Articles

It is difficult for us to imagine a world without printed matter. We find evidence of print everywhere around us – in books, journals, newspapers, prints of famous paintings, and also in everyday things like theatre programmes, official circulars, calendars, diaries, advertisements, cinema posters at street corners.

1. What does the geology of the peninsular plateau show?

The geology of the peninsular plateau shows that it constitutes one of the ancient landmasses on the earth’s surface. It was supposed to be one of the most stable blocks.

In 1900, a popular music publisher E.T. Paull produced a music book that had a picture on the cover page announcing the ‘Dawn of the Century’. At the centre of the picture is a goddess-like figure, the angel of progress, bearing the flag of the new century. She is gently perched on a wheel with wings, symbolising time.

In 1848, Frédéric Sorrieu, a French artist, prepared a series of four prints visualising his dream of a world made up of ‘democratic and social Republics’, as he called them. The first print of the series, shows the peoples of Europe and America - men and women of all ages and social classes - marching in a long train, and offering homage to the statue of Liberty as they pass by it.

The French Revolution opened up the possibility of creating a dramatic change in the way in which society was structured. Before the eighteenth century society was broadly divided into estates and orders and it was the aristocracy and church which controlled economic and social power.

A lot of this diversity is fast disappearing. Between 1700 and 1995, the period of industrialisation, 13.9 million sq km of forest or 9.3 per cent of the world’s total area was cleared for industrial uses, cultivation, pastures and fuelwood.

An event for an experiment is the collection of some outcomes of the experiment. The Probability of an event lies between 0 and 1 (0 and 1 inclusive).

An arithmetic progression is a list of numbers in which each term is obtained by adding a fixed number to the preceding term except the first term.

To locate the position of an object or a point in a plane, we require two perpendicular lines. One of them is horizontal, and the other is vertical. The plane is called the Cartesian, or coordinate plane and the lines are called the coordinate axes.

Facts or figures, collected with a definite purpose, are called data. Statistics is the area of study dealing with the presentation, analysis and interpretation of data. How data can be presented graphically in the form of bar graphs, histograms and frequency polygons.

A circle is the collection of all points in a plane, which are equidistant from a fixed point in the plane.

Area of a figure is a number (in some unit) associated with the part of the plane enclosed by that figure. Two congruent figures have equal areas but the converse need not be true.

Two figures are congruent, if they are of the same shape and of the same size. Two circles of the same radii are congruent. Two squares of the same sides are congruent.

The various components of an ecosystem are interdependent. The producers make the energy from sunlight available to the rest of the ecosystem. There is a loss of energy as we go from one trophic level to the next, this limits the number of trophic levels in a food-chain.

When we talk of ‘globalisation’ we often refer to an economic system that has emerged since the last 50 years or so. But as you will see in this chapter, the making of the global world has a long history - of trade, of migration, of people in search of work, the movement of capital, and much else.

As you have seen, modern nationalism in Europe came to be associated with the formation of nation-states. It also meant a change in people’s understanding of who they were, and what defined their identity and sense of belonging.

In this chapter you will read about nomadic pastoralists. Nomads are people who do not live in one place but move from one area to another to earn their living. In many parts of India we can see nomadic pastoralists on the move with their herds of goats and sheep, or camels and cattle.

In the spring of 1945, a little eleven-year-old German boy called Helmuth was lying in bed when he overheard his parents discussing something in serious tones.

One type of polynomial is the quadratic polynomial of the form ax² + bx + c, a ≠ 0. When you equate this polynomial to zero, you get a quadratic equation. Quadratic equations come up when you deal with many real-life situations.

Euclid’s division algorithm, as the name suggests, has to do with divisibility of integers. Stated simply, it says any positive integer a can be divided by another positive integer b in such a way that it leaves a remainder r that is smaller than b.

Trigonometry is one of the most ancient subjects studied by scholars all over the world. Trigonometry was invented because its need arose in astronomy. Since then the astronomers have used it, for instance, to calculate distances from the Earth to the planets and stars.

The word ‘trigonometry’ is derived from the Greek words ‘tri’ (meaning three), ‘gon’ (meaning sides) and ‘metron’ (meaning measure). trigonometry is the study of relationships between the sides and angles of a triangle.

A polynomial p(x) in one variable x is an algebraic expression in x of the form

An equation of the form ax + by + c = 0, where a, b and c are real numbers, such that a and b are not both zero, is called a linear equation in two variables. A linear equation in two variables has infinitely many solutions.

