#Relations and Functions Class 12 Maths

[ashishkumarletslearn]

Class 12 Maths Exercise 1.1 | Relations and Functions - MathYug

Delve into the realm of Relations and Functions in Class 12 Maths with MathYug's expert teacher Ashish Kumar, fondly known as Agam Sir. In this comprehensive video lecture, we unravel the complexities of NCERT Exercise 1.1, exploring empty relations, universal relations, and more.

Timestamps:

00:00:05 Introduction and How Ashish Sir is going to teach you Class 12 Maths on MathYug

00:06:37 Empty Relations and Universal Relations (Trivial Relations) Lecture 1 (NCERT Exercise 1.1, NCERT Exemplar, Board’s Question Bank)

00:12:27 Question 1 Let R be the relation in the set N given by R = {(a, b) : a = b – 2, b ≥ 6}. Choose the correct answer. A. (2, 4) ∈ R B. (3, 8) ∈ R C. (6, 8) ∈ R D. (8, 7) ∈ R (N)

00:15:17 Question 2 Let A= {1, 2, 3,} and define R = {(a, b): a – b = 12}. Show that R is an empty relation on Set A. (B)

00:17:47 Question 3 Let A be the set of all students of a boy’s school. Show that the relation R in A given by R = {(a, b) : a is the sister of b} is the empty relation and R′ = {(a, b) : the difference between the heights of a and b is less than 3 meters} is the universal relation. (N)

00:28:17 Question 4 If A is the set of students of a school then write, which of the following relations are Universal, Empty, or neither of the two. R1 = {(a, b) : a, b are ages of students and |a – b| > 0} R2 = {(a, b) : a, b are weights of students, and |a – b| > 0} R3 = {(a, b) : a, b are students studying in the same class} (B)

00:40:47 Question 5 Let A = {1, 2, 3,} and define R = {(a, b): a + b < 0}. Show that R is a universal relation on set A. (B)

Join us as we embark on a journey to master Class 12 Maths, guided by Agam Sir's expertise.

[rosesrded]

04.05.2025 (sun)

Day (25/30) DOP COLLAB CHALLENGE

There was no offline school today because of NEET (I have only a year left AHHHHH), but we did have online classes.

They started at 9, and I woke up at 9:05—but thankfully class actually began at 9:10. The teachers were struggling with the online setup and it totally took me back to COVID times lol.

Anyway, class ended around 12:40-ish, after which I procrastinated, cleaned my room (which was an absolute pig’s pen for the past week or so), ironed my uniform, and did other random stuff. I still haven’t even broomed my room yet—planning to do that tomorrow.

It’s almost 7 pm rn and these are the things I've still yet to do will have to end up pulling an all nighter just when I was planning to get my sleep schedule fixed wtf.

They gave us so much work just because we had Sunday, which wasn’t even technically off. Watch me as I die?

Also I’m most stressed about the speaking test in English which they count towards our internal marks so AHHHH.

Bio - test on reproductive health

Bio - record

Bio - notes +diagrams

Chem - haloalkanes and arenes test

Chem - notes

Phy - test on current and electricity

Math - relations and functions test

Math - hw

Eng - Speech

[religion-is-a-mental-illness]

By: Ross Pomeroy

Published: Jan 4, 2023

Boys are under-performing girls across all ages, education levels, and in most countries — and the divide is worsening.

A recently published study of 39,000 Italian tenth graders found that for male and female students who have identical subject-specific competence, teachers give higher grades to girls.

A simple solution to grading-related bias is for students to write their names at the very end of any test or assignment, so the grader only knows their identity after scoring the wo

Across all ages and nearly all areas of education, boys are under-performing girls.

“Girls are about a year ahead of boys in terms of reading ability in OECD nations, in contrast to a wafer-thin and shrinking advantage for boys in maths. Boys are 50 percent more likely than girls to fail at all three key school subjects: maths, reading, and science,” Richard Reeves, a senior fellow in Economic Studies and the Director of the Future of the Middle Class Initiative, wrote in his recent book Why the Modern Male is Struggling,

According to a 2018 Brookings Institution report, about 88% of American girls graduated high school on time, compared with 82% of boys. In 2020, six out of ten college students were women. Once on campus, they graduate at higher rates, receiving more associate’s, bachelor’s, master’s, and doctoral degrees in the process. As evidenced by declining college enrollment in the U.S., a drop for which men account for 71%, the gender disparity is continuing to worsen.

