Sets in mathematics, are simply a collection of distinct objects forming a group. A set can have any group of items, be it a collection of numbers, days of a week, types of vehicles, and so on. Every item in the set is called an element of the set. Curly brackets are used while writing a set. A very simple example of a set would be like this. Set A = {1, 2, 3, 4, 5}. In set theory, there are various notations to represent elements of a set. Sets are usually represented using a roster form or a set builder form. Let us discuss each of these terms in detail.

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Sets in mathematics, are simply a collection of distinct objects forming a group. A set can have any group of items, be it a collection of numbers, days of a week, types of vehicles, and so on. Every item in the set is called an element of the set. Curly brackets are used while writing a set. A very simple example of a set would be like this. Set A = {1, 2, 3, 4, 5}. In set theory, there are various notations to represent elements of a set. Sets are usually represented using a roster form or a set builder form. Let us discuss each of these terms in detail.

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Sets in mathematics, are simply a collection of distinct objects forming a group. A set can have any group of items, be it a collection of numbers, days of a week, types of vehicles, and so on. Every item in the set is called an element of the set. Curly brackets are used while writing a set. A very simple example of a set would be like this. Set A = {1, 2, 3, 4, 5}. In set theory, there are various notations to represent elements of a set. Sets are usually represented using a roster form or a set builder form. Let us discuss each of these terms in detail.

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Sets in mathematics, are simply a collection of distinct objects forming a group. A set can have any group of items, be it a collection of numbers, days of a week, types of vehicles, and so on. Every item in the set is called an element of the set. Curly brackets are used while writing a set. A very simple example of a set would be like this. Set A = {1, 2, 3, 4, 5}. In set theory, there are various notations to represent elements of a set. Sets are usually represented using a roster form or a set builder form. Let us discuss each of these terms in detail.

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Algebra is a branch of mathematics that deals with symbols and the arithmetic operations across these symbols. These symbols do not have any fixed values and are called variables. In our real-life problems, we often see certain values that keep on changing. But there is a constant need to represent these changing values. Here in algebra, these values are often represented with symbols such as x, y, z, p, or q, and these symbols are called variables. Further, these symbols are manipulated through various arithmetic operations of addition, subtraction, multiplication, and division, with the objective to find the values.

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Algebra is a branch of mathematics that deals with symbols and the arithmetic operations across these symbols. These symbols do not have any fixed values and are called variables. In our real-life problems, we often see certain values that keep on changing. But there is a constant need to represent these changing values. Here in algebra, these values are often represented with symbols such as x, y, z, p, or q, and these symbols are called variables. Further, these symbols are manipulated through various arithmetic operations of addition, subtraction, multiplication, and division, with the objective to find the values.

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Math formulas are expressions that have been created after several decades of research that help to solve questions quickly. It is easy to perform simple arithmetic calculations such as addition, subtraction, and so on. However, when it comes to algebraic expressions, geometry, and other topics you need mathematical formulas to simplify the process of reaching the answer and saving time in the process. At Cuemath you will not only find formulas for each and every topic but will also get an idea of how that equation was developed. Thus, you will not have to memorize formulas, as you understand the concept behind them.

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Combinations are also called selections. Combinations correspond to the selection of things from a given set of things. Here we do not intend to arrange things. We intend to select them. We denote the number of unique r-selections o combinations out of a group of n objects by Combinations are different from arrangements or permutations. Let us learn more about how to calculate combinations, combinations formula, differences between permutation and combinations, with the help of examples, FAQs

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Mathematical Induction is a technique used to prove that a mathematical statements P(n) holds for all natural numbers n = 1, 2, 3, 4, ... It is often referred as the principle of mathematical induction. To prove a result P(n) using the principle of mathematical induction, we prove that P(1) holds. If P(1) is true, then we assume that P(k) holds for some natural number k, and using this hypothesis, we prove that P(k+ 1) is true. If P(k+1) holds true, then the statement P(n) becomes true for all natural numbers.

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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. Here in the below content, we shall understand the basics of trigonometry, the various identities-formulas of trigonometry, and the real-life examples or applications of trigonometry.

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Permutations are different ways of arranging objects in a definite order. It can also be expressed as the rearrangement of items in a linear order of an already ordered set. The symbol nPr is used to denote the number of permutations of n distinct objects, taken r at a time. It locks schedules of buses, trains or flights, allocation of zip codes and phone numbers. These are a few situations where permutations are used. Permute means to position. Let us learn more about permutations along with a few solved examples.

