SEBA Class 10 Syllabus 2024 Maths

GENERAL MATHEMATICS
SUBJECT CODE - C2
Class IX-X

1. Board objectives :
Teaching of General Mathematics at the Secondary stage
helps the pupils:
- to know the Mathematical terms, concepts, principles
and processes required in carrying out his/her day-
to-day problems.
- to provide the necessary background for
understanding of the allied concepts of other subjects.
- to provide the necessary background for the study of
Mathematics.
- to develop interest in mathematical processes and
reasoning.
- to develop the habit of precision and accuracy.
- to develop appreciation for the role of Mathematics in
the development of other subjects.

2. Specific Objectives :
The teaching of General Mathematics in the Secondary
Schools helps the pupil:
(i) to develop :
- Knowledge and understanding of the real number
system (R) viz whole numbers; fractions including
decimals, irrational numbers and their basic
properties.
- Understanding of various forms of symbolic languages
i.e. graphs; formulae; equations, etc.
- ability to translate into and form symbolic language,
ability to generalise and build patterns of reasoning,
ability to solve problems (i.e. decide upon the
necessary facts and discard unnecessary; estimate

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results, analyse problems and select the appropriate
method and check results).
(ii) To develop the following qualities :
- an attitude of checking computations,
- systematic representation of arguments.
- power of observation and generalisation.
- doing calculations systematically and speedily.
(iii) To develop an appreciation of the contribution of
mathematics to life and to the development of other
subjects.
(iv) To develop the knowledge, understanding and
applications of the acquired knowledge, practical
works to be done.
(v) To develop the interest with the help of activity.

Mathematics laboratory works :
Mathematics laboratory is a room wherein we find
collection of different kinds of materials and teaching/
learning aids, needed for learning and students
understand the concepts through relevent, meaningful
and concrete activities. The year-end assessment of
activities and project work will be done during the
session. The following parameters may be kept in mind
for the same:
a) Internal examination may be organised as per the
convenience of the schools.
b) Every student may be asked to perform two given
activities (which are to be selected from the textbook)
during the allotted time. Special care may be taken
in choosing these two activities to ensure that the
students are not put to any kind of stress due to time
constraint.

C) Appendix
1: Profs in Mathematics.

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2. Introduction to Mathematical Modelling.
These two chapters are very important to develop
students’ power of reasoning and understanding of
mathematical logic. These two areas should be included in
practical mathematics. These are to be discussed in the
periods dedicated to practical mathematics, i.e. once in a
week.

General Guidelines : for Class-IX-X
1. All concepts/identities must be illustrated by situational
examples.
2. The language of ‘Word problems’ must be clear, simple,
and unambiguous.
3. All proofs to be produced in a non-didactic manner,
allowing the learner to see flow of reason. Wherever
possible give more than one proof.
4. Motivate most results. Prove explicitly those where a
short and clear argument reingorces mathematical
thanking and reasoning. There must be emphasis on
correct way of expressing their arguments.
5. The reason for doing ruler and compass construction is
to motivate and illustrate logical argument and reasoning.
All constructions must include an analysis of the
construction, and proof for the steps taken to do the
required construction must be given.

marks distribution on practicals/project works
Internal Assessment for Classes IX & X
1) Practicals 7
2) Project 3
Total 10

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GENERAL MATHEMATICS
Subject Code : C2

Class : X Time : 3 hours
Total Marks : 100 Pass Marks : 30
Theory : 90
Internal Assessment : 10
Pass Marks in Written Examination : 27
Units : Class - X
I. Number Systems
II. Algebra
III. Trigonometry
IV. Coordinate Geometry
V. Geometry
VI. Mensuration
VII. Statistics and Probability
Appendix : 1. Proof in Mathematics
2. Mathematical Modelling

Unit I. Number Systems
Real Numbers (Periods 15)
Euclid’s division lemma, Fundamental Theorem of
Arithmetic-statements after reveiwing work done earlier and
after illustrating and motivating through examples. Proofs of
results-irrationality of √2, √3, √5, decimal expansions of
rational numbers in terms of terminating/non-terminating
recurring decimals.

