Introduction We studied in the previous classes that the system of two linear equations in two variables namely $\mathrm{a_{1}x\:+\:b_{1}y\:=\:c_{1}\:and\:a_{2}x\:+\:b_{2}y\:=\:c_{2}}$ will have unique solution if $\mathrm{\frac{a_{1}}{b_{1}}\:\neq\:\frac{a_{2}}{b_{2}}\:i.e.\:a_{1}b_{2}\:-\:b_{1}a_{2}\:\neq\:0}$. Thus, $\mathrm{(a_{1}b_{2}\:-\:b_{1}a_{2})}$ is the determining factor for the system of two linear equations. We define $\mathrm{a_{1}b_{2}\:-\:b_{1}a_{2}}$ to be the determinant of the square matrix of order 2. In this tutorial we define the determinant of the square matrix of order 2 and 3 and understand the properties of determinants along with some solved examples. Determinant To every square matrix $\mathrm{A\:=\:[a_{ij}]}$ of order 𝑛, we can associate a real or complex number called ... Read More

Introduction The study of geometric figures using coordinate axes is known as coordinate geometry. Figures like circles, ellipses, polygons, and straight lines can be drawn and scaled on the coordinate axes with ease. Additionally, coordinate geometry facilitates algebraic operations and the study of the properties of geometric figures. Every location on this globe has coordinates that make it simple for us to find them on a map. Our planet's coordinate system is made up of fictitious lines known as latitudes and longitudes. We have the coordinate axes with the horizontal x-axis and the vertical y- axis, which are similar ... Read More

Introduction A triangle has three sides, and three angles these two are the important parameters in constructing a triangle. It is done using a few geometrical equipment like a protractor (to measure an angle), compass (to draw the arc for a given measured side), and ruler (to measure the side length). There are different types of triangles, and they can be constructed differently by knowing a few given sets of parameters. In this tutorial let’s see three of the cases. Construction of Triangles In general, the construction of triangles is easy when the following properties like SSS, SAS, ... Read More

Introduction When a solid surface like a cone is cut by a plane it forms different sections called conic sections. There are different conic sections like a circle, ellipse, parabola, and hyperbola based on the angle at which the plane intersects with the cone axis. Circle and ellipse are closed sections whereas parabola and hyperbola are not closed the curves of these figures extend till infinity. Definition of Section of Cone When a two-dimensional plane intersects a three-dimensional right circular cone the crop section formed on the plane is called a conic section. The plane intersects the ... Read More

Introduction Mathematical reasoning, a crucial skill that enables pupils to examine a given hypothesis without reference to a specific context or meaning, includes conditional statements. The reasoning is not based on an individual's opinion when a scientific investigation or assertion is investigated, to put it simply. The basis for deductions and proofs must be factual and scientific. To answer issues involving mathematical reasoning, one needs to possess critical thinking and logical reasoning abilities in mathematics. We will delve into the world of conditional statements in this quick session. Along with solved examples and interactive questions, we will go over ... Read More

Introduction Complex numbers make it simpler to find the square root of negative values. The concept of complex numbers was first presented when Hero of Alexandria, a Greek mathematician, attempted to compute the square root of a negative number in the first century. However, he made the integers' negative values positive and got their root values. Additionally, the identity of complex numbers was established when the third- and second-order polynomials' negative roots were discovered by the Italian mathematician Gerolamo Cardano in the sixteenth century. Numerous scientific research, including those involving signal processing, electromagnetism, fluid physics, quantum mechanics, and vibration ... Read More

What is Mathematica? Mathematica is a mathematical computation program that has been developed by using The Wolfram Language. The app comes with a lot of features like adaptive visualization load on demand curated data, processing of images and audio, and many more. The app can be used by professionals who are in the fields of science, engineering, mathematics, and computing fields. Why Mathematica Alternatives? The app consists of a large number of functions The syntax is different in comparison to other programming languages Type commands to get answers Many shortcut notations How to choose a Mathematica Alternative? There ... Read More

What is GeoGebra? GeoGebra is a software that has been developed to resolve all sorts of mathematical problems for all levels of education whether primary middle, graduation, etc. The platform can resolve problems related to different subjects like geometry, algebra, statistics, graphing, and many more. Another feature of the app is the offering of one million classrooms resources for free. These are multilingual classrooms managed by a community. Price Plans of GeoGebra GeoGebra is available for free and anybody can use it to resolve different types of mathematical problems. Why GeoGebra Alternatives? There are no cons for GeoGebra How to ... Read More

Introduction The average value of a set of data points, observations, or values is known as the Mean of the data. It is the measure of the central tendency. Mathematically, the mean is obtained by dividing the sum of values by the number of values or observations. It is also called the expected value. The mean itself is not restricted to this simple form but has different types such as the arithmetic mean, geometric mean, harmonic mean, and weighted average. It is given mathematically as, $$\mathrm{Mean=\frac{\sum x}{N}}$$ where, x = set of observations N = number of observations Different ... Read More

Differential and derivative are two fundamental concepts in calculus that are often used interchangeably. While they are related, they are not the same thing. Understanding the difference between differential and derivative is important in mastering calculus and its applications. In this guide, we will explore the difference between differential and derivative and their uses in calculus. What are Differentials? Differential is one of the fundamentals divisions of calculus, along with integral calculus. It is a subfield of calculus that deals with infinitesimal change in some varying quantity. The world we live in is full of interrelated quantities that change periodically. ... Read More