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Elements Of Mathematics Class 12
Question
Welcome to the world of mathematics. In this article, we’ll introduce you to some of the basic concepts of mathematics.
Integers
Integers are the numbers that can be written as fractions with no remainders. Integers include natural numbers (1, 2, 3), whole numbers (1, 2, 3) and their opposites (-1,-2,-3).
The set of integers is infinite. An integer can also be expressed as an algebraic expression where each term has a variable raised to a power that is greater than 1. For example:
- 4a + 5b = 4a+5b = 4a + 5b = 4ab
Rational numbers
The set of rational numbers includes all whole numbers, integers, and decimals. It is the largest collection of numbers that can be written as a fraction. This means that if you divide one rational number by another rational number, you will get an integer (a whole number) as the answer.
The denominator of a rational number must not be zero; otherwise it is an infinite quantity which cannot be represented by any finite quantity such as a fraction or decimal value.
Similarly for the numerator: it must not equal zero either because this would mean there could never be any positive values added together to make up this value!
Irrational numbers
In mathematics, the term “irrational” is used to describe a number that cannot be written as a fraction. It is an adjective that can be applied to any real number–not just integers or non-zero decimals. An example of an irrational number is pi (3.14159265358979323846264338327950288419702…), which cannot be written as a fraction because it never ends and doesn’t contain any repeating patterns.
Irrational numbers are important because they help us understand things like circles, ellipses and other geometrical shapes without having to define them with specific values such as 2 or 3 inches long or 5 cm wide. These shapes only exist because there are infinite points along their perimeter; we wouldn’t be able to draw these objects if every point were given its own value!
Real numbers
Real numbers are the set of all possible numbers that can be expressed as a ratio of two integers. They include rational and irrational numbers, but not transcendental numbers (such as pi). Real numbers were first conceived by Pythagoras and Euclid in the 5th century BC, who defined them as ratios to their simplest terms; however they did not explicitly define an operation on these ratios that would satisfy all properties expected from an algebraic structure at this time. This was finally achieved by Carl Friedrich Gauss in 1799 with his discovery of arithmetic operations on complex quantities, which led him to create the first theory about complex analysis and its applications in geometry and physics.[2]
Complex numbers
Complex numbers are numbers that can be expressed as the sum of a real number and an imaginary number. The real part is called the “real” part, and the imaginary part is called “imaginary”.
The imaginary number is written as a lowercase letter i. In other words, 1 + 2i = 3 + 4i
Takeaway:
In this article, you learned about the elements of mathematics. In particular, we looked at integers, rational numbers and real numbers. We also saw what complex numbers are and how they relate to other types of numbers.
We hope that this article has been useful for you in understanding these concepts!
In this article, we have looked at the basics of real numbers and complex numbers. We hope that you have gained some insight into how these concepts work and what they mean for mathematics as a whole.
Answers ( 2 )
Elements Of Mathematics Class 12
Math classes can be daunting, but thankfully, they don’t have to be. In this post, we’re going to introduce you to some of the most important concepts in mathematics and give you a crash course so that you can start understanding them. By the end of this post, you will have the basics you need to start tackling math classes again with confidence. So stick around—we promise it’s worth it!
What is mathematics?
Mathematics is the study of patterns and structures in our world. It is a branch of mathematics that deals with numbers, symbols, and shapes. Mathematics can be used to solve problems and understand how our world works.
In high school, most students take mathematics classes to prepare for college entrance exams such as the SAT or ACT. In college, students may major in mathematics if they want to focus on a specific area of the field or if they are interested in a career in math-related fields. Many people also use mathematics every day when they work on their taxes or figure out how to pay for their groceries.
The basic operations of mathematics
In mathematics, there are basic operations that we use all the time. The most common one is addition, which is when you add two numbers together. You can also add two fractions together, or two decimals together.
Another common operation is multiplication. This is when you multiply two numbers together. You can also multiply two fractions, or two decimals.
Another operation in mathematics is division. This is when you divide one number by another. You can also divide two fractions, or two decimals.
Basic concepts in mathematics
Mathematics is the study of relationships between numbers and shapes. These relationships can be expressed in equations, which are mathematical statements that can be solved to produce a solution that is compatible with the given equation. Mathematics is also used in physics, engineering, and other fields to solve problems.
One of the most basic concepts in mathematics is algebra. Algebra is the study of solving equations. In algebra, you will often need to use parentheses to indicate where an equation should be solved for certain variables. For example, if you want to know how much money John has in his bank account, you would write John’s bank account (1000) – 500 = 400. Notice that the parentheses are needed because the equation contains two variables (John’s bank account and 500).
Another important concept in mathematics is addition. Addition is the ability to combine two numbers together and get a new number as a result. To add 2 + 3, you would take the two numbers inside of the parentheses and add them together: 5 + 6 = 11. You can also do this using Roman numerals (I + II = III).
subtraction is also a very common math operation. To subtract 2 – 1, you would take the number inside of the parentheses and subtract it from 2: 1 – 2 = 1. You can also do this using Roman numerals (III – IV = II).
