Ecosystem. The in terlinkage and interdependence of all plants and animals in a given area form an ecosystem.
Biosphere. It is the narrow belt of living organisms.
Biosphere Reserve. It is the forest area where all types of flora and fauna are preserved in their natural environment.
Biomes. Plant species occurring in distinct groups in areas having similar climatic conditions.
Savanna. It is similar to grassland but with scattered trees. There is a rich growth of grasses during hot or wet season.
Coniferous forests. They are evergreen cone bearing trees with needle-shaped leaves found between 1,600 and 3000 metres above sea level, e.g., pine, spruce, cedar etc.
Deciduous forests. They consist of trees which shed their leaves for about six to eight weeks in summer, e.g., sal, teak, shisham etc.
Natural vegetation. A plant community that has not been disturbed over a long period.
Flora. The original natural vegetation cover consisting of forests, grasslands, and shrubs.
Alpine vegetation. Above coniferous forests, there lies the Alpine vegetation at an altitude of about 3,600 metres and above. This is the tree line in the Himalayas. It has dense scrub forests of silver fir, birch and junipers. The Alpine forests give way to the Alpine grassland and shrubs.
Tundra vegetation. At about 5000 metres (snowline) there is a permanent cover of ice and snow, tundra vegetation of moss and lichen is found in this region.
Thorn and Scrub forests. They are so called due to the dominance of thorny trees, bushes and scrubs. They grow in dry areas of less than 75 cm annual rainfall. These trees and bushes have long roots which spread in radial pattern, thick bark, sharp thorns and waxy leaves. These devices help them to preserve water and protect themselves from animals, e.g., Kiker, Babool, Datepalm etc.
Fauna. All forms of animals found on the earth in natural environment.
Biosphere. Narrow belt of living organisms.
National Parks. They are relatively large area where one or several ecosystems exist and where plant and animal species, geomorphological sites and habitats are of special educative and recreative interests, e.g., Jim Corbett Park.
Wildlife sanctuary. It is similar to national park but is dedicated to protect wildlife and conserve pecies, e.g., Gir Lion Sanctuary.
Biosphere reserve. It is a multipurpose protected area to preserve the genetic diversity in the representative ecosystem, e.g., Nanda Devi.
Endemic. They are purely Indian plant species,
Exotic plants. Plants which have come from outside India.
Virgin vegetation. Plants which have grown naturally without human effort.
Introduction to Disaster Management
1.Need for introducing project work in Social Science was being felt for quite some time. There is a need to have projects to enhance students' understanding of different concepts, principles provided in the subject. This also introduces an alternative node of learning in classrooms with a purpose to create students' interest in the abject and enabling them to express their viewpoints.
This year in Class IX also, students are required to take up Disaster Management as part of the project.
Preparation of Project Work
2.At the end of the stipulated term, each student will prepare and submit his/her reject report. The following requirements are to be fulfilled for its preparation and submission.
The total length of the project report will not be more than 15-20 written pages of full scape size (A-4).
The project report will be handwritten and credit will be awarded to original drawings, illustrations and creative use of materials.
Students should discuss the topic with their concerned teachers and prepare a draft before finalising the report.
The project report will be presented in a neatly bound simple folder.
The project report will be developed and presented in the following order:
(a) Cover page: Student's name, roll no., school's name, year and the title of the project.
(b) Content: It will contain all the subtopics of the presentation.
(c) Acknowledgements: To the institution, teachers, libraries, places visited and the persons who helped them in preparing the project.
(d) Chapters: These would be having relevant headings.
(e) Bibliography: It should acknowledge any website with specific weblink, books, their pages referred, author and publisher.
Allocation of Marks
A number which can be expressed in the form of \[\frac{p}{q}\], Where p and q are integers and \[q\ne 0\]is called a rational number.
Example:- \[\frac{1}{2},\frac{1}{3},\frac{2}{5}\] etc.
Representation of Rational Number as Decimals.
Case I:- When remainder becomes zero \[\frac{1}{2}=.5,\frac{1}{4}=.25,\frac{1}{8}=.125\] it is a terminating Decimal expansion.
