# CBSE Class 10 Mathematics Syllabus for 2021-22

On July 22, 2021, CBSE finalised the reduction in syllabus for the 2021-22 session as per the latest Term-based Examination Pattern.

CBSE Class 10 Syllabus has undergone drastic changes since the previous 2020-21 session. Due to the COVID-19 pandemic, the education system has been challenging for both teachers and students.

So, similar to the 30% reduction in the last session, CBSE decided to reduce the overall syllabus according to the Term-based Board Examination for the 2021-22 session again.

We, at Educart, were prompt about it and have updated the changes in all the subjects for you. Here, you can find:

• simple analysis of all the deleted topics/ chapters for 2021-22 Term-based Board Exam.

With all this information in hand, both teachers and students will have a defined structure to begin the learning process on time and efficiently.

Class 10 Mathematics Reduced Syllabus for 2021-22 (Reduced)

We have also provided the syllabus for the 2021-22 session that was previously restored so that you can compare the deleted and added topics.

Class 10 Mathematics Syllabus for 2021-22 (Restored Previously)

Now, let us take a look at the syllabus for Term I and Term II Board Exams in detail and try to understand what changes have been made.

Units Unit Name Marks
Term I Term II
I Number Systems 06 -
II Algebra 10 10
III Coordinate Geometry 06 -
IV Geometry 06 09
V Trigonometry: Introduction 05 -
Trigonometry: Applications - 07
VI Mensuration 04 06
VII Statistics & Probability: Probability 03 -
Statistics & Probability: Statistics - 08
INTERNAL ASSESSMENT
(Periodic Tests (03) + Multiple Assessments (02) +
Portfolio (02) + Student Enrichment Activities/
Practical Work (03))
10 10
TOTAL 100

## TERM I

<red> Marked in red: <red> Topics <red> removed <red> for 2021-22

### Unit I: Number Systems

1. Real Numbers

• <red> Euclid’s division lemma <red>
• Fundamental Theorem of Arithmetic - statements after reviewing work done earlier and after illustrating and motivating through examples.
• <red> Proofs of irrationality of √2, √3, √5. <red> Decimal representation of rational numbers in terms of terminating/non-terminating recurring decimals.

### Unit II: Algebra

2. Polynomials

• Zeros of a polynomial
• Relationship between zeros and coefficients of quadratic polynomials
• <red> Statement and simple problems on division algorithms for polynomials with real coefficients. <red>

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, by elimination and <red> by cross multiplication method. <red>
• Simple situational problems. Simple problems on equations reducible to linear equations.

### Unit III: Coordinate Geometry

6. Lines

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

### Unit IV: Geometry

7. 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.
• (Prove) The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.
<green> (This topic was removed for the previous session i.e. 2020-21 but now it is added back for the 2021-22 session.) <green>
• (Prove) In a right triangle, the square on the hypotenuse is equal to the sum of  the squares on the other two sides, other two sides, the angles opposite to the first side is a right angle.
• (Prove) 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.
<green> (This topic was removed for the previous session i.e. 2020-21 but now it is added back for the 2021-22 session.) <green>

### Unit V: Trigonometry

10. Introduction to Trigonometry

• Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined).
• <red> Motivate the ratios whichever are defined at 0° and 90°. <red>
• Values of the trigonometric ratios of 30°, 45° and 60°. Relationships between the ratios.

11. Trigonometric Identities

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

### Unit VI: Mensuration

13. 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 the segment of a circle, problems should be restricted to a central angle of 60°, 90° only. Plane figures involving triangles, simple quadrilaterals and circles should be taken.)
• <red> Problems should be restricted to a central angle of 120°. <red>

### Unit VII: Statistics and Probability

16. Probability

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

## TERM II

<red> Marked in red: <red> Topics <red> removed <red> for 2021-22

### Unit II: Algebra

• 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 formulas.
• Relationship between discriminant and nature of roots.
• Situational problems based on quadratic equations related to day to day activities to be incorporated <red> (problems on equations reducible to quadratic equations are excluded.) <red>

5. Arithmetic Progressions

• Motivation for studying Arithmetic Progression Derivation of the nth term and sum of the first n terms of A.P.
• Application in solving daily life problems <red> (applications based on sum to n terms of an A.P. are excluded.) <red>

### Unit III: Geometry

8. 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 of contact.
• (Prove) The lengths of tangents drawn from an external point to a circle are equal.
• <red> (Motivate) Alternate Segment theorem: If a chord is drawn through the point of contact of a tangent to a circle, then the angles made by the chord with the tangent are respectively equal to the angles subtended by the chord in the alternate segments. <red>

10. Construction

• Division of a line segment in a given ratio (internally).
• Tangents to a circle from a point outside it.
• <red> Construction of a triangle similar to a given triangle. <red>

### Unit V: Trigonometry

12. Some Applications of Trigonometry

• Heights And Distance : 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 VI: Mensuration

14. 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.
• <red> Frustum of a cone. <red>
• Problems involving converting one type of metallic solid into another and other mixed problems. (Problems with combinations of not more than two different solids must be taken).

### Unit VII: Statistics and Probability

15. Statistics

• Mean, median and mode of grouped data (bimodal situation to be avoided). Mean by Direct Method and Assumed Mean Method only.
• <red> Step deviation Method for finding the mean, Cumulative frequency graph. <red>

Our other latest CLASS 10 EDUCART QUESTION BANKS FOR 2022 EXAMS are a complete solution for exam preparation with new pattern chapter-wise questions, Toppers corner, Competency-based Q’s, Self Assessment Questions and Papers, and Topper Answers.

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