Unit II. Algebra
1. Polynomials (Periods 6)
Zeros of a polyomial. Relationship between zeros and
coefficients of a polynomial with particular reference to
quadratic polynomials. Statement and simple problems
on division algorithm for polynomials with real
coefficients.
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2. Pair of Liner Equations in Two Variables (Periods 15)
Pair of linear equations in two variables. Geometric
representation of different possibilities of solutions/
inconsistency.
Algebraic conditions for number of solutions.
Solution of pair of linear equations in two variables
algebraically-by substitution, by elimination and by cross
multiplication. Simple situational problems must be
included. Simple problems on equations reducible to
linear equations may be included.
3. Quadratic Equations (Periods 15)
2
Standard form of a quadratic equation ax + bx + c = 0,
(a ¹ 0). Solution of quadratic equations (only real roots)
by factorization and by completing the square, i.e. by
using quadratic formula. Relationship between
discriminant and nature of roots.
Problems related to day-to-day activities to be
incorporated.
4. Arithmetic Progressions (AP) (Periods 8)
Motivation for studying A.P. Derivation of standard results
of finding the nth terms and sum of first n terms.
Unit III : Trigonometry
1. Introduction to Trigonometry (Periods 18)
Trigonometric ratios of an acute angle of a right-angled
triangle. Proof of their existence (well defined); motivate
the ratios, whichever are defined at 00 and 900. Values
(with proof) of the trigonometric ratios of 300, 450 and
600. Relationship between the ratios.
Trigonometric Identities : Proof and applications of
the identity sin2 A + cos2A=1, sec2A - tan2A=1, cosec2A
- cot 2A = 1. Only simple identities to be given.
Trigonometric ratios of complementary angles.
2. Heights and Distances (Not from examination point
of view) (Periods 8)
Simple and believable problems on heights and
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distances. Problems should not involve more than two
right triangles. Angles of elevation/depression should
be only 300, 450, 600.
Unit IV : Coordinate Geometry
Lines (In two-dimensions) (Periods 15)
Review the concepts of coordinate geometry done
earlier including graphs of linear equations. Awareness
of geometrical representation of quadratic polynomials.
Distance between two points and section formula
(internal). Area of a triangle.
Unit V : Geometry
1. Triangles (Periods 15)
Definitions, examples, counter examples of similar
triangles.
i) (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.
ii) (Motivate) If a line divides two sides of a triangle in the
same ratio, the line is parallel to the third side.
iii) (Motivate) If in two triangles, the corresponding angles
are equal, their corresponding sides are proportional
and the triangles are similar.
iv) (Motivate) If the corresponding sides of two triangles
are proportional, their corresponding angles are equal
and two triangles are similar.
v) (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.
vi) (Motivate) If a perpendicular is drawn from the vertex of
the right angle to the hypotenuse, the triangles on each
side of the perpendicular are similar to the whole triangle
and to each other.
vii) (Prove) The ratio of the areas of two similar triangles is
equal to the ratio of the squares on their corresponding
sides.
viii) (Prove) In a right triangle, the square of the hypotenuse
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is equal to the sum of the squares of the other two sides.
ix) (Prove) In a triangle, if the square of one side is equal to
sum of the squares of the other two sides, the angle
opposite to the first side is a right triangle.
2. Circle (Periods - 8)
Tangent to a circle at any point on it is motivated by
chords drawn from points coming closer and closer to
the point.
i) (Prove) The tangent at any point of a circle is
perpendicular to the radius through the point of contact.
ii) (Prove) The lengths of tangents drawn from an external
point to a circle are equal.
3. Constructions (Periods - 8)
i) Division of a line segment in a given ratio (internally).
ii) Tangent to a circle from a point outside it.
iii) Construction of a triangle similar to a given triangle.
Unit : VI. Mensuration :
1. Areas Related to Circles (Periods 12)
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 600, 900, and
1200 only. Plane figures involving triangles, simple
quadrilaterals and circle should be taken.)
2. Surface Areas and Volumes (Periods 12)
i) Problems on finding surface areas and volumes of
combinations of any two of the following:
cubes, cuboids, spheres, hemispheres and right
circular cylinders/cones. Frustum of a cone.
ii) Problems involving converting one type of metalic solid
into another and other mixed problems. (Problems with
combination of not more than two different solids be
taken.)
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Unit : VII. Statistics and Probability
1. Statistics (Periods 15)
Mean, median and mode of grouped data (bimodal
situation to be avoided).
Cumulative frequency graph.
2. Probability (Periods 10)
Classical definition of probability. Connection with
probability as given in Class IX.
Simple problems on single events, not using set
notation.

Appendix
1. Proof in Mathematics
Futher discussion on concept of ‘statement’. ‘proof’ and
‘agrument’. Further illustrations of deductive proof with
complete arguments using simple results from
arithmetic, algebra and geometry. Simple theorems of
the “Given... and assuming... prove...”. Training of using
only the given facts (irrespective of their truths) to arrive
at the required conclusion. Explanation of ‘converse’,
‘negation’, constructing converses and negations of
given result/statements.
2. Mathematical Modelling
Reinforcing the concept of mathematical modelling,
using simple examples of models where some
constraints are ignored. Estimating probability of
occurence of certain events and estimating averages
may be considered. Modelling fair instalments payments,
using only simple interest and future value (use of AP).