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The first mention of the binomial theorem was in the 4th century BC by a famous Greek mathematician by name of Euclid's. The binomial theorem states the principle for expanding the algebraic expression (x + y)n and expresses it as a sum of the terms involving individual exponents of variables x and y. Each term in a binomial expansion is associated with a numeric value which is called coefficient.

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Sequence and series are used in mathematics as well as in our daily lives. A sequence is also known as progression and a series is developed by sequence. Sequence and series is one of the basic concepts in Arithmetic. Sequences are the grouped arrangement of numbers orderly and according to some specific rules, whereas a series is the sum of the elements in the sequence. For example, 2, 4, 6, 8 is a sequence with four elements and the corresponding series will be 2 + 4 + 6+ 8, where the sum of the series or value of the series will be 20. There are various types of sequences and series depending upon the set of rules that are used to form the sequence and series. Sequence and series are explained in detail below.

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Analytical Geometry is a combination of algebra and geometry. In analytical geometry, we aim at presenting the geometric figures using algebraic equations in a two-dimensional coordinate system or in a three-dimensional space. Analytical geometry includes the basic formulas of coordinate geometry, equations of a line and curves, translation and rotation of axes, and three-dimensional geometry concepts. Let us understand the various sub-branches of analytical geometry, and also check the examples and FAQs on analytical geometry.

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Analytical Geometry is a combination of algebra and geometry. In analytical geometry, we aim at presenting the geometric figures using algebraic equations in a two-dimensional coordinate system or in a three-dimensional space. Analytical geometry includes the basic formulas of coordinate geometry, equations of a line and curves, translation and rotation of axes, and three-dimensional geometry concepts. Let us understand the various sub-branches of analytical geometry, and also check the examples and FAQs on analytical geometry.

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Determinants are the scalar quantities obtained by the sum of products of the elements of a square matrix and their cofactors according to a prescribed rule. They help to find the adjoint, inverse of a matrix. Further to solve the linear equations through the matrix inversion method we need to apply this concept. The cross-product of two vectors is remembered easily through the calculation of determinants. In this article, let's learn more about the process of finding determinants of different orders and their properties, and we will work on a few solved examples.

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Determinants are the scalar quantities obtained by the sum of products of the elements of a square matrix and their cofactors according to a prescribed rule. They help to find the adjoint, inverse of a matrix. Further to solve the linear equations through the matrix inversion method we need to apply this concept. The cross-product of two vectors is remembered easily through the calculation of determinants. In this article, let's learn more about the process of finding determinants of different orders and their properties, and we will work on a few solved examples.

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Determinants are the scalar quantities obtained by the sum of products of the elements of a square matrix and their cofactors according to a prescribed rule. They help to find the adjoint, inverse of a matrix. Further to solve the linear equations through the matrix inversion method we need to apply this concept. The cross-product of two vectors is remembered easily through the calculation of determinants. In this article, let's learn more about the process of finding determinants of different orders and their properties, and we will work on a few solved examples.

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Properties of determinants are needed to find the value of the determinant with the least calculations. The properties of determinants are based on the elements, the row, and column operations, and it helps to easily find the value of the determinant. In this article, we will learn more about the properties of determinants and go through some solved examples for a better understanding of the concept.

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The parallelogram law of vector addition is a method that is used to find the sum of two vectors in vector theory. We study two laws for the addition of vectors - the triangle law of vector addition and the parallelogram law of vector addition. The parallelogram law of vector addition is used to add two vectors when the vectors that are to be added form the two adjacent sides of a parallelogram by joining the tails of the two vectors. Then, the sum of the two vectors is given by the diagonal of the parallelogram passing through the tail of the two vectors.

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3D shapes are solid shapes or objects that have three dimensions (which are length, width, and height), as opposed to two-dimensional objects which have only a length and a width. Other important terms associated with 3D geometric shapes are faces, edges, and vertices. They have depth and so they occupy some volume. Some 3D shapes have their bases or cross-sections as 2D shapes. For example, a cube has all its faces in the shape of a square. Let us now learn about each 3-dimensional shape (3D shape) in detail. 3D shapes are classified into several categories. Some of them have curved surfaces; some are in the shape of pyramids or prisms.

