CBSE Class 10 (Math) New Syllabus

This is a new syllabus of maths after the reduction of the old syllabus.

Now you have to learn this new syllabus for your upcoming examination.

**UNIT
I: NUMBER SYSTEMS**

**1.
REAL NUMBER**

Fundamental Theorem of Arithmetic - statements after reviewing work done earlier and

after illustrating and motivating through
examples, Proofs of irrationality of **2^1/2,3^1/2,5^1/2**

Decimal representation of rational numbers interms 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 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.

Simple problems on equations reducible to linear equations.

**3.
QUADRATIC EQUATIONS **

Standard form of a quadratic equation **ax^2+ 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.

**4.
ARITHMETIC PROGRESSIONS **

Motivation for studying Arithmetic Progression Derivation of the nth term and sum of the

first n terms of A.P.

**UNIT
III: COORDINATE GEOMETRY**

**1.
LINES (In two-dimensions) **

Review: Concepts of coordinate geometry, graphs of linear equations. Distance formula.

Section formula (internal division).

**UNIT
IV: GEOMETRY**

**1.
TRIANGLES **

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)
In a right triangle, the square on the hypotenuse is equal to the sum of the

squares on the other two sides.

**2.
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.

**3.
CONSTRUCTIONS **

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

**[2.]**
Tangents to a circle from a point outside it.

**UNIT
V: TRIGONOMETRY**

**1.
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 300,450and 600.

**Relationships
between the ratios.**

**2.
TRIGONOMETRIC IDENTITIES **

Proof and applications of the identity sin2A + cos2A = 1. Only simple identities to be

given.

**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 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°and

90° only. Plane figures involving triangles, simple quadrilaterals and circle should be

taken.)

**2.
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
VII: STATISTICS AND PROBABILITY**

**1.
STATISTICS **

Mean, median and mode of grouped data (bimodal situation and step deviation method

for finding the mean to be avoided).

**2.
PROBABILITY **

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

event.

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