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TRIGNOMETRY

trigonometry, the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly used in trigonometry.

Integration maths

integration, in mathematics, technique of finding a function g(x) the derivative of which, Dg(x), is equal to a given function f(x). This is indicated by the integral sign “∫,” as in ∫f(x), usually called the indefinite integral of the function.

DIFFERENTIATION

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.

Algebra

Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols.

Geometry

Geometry is a branch of mathematics that studies the sizes, shapes, positions, angles, and dimensions of things.

POLYNOMIAL

Polynomials are algebraic expressions that consist of variables and coefficients. Variables are also sometimes called indeterminates.

FACTORISATION

In Mathematics, factorisation or factoring is defined as the breaking or decomposition of an entity (for example a number, a matrix, or a polynomial) into a product of another entity, or factors, which when multiplied together give the original number or a matrix, etc

COMPLEX NUMBER

A complex number is a number of the form a + bi, where a and b are real numbers ; This way, a complex number is defined as a polynomial

TRIANGLE

In Geometry, a triangle is a three-sided polygon that consists of three edges and three vertices

Applications of Derivatives

Applications of derivatives are varied not only in maths but also in real life. To give an example, derivatives have various important applications in Mathematics such as to find the Rate of Change of a Quantity, to find the Approximation Value, to find the equation of Tangent and Normal to a Curve, and to find the Minimum and Maximum Values of algebraic expressions.

STRAIGHT LINE

A line is a one-dimensional figure, which has length but no width. A line is made of a set of points which is extended in opposite directions infinitely. It is determined by two points in a two-dimensional plane. The two points which lie on the same line are said to be collinear points.

RATIONALIZATION

Rationalization is a process that finds application in elementary algebra, where it is used to eliminate the irrational number in the denominator. There are many rationalizing techniques which are used to rationalize the denominator

Arithmetic Progression

An arithmetic progression (AP) is a sequence in which the differences between each successive term are the same. It is possible to derive a formula for the AP’s nth term from an arithmetic progression. The sequence 2, 6, 10, 14,…, for example

QUADRATIC EQUATION

Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax2 + bx + c = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where ‘a’ is called the leading coefficient and ‘c’ is called the absolute term of f (x). The values of x satisfying the quadratic equation are the roots of the quadratic equation (α, β)

Co-ordinate Geometry

Coordinate geometry is defined as the study of geometry using the coordinate points. Using coordinate geometry, it is possible to find the distance between two points, dividing lines in m:n ratio, finding the mid-point of a line, calculating the area of a triangle in the Cartesian plane, etc.

PROBABILITY

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in Maths to predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen.

MATRIX

A rectangular array of m × n numbers (real or complex) in the form of m horizontal lines (called rows) and n vertical lines (called columns), is called a matrix of order m by n, written as m × n matrix. Such an array is enclosed by [ ] or ( ). In this article, we will learn the meaning of matrices, types of matrices, important formulas, etc.

Limits and Derivatives

Limits and derivatives are extremely crucial concepts in Maths whose application is not only limited to Maths but are also present in other subjects like physics. In this article, the complete concepts of limits and derivatives along with their properties, and formulas are discussed

Binomial Theorem

As the power increases the expansion becomes lengthy and tedious to calculate. A binomial expression that has been raised to a very large power can be easily calculated with the help of the Binomial Theorem

LINEAR INEQUALTIES

Linear inequalities are the expressions where any two values are compared by the inequality symbols such as, ‘<’, ‘>’, ‘≤’ or ‘≥’. These values could be numerical or algebraic or a combination of both.

Vector Algebra

Vector algebra is one of the essential topics of algebra. It studies the algebra of vector quantities. As we know, there are two types of physical quantities, scalars and vectors. The scalar quantity has only magnitude, whereas the vector quantity has both magnitude and direction.

Three Dimensional Geometry

3-Dimensional geometry involves the mathematics of shapes in 3D space and involves 3 coordinates in the XYZ plane which are x-coordinate, y-coordinate, and z-coordinate. The shapes that occupy space are called 3D shapes. 3D shapes can also be defined as solid shapes having three dimensions length, width, and height.

Linear Programming

linear programming is a method of optimising operations with some constraints. The main objective of linear programming is to maximize or minimize the numerical value. It consists of linear functions which are subjected to the constraints in the form of linear equations or in the form of inequalities.