Case II:- When Remainder never becomes zero..
Example:- \[\frac{1}{3}=.3333,\frac{2}{3}=.6666\]it is a non - terminating Decimal expansion.
There are infinitely rational numbers between any two given rational numbers.
Irrational Number: The number which cannot be part in form of \[\frac{p}{q}\]and neither there are terminating nor recurring are known as irrational Number.
Example:- \[\sqrt{2},\sqrt{3}\text{ }etc.\]
Rationalization: "Changing of an irrational number into rational number is called rationalization and the factor by which we multiply and divide the number is called rationalizing factor.
Example:- Rationalizing factor of \[\frac{1}{2-\sqrt{3}}\]is \[2+\sqrt{3}\,.\]
Rationalizing factor of \[\sqrt{3}+\sqrt{2}\]is\[\sqrt{3}-\sqrt{2}\]
LAW OF EXPONENTS FOR REAL NUMBERS
\[{{a}^{m}}\times {{a}^{n}}={{a}^{m+n}}\]
\[\frac{{{a}^{m}}}{{{a}^{n}}}={{a}^{m-n}}\]
\[{{\left( {{a}^{m}} \right)}^{n}}={{a}^{mn}}\]
\[{{a}^{{}^\circ }}=1\]
Some useful results on irrational number
Negative of an irrational number is an irrational number.
The sum of a rational and an irrational number is an irrational number.
The product of a non - zero rational number and an irrational number is an irrational
An algebraic expression in which the variables involved have only non – negative integral powers is called a polynomial.
GENERAL FORM OF A POLYNOMIALS
\[P(x)={{a}_{0}}+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+....+{{a}_{n}}{{x}^{n}}\] is a polynomials in variable x, where \[{{a}_{0}},{{a}_{1}},{{a}_{2}},{{a}_{3}}....,{{a}_{n}}\]are real numbers and n is a non - negative integer.
Examples:- (i) \[7{{x}^{3}}+4{{x}^{2}}+6x-2\]is a polynomial in one variable x.
(ii) \[3+2{{x}^{3}}-5{{x}^{2}}y+6x{{y}^{2}}\]is a polynomial in two variables x and y.
Coefficients:- In the polynomials \[5{{x}^{3}}-3{{x}^{2}}+2x-7\], coefficients of \[{{x}^{3}},{{x}^{2}}\] and \[x\] are 5, -3, and 2 respectively and -7 is the constant term in it.
DEGREE OF A POLYNOMIAL IN TWO OR MORE VARIABLES
Variables:- In case of polynomials in more than one variable, the sum of the powers of the variable in each term is taken up and the highest sum so obtained is called the degree of polynomials.
Example:- \[7{{x}^{3}}-5{{x}^{2}}{{y}^{2}}+3xy+7y+9\]is a polynomial in x and y of degree 4.
Linear polynomial:- A polynomial of degree 1 is called a linear polynomial.
Quadratic polynomial:- A polynomial of degree 2 is called a quadratic polynomial.
Cubic Polynomial:- A polynomial of degree 3 is called a cubic polynomial
Biquadratic polynomial:- A polynomial of degree 4 is called a biquadratic polynomial.
Monomial:- A polynomial containing one non-zero term.
Binomial:- A polynomial containing two non-zero terms.
Trinomial:- A polynomial containing three non-zero terms.
Constant polynomial:- A polynomial containing one term only consisting of a constant term is called a constant polynomial.
Zero polynomial:- A polynomial consisting of one term namely zero is called a zero polynomial. The degree of a zero polynomial is not defined.
Remainder theorem:- Let f(x) be a polynomial of degree \[x\ge 1\] and let a be the any real number. When f(x) is divided by (x - a), then the remainder is f(a).
Factor theorem:- Let f(x) be a polynomial of degree greater than or equal to 1 and a be a real number such that p(a) = 0, then (x-a) is a factor off(x).
GCD:- The GCD of two polynomials P(x) and q(x) is that common divisor which has the highest degree among all common divisors and the coefficient of the highest degree term is positive.
