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CBSE Class 10

CBSE Class 10 Maths Syllabus

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Mathematics, Class 10 CBSE

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.

Exam Structure and Important Chapters
Syllabus

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
Syllabus
  1. Real Numbers
  2. Polynomials
  3. Pair of Linear Equation in Two Variables
  4. Quadratic Equations
  5. Arithmetic Progressions
  6. Triangles
  7. Coordinate Geometry
  8. Introduction to Trigonometry
  9. Some Applications of Trigonometry
  10. Circles
  11. Constructions
  12. Area related to circles
  13. Surface area and volumes
  14. Statistics
  15. Probability
Exam Structure
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
Unit I: Number Systems
1. Real Numbers

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

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 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.

3. Quadratic Equations

Standard form of a quadratic equation ax2+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.

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
1. Lines (In two-dimensions)

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

Unit IV: Geometry
1. Triangles

Definitions, examples, counter examples of similar triangles.

  1. 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. If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side.
  3. If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar.
  4. If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar.
  5. 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.
  6. 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.
  7. The ratio of the areas of two similar triangles is equal to the ratio of the squares on their corresponding sides.
  8. In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.
  9. 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.
2. Circles
  1. The tangent at any point of a circle is perpendicular to the radius through the point of contact.
  2. The lengths of tangents drawn from an external point to circle are equal.

3. Constructions

  1. Division of a line segment in a given ratio (internally).
  2. Tangent to a circle from a point outside it.
  3. Construction of a triangle similar to a given triangle.
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 (with proofs) of the trigonometric ratios of 30°, 45° and 60°. Relationships between the ratios.

2. Trigonometric Identities

Proof and applications of the identity sin2A + cos2A = 1. Only simple identities to be given. Trigonometric ratios of complementary angles.

3. Heights and Distances

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°.

Unit VI: Mensuration
1. 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 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).

Unit VII: Statistics and Probability
1. Statistics

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

2. Probability

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