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List of units along with their marks
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Complete syllabus of Mathematics for Class 10
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 sqrt (2), sqrt (3) and sqrt (5).
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.
3.
QUADRATIC EQUATIONS
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.
4. 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.
UNIT III:
COORDINATE GEOMETRY
Coordinate
Geometry
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.
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.
UNIT V: TRIGONOMETRY
1. INTRODUCTION TO
TRIGONOMETRY
Trigonometric
ratios of an acute angle of a right-angled triangle. Proof of their existence
(well defined); motivate the ratios whichever are defined at 0oand 90o. Values of the trigonometric ratios
of 30o, 45oand
60o. 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.
Simple
problems on heights and distances. Problems should not involve more than two
right triangles. Angles of elevation / depression should be only 30o, 45o, and
60o.
UNIT VI:
MENSURATION
1. AREAS
RELATED TO CIRCLES
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.
2. 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.
UNIT VII:
STATISTICS AND PROBABILITY
1. STATISTICS
Mean, median and mode of grouped data (bimodal situation to be avoided).
2. PROBABILITY
Classical definition of probability. Simple problems on
finding the probability of an event.
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