The reasons for this expanding educational divide have been vociferously debated and discussed. A startling shortage of male K-12 teachers (just 24%), the hands-off, tedious structure of school, and poor parenting are a few of the explanations offered. Another, less frequently discussed, is starting to emerge from the scientific literature: Boys appear to be graded more harshly than girls.

Boys vs. girls

When researchers across the world — from Israel and Sweden to France and Czechia — explored teachers’ grading behaviors, either by having educators grade hypothetical students’ identical works while only changing the students’ gender, or comparing grades achieved by “similarly competent” male and female students, they found that girls consistently receive higher grades than boys.

Further cementing this pattern is a recently published study conducted on nearly 39,000 10th grade students in Italy.

Authors Ilaria Lievore and Moris Triventi, both in the department of sociology and social research at the University of Trento, found that for students with the same level of “subject-specific competence,” as measured by standardized test scores, girls are graded more generously than boys. In Italy, students are graded on a one to ten scale, with six being a passing score. In mathematics, girls are graded about 0.4 points higher than similarly competent boys. In language, the gender grading premium is 0.3 points in favor of girls.

Since the researchers also procured data on students’ teachers and classroom characteristics, they explored whether the teacher’s gender or the classroom size had any effect on the difference in grading. Alas, they didn’t see any sign that male teachers were kinder graders to boys. Moreover, fewer students in a classroom did not mitigate the effect.

The researchers were thus left to speculate about the cause of the grading imbalance.

Teacher bias?

“One related theoretical stream interprets gender grading mismatch as also being a function of students’ observed behaviours,” they wrote. “School and classroom environments might indeed be adapted to traditionally female behaviours. Female students might thus adopt such actual behaviours during class, including precision, order, modesty, and quietness, which go beyond the individuals’ academic performance, but which teachers may highly reward in terms of grades.��

The simple fact is that, despite their best intentions, teachers can be swayed by the same unconscious biases as the rest of us. As one anonymous teacher pointed out on Reddit, “Teacher’s mood plays into grades. How the student acts in class affects grading. How the students’ parents act plays into grades.”

Thus, a simple solution to grading-related bias is for students to write their names at the very end of any test or assignment, so the grader only knows their identity after scoring the work.

==

Teacher bias has been studied quite extensively.

Abstract

Schools and teachers are often said to be a source of stereotypes that harm girls. This paper tests for the existence of gender stereotyping and discrimination by public high-school teachers in Israel. It uses a natural experiment based on blind and non-blind scores that students receive on matriculation exams in their senior year. Using data on test results in several subjects in the humanities and sciences, I found, contrary to expectations, that male students face discrimination in each subject. These biases widen the female–male achievement difference because girls outperform boys in all subjects, except English, and at all levels of the curriculum. The bias is evident in all segments of the ability and performance distribution and is robust to various individual controls. Several explanations based on differential behavior between boys and girls are not supported empirically. However, the size of the difference is very sensitive to teachers' characteristics, suggesting that the bias against male students is the result of teachers', and not students', behavior.

Abstract

In this paper, we study the presence of systematic differences between teacher non-blind assessments and external blindly graded standardized tests as a measure of grading misalignment. Using a large administrative database covering two student cohorts (N = 31, 183 pupils) from publicly-funded schools in the Basque Country (Spain), we explore the grading gaps found between these two type of assessments for several student characteristics using fixed effects modeling. We find that, after controlling for standardized achievement, systematic teachers’ under-assessment exists for student groups that, on average, lag behind in school: boys, children from an immigrant background, and low SES students. The observed data patterns withstand several robustness checks, including the use of instrumental variables approach (IV) and other alternative regression specifications.

Abstract

The ‘boy crisis’ prompts the question of whether people interpret inequalities differently depending on whether males or females are lagging behind. We study this question in a novel large-scale distributive experiment involving more than 5,000 Americans. Our data provide strong evidence of a gender bias against low-performing males, particularly among female participants. A large set of additional treatments establishes that the gender bias reflects statistical fairness discrimination. The study provides novel evidence on the nature of discrimination and on how males falling behind are perceived by society.

Abstract

Teachers’ evaluations of students do not consider only academic competence, but are imbued with social considerations related to individual teacher and student characteristics, their interactions, and the surrounding context. The aim of this paper is understanding the extent to which teachers grade girls more generously than boys, and which characteristics of teachers and classrooms are likely to reduce this gender grading gap. We use Italian data from INVALSI-SNV, providing information on 10th-grade students linked with their teachers. The analysis relies on grade equation models in multilevel regression analysis, with students as first level, teachers/classrooms as second level, and schools as third level. Results show that, when comparing students who have identical subject-specific competence, teachers are more likely to give higher grades to girls. Furthermore, they demonstrate for the first time that this grading premium favouring girls is systemic, as teacher and classroom characteristics play a negligible role in reducing it.

