MATHEMATICS (IX-X)
Session
2020-21
The Syllabus in the subject of
Mathematics has undergone changes from time to time in accordance with growth
of the subject and emerging needs of the society. The present revised syllabus
has been designed in accordance with National Curriculum Framework 2005 and as
per guidelines given in the Focus Group on Teaching of Mathematics which is to
meet the emerging needs of all categories of students. For motivating the
teacher to relate the topics to real life problems and other subject areas,
greater emphasis has been laid on applications of various concepts.
The curriculum at Secondary
stage primarily aims at enhancing the capacity of students to employ
Mathematics in solving day-to-day life problems and studying the subject as a
separate discipline. It is expected that students should acquire the ability to
solve problems using algebraic methods and apply the knowledge of simple
trigonometry to solve problems of height and distances. Carrying out
experiments with numbers and forms of geometry, framing hypothesis and
verifying these with further observations form inherent part of Mathematics
learning at this stage. The proposed curriculum includes the study of number
system, algebra, geometry, trigonometry, mensuration, statistics, graphs and
coordinate geometry, etc.
The teaching of Mathematics
should be imparted through activities which may involve the use of concrete
materials, models, patterns, charts, pictures, posters, games, puzzles and
experiments.
Objectives
The broad objectives of teaching
of Mathematics at secondary stage are to help the learners to:
•
consolidate the Mathematical knowledge and
skills acquired at the upper primary stage;
•
acquire knowledge and understanding,
particularly by way of motivation and visualization, of basic concepts, terms,
principles and symbols and underlying processes and skills;
•
develop mastery of basic algebraic skills;
•
develop drawing skills;
•
feel the flow of reason while proving a result
or solving a problem;
•
apply the knowledge and skills acquired to solve
problems and wherever possible, by more than one method;
•
to develop ability to think, analyze and
articulate logically;
•
to develop awareness of the need for national
integration, protection of environment, observance of small family norms,
removal of social barriers, elimination of gender biases;
•
to develop necessary skills to work with modern
technological devices and mathematical software's.
•
to develop interest in mathematics as a
problem-solving tool in various fields for its beautiful structures and
patterns, etc.
•
to develop reverence and respect towards great
Mathematicians for their contributions to the field of Mathematics;
•
to develop interest in the subject by
participating in related competitions;
•
to acquaint students with different aspects of
Mathematics used in daily life;
•
to develop an interest in students to study
Mathematics as a discipline.
COURSE STRUCTURE CLASS –IX
|
Units |
Unit Name |
Marks |
|
I |
NUMBER SYSTEMS |
08 |
|
II |
ALGEBRA |
17 |
|
III |
COORDINATE GEOMETRY |
04 |
|
IV |
GEOMETRY |
28 |
|
V |
MENSURATION |
13 |
|
VI |
STATISTICS &
PROBABILITY |
10 |
|
|
Total |
80 |
UNIT I: NUMBER SYSTEMS
1.
REAL NUMBERS (16 Periods)
1. Review
of representation of natural numbers, integers, rational numbers on the number
line. Representation of terminating / non-terminating recurring decimals onthe
number line through successive magnification. Rational numbers as recurring/
terminating decimals. Operations on real numbers.
2. Examples
of non-recurring/non-terminating decimals. Existence of non-rational numbers
(irrational numbers) such as- and their representation on the number line.
Explaining that every real number is represented by a unique point on the
number line and conversely, viz. every point on the number line represents a
unique real number.
3. Definition
of nth root of a real number.
4. Rationalization (with precise meaning) of real numbers of the type (and their combinations) where x and y are natural number and a and b are
integers.
5. Recall
of laws of exponents with integral powers. Rational exponents with positive
real bases
(to be done by particular cases, allowing learner to
arrive at the general laws.)
UNIT II: ALGEBRA
1. POLYNOMIALS (23) Periods
Definition of a polynomial in one variable, with
examples and counter examples. Coefficients of a polynomial, terms of a
polynomial and zero polynomial. Degree of a polynomial. Constant, linear,
quadratic and cubic polynomials. Monomials, binomials, trinomials. Factors and
multiples. Zeros of a polynomial. Motivate and State the Remainder Theorem with
examples. Statement and proof of the Factor Theorem. Factorization of ax2
+ bx + c, a ≠ 0 where a, b and c are real numbers, and of cubic polynomials
using the Factor Theorem.
