This document provides the syllabus for Sets and Functions from the 10th standard Tamil Nadu state board curriculum. It outlines the key topics to be covered, including introduction to sets, operations on sets, properties of set operations, De Morgan's laws, functions, and cardinality of sets. The expected learning outcomes and number of periods allocated for each topic are also specified. Teaching strategies like using Venn diagrams, real-life examples, and pattern approaches are recommended to help students understand the concepts.

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X Std. SYLLABUS
Transactional
Expected Learning No. of
Topic Content Teaching
Outcomes Periods
Strategy
i. Introduction • To revise the basic con- Use Venn
ii. Properties of operations on cepts on Set operations diagrams for all
sets • To understand the proper- illustrations
iii. De Morgan’s laws-verifi- ties of operations of sets
cation using example Venn - commutative, associative,
diagram and distributive restricted Give examples
to three sets.
I. Sets and Functions
iv. Formula for of functions from
v. Functions • To understand the laws of economics, medi-
complementation of sets. cine, science etc.
• To understand De Mor-
gan’s laws and demonstrat-
ing them by Venn diagram 26
as well.
• To solve word problems
using the formula as well
as Venn diagram.
• To understand the defini-
tion , types and representa-
tion of functions.
• To understand the types
of functions with simple
examples.
i. Introduction • To understand to identify Use pattern ap-
ii. Sequences an Arithmetic Progression proach
iii. Arithmetic Progression and a Geometric Progres-
II. Sequences and Series of
(A.P) sion. Use dot pattern as
iv. Geometric Progression • Able to apply to find the teaching aid
Real Numbers
(G.P) nth term of an Arithmetic
v. Series Progression and a Geomet- Use patterns to
ric Progression. derive formulae 27
• To determine the sum of
n terms of an Arithmetic Examples to be
Progression and a Geomet- given from real
ric Progression. life situations
• To determine the sum of
some finite series.
i. Solving linear equations • To understand the idea about Illustrative
ii. Polynomials pair of linear equations in examples –
iii. Synthetic division two unknowns. Solving a
iv. Greatest common divisor pair of linear equations in Use charts as
III. Algebra
(GCD) two variables by elimination teaching aids
and Least common mul- method and cross multipli-
tiple (LCM) cation method. Recall GCD and
v. Rational expressions • To understand the relation- LCM of numbers
vi. Square root ship between zeros and co- initially
vii. Quadratic Equations efficients of a polynomial
with particular reference to
quadratic polynomials.
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• To determine the remain- Compare with
der and the quotient of operations on
the given polynomial fractions
using Synthetic Division
Method.
• To determine the factors
of the given polynomial
using Synthetic Division
Method.
• Able to understand the dif-
ference between GCD and Compare with the
LCM, of rational expres- square root opera-
sion. tion on numerals.
• Able to simplify rational
expressions (Simple Prob- Help students
visualize the
lems),
III. Algebra
nature of roots
• To understand square
algebraically and
roots.
graphically.
• To understand the standard
40
form of a quadratic equa-
tion .
• To solve quadratic equa-
tions (only real root) - by
factorization, by complet-
ing the square and by using
quadratic formula.
• Able to solve word prob-
lems based on quadratic
equations.
• Able to correlate relation-
ship between discriminant
and nature of roots.
• Able to Form quadratic
equation when the roots
are given.
i. Introduction • Able to identify the order Using of rect-
ii. Types of matrices and formation of matrices angular array of
iii. Addition and subtraction • Able to recognize the types numbers.
iv. Multiplication of matrices
v. Matrix equation • Able to add and subtract Using real life
the given matrices. situations.
• To multiply a matrix by a
IV. Matrices
scalar, and the transpose of Arithmetic opera-
a matrix. tions to be used 16
• To multiply the given
matrices (2x2; 2x3; 3x2
Matrices).
• Using matrix method solve
the equations of two vari-
ables.