Application of Integrals

Application of Integrals is applied in various fields like Mathematics, Science, Engineering etc. For the calculation of areas, we use majorly integrals formulas. So let us give here a brief introduction on integrals based on the Mathematics subject to find areas under simple curves, areas bounded by a curve and a line and area between two curves, and also the application of integrals in the mathematical disciplines along with the solved problem.

DIVISION OF ALGEBRAIC EXPRESSIONS

algebraic expression in Maths is an expression which is made up of constants, variables and arithmetic operators. We have learnt about addition, subtraction, multiplication of an algebraic expression.

LINEAR EQUATION IN ONE VARIABLE

The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution. For example, 2x+3=8 is a linear equation having a single variable in it. Therefore, this equation has only one solution, which is x = 5/2.

COMPOUND INTEREST

Compound interest is the interest imposed on a loan or deposit amount. It is the most commonly used concept in our daily existence. The compound interest for an amount depends on both Principal and interest gained over periods.

DIRECT AND INVERSE VARIATIONS

The variables in a direct variation are said to be directly proportional. If the value of one variable increases, the value of the other variable also increases and vice versa. Assuming k to be constant, a direct variation can be expressed as: Y=KX, AND The variables in an inverse variation are said to be inversely proportional. If the value of one variable increases, the value of the other variable decreases and vice versa. Assuming k to be constant, an inverse variation can be expressed as: Y=K/X

TIME AND WORK

A certain amount of time (T) is taken to complete a certain work (W). The number of units of work done per unit time is called the rate of work (R). Hence, Work (W) = Rate (R) Time (T) Whenever some work is done, the total work itself can be taken as one unit.

PROFIT & LOSS

The term profit and loss (P&L) statement refers to a financial statement that summarizes the revenues, costs, and expenses incurred during a specified period, usually a quarter or fiscal year.

PERCENTAGE

percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity.

APPLICATION OF TRIGNOMETRY

Trigonometry can be defined as calculations with triangles involved in the study of lengths, heights and angles. Trigonometry and its functions have an enormous number of uses in our daily life. For instance, it is used in geography to measure the distance between landmarks, in astronomy to measure the distance of nearby stars and also in the satellite navigation system.

Surface Area and Volume

The surface area of any given object is the area or region occupied by the surface of the object. Whereas volume is the amount of space available in an object

RELATION AND FUNCTION

The relation shows the relationship between INPUT and OUTPUT. Whereas, a function is a relation which derives one OUTPUT for each given INPUT. All functions are relations, but not all relations are functions.

INVERSE TRIGNOMETRY FUNCTIONS

Inverse trigonometric functions are also called “Arc Functions” since, for a given value of trigonometric functions, they produce the length of arc needed to obtain that particular value. The inverse trigonometric functions perform the opposite operation of the trigonometric functions such as sine, cosine, tangent, cosecant, secant, and cotangent.

DETERMINANTS

The development of determinants took place when mathematicians were trying to solve a system of simultaneous linear equations.

CONTINUITY AND DIFFERENTIABILITY

t implies that if the left hand limit (L.H.L), right hand limit (R.H.L) and the value of the function at x=a exists and these parameters are equal to each other, then the function f is said to be continuous at x=a.f(x) is said to be differentiable at the point x = a if the derivative f ‘(a) exists at every point in its domain.

DIFFERENTIAL EQUATIONS

A differential equation is an equation which contains one or more terms and the derivatives of one variable (i.e., dependent variable) with respect to the other variable (i.e., independent variable)

PROBABILITY

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics

SETS

In Maths, sets are a collection of well-defined objects or elements. A set is represented by a capital letter symbol and the number of elements in the finite set is represented as the cardinal number of a set in a curly bracket {…}.

RELATION AND FUNCTIONS

The relation shows the relationship between INPUT and OUTPUT. Whereas, a function is a relation which derives one OUTPUT for each given INPUT. All functions are relations, but not all relations are functions.

PRINCIPAL OF MATHEMATICAL INDUCTION

Mathematical Induction is a technique of proving a statement, theorem or formula which is thought to be true, for each and every natural number n

SEQUENCES AND SERIES

An itemized collection of elements in which repetitions of any sort are allowed is known as a sequence, whereas a series is the sum of all elements

CONIC SECTIONS

a conic section (or simply conic, sometimes called a quadratic curve) is a curve obtained as the intersection of the surface of a cone with a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse;

INTRODUCTION TO THREE DIMENSIONAL GEOMETRY

3-Dimensional geometry involves the mathematics of shapes in 3D space and involves 3 coordinates in the XYZ plane which are x-coordinate, y-coordinate, and z-coordinate.