Recall of algebraic expressions and identities.
Verification of identities:
and their use in factorization of
polynomials.
2. LINEAR EQUATIONS IN TWO VARIABLES (14) Periods
Recall of linear equations in one variable.
Introduction to the equation in two variables.
Focus on linear equations of the type ax+by+c=0.
Explain that a linear equation in two variables has infinitely many solutions
and justify their being written as ordered pairs of real numbers, plotting them
and showing that they lie on a line. Graph of linear equations in two
variables. Examples, problems from real life, including problems on Ratio and
Proportion and with algebraic and graphical solutions being done
simultaneously.
UNIT III: COORDINATE GEOMETRY
COORDINATE GEOMETRY (6) Periods
The Cartesian plane, coordinates of a point, names
and terms associated with the coordinate plane, notations, plotting points in
the plane.
UNIT IV: GEOMETRY
1. INTRODUCTION TO EUCLID'S GEOMETRY (Not for assessment)
History - Geometry in India and Euclid's geometry.
Euclid's method of formalizing observed phenomenon into rigorous Mathematics
with definitions, common/obvious notions, axioms/postulates and theorems. The
five postulates of Euclid. Equivalent versions of the fifth postulate. Showing
the relationship between axiom and theorem, for example:
(Axiom) 1. Given two distinct points, there exists
one and only one line through them.
(Theorem) 2.
(Prove) Two distinct lines cannot have more than one point in common.
2. LINES AND ANGLES (13) Periods
1. (Motivate)
If a ray stands on a line, then the sum of the two adjacent angles so formed is
180O and the converse.
2. (Prove)
If two lines intersect, vertically opposite angles are equal.
3. (Motivate)
Results on corresponding angles, alternate angles, interior angles when a
transversal intersects two parallel lines.
4. (Motivate)
Lines which are parallel to a given line are parallel.
5. (Prove)
The sum of the angles of a triangle is 180O.
6. (Motivate)
If a side of a triangle is produced, the exterior angle so formed is equal to
the sum of the two interior opposite angles.
3. TRIANGLES (20) Periods
1. (Motivate)
Two triangles are congruent if any two sides and the included angle of one triangle
is equal to any two sides and the included angle of the other triangle (SAS
Congruence).
2. (Prove)
Two triangles are congruent if any two angles and the included side of one
triangle is equal to any two angles and the included side of the other triangle
(ASA Congruence).
3. (Motivate)
Two triangles are congruent if the three sides of one triangle are equal to
three sides of the other triangle (SSS Congruence).
4. (Motivate)
Two right triangles are congruent if the hypotenuse and a side of one triangle
are equal (respectively) to the hypotenuse and a side of the other triangle.
(RHS Congruence)
5. (Prove)
The angles opposite to equal sides of a triangle are equal.
6. (Motivate)
The sides opposite to equal angles of a triangle are equal.
7. (Motivate)
Triangle inequalities and relation between ‘angle and facing side' inequalities
in triangles.
4. QUADRILATERALS (10) Periods
1. (Prove)
The diagonal divides a parallelogram into two congruent triangles.
2. (Motivate)
In a parallelogram opposite sides are equal, and conversely.
3. (Motivate)
In a parallelogram opposite angles are equal, and conversely.
4. (Motivate)
A quadrilateral is a parallelogram if a pair of its opposite sides is parallel
and equal.
5. (Motivate)
In a parallelogram, the diagonals bisect each other and conversely.
6. (Motivate)
In a triangle, the line segment joining the mid points of any two sides is
parallel to the third side and in half of it and (motivate) its converse.
5. AREA (7) Periods
Review concept of area, recall area of a rectangle.
1. (Prove)
Parallelograms on the same base and between the same parallels have equal area.
2. (Motivate)
Triangles on the same base (or equal bases) and between the same parallels are
equal in area.
6. CIRCLES (15) Periods
Through examples, arrive at definition of circle and
related concepts-radius, circumference, diameter, chord, arc, secant, sector,
segment, subtended angle.
1. (Prove)
Equal chords of a circle subtend equal angles at the center and (motivate) its
converse.
