CBSE 10TH MATHS SYLLABUS
1. REAL NUMBER 2021-2022
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. ( Deleted for 2022-2023)
1.
REAL NUMBER 2022-2023
Fundamental Theorem of Arithmetic - statements after
reviewing work done earlier and after illustrating and motivating through
examples, Proofs
of irrationality of Root 2 , Root 3 and Root 5 .
2.
POLYNOMIALS
2021-2022
Zeroes of a
polynomial. Relationship between
zeroes and coefficients of quadratic polynomials only.
2.
POLYNOMIALS
2022-2023
Zeros of a
polynomial. Relationship between
zeros and coefficients of quadratic polynomials.
3.
PAIR OF LINEAR EQUATIONS IN TWO VARIABLES 2021-2022
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 equations.
3. PAIR OF
LINEAR EQUATIONS IN TWO VARIABLES
(
2022-2023)
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. Simple
situational problems.
4. QUADRATIC
EQUATIONS ( 2021-2022)
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)
( Included for 2022-2023 )
4. QUADRATIC
EQUATIONS ( 2022-2023)
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 to be incorporated.
5. ARITHMETIC
PROGRESSIONS ( 2021-2022)
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)
( Included for 2022-2023 )
5. ARITHMETIC
PROGRESSIONS ( 2022-2023)
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.
6. TRIANGLES (
2021-2022)
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. (Motivate) 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. (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. ( Deleted for
2022-2023)
6. TRIANGLES ( 2022-2023)
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.
7. COORDINATE GEOMETRY
LINES
(In two-dimensions) ( 2021-2022)
Review:
Concepts of coordinate geometry, graphs of linear equations. Distance formula.
Section formula (internal division)
7. Coordinate Geometry (
2022-2023)
Review:
Concepts of coordinate geometry, graphs of linear
equations. Distance formula. Section formula (internal division).
8. INTRODUCTION
TO TRIGONOMETRY ( 2021-2022)
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 ( 2021-2022)
Proof and applications of the
identity sin2A + cos2A = 1. Only simple identities to be
given.
8. INTRODUCTION
TO TRIGONOMETRY ( 2022-2023)
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 of
the trigonometric ratios of 300, 450 and 600.
Relationships between the ratios.
TRIGONOMETRIC IDENTITIES (
2022-2023)
Proof and applications of the
identity sin2A + cos2A = 1. Only simple identities
to be given.
9.
SOME APPLICATIONS OF TRIGONOMETRY ( 2021-2022)
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°.
9. HEIGHTS AND
DISTANCES: ( 2022-2023)
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°, and 60°.
10. CIRCLES ( 2021-2022)
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.
10. CIRCLES ( 2022-2023)
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.
11.CONSTRUCTIONS
( 2021-2022)
1.
Division of a line segment in a given ratio (internally).
2. Tangents to a circle from a
point outside it.
( excluded for 2022-2023)
12. AREAS RELATED TO
CIRCLES ( 2021-2022)
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.)
12.AREAS RELATED
TO CIRCLES ( 2022-2023)
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.
13. SURFACE AREAS AND VOLUMES ( 2021- 2022)
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).
(
Excluded for 2022-2023)
13. SURFACE AREAS AND VOLUMES ( 2022-2023)
Surface
areas and volumes of combinations of any two of the following: cubes, cuboids,
spheres, hemispheres and right circular cylinders/cones.
14. STATISTICS ( 2021-2022)
Mean, median and mode of grouped data (bimodal
situation to be avoided). Mean by Direct Method and Assumed Mean Method only.
|
14. STATISTICS ( 2022-2023) |
|
|
Mean, median and mode of grouped data (bimodal situation to be
avoided). |
|
( Direct method , Assumed Mean method and Step
deviation method )
15. PROBABILITY ( 2021-2022)
Classical definition of probability. Simple problems
on finding the probability of an event.
15.
PROBABILITY ( 2022-2023)
Classical definition of probability. Simple problems on finding the probability of an event.
10th Maths Syllabus - Deleted portion - 2022-2023
_page-0001.jpg)
0 Comments