Class 10 Maths NCERT

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.

If p(x) is a polynomial in x, the highest power of x in p(x) is called the degree of the polynomial p(x). For example, 4x + 2 is a polynomial in the variable x of degree 1, 2y² - 3y + 4 is a polynomial in the variable y of degree 2.

An equation which can be put in the form ax + by + c = 0, where a, b and c are real numbers, and a and b are not both zero, is called a linear equation in two variables x and y. Solution of such an equation is a pair of values, one for x and the other for y, which makes the two sides of the equation equal.

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.

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.

Two figures having the same shape but not necessarily the same size are called similar figures. All the congruent figures are similar but the converse is not true.

To locate the position of a point on a plane, you require a pair of coordinate axes. The distance of a point from the y-axis is called its x-coordinate, or abscissa. The distance of a point from the x-axis is called its y-coordinate, or ordinate.

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.

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.

A circle is a collection of all points in a plane which are at a constant distance (radius) from a fixed point (centre).

Many objects that we come across in our daily life are related to the circular shape in some form or the other. Cycle wheels, wheel barrow (thela), dartboard, round cake, papad, drain cover, various designs, bangles, brooches, circular paths, washers, flower beds. are some examples of such objects.

In this chapter, you will study how to determine the surface area of an object formed by combining any two of the basic solids - cuboid, cone, cylinder, sphere and hemisphere.

In this chapter, you will study how to measure mean, median and mode of grouped data. You will also learn the concept of cumulative frequency, the cumulative frequency distribution and how to draw cumulative frequency curves, called ogives.

In Class IX, you have studied about experimental (or empirical) probabilities of events which were based on the results of actual experiments. Experimental probabilities are based on the results of actual experiments and adequate recordings of the happening of the events.