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Relations and Functions in real life give us the link between any two entities. In our daily life, we come across many patterns and links that characterize relations such as a relation between a father and a son, brother and sister, etc. In mathematics also, we come across many relations between numbers such as a number x is less than y, line l is parallel to line m, etc. Relation and function map elements of one set (domain) to the elements of another set (codomain). Functions are nothing but special types of relations that define the precise correspondence between one quantity with the other. In this article, we will study how to link pairs of elements from two sets and then define a relation between them, different types of relations and functions, and the difference between relation and function.

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Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x. Mapping or transformation is used to denote a function in math. These functions are usually denoted by letters such as f, g, and h. The domain is defined as the set of all the values that the function can input while it can be defined. The range is all the values that come out as the output of the function involved. Co-domain is the set of values that have the potential of coming out as outputs of a function. Let us explore the world of functions in math.

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The types of functions are defined on the basis of the mapping, degree, and math concepts. The expression used to write the function is the prime defining factor for a function. Along with expression, the relationship between the elements of the domain set and the range set also accounts for the type of function. The classification of functions helps to easily understand and learn the different types of functions.Every mathematical expression which has an input value and a resulting answer can be conveniently presented as a function provided that every input has only one output. Here we shall learn about the types of functions and their definitions along with their graphs and examples.

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The composition of functions is the process of combining two or more functions into a single function. A function represents some work. Let us take the preparation of bread. Let x is the flour, the food processor is doing the function of preparing the dough using the flour (and let this function be g(x)) and let the oven is doing the function of making the bread (and let this function be f(x)). To prepare bread, the output of g(x) should be placed in the function f(x) (i.e., the prepared dough should be placed in the oven). The result is denoted by f(g(x)) and is a composition of functions f(x) and g(x).

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Euclid's division algorithm is a way to find the HCF of two numbers by using Euclid's division lemma. It states that if there are any two integers a and b, there exists q and r such that it satisfies the given condition a = bq + r where 0 ≤ r < b. Let's learn more about it in this lesson.

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An arithmetic progression (AP) is a sequence where the differences between every two consecutive terms are the same. For example, the sequence 2, 6, 10, 14, … is an arithmetic progression (AP) because it follows a pattern where each number is obtained by adding 4 to the previous term. A real-life example of an AP is the sequence formed by the annual income of an employee whose income increases by a fixed amount of $5000 every year. In this video, we will explore the concept of arithmetic progression, the AP formulas to find its nth term, common difference, and the sum of n terms of an AP. We will solve various examples based on the arithmetic progression formula for a better understanding of the concept.

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A series can be defined as the sum of all the numbers of the given sequence. The sequences are finite as well as infinite. In the same way, the series can also be finite or infinite. For example, consider a sequence as 1, 3, 5, 7, … Then the series of these terms will be 1 + 3 + 5 + 7 + ….. The series special in some way or the other is called a special series. The following are the three types of special series.

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The greatest common divisor of a and b is the greatest number by which a and b are both divided without a remainder. To understand this definition well, substitute any two numbers instead of variables a and b. For example, instead of the variable a we use the number 12, and instead of the variable b we use the number 9. Now let's try to read this definition: The greatest common divisor of 12 and 9 is the greatest number by which 12 and 9 are divided without a remainder. It is clear from the definition that we are talking about the common divisor of the numbers 12 and 9. The divisor is the greatest of all existing divisors. This greatest common divisor (GCD) must be found. There are three ways to find the greatest common divisor of two numbers. The first way is quite time consuming, but it gives you a good understanding of the subject and a sense of its meaning. The second and third ways are quite simple and allow you to quickly find the GCD. Consider all three methods. It is up to you to choose which one to use in practice.

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Rational expressions are fractions with variables. In a rational expression, both numerator and denominator are polynomials. i.e., it is of the form p(x)/q(x), where q(x) ≠ 0 and p(x) and q(x) are polynomials. Since rational expressions are nothing but fractions, we operate on them just the way we operate the Fractions. Here are some examples of rational expressions: (x + 1) / (x2 - 5), (x3 + 3x2 - 5) / (4x - 2), etc. Note that if one of the numerator and denominator is NOT a polynomial, then the fraction is NOT called as a rational expression.

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A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term. The important condition for an equation to be a quadratic equation is the coefficient of x2 is a non-zero term (a ≠ 0). For writing a quadratic equation in standard form, the x2 term is written first, followed by the x term, and finally, the constant term is written.

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Use the below simulation to find the nature of roots of a quadratic equation graphically. Use the sliders to adjust the values of a,ba,b, and cc, the simulation then gives the value of the discriminant, the number of real roots, and shows the graph of the quadratic equation.

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Matrices is a plural form of a matrix, which is a rectangular array or a table where numbers or elements are arranged in rows and columns. They can have any number of columns and rows. Different operations can be performed on matrices such as addition, scalar multiplication, multiplication, transposition, etc. There are certain rules to be followed while performing these matrix operations like they can be added or subtracted if only they have the same number of rows and columns whereas they can be multiplied if only columns in first and rows in second are exactly the same. Let us understand the different types of matrices and these rules in detail.

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The Pythagoras theorem states that if a triangle is a right-angled triangle, then the square of the hypotenuse is equal to the sum of the squares of the other two sides. Observe the following triangle ABC, in which we have BC2 = AB2 + AC2​​. Here, ​​​​AB is the base, AC is the altitude (height), and BC is the hypotenuse. It is to be noted that the hypotenuse is the longest side of a right-angled triangle.