ABSTRACT

We study if the Italian school system suffers from gender bias when judging students. To this aim, we use a differences-in-differences approach that compares the teachers' assessments and the standardized test scores that the students receive during the school year. We have census data for all Italian fifth and sixth graders in two different subjects, math and language, that include a rich set of additional controls. Our evidence reveals that, since primary school, boys are graded less favourably than girls in both math and language. This result is also confirmed for middle school students (sixth graders), and it holds even when (a) we separate the analysis between the most and least developed Italian regions, (b) we control for possible gender-specific attitude towards cheating and teachers' manipulation and (c) we introduce class and school fixed effects in the models. Comparing the results obtained across different levels of schooling and subjects, we cannot clearly identify the role of specific mechanisms in determining the gender bias. Overall the analysis suggests further study on the role of teachers' characteristics.

Abstract

I use a combination of blind and non-blind test scores to show that middle school teachers favor girls in their evaluations. This favoritism, estimated as individual teacher effects, has long-term consequences: as measured by their national evaluations three years later, male students make less progress than their female counterparts. On the other hand, girls who benefit from gender bias in math are more likely to select a science track in high school. Without teachers’ bias in favor of girls, the gender gap in choosing a science track would be 12.5% larger in favor of boys.

2.1 Grading bias and teacher assessments

The OECD found that girls are more likely to receive better marks from their teachers (in class tests), even when compared to boys who perform equally well in PISA (anonymous, surprise test), and they report similar attitudes and behaviors (amount of time spent reading and on homework, school enjoyment, etc.) [15]. Students’ expectations of their future and ambitions were shown to be linked to their grades. It is concluded that because of the grading bias, boys are more likely to not go to college and to end their education earlier than girls who perform equally well at PISA and display similar behaviors.

The OECD is not alone in their observation of the grading bias. Researcher Camille Terrier found that this favouritism towards girls has long-term negative consequences for boys’ progress. In particular, she notes that “without teachers’ bias in favour of girls, the gender gap in choosing a science track would be 12.5% larger in favour of boys” [16]. She also finds that, contradicting the OECD report’s speculation1, “girls’ better behaviour in class is not behind this nudge forwards”.

Another study analysed the grades of almost 30,000 pupilsfrom 300 Israeli schools, across multiple cohorts of high school seniors, and found a grading bias against males across nine subjects by comparing blind grades from external state exams with non-blind teacher grades [17]. These findings were consistent even in schools where boys outperformed girls on average. As this study is a natural experiment, the findings have a high degree of generalisability.

A very recent study from Italy reports that, among students with identical subject-specific competence, teachers tend to give higher marks to girls [18]. The study further reveals that this bonus in favour of girls is systemic, as teacher and classroom characteristics have minimal impact on reducing it. Thus, a holistic approach may be needed in order to solve the problem which may not be caused by any one particular failing. Notably, the authors conclude: “[…] the magnitude of the bias against male students in not negligible, and may have negative consequences. This is especially true regarding Mathematics, where a teacher penalty may translate into a failing grade, since the average teacher grade for boys falls right on the passing mark.” [emphasis added]

[gaydivorcetual]

theres multiple grandmasters??? well. it makes sense that its a title. news to me

Yeah !! "Grandmaster" is just the name for the "owner"/leader of Koro at the time (technically Koro [the city/settlement] is run by Koro [the AI], but since it isnt 100% functional rn, the de facto leader is The Grandmaster- they're the one who manages project Koro and oversees any settlements incorporated into Koro [the city]). Its mostly a familial line (being the Grandmaster is suuuuper reliant on the person having this One Specific Fear or else it doesnt work, so if the persons kid doesnt develop/they dont have a kid, the title is passed down to a non-related heir, who is then adopted into the family). Yoki and the first Grandmaster dated for a bit wayyyy back like. even before he got his cellres bug.

Sooo. If the grandmaster title has been around since b4 Yoki got a bug ,,, 400 years post-bomb and he got his bug 80 years b4 that, but the first guy probably didnt take on the alias until he was in his 30s-40s. Yoki n him dated as teens n Yoki was in his 20s when he got the bug. Lets say 15 years after that the Grandmaster appeared, so 80-15 is 65. So ~465 years of grandmasters. The title is only transferred upon death, n lets average an age of death of 60 since a lot of them probably died younger than usual after the bomb. I'll say each grandmaster has a kid at ~20 then dies at 60, so the new grandmaster gets it at age 40,, i havent had a math class in years oh my god. 465/40 is ~11.6

So theres been around 12 grandmasters total so far !!