2. (Motivate)
The perpendicular from the center of a circle to a chord bisects the chord and
conversely, the line drawn through the center of a circle to bisect a chord is
perpendicular to the chord.
3. (Motivate)
There is one and only one circle passing through three given non-collinear
points.
4. (Motivate)
Equal chords of a circle (or of congruent circles) are equidistant from the
center (or their respective centers) and conversely.
5. (Prove)
The angle subtended by an arc at the center is double the angle subtended by it
at any point on the remaining part of the circle.
6. (Motivate)
Angles in the same segment of a circle are equal.
7. (Motivate)
If a line segment joining two points subtends equal angle at two other points
lying on the same side of the line containing the segment, the four points lie
on a circle.
8. (Motivate)
The sum of either of the pair of the opposite angles of a cyclic quadrilateral
is 180° and its converse.
7. CONSTRUCTIONS (10) Periods
1. Construction
of bisectors of line segments and angles of measure 60o, 90o,
45o etc., equilateral triangles.
2. Construction
of a triangle given its base, sum/difference of the other two sides and one
base
angle.
3. Construction
of a triangle of given perimeter and base angles.
UNIT V: MENSURATION
1. AREAS(4) Periods
Area of a triangle using Heron's formula (without
proof) and its application in finding the area of a quadrilateral.
2.
SURFACE AREAS AND VOLUMES (12) Periods
Surface areas and volumes of cubes, cuboids, spheres
(including hemispheres) and right circular cylinders/cones.
UNIT
VI: STATISTICS & PROBABILITY
1. STATISTICS (13) Periods
Introduction to Statistics: Collection of data,
presentation of data — tabular form, ungrouped / grouped, bar graphs,
histograms (with varying base lengths), frequency polygons. Mean, median and
mode of ungrouped data.
2. PROBABILITY (9) Periods
History, Repeated experiments and
observed frequency approach to probability.
Focus is on empirical probability. (A large amount
of time to be devoted to groupand to individual activities to motivate the
concept; the experiments to be drawn from real - life situations, and from
examples used in the chapter on statistics).
MATHEMATICS QUESTION PAPER DESIGN CLASS – IX (2020-21)
Time: 3 Hrs.
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 |
DECUCTED
PORTION
CLASS IX
|
CHAPTER |
TOPICS REMOVED |
|
UNIT I-NUMBER SYSTEMS |
|
|
•
Explaining that every real number
is represented by a unique point on the number line and conversely, viz.
every point on the number line represents a unique real number. •
Definition of nth root of a real
number. |
|
|
UNIT II-ALGEBRA |
|
|
POLYNOMIALS |
• Motivate
and State the Remainder Theorem with examples. Statement and proof of the
Factor Theorem. • x3+y3+z3-3xyz
|
|
LINEAR EQUATIONS IN TWO VARIABLES |
Examples, problems on Ratio and Proportion
|
|
UNIT III-COORDINATE GEOMETRY |
|
|
COORDINATE GEOMETRY |
No deletion |
|
UNIT IV-GEOMETRY |
|
|
INTRODUCTION
TO EUCLID'S GEOMETRY |
Delete the Chapter |
|
LINES AND ANGLES |
No deletion |
|
TRIANGLES |
•
Proof of the theorem deleted- Two
triangles are congruent if any two angles and the included side of one
triangle is equal to any two angles and the included side of the other
triangle (ASA Congruence). • Topic
Deleted-Triangle inequalities and relation between ‘angle and facing side'
inequalities in triangles |
|
QUADRILATERALS |
No deletion |
|
AREA |
Delete the Chapter |
|
CIRCLES |
•
There is one and only one circle
passing through three given non-collinear points. • If
a line segment joining two points subtends equal angle at two other points
lying on the same side of the line containing the segment, the four points
lie on a circle. |
|
CONSTRUCTIONS |
Construction of a triangle of given perimeter and base angles |
|
UNIT V-MENSURATION |
|
|
AREAS |
Application of Heron’s Formula in finding the area of a
quadrilateral. |
|
SURFACE AREAS AND VOLUMES |
No
deletion |
|
UNIT VI-STATISTICS & PROBABILITY |
|
|
STATISTICS |
•
Histograms (with varying base
lengths), Frequency polygons. •
Mean, median and mode of ungrouped
data. |
|
PROBABILITY |
No
deletion |
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