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Geometry is the branch of mathematics that relates the principles covering distances, angles, patterns, areas, and volumes. All the visually and spatially related concepts are categorized under geometry. There are three types of geometry: Euclidean Hyperbolic Elliptical

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Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc. Let's learn how to calculate the area of different geometric shapes through examples and practice questions.

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A straight line is an infinite length line that does not have any curves on it. A straight line can be formed between two points also but both the ends extend to infinity. A straight line is a figure formed when two points A (x1, y1) and B (x2, y2) are connected with the shortest distance between them, and the line ends are extended to infinity.

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Trigonometry is the branch of mathematics that deals with the relationship between ratios of the sides of a right-angled triangle with its angles. The ratios used to study this relationship are called trigonometric ratios, namely, sine, cosine, tangent, cotangent, secant, cosecant. The word trigonometry is a 16th century Latin derivative, and the concept was given by the Greek mathematician Hipparchus.

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Mensuration can be explained as an act of measurement. We live in a three-dimensional world. The concept of measurement plays an important role in primary as well as secondary school mathematics. Moreover, measurement has a direct connection to our everyday lives. When learning to measure objects we learn to do so for both 3D shapes and 2D shapes. Objects or quantities can be measured using both standard and nonstandard units of measurement. For example, a non-standard unit of measuring length would be handspans. You can even do an activity on it by asking children to measure the length of objects using handspans. Let children notice that while measuring objects using non-standard units there will always be a scope of a discrepancy. Hence the need for standard units of measurement. To measure parameters like length, weight, and capacity we now have units like kilometer, meter, kilogram, gram, liter, milliliter, etc.

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Mensuration can be explained as an act of measurement. We live in a three-dimensional world. The concept of measurement plays an important role in primary as well as secondary school mathematics. Moreover, measurement has a direct connection to our everyday lives. When learning to measure objects we learn to do so for both 3D shapes and 2D shapes. Objects or quantities can be measured using both standard and nonstandard units of measurement. For example, a non-standard unit of measuring length would be handspans. You can even do an activity on it by asking children to measure the length of objects using handspans. Let children notice that while measuring objects using non-standard units there will always be a scope of a discrepancy. Hence the need for standard units of measurement. To measure parameters like length, weight, and capacity we now have units like kilometer, meter, kilogram, gram, liter, milliliter, etc.

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Mensuration can be explained as an act of measurement. We live in a three-dimensional world. The concept of measurement plays an important role in primary as well as secondary school mathematics. Moreover, measurement has a direct connection to our everyday lives. When learning to measure objects we learn to do so for both 3D shapes and 2D shapes. Objects or quantities can be measured using both standard and nonstandard units of measurement. For example, a non-standard unit of measuring length would be handspans. You can even do an activity on it by asking children to measure the length of objects using handspans. Let children notice that while measuring objects using non-standard units there will always be a scope of a discrepancy. Hence the need for standard units of measurement. To measure parameters like length, weight, and capacity we now have units like kilometer, meter, kilogram, gram, liter, milliliter, etc.

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Mensuration can be explained as an act of measurement. We live in a three-dimensional world. The concept of measurement plays an important role in primary as well as secondary school mathematics. Moreover, measurement has a direct connection to our everyday lives. When learning to measure objects we learn to do so for both 3D shapes and 2D shapes. Objects or quantities can be measured using both standard and nonstandard units of measurement. For example, a non-standard unit of measuring length would be handspans. You can even do an activity on it by asking children to measure the length of objects using handspans. Let children notice that while measuring objects using non-standard units there will always be a scope of a discrepancy. Hence the need for standard units of measurement. To measure parameters like length, weight, and capacity we now have units like kilometer, meter, kilogram, gram, liter, milliliter, etc.

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Statistics is used mainly to gain an understanding of the data and focus on various applications. Statistics is the process of collecting data, evaluating data, and summarizing it into a mathematical form. Initially, statistics were related to the science of the state where it was used in the collection and analysis of facts and data about a country such as its economy, population, etc. Mathematical statistics applies mathematical techniques like linear algebra, differential equations, mathematical analysis, and theories of probability. There are two methods of analyzing data in mathematical statistics that are used on a large scale: Descriptive Statistics Inferential Statistics

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Mean of grouped data is the data set formed by aggregating individual observations of a variable into different groups. Grouped data is data that is grouped together in different categories. Mean is considered as the average of the data. For the mean of grouped data, it might be difficult to find the exact value however, we can always estimate it. Let us learn more about the mean of grouped data, the methods to find the mean of grouped data, and solve a few examples to understand this concept better.

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Probability defines the likelihood of occurrence of an event. There are many real-life situations in which we may have to predict the outcome of an event. We may be sure or not sure of the results of an event. In such cases, we say that there is a probability of this event to occur or not occur. Probability generally has great applications in games, in business to make predictions, and also it has extensive applications in this new area of artificial intelligence. The probability of an event can be calculated by the probability formula by simply dividing the favorable number of outcomes by the total number of possible outcomes. The value of the probability of an event happening can lie between 0 and 1 because the favorable number of outcomes can never be more than the total number of outcomes. Also, the favorable number of outcomes cannot be negative.

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