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i. Introduction • To recall the distance Simple geometri-
ii. Revision :Distance be- between two points, and cal result related
tween two points locate the mid point of two to triangle and
iii. Section formula, Mid given points. quadrilaterals to
point formula, Centroid • To determine the point be verified as ap-
formula of division using section plications.
iv. Area of a triangle and formula (internal).
quadrilateral • To calculate the area of a the form
v. Straight line triangle. y = mx + c to be
V. Coordinate Geometry
• To determine the slope of taken as the start-
a line when two points are ing point
given, equation is given. 25
• To find an equation of line
with the given information.
• Able to find equation of
a line in: slope-intercept
form, point -slope form,
two -point form, intercept
form.
• To find the equation of
a straight line passing
through a point which is (i)
parallel (ii) perpendicular
to a given straight line.
i. Basic proportionality theo- • To understand the theo- Paper folding
rem (with proof) rems and apply them to symmetry and
ii. Converse of Basic propor- solve simple problems transformation
tionality theorem only. techniques to be
(with proof) adopted.
iii. Angle bisector theorem
Formal proof to
(with proof - internal case
VI. Geometry
be given
only)
iv. Converse of Angle bisec- Drawing of 20
tor theorem (with proof figures
- internal case only)
v. Similar triangles (theo- Step by step
rems without proof) logical proof with
diagrams to be
explained and
discussed
i. Introduction • Able to identify the By using Alge-
ii. Identities Trigonometric identities braic formulae
VII. Trigonometry
iii. Heights and distances and apply them in simple
problems. Using trigonomet-
• To understand trigonomet- ric identities. 21
ric ratios and applies them
to calculate heights and The approximate
distances. nature of values
(not more than two right to be explained
triangles)
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i. Introduction • To determine volume and Use 3D models to
ii. Surface Area and Volume surface area of cylinder, create combined
VIII. Mensuration of Cylinder, Cone, Sphere, cone, sphere, hemisphere, shapes
Hemisphere, Frustum frustum
iii. Surface area and volume • Volume and surface area Use models and
of combined figures of combined figures (only pictures ad teach-
iv. Invariant volume two). ing aids. 24
• Some problems restricted
to constant Volume. Choose examples
from real life situ-
ations.
i. Introduction • Able to construct tangents To introduce
ii. Construction of tangents to circles. algebraic verifica-
to circles • Able to construct triangles, tion of length of
IX. Practical Geometry
iii. Construction of Triangles given its base, vertical tangent segments.
iv. Construction of cyclic angle at the opposite vertex
quadrilateral and Recall related
(a) median properties of
(b) altitude angles in a circle 15
(c) bisector. before construc-
• Able to construct a cyclic tion.
quadrilateral
Recall relevant
theorems in theo-
retical geometry
i. Introduction • Able to solve quadratic Interpreting skills
ii. Quadratic graphs equations through graphs also to be taken
iii. Some special graphs • To solve graphically the care of graphs
X. Graphs
equations of quadratics to
. precede algebraic
• Able to apply graphs to treatment. 10
solve word problems
Real life situa-
tions to be intro-
duced.
i. Recall Measures of central • To recall Mean for grouped Use real life situa-
tendency and ungrouped data situa- tions like perfor-
ii. Measures of dispersion tion to be avoided). mance in exami-
XI. Statistics
iii. Coefficient of variation • To understand the concept nation, sports, etc.
of Dispersion and able 16
to find Range, Standard
Deviation and Variance.
• Able to calculate the coef-
ficient of variation.
i. Introduction • To understand Random Diagrams and
ii. Probability-theoretical ap- experiments, Sample space investigations
proach and Events – Mutually on coin tossing,
XII. Probability
iii. Addition Theorem on Exclusive, Complemen- die throwing and
Probability tary, certain and impossible picking up the
events. cards from a deck 15
• To understand addition of cards are to be
Theorem on probability used.
and apply it in solving
some simple problems.
