REVISED SYLLABUS Mathematics 2020-21
REVISED SYLLABUS
COURSE STRUCTURE
CLASS –X
Mathematics
|
Units |
Unit Name |
Marks |
|
I |
NUMBER SYSTEMS |
06 |
|
II |
ALGEBRA |
20 |
|
III |
COORDINATE GEOMETRY |
06 |
|
IV |
GEOMETRY |
15 |
|
V |
TRIGONOMETRY |
12 |
|
VI |
MENSURATION |
10 |
|
VII |
STATISTICS & PROBABILTY |
11 |
|
|
Total |
80 |
UNIT I: NUMBER
SYSTEMS
1. REAL NUMBER (8) Periods
Fundamental Theorem of Arithmetic - statements after
reviewing work done earlier and after illustrating and motivating through
examples, Proofs of irrationality of 
Decimal representation of rational
numbers interms of terminating/non-terminating recurring decimals.
UNIT II: ALGEBRA
1.
POLYNOMIALS (4) Periods
Zeros of a polynomial. Relationship between zeros and coefficients of quadratic polynomials.
2.
PAIR OF LINEAR EQUATIONS IN TWO VARIABLES (11) Periods
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 (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.
4.
ARITHMETIC PROGRESSIONS (4) Periods
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) (10) Periods
Review: Concepts of coordinate geometry, graphs of linear equations. Distance formula. Section formula (internal division).
UNIT IV: GEOMETRY
1.
TRIANGLES (10) Periods
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 (8) Periods
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 (4) Periods
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 (8) Periods
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.
2.
TRIGONOMETRIC IDENTITIES (10) Periods
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 (10) Periods
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 (8) Periods
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 (10) Periods
Mean, median and mode of grouped data (bimodal situation and step deviation method for finding the mean to be avoided).
2. PROBABILITY (10) Periods
Classical definition of probability. Simple problems on finding the probability of an event.
MATHEMATICS-Standard QUESTION PAPER DESIGN
CLASS – X (2020-21)
Time :
3 Hours Max.
Marks: 80
|
S. No. |
Typology
of Questions |
Total Marks |
% Weightage (approx.) |
|
1 |
Remembering:
Exhibit memory of previously learned material by recalling facts,
terms, basic concepts, and answers. Understanding: Demonstrate
understanding of facts and ideas by organizing, comparing, translating,
interpreting, giving descriptions, and stating main ideas |
43 |
54 |
|
2 |
Applying: Solve problems to new situations
by applying acquired knowledge, facts, techniques and rules in a different
way. |
19 |
24 |
|
3 |
Analysing : Examine
and break information into parts by identifying motives or causes. Make
inferences and find evidence to support generalizations Evaluating: Present
and defend opinions by making judgments about information, validity of ideas,
or quality of work based on a set of criteria. Creating: Compile
information together in a different way by combining elements in a new
pattern or proposing alternative solutions |
18 |
22 |
|
|
Total |
80 |
100 |
|
INTERNAL
ASSESSMENT |
20 MARKS |
|
Pen Paper Test and Multiple Assessment (5+5) |
10 Marks |
|
Portfolio |
05 Marks |
|
Lab Practical (Lab activities to be done from the
prescribed books) |
05 Marks |
MATHEMATICS-Basic
QUESTION PAPER DESIGN CLASS – X (2020-21)
Time : 3Hours Max.
Marks: 80
|
S. No. |
Typology of
Questions |
Total Marks |
% Weightage (approx.) |
|
1 |
Remembering: Exhibit memory of previously
learned material by recalling facts, terms, basic concepts, and answers. Understanding: Demonstrate understanding
of facts and ideas by organizing, comparing, translating, interpreting,
giving descriptions, and stating main ideas |
60 |
75 |
|
2 |
Applying: Solve problems to new situations
by applying acquired knowledge, facts, techniques and rules in a different
way. |
12 |
15 |
|
3 |
Analysing : Examine
and break information into parts by identifying motives or causes. Make inferences and find evidence to support generalizations Evaluating: Present
and defend opinions by making judgments about information, validity of ideas,
or quality of work based on a set of criteria. Creating: Compile
information together in a different way by combining elements in a new pattern or proposing alternative solutions |
8 |
10 |
|
|
Total |
80 |
100 |
|
INTERNAL
ASSESSMENT |
20 MARKS |
|
Pen Paper Test and Multiple Assessment (5+5) |
10 Marks |
|
Portfolio |
05 Marks |
|
Lab Practical (Lab activities to be done from the
prescribed books) |
05 Marks |
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.
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