LCM:- The LCM of two polynomials p(x) and q(x) is a polynomial of lowest degree of which p(x) and q(x) are multiples.
An equation of the form \[ax+by+c=0,\]where a, b, c are real numbers \[(a\ne 0,b\ne 0)\] is called a linear equation in two variables x and y.
Example:- \[(i)\,\,3x+4y-2=0\]
\[\left( ii \right)\,\,4x+7y=3\]
Are the linear equations in x and y?
Solution:- Any point of values of x and y which satisfies the equation ax \[4x+by+=0\] is called a solution of it.
Example:- \[x=3,y=2\] is a solution of \[3x+2y=13\] because, when \[x=3\] and \[y=2,\] we have\[L.H.S=3\times 3+2\times 2=13=R.H.S\]
A linear equation in two variables has infinite solutions.
The graph of a two variables linear equation in two variables is a straight line.
Example:- \[x+2y=7\]
X
1
3
-1
-3
Y
3
2
4
5
The graph of equation parallel to y-axis The graph of equation parallel to x-axis
\[x=2\] \[y=2\]
Every point on the graph of a linear equation in two variables is a solution of the equation conversely every solution of the linear equation in two variable represents a point on the graph of the equation.
Let the two line represented by the equations \[{{x}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0\,and\,{{x}_{2}}x+{{b}_{2}}y+c=0\]
Line Segment:- A part of line with two end points is called a line segment.
Here, line segment is denoted by \[\overline{AB}\].
Ray;- A part of a line with one end point is called ray.
Angle:- An angle is the union of two rays with a common initial point. It is denoted by \[\angle \].
The angle formed by two rays OX and OY is \[\angle XOY\] and \[\angle YOX.\]
Acute angle:- Greater than \[{{0}^{{}^\circ }}\] but less than\[{{90}^{{}^\circ }}\].
Here, \[\theta \] is an obtuse angle.
Obtuse angle:- Greater than 90° but less than \[{{180}^{{}^\circ }}\]
Here, \[\theta \] is a straight angle.
Right angle:- Equal to \[{{90}^{{}^\circ }}\]
Here, \[\theta \] is a right angle.
Straight angle:- Exactly equal to \[{{180}^{{}^\circ }}\]
Here, \[\theta \] is an acute angle.
Reflex angle:- Greater then \[{{180}^{{}^\circ }}\] but less then \[{{360}^{{}^\circ }}\]
Here, \[\theta \] is reflex angle
Complementary angle:- Two angles whose sum is \[90{}^\circ \] are called complementary angles.
\[\angle XOZ\] and \[\angle YOZ\] are complementary angles.
Supplementary angle:- Two angles whose sum is \[180{}^\circ \] are called supplementary angles.
\[\angle XOZ\] and \[\angle YOZ\] are supplementary angles.
Adjacent angle:- Two angles are said to be adjacent angle if they have the same vertex and a common arm and uncommon arm on the either side of the common arm.
\[\angle 1\] and \[\angle 2\]are called Adjacent angles.
Linear pair of angles:- Two adjacent angles are called linear pair of angles if their non- common arms are two opposite rays. These angles are supplementary.
Angle \[\angle 1\] and \[\angle 2\] are linear pair of angles.
Vertically opposite angle:- Two angles are called vertically opposite angles if their arms form two pairs of opposite rays. These two vertically opposite angles are equal.
\[\angle 1\] and \[\angle 3\] are vertically opposite angles and also \[\angle 2\] and \[\angle 4\] are vertically opposite angles.
\[\angle B=\angle Y={{90}^{{}^\circ }}\] \[BC=YZ\], then \[\Delta ABC\cong \Delta XYZ.\]
SIMILARITY OF A TRIANGLE
Two triangles are similar if their corresponding angles are equal and also their corresponding sides are in the same ratio
\[\Delta ABC\] and \[\Delta XYZ\] are similar if \[\angle A=\angle X,\angle B=\angle Y,\text{ }\angle C=\angle Z\] and \[\frac{AB}{XY}\text{=}\frac{BC}{YZ}=\frac{AC}{XZ}\]
Centroid of a triangle:- Point of intersection of all the three medians.
