PROGRAMME AT SCHOOL
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Trigonometry
Trigonometry is the one of the branches of mathematics which means the measurement of triangle. Trigonometric Ratios: The side that is opposite to the right angle is called the Hypotenuse. This is the longest in a right triangle. The side that is opposite to the angle 𝛳 is called the opposite side. The side that runs alongside the angle 𝛳 and which is not the Hypotenuse is called the Adjacent side. Let 𝛳 be an acute angle of a right triangle. Then the six trigonometric Ratios of 𝛳 and the trigonometric table are as follows, Example: Trigonometric Ratios of Complementary Angles Let 𝛳 be an acute angle of a right triang le. Then we have the following identities for the trigonometric rat ios of Complementary angles, Sin 𝛳 = Cos ( 90⁰ - 𝛳 ) Cos 𝛳 = Sin ( 90⁰ - 𝛳 ) tan 𝛳 = cot ( 90⁰ - 𝛳
Algebra
The mathematical term "Algebra" was derived from the Arabic word 'al-jabr' Indian mathematicians like Aryabhatta , Bhrahmagupta, Mahavir, Bhaskara Ⅱ, Sridhara have contribute a lot to this branch of mathematics. The Greek mathematician, Diophantus of Alexandria had developed this branch to a greater extent. Hence he is called as "The father of Algebra" Basic concepts of Polynomial: Monomial: An Algebraic expression that contains only one term is called a monomial. Examples: 2x², 3ab,81xyz Binomial: An Algebraic expression that contains only two terms is called a binomial. Examples: x + y, 4a - 3b , l² -7m Trinomial: An Algebraic expression that contains only three ter
Pythagoras Theorem
Pythagoras theorem is the important one which gives the relation between the three sides of the right angled triangle. This theorem was discoveredby a famous mathematician"PYTHAGORAS" Statement: In a right angled triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides. Let us consider ∆ ABC with ∠C = 90⁰ , BC = a , CA = b and AB = c , then a² + b² = c² Application: In ∆ ABC , ∠ B = 90⁰ , AB = 18 cm and BC = 24 cm. Calculate the length of AC. Solution: Given: ∠ B = 90⁰ , AB = 18 cm , BC = 24 cm. By Pythagoras Theorem, AC² = BC² + AB² =18² + 24 ² = 324 + 576 AC² = 900 Th
Angles
Two rays starting from a common point from an angle. Types of angles: Acute angle: An angle whose measure is greater than 0⁰ but less than 90⁰ is called an acute angle. Examples: 15⁰ , 30⁰. Right angle: An angle whose measure is 90⁰ is called a right angle. Obtuse angle: An angle whose is greater than 90⁰ and less than 180⁰ is called an obtuse angle. Examples: 100⁰ , 110⁰ , 140⁰ Straight angle: When the rays of an angle are opposite rays forming a straight line, the angle thus formed is a straight angle and its measure is 180⁰ Reflex angle: An angle whose measure is more than 180⁰ but less than 360⁰ is called a reflex angle. Complete angle: An angle whose measure is 360⁰ is called a complete angle.
Theory of Sets
A set is a collection of well defined objects. The objects of a set are called elements or members of the set. A set is denoted by the capital letters. Example: The collection of jewels in your home. Cardinal Number: The number of elements in a set "A" is called the cardinal number of a set and it is denoted by n(A). Different kinds of sets: The empty set: A set which containing no elements is called the empty set or null set or void set. The cardinal number of the empty set is zero. Finite set: If the number of elements in a set is zero or finite,then the set is called a finite set. The cardinal number of a finite set is finite. Infinite set: A set is said to be an infinite set if the number of elements in a set is infinite. The cardinal number of a infinite set is not a finite number. Sin
Measurement
Introduction: Measurement is the branch of Mathematics which deals with the measure of lengths,angles,areas,perimeters in plane figures and surface areas,volumes in solid figures. Area: Area is the portion inside the closed figure in a plane surface. Perimeter: The perimeter of a closed figure is the total measure of the boundary. Formulae: Circle: Area A = ℼ r² sq.units. Perimeter P = 2ℼr units. Semicircle: Area A = ½ ℼ r² sq.units. Perimeter P = ( ℼ + 2 ) r units. Quadrant of a circle: Area A = ¼ ℼ r² sq.units. Perimeter P = ( ½ ℼ + 2 ) r units.
Geometry
Geometry is the branch of Mathematics that deals with the properties of various geometrical shapes and figures.In Greek the word "Geometry" means "Earth Measurement".Geometry deals with the shape,size,position and other geometrical properties of various objects.Geometry is useful in studying space,architecture,design and engineering. Basic Geometrical Concepts: Point: A fine dot made with a sharp pencil may be taken as roughly representing a point. A point has a position but it has no length,breadth or thickness. It is denoted by the capital letters. Example: ● ● A B Line: A line is traced out by a moving point. If the point of a pencil is moved over a sheet of the paper,the trace left represent a line. A line has length,but it has no breadth. A line has no end points. A line is named with the small letters. Ray: A ray has a starti
Real Number System
INTRODUCTION: In the development of science,we should know about properties and operations on numbers which are very important in our daily life.In the earlier classes,we have studied about the whole numbers and the fundamental operations on them.Now,we extend our study to the integers,rations,decimals,fractions and powers in this chapter. NUMBERS: In real life, we use HINDU ARABIC numerals- a system which consists of the symbols 0 to 9.This system of reading and writing numerals is called,'Base ten system' or 'decimal number system'. NATURAL NUMBERS: Counting numbers are called natural numbers.These numbers start with smallest number 1 and go on without end. The set of all natural numbers is denoted by the symbol 'N' N={1,2,3,4,5.........} is the set of all natural numbers. WHOLE NUMBERS: Natural numbers together with zero (0) are called whole