Board | CBSE |

Class | 10 |

Session | 2023-24 |

Subject | Mathematics (041) |

Type | Syllabus |

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

**MATHEMATICS (Code No. 041)**

**CLASS – X (2023-24)**

- Theory – 80 Marks
- Internal Assessment – 20 Marks

**COURSE STRUCTURE CLASS –X**

Units | Unit Name | Marks |

I | Number Systems | 06 |

II | Algebra | 20 |

III | Coordinate Geometry | 06 |

IV | Geometry | 15 |

V | Trigonometry | 12 |

VI | Mensuration | 10 |

VII | Statistics & Probability | 11 |

Total | 80 |

**UNIT I: NUMBER SYSTEMS**

**1. REAL NUMBER**

Fundamental Theorem of Arithmetic - statements after reviewing work done earlier and after illustrating and motivating through examples, Proofs of the irrationality of √2, √3, √5.

**UNIT II: ALGEBRA**

**1.** **POLYNOMIALS**

Zeros of a polynomial. Relationship between zeros and coefficients of quadratic polynomials.

**2.** **PAIR OF LINEAR EQUATIONS IN TWO VARIABLES**

Pair of linear equations in two variables and graphical method of their solution, consistency/inconsistency.

Algebraic conditions for the number of solutions. Solution of a pair of linear equations in two variables algebraically - by substitution, by elimination. Simple situational problems.

**3.** **QUADRATIC EQUATIONS**

The standard form of a quadratic equation *ax ^{2} + bx + c = 0, (a ≠ 0). *Solutions of quadratic equations (only real roots) by factorization, and by using the quadratic formula. Relationship between discriminant and nature of roots.

Situational problems based on quadratic equations related to day-to-day activities to be incorporated.

**4.** **ARITHMETIC PROGRESSIONS**

Motivation for studying Arithmetic Progression Derivation of the nth term and sum of the first n terms of A.P. and their application in solving daily life problems.

**UNIT III: COORDINATE GEOMETRY**

**COORDINATE GEOMETRY**

**Review: **Concepts of coordinate geometry, graphs of linear equations. Distance formula. Section formula (internal division).

**UNIT IV: GEOMETRY**

**1.** **TRIANGLES**

Definitions, examples, and counter examples of similar triangles.

1. (Prove) If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.

2. (Motivate) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side.

3. (Motivate) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar.

4. (Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar.

5. (Motivate) If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are proportional, the two triangles are similar.

**2.** **CIRCLES**

Tangent to a circle at the point of contact

1. (Prove) The tangent at any point of a circle is perpendicular to the radius through the point of contact.

2. (Prove) The lengths of tangents drawn from an external point to a circle are equal.

**UNIT V: TRIGONOMETRY**

**1.** **INTRODUCTION TO TRIGONOMETRY**

Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined); motivate the ratios whichever are defined at 0° and 90°. Values of the trigonometric ratios of 30°, 45°, and 60°. Relationships between the ratios.

**2.** **TRIGONOMETRIC IDENTITIES**

Proof and applications of the identity sin^{2}A + cos^{2}A = 1. Only simple identities are to be given.

**3. HEIGHTS AND DISTANCES: Angle of elevation, Angle of Depression.**

Simple problems on heights and distances. Problems should not involve more than two right triangles. Angles of elevation/depression should be only 30°, 45°, and 60°.

**UNIT VI: MENSURATION**

**1.** **AREAS RELATED TO CIRCLES**

Area of sectors and segments of a circle. Problems based on areas and perimeter /circumference of the above-said plane figures. (In calculating the area of a segment of a circle, problems should be restricted to the central angles of 60°, 90°, and 120° only.

**2.** **SURFACE AREAS AND VOLUMES**

Surface areas and volumes of combinations of any two of the following: cubes, cuboids, spheres, hemispheres, and right circular cylinders/cones.

**UNIT VII: STATISTICS AND PROBABILITY**

**1. ****STATISTICS**

Mean, median, and mode of grouped data (bimodal situation to be avoided).

**2.** **PROBABILITY**

The classical definition of probability. Simple problems in finding the probability of an event.

**List of Deleted Topics from NCERT:**

Chapter | Page No. | Dropped Topics/Chapter |

Chapter 1: Real Number | 2-7 15-18 |
1.2 Euclid’s division lemma 1.5 Revisiting rational numbers and their decimal expansions |

Chapter 2: Polynomials | 33-37 | 2.4 Division algorithm for polynomials |

Chapter 3: Pair of Linear Equations in Two Variables | 39-46 57-69 |
3.2 Pair of linear equations in two variables 3.3 Graphical method of solution of a pair of linear equations 3.4.3 Cross-multiplication method 3.5 equation reducible to a pair of linear equations in two variables |

Chapter 4: Quadratic Equations | 76-88 91-92 |
4.4 Solution of a quadratic equation by completing the squares |

Chapter 6: Triangles | 141-144 144-154 |
6.5 Areas of similar triangles 6.6 Pythagoras theorem |

Chapter 7: Coordinate Geometry | 168-172 | 7.4 Area of a triangle |

Chapter 8: Introduction to Trigonometry | 187-190 193-194 |
8.4 Trigonometric ratios of complementary angles |

Chapter 9: Some Applications of Trigonometry | 195-196 205 |
9.1 Introduction |

Chapter 11: Construction | 216-222 | 11.1Introduction 11.2 Division of a line segment 11.3 Construction of tangents to a circle 11.4 Summary |

Chapter 12: Areas Related to Circles | 223 224-226 231-238 |
12.1 Introduction 12.2 Perimeter and area of a circle — A review 12.4 Areas of combinations of plane figures |

Chapter 13: Surface Areas and Volumes | 248-252 252-259 |
13.4 Conversion of solid from one shape to another 13.5 Frustum of a cone |

Chapter 14: Statistics | 289-294 | 14.5 Graphical representation of cumulative frequency distribution |

Chapter 15: Probability | 295-296 311-312 |
15.1 Introduction Exercise 15.2 (Optional) |

Good guidance

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