Gebra and trigonometry
Trigonometry is a branch of mathematics that deals with the properties of triangles and other polygons. Gebra is a Japanese puzzle game that uses trigonometry to solve puzzles.
Calculus
In calculus, students learn to use the derivative and integral signs to calculate rates of change and work out solutions to integrals. Calculus is used in many fields, including engineering, physics, chemistry, and maths.
Probability and statistics
In mathematics, probability and statistics are two important fields that deal with the collection, analysis, interpretation, presentation, and organization of data. Probability is the study of how likely events are to occur. Statistics is the use of data to gain knowledge about patterns or trends.
Probability can be used to understand random phenomena such as dice throwing or coin flipping. Statistical analysis can help us understand how groups of people behave, what factors affect their behavior, and how we can predict future events based on past ones.
Both probability and statistics have applications in a wide range of disciplines, from finance to engineering to medicine. In fact, many scientists and engineers use probability and statistics when they are trying to find solutions to problems.
Conclusion
Thank you for reading our article on the Elements of Mathematics Class 12. We hope that this article has provided you with a comprehensive overview of all that is covered in this course and has given you some ideas about what topics might be of interest to you. We would be happy to answer any questions that you may have and we encourage you to explore our website further, as there is much more content available on our site if you areinterested in learning more about mathematics or other subjects. Thankyou once again for taking the time to read this article and we look forward to hearing from you soon.
Many students find mathematics to be a challenging subject. The following is an attempt to simplify some of the concepts and make them easier to understand, so that you can do well in your mathematics class.
Number System
A number is a symbol that represents a quantity. It can be written as an Arabic numeral or as a word (e.g., two hundred). There are many types of numbers: whole numbers, fractions, decimals and irrational numbers. A digit is one of the symbols used to write down numbers; these include 0-9 in our decimal system and 1-9 in other systems such as Roman numerals. The position of each digit within a given number has importance; for example 676 means something different from 767 or 76$. You can find more information about writing and reading numbers here!
Numbers have properties such as divisibility by 2, 3 and 5 which we will learn later on in this section!
Introduction to Functions
Functions are a common topic in mathematics. They are used to describe many real-world processes and relationships, such as the relationship between height and weight, or between voltage and current. In this section, we will talk about what functions are, how they can be represented mathematically (with graphs), how one function relates to another (such as an inverse function), and some examples of functions that you might have seen before.
Inverse Functions:
An inverse relation is one where the product of two numbers is always equal to another number that has an opposite sign in front of it; for example -1 times 2 = -2 or +1/2 = -1/2
Functions and their Graphs
Functions are a key concept in linear algebra. They allow us to define relationships between two variables, and they can be used to model many real-world situations.
Inverse Trigonometric Functions and their Graphs
Inverse trigonometric functions are inverse of the corresponding trigonometric functions. They are written as:
`f(x)=g^(-1)(x)` or `f(x)=g(cos(theta),sin(theta))` with `g=tan^(-1),sec^(-1),csc^(-1)`. The graphs of these inverse trigonometric functions are obtained by reflecting the graphs of corresponding basic trigonometric functions across y-axis.
Trigonometry
Trigonometry is the branch of mathematics that studies relationships involving lengths and angles of triangles. It has many applications in fields such as astronomy, engineering, physics and surveying. The etymology of trigonometry is from Greek “trigonon” meaning “triangle” plus “metron” meaning “measure”.
Trig functions are used to solve right triangle problems such as finding missing lengths or angles when two sides or angles are known. The sine function can be used to find the length (or height) of one side if you know another side’s length and angle measure; similarly cosine can be used for this purpose too (and tangent works similarly).
Complex Numbers
Complex numbers are numbers that have a real part and an imaginary part. The imaginary part, which is usually written as i, is defined as the square root of -1.
When we use complex arithmetic operations on them, it can be confusing to know what to do first with the real or imaginary parts. For example:
z1 = 2 + 3i; 2×2-z2=0
Takeaway:
Mathematics is a subject that is essential for everyone to learn. It has been around since time immemorial and has helped people in many ways. It can be used to solve problems of everyday life, at work or school, or even while playing games like chess or poker.
Mathematics helps us understand the world around us better by allowing us to predict results based on certain inputs. This can range from calculating how much money you will make if you invest in stocks or bonds (interest rates), determining which route is fastest between two locations (distance traveled), estimating how long it takes for something to decay over time (half-life), etcetera! Mathematics also helps us explain natural phenomena such as why planets orbit around stars instead of crashing into them like asteroids do when they come too close together during their orbits around each other due towards gravitational forces acting upon them constantly pulling each other inward towards one another until eventually their paths intersected again causing both celestial bodies’ orbits around each other never intersecting again afterwards unless disturbed again later down the line by another approaching object causing another series of collisions which repeats itself endlessly until all matter within its vicinity becomes unstable enough not only due to the constant collisions between celestial bodies of all sizes but also due to the sheer force of gravity exerted upon them by each star themselves causing them to collapse inward on themselves and eventually implode becoming black holes that suck up everything around them not just nearby planets and asteroids but entire solar systems as well.
We hope that this article helped you understand the basic concepts of trigonometry and the functions associated with it. You can now go ahead and apply these concepts in your life as well as career!