STATISTICS

Statistics is a branch of applied mathematics that involves the collection, description, analysis, and inference of conclusions from quantitative data.

PROBABILITY

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics

REAL NUMBERS

Real numbers can be defined as the union of both rational and irrational numbers. They can be both positive or negative and are denoted by the symbol “R”. All the natural numbers, decimals and fractions come under this category.

PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

Linear equations in two variables are equations which can be expressed as ax + by + c = 0, where a, b and c are real numbers and both a, and b are not zero.

INTRODUCTION TO TRIGNOMETRY

trigonometry, the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc)

CIRCLES

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “centre”. Every line that passes through the circle forms the line of reflection symmetry.

CONSTRUCTIONS

"Construction" in Geometry means to draw shapes, angles or lines accurately. These constructions use only compass, straightedge (i.e. ruler) and a pencil.

AREA RELATED TO CIRCLE

Area of a circle is πr2, where π=22/7 or ≈ 3.14 (can be used interchangeably for problem-solving purposes) and r is the radius of the circle.

SURFACE AREAS AND VOLUMES

The surface area of any given object is the area or region occupied by the surface of the object. Whereas volume is the amount of space available in an object.

STATISTICS

Statistics is a branch of applied mathematics that involves the collection, description, analysis, and inference of conclusions from quantitative data

NUMBER SYSTEM

A number system is defined as a system of writing to express numbers

POLYNOMIAL

Polynomials are algebraic expressions that consist of variables and coefficients. Variables are also sometimes called indeterminates.

Co-ordinate Geometry

Coordinate geometry is defined as the study of geometry using the coordinate points. Using coordinate geometry, it is possible to find the distance between two points, dividing lines in m:n ratio, finding the mid-point of a line, calculating the area of a triangle in the Cartesian plane, etc.

PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

Linear equations in two variables are equations which can be expressed as ax + by + c = 0, where a, b and c are real numbers and both a, and b are not zero.

INTRODUCTION TO EUCLID'S GEOMETRY

Euclidean geometry is the study of geometrical shapes (plane and solid) and figures based on different axioms and theorems.

LINES AND ANGLES

A line is defined as a row of closely spaced dots that extends infinitely in two directions

TRIANGLES

In Geometry, a triangle is a three-sided polygon that consists of three edges and three vertices

QUADRILATERALS

A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles.

AREAS OF PARALLELOGRAMS AND TRIANGLES

If a triangle and a parallelogram are on a common base and between the same parallels, then the area of the triangle is equal to half the area of the parallelogram.

CIRCLES

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “centre”. Every line that passes through the circle forms the line of reflection symmetry.

CONSTRUCTIONS

"Construction" in Geometry means to draw shapes, angles or lines accurately. These constructions use only compass, straightedge (i.e. ruler) and a pencil.

HERON'S FORMULA

To find the area of a triangle using Heron's formula,semi-perimeter of the given triangle; S = (a+b+c)/2. find the area of a triangle (√(s(s – a)(s – b)(s – c)))

SURFACE AREAS AND VOLUMES

The surface area of any given object is the area or region occupied by the surface of the object. Whereas volume is the amount of space available in an object.

PROBABILITY

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics

STATISTICS

Statistics is a branch of applied mathematics that involves the collection, description, analysis, and inference of conclusions from quantitative data.

FACTORISATION

Factorisation of an algebraic expression means writing the given expression as a product of its factors. These factors can be numbers, variables, or an algebraic expression

Rational Numbers

rational number, in arithmetic, a number that can be represented as the quotient p/q of two integers such that q ≠ 0. In addition to all the fractions, the set of rational numbers includes all the integers, each of which can be written as a quotient with the integer as the numerator and 1 as the denominator.

Linear Equations in One Variable

The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution. For example, 2x+3=8 is a linear equation having a single variable in it.

Understanding Quadrilaterals

These four lines enclose a quadrilateral.

Practical Geometry

Practical geometry is an important branch of Mathematics concerning the evaluation of different shapes, sizes, etc. Besides, it also involves constructing different geometrical patterns.

Data Handling

Data handling is the process of ensuring that research data is stored, archived or disposed off in a safe and secure manner during and after the conclusion of a research project.

Square and Square Roots

Squares are the numbers, generated after multiplying a value by itself. Whereas square root of a number is value which on getting multiplied by itself gives the original value

Cube and Cube Roots

Cube is defined as the multiplication of a number to itself three times and Cube Root is defined as the reverse of Cube.