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LIST OF PRACTICALS IN MATHEMATICS
PRESCRIBED
FOR CLASS-X

1. Solve a pair of linear equation by graphical method and
to verify the result by any other algebraic method.
(Chapter-3)
2. To find the zeros of a quadratic polynomial graphically
and verification of the result by any other algebraic method
(Chapter-2)
3. Verification of the formula for :- (chapter-5)
i. Sum of first n terms of an AP
ii. Sum of first n natural numbers
iii. Sum of first n odd natural numbers
iv. Sum of first n even natural numbers
4. Verification of Basic Proportionality Theorem.
(Chapter-6)
5. Verification of converse of Basic Proportionality theorem.
chapter-6)
6. To verify that the ratio of the area of to two similar
triangles is equal to the ratio of the squares of their
correspoding sides. (Chapter-6)
7. Verification of Phythagoras Theorem.
8. Verification of the formula of area of triangle (in co-
ordinate geometry) with the help of the formula of plane
geometry. (Chapter-7)
9. Construction of a tangent to a circle at any point on it,
when the centre of the circle is given (Chapter-10)
10. To verify that the length of the tangents the drawn from
an external point to a circle are equal. (Chapter-10)
11. To obtain the formula for the area of a circle with radius
r. (Chapter -12)
12. To construct a right circular cylinder with given height

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and circumference. (Chapter-13)
13. To construct a right circular cone with given height and
circumference of the circular base. For the cone so
formed, to determine its radius and height. (Chapter-13)
14. To construct a quadrilateral with given measure and then
to construct a similar quadrilateral.
15. To find mean, median and mode from a primary data
collected by the students in a specific subject.
16. To Find the median from a given distribution using graph
mentioned below and to verify the result. (Chapter-14)
(i) Using less than type ogive.
(ii) Using more than type ogive.
(iii) Using both less than and more than type
ogive
17. Probability : (Chapter-15)
(a) To find the probability of getting head or tail from
the experiment of tossing a coin 100 times.
(b) To obtain the probability of an event associated
with throwing a pair of dice.
18. Displacement and rotation of triangle. (Chapter-7)
To verify that under any displacement and rotation of a
triangle-
(a) Distance between the verities remain unchanged.
(b) Area of the triangle remains unaltered.
19. Project :
1) (a) Write a note on Euclid’s Division Lemma
(b) Write a note on Pythagoras Theorem
2) Write short life history of 3/4 great Mathematicians
N.B. : Students should do at least 15 practicals and at least
one project work.

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Revised syllabus of Mathematics, Class-X
GENERAL MATHEMATICS
Subject Code : C2
Class : X Time : 3 hours
Full Marks : 100 Pass Marks : 30
Theory : 90
Internal Assessment : 10
Pass marks in written examination : 27

Chapter Units Units Marks
Chapter Name Half HSLC
No. Required Omitted
Yearly Exam.
Revision Chapter Part I & Part III 10 6
Part II
1. Real Number Whole Nil 10 5
chapter
2. Polynomials Whole Nil 12 8
chapter
3. Pair of Linear Equations in two Whole Nil 12 7
variables chapter
4. Quadratic Equations Whole Nil 12 6
chapter
5. Arithmetic Progressions Whole Nil – 6
chapter
6. Triangles Upto unit Unit 6.5 12 6
6.4 (i.e. upto onwards
Exercise 6.3)
7. Coordinate Geometry Whole Nil 10 7
chapter
8. Introduction to Trigonometry Whole Nil 12 7
chapter
9. * * * – *
10. Circles Whole Nil – 6
chapter
11. Constructions Upto unit Unit 11.3 – 4
11.2 (i.e. onwards
Upto
Exercise
11.1)
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Chapter Units Units Marks
Chapter Name Half HSLC
No. Required Omitted
Yearly Exam.
12. Areas Related to Circles Upto unit Unit 12.4 – 6
12.3 (i.e. onwards
Upto
Exercise
12.2
13. Surface Area and Volume Upto unit Unit 13.4 – 6
13.3 (i.e. onwards
Upto
Exercise
13.2)
14. Statistics Upto unit Unit 14.5 – 5
14.4 (i.e. onwards
Upto
Exercise
14.3)
15. Probability Whole Nil – 5
chapter
Theory Total – 90
Internal Assessments – 10
Grand Total – 100

* Chapter 9 is totally excluded from the syllabus.
Textbook : Mathematics (for class X), published by The Assam State
Textbook Production and Publication Corporation Ltd.,
Guwahati-1

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