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Vectors algebra involves algebraic operations across vectors. The algebraic operations involving the magnitude and direction of vectors is performed in vector algebra. Vector algebra helps for numerous applications in physics, and engineering to perform addition and multiplication operations across physical quantities, represented as vectors in three-dimensional space. Let us learn more about vector algebra, operations in vector algebra, vector types, with the help of solved examples, and practice questions.

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The continuity of a function and the differentiability of a function are complementary to each other. The function y = f(x) needs to be first proved for its continuity at a point x = a, before it is proved for its differentiability at the point x = a. The concepts of continuity and differentiability can be proved both geometrically and algebraically.

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Trigonometric identities are a fundamental aspect of trigonometry, which is the study of the relationships between the angles and sides of triangles. These identities are mathematical equations that involve trigonometric functions, such as sine, cosine, and tangent, and are true for all values of the variables involved. Trigonometry identities are useful for simplifying expressions, solving equations, and proving mathematical theorems in various fields of science and engineering. Understanding the properties and applications of these identities is essential for students and professionals in fields such as mathematics, physics, and engineering.

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The process of finding derivatives of a function is called differentiation in calculus. A derivative is the rate of change of a function with respect to another quantity. The laws of Differential Calculus were laid by Sir Isaac Newton. The principles of limits and derivatives are used in many disciplines of science. Differentiation and integration form the major concepts of calculus. Let us learn the techniques of differentiation to find the derivatives of algebraic functions, trigonometric functions, and exponential functions.

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The process of finding derivatives of a function is called differentiation in calculus. A derivative is the rate of change of a function with respect to another quantity. The laws of Differential Calculus were laid by Sir Isaac Newton. The principles of limits and derivatives are used in many disciplines of science. Differentiation and integration form the major concepts of calculus. Let us learn the techniques of differentiation to find the derivatives of algebraic functions, trigonometric functions, and exponential functions.

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Theorem is an important theorem in calculus. The first form of the mean value theorem was proposed in the 14th century by Parmeshwara, a mathematician from Kerela, India. Further, a simpler version of this was proposed by Rolle in the 17th century: Rolle's Theorem, which was proved only for polynomials and was not a part of the calculus. Finally, the present version of the Mean Value Theorem was proposed by Augustin Louis Cauchy in the year 1823. The mean value theorem states that for a curve passing through two given points there is one point on the curve where the tangent is parallel to the secant passing through the two given points. Rolle's theorem has been derived from this mean value theorem.

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Integral calculus helps in finding the anti-derivatives of a function. These anti-derivatives are also called the integrals of the function. The process of finding the anti-derivative of a function is called integration. The inverse process of finding derivatives is finding the integrals. The integral of a function represents a family of curves. Finding both derivatives and integrals form the fundamental calculus. In this topic, we will cover the basics of integrals and evaluating integrals.

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Integrals are the values of the function found by the process of integration. The process of getting f(x) from f'(x) is called integration. Integrals assign numbers to functions in a way that describe displacement and motion problems, area and volume problems, and so on that arise by combining all the small data. Given the derivative f’ of the function f, we can determine the function f. Here, the function f is called antiderivative or integral of f’.

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mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables. In this article, we will discuss the concept of expressions in math and their different types. We will also understand the difference between an expression and an equation in a tabular way and different types of expressions with the help of examples for a better understanding.

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Probability theory is a branch of mathematics that investigates the probabilities associated with a random phenomenon. A random phenomenon can have several outcomes. Probability theory describes the chance of occurrence of a particular outcome by using certain formal concepts. Probability theory makes use of some fundamentals such as sample space, probability distributions, random variables, etc. to find the likelihood of occurrence of an event. In this article, we will take a look at the definition, basics, formulas, examples, and applications of probability theory.

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It is a measure of the likelihood of a particular outcome, and it is generally calculated by the ratio of the number of favorable outcomes to the number of unfavorable outcomes

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The theorem of total probability is useful to compute the probability of happening of an event, which is the result of the probabilities of happening of this event from the different partitions of the sample space. Here we assume the sample space S to be divided into different partitions {E1, E2, E3, ......En} such that {E1 U E2 U E3, .....U En} = S, and the probability of happening of an event A is the summation of the probability of happening of this event from the different partitions of the sample space.

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