Comparing Quantities

Comparing quantities is the method of determining the amount of comparing units with respect to another standard or reference unit.

Algebraic Expressions and Identities

An algebraic expression is an expression which consists of variables and constants. In expressions, a variable can take any value. Thus, the expression value can change if the variable values are changed. But algebraic identity is equality which is true for all the values of the variables.

Visualizing Solid Shapes

A three-dimensional object or shape can look differently from different positions (or sides) so they can be drawn from different perspectives, this is called visualising a solid shape. For example, views of a hut and a solid with three cubes from different sides are given below.

Mensuration

geometry applied to the computation of lengths, areas, or volumes from given dimensions or angles

Exponents and Powers

Exponents and powers are ways used to represent very large numbers or very small numbers in a simplified manner. For example, if we have to show 3 x 3 x 3 x 3 in a simple way, then we can write it as 34, where 4 is the exponent and 3 is the base.

Direct and Inverse Proportions

A direct and inverse proportion are used to show how the quantities and amount are related to each other. They are also mentioned as directly proportional or inversely proportional. The symbol used to denote the proportionality is ‘∝‘. For example, if we say, a is proportional to b, then it is represented as “a ∝ b” and if we say, a is inversely proportional to b, then it is denoted as ‘a∝1/b’.

Factorization

Factorisation means write an expression as a product of' its factors. • Like prime factors, an irreducible factor, a factor which cannot be expressed further as a product of factors

Introduction to Graphs

The purpose of the graph is to show numerical facts in visual form so that they can be understood quickly, easily and clearly. Thus graphs are visual representations of data collected.

Playing with Numbers

Playing with numbers involves activities like arranging the numbers, understanding BODMAS rule, finding out whether a given number is a factor of another number or a multiple of another number, and understanding the properties of factors and multiples.

Integers

An integer is a whole number (not a fractional number) that can be positive, negative, or zero.

Fractions and Decimals

A fraction is just another way of expressing division. The expression 12/17 is exactly the same thing as 12 divided by 17. a/c is a divided by c. Fractions can also be expressed as Part/Whole.Decimals are real numbers having decimal point. Decimals are another form of fractions. When decimals are added or subtracted, the decimal points must be placed one under the other

Data Handling

Data handling is the process of ensuring that research data is stored, archived or disposed off in a safe and secure manner during and after the conclusion of a research project.

Simple Equations

What is Simple Equation? A mathematical equation which represents the relationship of two expressions on either side of the sign. It mostly has one variable and equal to symbol. Example: 2x – 4 = 2

Lines and Angles

Lines are straight and have negligible depth or width. There are a variety of lines you will learn about, such as perpendicular lines, intersecting lines, transversal lines, etc. An angle is a figure in which two rays emerge from a common point. You may also come across alternate and corresponding angles in this field.

The Triangles and Its Properties

In Geometry, a triangle is a three-sided polygon that consists of three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees. This property is called angle sum property of triangle.

Congruence of Triangles

Congruence of triangles: Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.

Comparing Quantities

Comparing quantities is the method of determining the amount of comparing units with respect to another standard or reference unit.

Rational Numbers

rational number, in arithmetic, a number that can be represented as the quotient p/q of two integers such that q ≠ 0. In addition to all the fractions, the set of rational numbers includes all the integers, each of which can be written as a quotient with the integer as the numerator and 1 as the denominator.

Practical Geometry

Practical geometry is an important branch of Mathematics concerning the evaluation of different shapes, sizes, etc. Besides, it also involves constructing different geometrical patterns.

Perimeter and Area

Area and perimeter, in Maths, are the two important properties of two-dimensional shapes. Perimeter defines the distance of the boundary of the shape whereas area explains the region occupied by it.

Algebraic Expressions

An algebraic expression is an expression which consists of variables and constants. In expressions, a variable can take any value. Thus, the expression value can change if the variable values are changed.

Exponents and Powers

Exponents and powers are ways used to represent very large numbers or very small numbers in a simplified manner. For example, if we have to show 3 x 3 x 3 x 3 in a simple way, then we can write it as 34, where 4 is the exponent and 3 is the base.

Symmetry

the state of having two halves that match each other exactly in size, shape, etc.

Visualising Solid Shapes

A three-dimensional object or shape can look differently from different positions (or sides) so they can be drawn from different perspectives, this is called visualising a solid shape. For example, views of a hut and a solid with three cubes from different sides are given below.

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