’s Formula | 197-199 203-207 |
12.1 Introduction 12.3 Application of Heron’s formula in finding areas of quadrilaterals |

Chapter 13: Surface Area and Volume | 208-217 226-231 236-237 |
13.1 Introduction 13.2 Surface area of a cuboid and cube 13.3 Surface area of right circular cylinder 13.6 Volume of cuboid 13.7 Volume of cylinder |

Chapter 14: Statistics | 238-246 261-270 |
14.1 Introduction 14.2 Collection of data 14.3 Presentation of data 14.5 Measure of central tendency 14.6 Summary |

Chapter 15: Probability | 271-285 | Full chapter |

Also See:CBSE Class 9 English Language & Literature Syllabus for 2023-24 CBSE Class 9 Science Syllabus for 2023-24 CBSE Class 9 Social Science Syllabus for 2023-24 |