A number r is called a rational number, if it can be written in the form p/q, where p and q are integers and q ≠ 0. A number s is called a irrational number, if it cannot be written in the form p/q, where p and q are integers and q ≠ 0.

So far, you have been dealing with figures that can be easily drawn on our notebooks or blackboards. These are called plane figures.

Light seems to travel in straight lines. Mirrors and lenses form images of objects. Images can be either real or virtual, depending on the position of the object.

Carbon is a versatile element that forms the basis for all living organisms and many of the things we use. This large variety of compounds is formed by carbon because of its tetravalency and the property of catenation that it exhibits.

A compass needle is a small magnet. Its one end, which points towards north, is called a north pole, and the other end, which points towards south, is called a south pole. A magnetic field exists in the region surrounding a magnet, in which the force of the magnet can be detected.

Control and coordination are the functions of the nervous system and hormones in our bodies. The responses of the nervous system can be classified as reflex action, voluntary action or involuntary action.

Sum of the

If a ray stands on a line, then the sum of the two adjacent angles so formed is 180° and vice-versa. This property is called as the Linear pair axiom. If two lines intersect each other, then the vertically opposite angles are equal.

Movement of various types can be taken as an indication of life. Maintenance of life requires processes like nutrition, respiration, transport of materials within the body and excretion of waste products.

Variations arising during the process of reproduction can be inherited. These variations may lead to increased survival of the individuals. Sexually reproducing individuals have two copies of genes for the same trait. If the copies are not identical, the trait that gets expressed is called the dominant trait and the other is called the recessive trait.

Elements can be classified as metals and non-metals. Metals are lustrous, malleable, ductile and are good conductors of heat and electricity. They are solids at room temperature, except mercury which is a liquid. Metals can form positive ions by losing electrons to non-metals.

A stream of electrons moving through a conductor constitutes an electric current. Conventionally, the direction of current is taken opposite to the direction of flow of electrons. The SI unit of electric current is ampere.

Much of mathematics is about finding a pattern - a recognisable link between quantities that change. In our daily life, we come across many patterns that characterise relations such as brother and sister, father and son, teacher and student.

The word ‘trigonometry’ is derived from the Greek words ‘trigon’ and ‘metron’ and it means ‘measuring the sides of a triangle’. The subject was originally developed to solve geometric problems involving triangles.

The equation x² + 1 = 0 has no real solution as x² + 1 = 0 gives x² = -1 and square of every real number is non-negative.

If we interchange any two rows (or columns), then sign of determinant changes. If any two rows or any two columns are identical or proportional, then value of determinant is zero.

A real valued function is continuous at a point in its domain if the limit of the function at that point equals the value of the function at that point. A function is continuous if it is continuous on the whole of its domain.

If a quantity y varies with another quantity x, satisfying some rule y = f(x), then f'(x) represents the rate of change of y with respect to x.

Differential Calculus is centred on the concept of the derivative. The original motivation for the derivative was the problem of defining tangent lines to the graphs of functions and calculating the slope of such lines.

In geometry, we have learnt formulae to calculate areas of various geometrical figures including triangles, rectangles, trapezias and circles. Such formulae are fundamental in the applications of mathematics to many real life problems.

In Class XI and in Chapter 5 of the present book, we discussed how to differentiate a given function f with respect to an independent variable, i.e., how to find f'(x) for a given function f at each x in its domain of definition.

In our day to day life, we come across many queries such as - What is your height? How should a football player hit the ball to give a pass to another player of his team? Observe that a possible answer to the first query may be 1.6 meters, a quantity that involves only one value (magnitude) which is a real number. Such quantities are called scalars.

In Class XI, while studying Analytical Geometry in two dimensions, and the introduction to three dimensional geometry, we confined to the Cartesian methods only. In the previous chapter of this book, we have studied some basic concepts of vectors.

In earlier classes, we have discussed systems of linear equations and their applications in day to day problems. In Class XI, we have studied linear inequalities and systems of linear inequalities in two variables and their solutions by graphical method. Many applications in mathematics involve systems of inequalities or equations.

In earlier Classes, we have studied the probability as a measure of uncertainty of events in a random experiment. We discussed the axiomatic approach formulated by Russian Mathematician, A.N. Kolmogorov (1903-1987) and treated probability as a function of outcomes of the experiment.

In this chapter, you study different types of relations and equivalence relation, composition of functions, invertible functions and binary operations.