Here, Point G is centroid of triangle ABC
In Centre:- Meeting Point of all the three angle bisectors of a more...
Circle:- The collection of all the points in a plane which are equidistant from a fixed point in the plane is called a circle.
Centre:- The fixed point O is called the centre of the circle.
Radius:- Radius is the distance from centre of a circle in any point on its circumferences Here, OX is a radius.
Chord:- A line segment whose end points on the circumference of a circle is called a chord.
Here, XY is a chord.
Diameter:- A chord passing through, the centre O of the circle is called a diameter of the circle . It is largest chord of the circle and twice that of the radius.
Here, XY is a diameter.
Semi-circle:- A diameter of a circle divides it into two equal parts and each part is called a semi-circle.
Segments: A chord divides a circle into two parts,, which are called segments, smaller parts of the circle called minor segment: and larger part is called major segment
Tangents:- A line that touches the circle at one end point only is called a tangent.
When two circles touch each other externally, then 3 tangents can be drawn.
When two circles intersect each other externally, then two tangents can be drawn.
When one circle touches another circle internally, then only one tangent can be drawn.
If two circles do not touches each other then 4 tangents can be drawn.
The angle in a semi - circle is a right angle i.e., \[\angle XZY={{90}^{{}^\circ }}\]
Angles in the same segment of a circle are equal.
i.e., \[\angle 1=\angle 2\]
The angle subtended by an arc of a circle at the centre is twice the angle subtended by it at its circumference.
Here, line segment is denoted by \[\overline{AB}\].
The angle formed by two rays OX and OY is \[\angle XOY\] and \[\angle YOX.\]
Here, \[\theta \] is an obtuse angle.
Here, \[\theta \] is a straight angle.
Here, \[\theta \] is a right angle.
Here, \[\theta \] is an acute angle.
Here, \[\theta \] is reflex angle
\[\angle XOZ\] and \[\angle YOZ\] are complementary angles.
\[\angle XOZ\] and \[\angle YOZ\] are supplementary angles.
\[\angle 1\] and \[\angle 2\]are called Adjacent angles.
Angle \[\angle 1\] and \[\angle 2\] are linear pair of angles.
\[\angle 1\] and \[\angle 3\] are vertically opposite angles and also \[\angle 2\] and \[\angle 4\] are vertically opposite angles.
i.e., \[\angle A=\angle B=\angle C\] and also \[AB=BC=AC\]
i.e., \[\angle B=\angle C\ne \angle A\] \[AB=AC\]
i.e., \[AB\ne BC\ne AC\]
and \[\angle A\ne \angle B\ne \angle C\]
\[\angle A=\angle X\], \[\angle B=\angle Y\], \[\angle C=\angle Z\]
\[AB=XY\], \[BC=YZ\], \[AC=XZ\]
\[AB=XY,BC=YZ\] and \[AC=XZ\]
Then \[\Delta ABC\cong \Delta XYZ\]
\[AB=XY\], \[BC=YZ\] and \[\angle B=\angle Y\]
Then \[\Delta ABC\cong \Delta XYZ\]
\[\angle B=\angle Y,\text{ }\angle C=\angle Z,\text{ }BC=YZ\]
Then, \[\Delta ABC\cong \Delta XYZ\]
\[\angle B=\angle Y={{90}^{{}^\circ }}\] \[BC=YZ\], then \[\Delta ABC\cong \Delta XYZ.\]
SIMILARITY OF A TRIANGLE
\[\Delta ABC\] and \[\Delta XYZ\] are similar if \[\angle A=\angle X,\angle B=\angle Y,\text{ }\angle C=\angle Z\] and \[\frac{AB}{XY}\text{=}\frac{BC}{YZ}=\frac{AC}{XZ}\]
Here, Point G is centroid of triangle ABC
In Centre:- Meeting Point of all the three angle bisectors of a
