# CBSE Class 10 Mathematics Syllabus for Board Exam 2019

For the CBSE Class 10 Maths exam that is going to be conducted tomorrow (March 07, 2019), here we are providing the complete CBSE syllabus. Students must go through the complete syllabus for one last time to check if they don't miss any important topic and know the weightage alloted to various chapters of Maths.

This syllabus is according to the assessment structure that was introduced in class 10 from the last academic session. Under this assessment scheme the board examinations were made mandatory for all students of CBSE Class 10. Now students are assessed on the basis of a final exam in all scholastic subjects which carries 100 marks with an 80 marks component for class 10 Board examination and a 20 marks component for Internal Assessment (IA). IA comprises Periodic Tests (PT) with weightage of 10 marks, Notebook Submission of 5 marks and Subject Enrichment Activities of 5 marks. Students must know the entire syllabus before starting preparing for the exams.

In the CBSE Class 10 Maths syllabus 2019, you will find:

• Topics to be studied during the complete course
• Weightage allotted to each unit
• Question paper design for the board examination
• Components of Internal Assessment
• Prescribed books

Find below the complete syllabus for CBSE Class 10 Mathematics:

CBSE Class 10 Mathematics Unit-Wise Weightage

 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 & PROBABILTY 11 Total 80

CBSE Class 10 Mathematics Sample Paper and Marking Scheme 2019

CBSE Class 10 Mathematics Course Structure:

UNIT I: NUMBER SYSTEMS

1. Real Numbers  (15 Periods)

Euclid’s division lemma, Fundamental Theorem of Arithmetic - statements after  reviewing work done earlier and after illustrating and motivating through examples, Proofs of irrationality of Decimal representation of rational numbers in terms of terminating/non-terminating recurring decimals.

UNIT II: ALGEBRA

1. Polynomials  (7 Periods)

Zeros of a polynomial. Relationship between zeros and coefficients of quadratic polynomials. Statement and simple problems on division algorithm for polynomials with real coefficients.

CBSE Class 10 Mathematics Solved Sample Paper 2019

2. Pair of Linear Equations in Two Variables (15 Periods)

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

Algebraic conditions for number of solutions. Solution of a pair of linear equations in two variables algebraically - by substitution, by elimination and by cross multiplication method. Simple situational problems. Simple problems on equations reducible to linear equations.

3. Quadratic Equations (15 Periods)

Standard form of a quadratic equation ax2 + bx + c = 0, (a ≠ 0). Solutions of 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 (8 Periods)

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

CBSE Class 10 Mathematics Exam 2019: Important questions with solutions

UNIT III: COORDINATE GEOMETRY

1. Lines (In two-dimensions) (14 Periods)

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

UNIT IV: GEOMETRY

1. Triangles (15 Periods)

Definitions, examples, 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.

6. (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 each other.

7. (Prove) The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.

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

9. (Prove) 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 angle.

CBSE Class 10 Mathematics Previous Years' Solved Question Papers (2010-2018)

2. Circles (8 Periods)

Tangent to a circle at, 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.

3. Constructions (8 Periods)

1. Division of a line segment in a given ratio (internally).

2. Tangents 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 (10 Periods)

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

2. Trigonometric Identities (15 Periods)

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

3.  Heights and Distances: Angle of elevation, Angle of Depression. (8 Periods)

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

UNIT VI: MENSURATION

1. Areas Related to Circles (12 Periods)

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 (12 Periods)

1. 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.

2. 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 (18 Periods)

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

2. Probability (10 Periods)

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

QUESTIONS PAPER DESIGN 2017–18

CLASS–X

Mathematics (Code No. 041)            Time : 3 hrs                                         Marks: 80

 Typology of Questions Number of questions of different types Total Marks Remembering (Knowledge based- Simple recall questions, to know specific facts, terms, concepts, principles or theories; Identify, define, or recite, information) VSA – 2 20 SA (I) - 2 SA (II) - 2 LA - 2 Understanding (Comprehension- to be familiar with meaning and to understand conceptually, interpret, compare, contrast, explain, paraphrase, or interpret information) VSA – 2 23 SA (I) – 1 SA (II) – 1 LA - 4 Application (Use abstract information in concrete situation, to apply knowledge to new situation; Use given content interpret a situation, provide example, or solve a problem) VSA – 2 19 SA (I) – 2 SA (II) – 3 LA - 1 Higher Order Thinking Skills (Analysis & Synthesis-Classify,compare, contrast, or differentiate between different pieces of information; Organize and /or integrate unique pieces of information from  variety of sources) VSA - None 14 SA (I) – 1 SA (II) – 4 LA - None Evaluation ( Judge, and/or justify the value or worth of a decision or outcome, or to predict outcomes based on values) VSA – None 4 SA (I) – None SA (II) – None LA -1 Total 80

Abbreviations used are:

VSA: Very Short Answer (1 Mark)

SA (I): Short Answer –I (2 Marks)

SA (II): Short Answer –II (3 Marks)

LA (I): Long Answer (4 Marks)

NCERT Solutions for CBSE Class 10 Maths: All Chapters

 Internal Assessment 20 Marks Periodical Test 10 Marks Note Book Submission 05 Marks Lab Practical (Lab activities to be done from the prescribed books) 05 Marks

PRESCRIBED BOOKS:

 1. Mathematics - Textbook for class X - NCERT Publication 2. Guidelines for Mathematics Laboratory in Schools, class X - CBSE Publication 3. Laboratory Manual - Mathematics, secondary stage - NCERT Publication 4. Mathematics exemplar problems for class X, NCERT publication.

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