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CONTENTS
1. SETS AND FUNCTIONS 1-33
1.1 Introduction 1
1.2. Sets 1
1.3. Operations on Sets 3
1.4. Properties of Set Operations 5
1.5. De Morgan’s Laws 12
1.6. Cardinality of Sets 16
1.7. Relations 19
1.8. Functions 20
2. SEQUENCES AND SERIES OF REAL NUMBERS 34-67
2.1. Introduction 34
2.2. Sequences 35
2.3. Arithmetic Sequence 38
2.4. Geometric Sequence 43
2.5. Series 49
3. ALGEBRA 68-117
3.1 Introduction 68
3.2 System of Linear Equations in Two Unknowns 69
3.3 Quadratic Polynomials 80
3.4 Synthetic Division 82
3.5 Greatest Common Divisor and Least Common Multiple 86
3.6 Rational Expressions 93
3.7 Square Root 97
3.8 Quadratic Equations 101
4. MATRICES 118-139
4.1 Introduction 118
4.2 Formation of Matrices 119
4.3 Types of Matrices 121
4.4 Operation on Matrices 125
4.5 Properties of Matrix Addition 128
4.6 Multiplication of Matrices 130
4.7 Properties of Matrix Multiplication 132
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5. COORDINATE GEOMETRY 140-170
5.1 Introduction 140
5.2 Section Formula 140
5.3 Area of a Triangle 147
5.4 Collinearity of Three Points 148
5.5 Area of a Quadrilateral 148
5.6 Straight Lines 151
5.7 General form of Equation of a Straight Line 164
6. GEOMETRY 171-195
6.1 Introduction 171
6.2 Similar Triangles 182
6.3 Circles and Tangents 189
7. TRIGONOMETRY 196-218
7.1 Introduction 196
7.2 Trigonometric Identities 196
7.3 Heights and Distances 205
8. MENSURATION 219-248
8.1 Introduction 219
8.2 Surface Area 219
8.3 Volume 230
8.4 Combination of Solids 240
9. PRACTICAL GEOMETRY 249- 266
9.1 Introduction 249
9.2 Construction of Tangents to a Circle 250
9.3 Construction of Triangles 254
9.4 Construction of Cyclic Quadrilaterals 259
10. GRAPHS 267-278
10.1 Introduction 267
10.2 Quadratic Graphs 267
10.3 Some special Graphs 275
11. STATISTICS 279-298
11.1 Introduction 279
11.2 Measures of Dispersion 280
12. PROBABILITY 299 - 316
12.1 Introduction 299
12.2 Classical Definition of Probability 302
12.3 Addition theorem on Probability 309
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1 SETS AND
FUNCTIONS
A set is Many that allows itself to be thought of as a One
- Georg Cantor
 Introduction
 Sets 1.1 Introduction
The concept of set is one of the fundamental concepts
 Properties of set operations
in mathematics. The notation and terminology of set theory
 De Morgan’s Laws
is useful in every part of mathematics. So, we may say that
 Functions set theory is the language of mathematics. This subject, which
originated from the works of George Boole (1815-1864) and
Georg Cantor (1845-1918) in the later part of 19th century,
has had a profound influence on the development of all
branches of mathematics in the 20th century. It has helped
in unifying many disconnected ideas and thus facilitated the
advancement of mathematics.
In class IX, we have learnt the concept of set, some
GeorGe Boole
operations like union, intersection and difference of two sets.
Here, we shall learn some more concepts relating to sets and
(1815-1864)
England another important concept in mathematics namely, function.
First let us recall basic definitions with some examples. We
Boole believed that there was
a close analogy between symbols that denote all positive integers (natural numbers) by N and all
represent logical interactions and real numbers by R .
algebraic symbols. 1.2 Sets
He used mathematical symbols Definition
to express logical relations. Although
computers did not exist in his A set is a collection of well-defined objects. The objects
day, Boole would be pleased to in a set are called elements or members of that set.
know that his Boolean algebra Here, “well-defined” means that the criteria for
is the basis of all computer arithmetic. deciding if an object belongs to the set or not, should be
As the inventor of Boolean defined without confusion.
logic-the basis of modern digital For example, the collection of all “tall people” in
computer logic - Boole is regarded in
Chennai does not form a set, because here, the deciding criteria
hindsight as a founder of the field of
“tall people” is not clearly defined. Hence this collection does
computer science.
not define a set.