Quantitative Ability or Mathematics is the base of human civilization. From cutting vegetables to arranging books on the shelves, from tailoring clothes to motion of Planets - Mathematics applies everywhere. Mathematics as a discipline has its own importance as it prepares you to develop **problems solving skills**.

Rotate a semicircle about its diameter. The solid so generated with this rotation is called a **sphere**.

A part of a circular region enclosed between two radii of the corresponding circle is called a **sector of the circle**.

The **circumference (perimeter)** of a circle is 2πr and its **area** is πr^{2}, where r is the radius of the circle and π is a constant equal to the ratio of circumference of a circle to its diameter.

The distance covered around a closed figure on a plane is called its perimeter.

Read more ...The area of parallelogram is equal to base multiplied by its corresponding height.

Read more ...The square is a **special rectangle** in which length and breadth are equal.

The centroid of a triangle is the point of concurrency of its medians and divides each median in the ratio of 2 : 1.

Read more ...To find the co-ordinates of a point, which divides the line segment joining two points, in a given ratio internally.

Read more ...The co-ordinates of the mid-point of the line segment joining two points (x_{1}, y_{1}) and (x_{2}, y_{2}) can be obtained by taking m = n in the section formula.

The distance between any two points P(x_{1}, y_{1}) and Q(x_{2}, y_{2}) in the plane is the length of the line segment PQ.

The position of a point is given by two numbers, called co-ordinates which refer to the distances of the point from these two axes. By convention the first number, the x-co-ordinate (or **abscissa**), always indicates the distance from the y-axis and the second number, the y-coordinate (or **ordinate**) indicates the distance from the x-axis.

The position of a **point** in a plane is fixed w.r.t. to its distances from two axes of reference, which are usually drawn by the two graduated number lines XOX′ and YOY′, at right angles to each other at O.

The Lowest Common Multiple (LCM) of two or more given numbers is the lowest (or smallest or least) of their common multiples. For example, the common multiples of 4 and 6 are 12, 24, 36, ... . The lowest of these is 12. So, the lowest common multiple of 4 and 6 is 12.

Read more ...You can find the **common factors** of any two numbers. For example, the common factors of 12 and 16 are 1, 2 and 4. The highest of these common factors is 4.

You can find a pattern that can tell whether a number is divisible by 2, 3, 4, 5, 6, 8, 9, 10 or 11.

Read more ...In the numbers 2, 4, 6, 8, 10, 12, 14, ... each of them is a multiple of 2. These are called even numbers.

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There are numbers, having exactly two factors 1 and the number itself. Such number are 2, 3, 5, 7, 11, and so on. These numbers are prime numbers.

Read more ...The decimal expansion of a rational number is either terminating or is a non-terminating and repeating decimal. A decimal expansion which is neither terminating nor is repeating represents an **irrational number**.

The process of expressing a rational number into decimal form is to carry out the process of **long division** using decimal notation.

Carl Friedrich Gauss, the great German mathematician, was in elementary school, when his teacher asked the class to find the sum of first 100 natural numbers. While the rest of the class was struggling with the problem, Gauss found the answer within no time.

Read more ...A pattern in which each term except the first is obtained by adding a fixed number (positive or negative) to the previous term is called an **Arithmetic Progression (A.P.)**.

**1.** The sum of squares of two consecutive odd natural numbers is 74. Find the numbers.

A zero of a polynomial is that real number, which when substituted for the variable makes the value of the polynomial zero. In case of a quadratic equation, the value of the variable for which LHS and RHS of the equation become equal is called a **root or solution** of the quadratic equation.

A polynomial of degree two is called a **quadratic polynomial**. When a quadratic polynomial is equated to zero, it is called a quadratic equation.

**1. **The perimeter of a rectangular garden is 20 m. If the length is 4 m more than the breadth, find the length and breadth of the garden.

An equation which contains two variables and the exponents of each variable is one and has no term involving product of variables is called a linear equation in two variables.

Read more ...Suppose a **coin** is tossed at random. You have two possible outcomes, Head (H) and Tail (T). We may assume that each outcome H or T is as likely to occur as the other. In other words, we say that the two outcomes H and T are **equally likely**.

The words **may, likely, unlikely, chances, doubt** show that the event, we are talking about , is not certain to occur. It may or may not occur. Theory of probability is a branch of Mathematics which has been developed to deal with situations involving **uncertainty**.

Mode is one of the measures of central tendency. The observation that occurs **most frequently** in the data is called mode of the data.

The mean is affected by the **extreme values** of the observations in the data. This weakness of mean drives us to look for another average which is unaffected by a few extreme values. Median is one such a measure of central tendency.

To calculate the mean of raw data, all the observations of the data are added and their sum is divided by the number of observations.

Read more ...A **continuous grouped frequency distribution** can be represented graphically by a histogram. A histogram is a vertical bar graph with no space between the bars.

Graphical representation is more convenient for the purpose of comparison among the individual items. **Bar chart (graph)** is one of the graphical representation of numerical data.

When the work of collection of data is over, the next step to the investigator is to find ways to condense and organise them in order to study their salient features. Such an arrangement of data is called **presentation of data**.

**Statistics** is the science which deals with the collection, organisation, analysis and interpretation of the numerical data.

Trigonometry can be used to determine the distance between the objects or the distance between the objects or the heights of objects.

Read more ...Let a ray OA start from OX and rotate in anti-clockwise direction and make an angle of 60° with x-axis. Take any point P on OA.

Read more ...Let a ray OA start from OX and rotate in the anti clockwise direction and make an angle of 30° with x-axis.

Read more ...Let a ray OA start from OX and rotate in the anti-clockwise direction and make an angle of 45° with the x-axis.

Read more ...Two angles are **complementary** if their sum is 90°. If the sum of two angles A and B is 90°, then ∠A and ∠B are complementary angles and each of them is complement of the other.

When equation involving a variable is true for all values of the variable, it is called an **identity**.

Let there be a right triangle ABC, right angled at B. Here ∠A (∠CAB) is an acute angle, AC is hypotenuse, side BC is opposite to ∠A and side AB is adjacent to ∠A.

Read more ...If the base and corresponding altitude of a triangle are known, you can find the area of a triangle. However, sometimes you are not given the altitude (height) corresponding to the given base of a triangle. Instead, you are given the three sides of the triangle.

Read more ...Rotate a right triangle ABC right angled at B about one of its side AB containing the right angle. The solid generated as a result of this rotation is called a **right circular cone**. In daily life, we come across many objects of this shape, such as Joker's cap, tent, ice cream cones.

Rotate a rectangle ABCD about one of its edges say AB. The solid generated as a result of this rotation is called a **right circular cylinder**. In daily life, we come across many solids of this shape such as water pipes, tin cans, drums, powder boxes.

A brick, chalk box, geometry box, match box, a book, are all examples of a cuboid. A cuboid has six rectangular regions as its **faces**.

The **counting numbers 1, 2, 3,...** constitute the system of natural numbers. These are the numbers which are used in day-to-day life.

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