# CBSE Class 10 Syllabus Maths

The Central Board of Secondary Education (CBSE) is one of the most prestigious and preferred educational boards in India. It aims to provide holistic and healthy education to all its learners so that students can get adequate space to develop mentally and physically. CBSE is known for its comprehensive syllabus and well structured exam pattern which helps students to get a detailed idea about the entire curriculum. There are around 20,102 schools under the board which follow the NCERT curriculum.

The CBSE class 10 board exam is undoubtedly the first important exam in an individualâ€™s life because this phase of life shapes the future of the students for their next successive years. The CBSE class 10 board exam is the first nationalised external exam that the students undertake and hence gives a nightmare to many students appearing for the exam.

The subjects are designed very strategically and help the students to get influenced by the lessons and knowledge imparted to them. The subjects, especially science and maths require the students to get completely immersed in them and enjoy learning along with gathering knowledge.

**COURSE STRUCTURE**

**CLASS â€“X (2021-22)**

**FIRST TERM**

**Time: 90 Minutes**

NO. |
UNIT NAME |
MARKS |

I | NUMBER SYSTEMS | 6 |

II | ALGEBRA | 10 |

III | COORDINATE GEOMETRY | 6 |

IV | GEOMETRY | 6 |

V | TRIGONOMETRY | 5 |

VI | MENSURATION | 4 |

VII | STATISTICS & PROBABILITY | 3 |

Â |
Total |
40 |

INTERNAL ASSESSMENT | 10 | |

Â |
TOTAL |
50 |

INTERNAL ASSESSMENT |
MARKS |
TOTAL MARKS |

Periodic Tests | 3 | |

Multiple Assessments | 2 | |

Portfolio | 2 | 10 marks for the term |

Student Enrichment Activities-practical work | 3 |

**UNIT-NUMBER SYSTEMS**

**1. REAL NUMBER**

Fundamental Theorem of Arithmetic – statements after reviewing work done earlier and after illustrating and motivating through examples. The decimal representation of rational numbers in terms of terminating/non-terminating recurring decimals.

**UNIT-ALGEBRA**

**2. POLYNOMIALS**

Zeroes of a polynomial. Relationship between zeroes and coefficients of quadratic polynomials only.

**3. 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 a number of solutions. Solution of a pair of linear equations in two variables algebraically – by substitution and by elimination. Simple situational problems. Simple problems on equations are reducible to linear equations.

**UNIT-COORDINATE GEOMETRY**

**4. COORDINATE GEOMETRY**

LINES (In two dimensions)

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

**UNIT-GEOMETRY**

**5. TRIANGLES**

Definitions, examples, counterexamples of similar triangles.

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

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

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

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

(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 areÂ similar.

(Motivate) If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse, the triangles on each side of the perpendicular are similar to the whole triangle and to eachÂ other.

(Motivate) The ratio of the areas of two similar triangles is equal to the ratio of the squares of their correspondingÂ sides.

(Prove) In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other twoÂ sides.

(Motivate) In a triangle, if the square on one side is equal to the sum of the squares on the other two sides, the angle opposite to the first side is a right angle.

**UNIT- TRIGONOMETRY**

**6. INTRODUCTION TO TRIGONOMETRY**

Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined). Values of the trigonometric ratios of $30^{circ}, 45^{circ}$ and $60^{circ} .$ Relationships between the ratios.

TRIGONOMETRIC IDENTITIES

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

**UNIT-MENSURATION**

**7. AREAS RELATED TO CIRCLES**

Motivate the area of a circle, 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 angle of $60^{circ}$ and $90^{circ}$ only. Plane figures involving triangles, simple quadrilaterals, and circles should be taken.)

**Â **

**UNIT- STATISTICS & PROBABILITY**

**8. PROBABILITY**

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

**Â **

**SECOND TERM**

NO. |
UNIT NAME |
MARKS |

I | ALGEBRA(Cont.) | 10 |

II | GEOMETRY(Cont.) | 9 |

III | TRIGONOMETRY(Cont.) | 7 |

IV | MENSURATION(Cont.) | 6 |

V | STATISTICS & PROBABILITY(Cont.) | 8 |

Â |
Total |
40 |

INTERNAL ASSESSMENT | 10 | |

Â |
TOTAL |
50 |

**UNIT-ALGEBRA**

**1. QUADRATIC EQUATIONS**

Standard form of a quadratic equation $a x^{2}+b x+c=0,(a neq 0)$. Solutions of

quadratic equations (only real roots) by factorization, and by using quadratic

formula. Relationship between discriminant and nature of roots. Situational

problems based on quadratic equations related to day-to-day activities (problems on equations reducible to quadratic equations are excluded)

**Â 2. 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. (Applications based on the sum to n terms of an A.P. are excluded)

**Â **

**UNIT- GEOMETRY**

**3. CIRCLES**

Tangent to a circle at, point of contact

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

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

**4. CONSTRUCTIONS**

Division of a line segment in a given ratioÂ (internally).

Tangents to a circle from a point outsideÂ it.

**UNIT-TRIGONOMETRY**

**5. SOME APPLICATIONS OF TRIGONOMETRY**

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 $30^{circ}, 45^{circ}, 60^{circ}$.

**UNIT-MENSURATION**

**6. 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.

Problems involving converting one type of metallic solid into another and other mixed problems. (Problems with combination of not more than two different solids beÂ taken).

**UNIT-STATISTICS & PROBABILITY**

**7. STATISTICS**

Mean, median, and mode of grouped data (bimodal situation to be avoided). Mean by Direct Method and Assumed Mean Method only

INTERNAL ASSESSMENT |
MARKS |
TOTAL MARKS |

Periodic Tests | 3 | 10 marks for the term |

Multiple
Assessments |
2 | |

Portfolio | 2 | |

Student Enrichment Activities-practical
work |
3 |

**PRESCRIBED BOOKS**

Mathematics – Textbook for Class IX – NCERT Publication

Mathematics – Textbook for Class X – NCERT Publication

Guidelines for Mathematics Laboratory in Schools, class IX – CBSEÂ Publication

Guidelines for Mathematics Laboratory in Schools, class X – CBSEÂ Publication

Laboratory Manual – Mathematics, secondary stage – NCERTÂ Publication

Mathematics exemplar problems for class IX, NCERTÂ publication.

Mathematics exemplar problems for class X, NCERTÂ publication.