CBSE Class 10

The Central Board of Secondary Education (CBSE) is one of the most prestigious and preferred educational boards in India. It aims to provide a 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 follows the NCERT curriculum.

The CBSE class 10 board exam is undoubtedly the first important exam in an individual’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 helps 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.

Students studying in CBSE board are assessed in two areas: Co-scholastic and Scholastic. The academic year of the Scholastic areas is divided into two terms which are Term 1 and Term 2 and two types of tests which are Formative Assessment and Summative Assessment are conducted to evaluate the academic subjects.

- Formative Assessment: In the primary classes, the formative assessment tests are in the form of oral tests, dictation, homework, class test, projects & assignments, storytelling, elocution, memory test, quiz, etc.
- Summative Assessment: Here students are tested internally. The Summative Assessment (SA) tests are in the form of pen and paper. The tests are conducted by the school. The Summative Assessment is conducted at the end of each term two times each year.

Marks | Number of Questions |
---|---|

1 Mark | 06 |

2 Marks | 06 |

3 Marks | 10 |

4 Marks | 08 |

Total | 30 |

- Real Numbers
- Polynomials
- Pair of Linear Equation in Two Variables
- Quadratic Equations
- Arithmetic Progressions
- Triangles
- Coordinate Geometry
- Introduction to Trigonometry
- Some Applications of Trigonometry
- Circles
- Constructions
- Area related to circles
- Surface area and volumes
- Statistics
- Probability

Unit No. | Unit | Marks |
---|---|---|

I | Number Systems | 06 |

II | Algebra | 20 |

III | Coordinate Geometry | 06 |

IV | Geometry | 15 |

V | Trigonometry | 12 |

VI | Mensuration | 10 |

VII | Statistics and Probability | 11 |

Total | 80 |

Euclid's division lemma, Fundamental Theorem of Arithmetic -, Proofs of results - irrationality of √2, √3, √5, terms of terminating/non-terminating recurring decimals.

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

Pair of linear equations in two variables and their graphical solution. Geometric representation of different possibilities of solutions/inconsistency.

Solution of a pair of linear equations in two variables algebraically - by substitution, by elimination and by cross multiplication method. Simple situational problems must be included. Simple problems on equations reducible to linear equations.

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

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

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

Concepts of coordinate geometry, graphs of linear equations. Distance formula. Section formula (internal division). Area of a triangle.

Definitions, examples, counter examples of similar triangles.

- 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.
- If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side.
- If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar.
- If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar.
- 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.
- 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 each other.
- The ratio of the areas of two similar triangles is equal to the ratio of the squares on their corresponding sides.
- In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.
- In a triangle, if the square on one side is equal to sum of the squares on the other two sides, the angles opposite to the first side is a right triangle.

- The tangent at any point of a circle is perpendicular to the radius through the point of contact.
- The lengths of tangents drawn from an external point to circle are equal.

3. Constructions

- Division of a line segment in a given ratio (internally).
- Tangent to a circle from a point outside it.
- Construction of a triangle similar to a given triangle.

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 (with proofs) of the trigonometric ratios of 30°, 45° and 60°. Relationships between the ratios.

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

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

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 area of segment of a circle, problems should be restricted to central angle of 60°, 90° and 120° only. Plane figures involving triangles, simple quadrilaterals and circle should be taken).

2. Surface Areas and Volumes

(i) Problems on finding surface areas and volumes of combinations of any two of the following: cubes, cuboids, spheres, hemispheres and right circular cylinders/cones. Frustum of a cone.

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

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

Classical definition of probability. Simple problems on single events (not using set notation).

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