 ## CBSE Class 10th Math Syllabus 2022

Mathematics is one of the crucial subject for class 10th students to secure good percentage in the CBSE Class 10th Academic exam also one of the toughest subject to score. With a hard practice students can  score best marks.

Securing good marks in class 10th students need to go through CBSE Class 10th Math Syllabus 2022 for brief subject wise marks and internal assessment marks.

### CBSE Class 10th Math Syllabus 2022 (TERM - 1)

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

TOTAL

40

INTERNAL ASSESSMENT

10

GRAND 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 1- NUMBER SYSTEM

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

### UNIT 2-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 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 reducible to linear

### UNIT 3-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 4-GEOMETRY

5. TRIANGLES
Definitions, examples, counter examples of similar triangles.

• (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.
• (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 are 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 are 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 each other.
• (Motivate) The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.
• (Prove) In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.
• (Motivate) In a triangle, if the square on one side is equal to sum of the squares on the other two sides, the angle opposite to the first side is a right angle.

### UNIT 5- 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 300 , 450 and 600. Relationships between the ratios.
TRIGONOMETRIC IDENTITIES
Proof and applications of the identity sin2A + cos2A = 1. Only simple identities to be given.

### UNIT 6-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 area of segment of a circle, problems should be restricted to central angle of 60° and 90° only.
Plane figures involving triangles, simple quadrilaterals and circle should be taken.)

### UNIT 7- STATISTICS & PROBABILITY

8. PROBABILITY
Classical definition of probability. Simple problems on finding the probability of an event.

### CBSE Class 10th Math Syllabus 2022 (TERM - 2)

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

TOTAL

40

INTERNAL ASSESSMENT

10

GRAND 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-ALGEBRA

(10) Periods
Standard form of a quadratic equation ax2 + bx + c = 0, (a ≠ 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)
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 sum to n terms of an A.P. are excluded)

### UNIT- GEOMETRY

3. CIRCLES
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.
4. CONSTRUCTIONS
1. Division of a line segment in a given ratio (internally).
2. Tangents to a circle from a point outside 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°, 45°, 60°.

### UNIT-MENSURATION

6. SURFACE AREAS AND VOLUMES
1. Surface areas and volumes of combinations of any two of the following: cubes,cuboids, spheres, hemispheres and right circular cylinders/cones.
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-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.

### PRESCRIBED BOOKS

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