[ddaleishere45]

Exploring S.T.E.M

By Dale V. Aldea (Grade 11-Perfection)

As a senior high school student, you've probably heard the term "STEM" being talked around countless times. Maybe you have heard that this strand is for students who wants to be a Doctor, an Engineer, even a Software Genius! But what exactly is STEM? Is it just more than just a senior high school strand? In this blog, we'll dive into the fascinating world of the STEM strand.

S.T.E.M and its origins

STEM is one of many strands you can take up in Senior High School. It stands for Science, Technology, Engineering, and Mathematics. The S.T.E.M acronym was first introduced in 2001 by a a group of scientific administrators at the U.S. National Science Foundation (Hallinen, 2023). The organization previously used the acronym SMET when referring to the career fields in those disciplines or a curriculum that integrated knowledge and skills from those fields but was later changed to STEM and since then, STEM-focused curriculum has been extended to many countries like the United States, Australia, China, France, South Korea, Taiwan, United Kingdom, and was later introduced here in the Philippines by the K-12 program.

Decoding the Acronym

S.T.E.M - SCIENCE Science is all about understanding the natural world, from the smallest particles to the vastness of the space. It involves asking questions, making hypotheses, conducting experiments, and analyzing data to discover the basic principles that govern the universe. If you aim to take science related courses or medicine in college, well you're in luck because this strand offers primary education for the said courses.

S.T.E.M - TECHNOLOGY

Technology is everything from smartphones and laptops to life-saving medical devices and cutting-edge space exploration equipment. It's the practical application of scientific knowledge to create tools, systems, and solutions that make our lives more efficient, convenient, and safe. If you're interested in software development, computer engineering, or even app designs in college, this strand is for you.

S.T.E.M - ENGINEERING

Engineering is the art of using scientific and technical knowledge and using it to design and make solutions. From bridges and skyscrapers to renewable energy systems and electric cars, engineers turn ideas into real, functional realities. The field of engineering is big, with specialties like civil engineering, mechanical engineering, electrical engineering, and aerospace engineering, to name just a few. Well in this strand you can learn the basics of those courses to prepare yourselves in college.

S.T.E.M - MATHEMATICS

Mathematics serves as the language of STEM. It is the foundation upon which all the other subjects are based. Our high school math classes help us develop critical thinking skills, problem-solving abilities, and logical reasoning qualities that are highly sought after in any profession. Whether you are planning on taking a career directly related to mathematics or use it as a tool to excel in another S.T.E.M field, its importance cannot be overstated.

Is STEM important?

The S.T.E.M strand in senior high school very important for students like me. The strand prepares students who are planning on taking on courses that are related to science, technology things, engineering, architecture and many more. The strand also focuses on enhancing the students problem-solving skills, critical thinking and creativity. This is a big help, giving us students a big boost in knowledge in the fields of science and math for college.

So keep this in mind, STEM isn't just a some random acronym made for Senior High School, it is a gateway of understanding the world around us. The strand equips students with knowledge and curiosity for the fields in science, technology, engineering and mathematics, creating a path for a bright future. STEM is more than just a strand, it is a journey of discovery and learning to limitless possibilities.

References:

[mbti-notes]

Anon wrote: Hello, I am 16 years old. I have taken many tests, and read your blogs and descriptions about the Cognitive Functions and processes. I have narrowed my decisions down to two types. INTP AND ISTP. If you are able to find it, I could your advice as a resource to help me find my official type.

Dominant Ti- INTP and ISTP argument.

Between the ages of 6-12 and before some steess happened to me, I was a very curious child, watching many videos about how things worked, many History and Science Vids just to learn for fun. I tend to notice inconsistencies with data, and real life systems such as schools. Additionally, I also tend to have my own framework on how the world works. Such as me thinking that relationships are like an abstract system were you have to stabilize it at all angles to keep it running. I also think that many concepts like Newtons Laws can be applicable to many things like relationships . Like the 3rd Law where for every reaction, there is an equal and opposite reaction. A good example of this is that the more you love the person in a relationship, the more it will hurt when you break up. My one family member, who is an ISTJ btw told me that my logic makes sense and that it is kind of weird. I also have the thinking that School is just a chore, and that School is not real knowledge to me. I also tend to like to analyze things I am interested in such as Personality Theory, History, Science, and Math and knowing how they were formed and how it happened so I can expand my logical framework into a rich innerworld full of knowledge.

Inferior Fe-

One time when I got stressed, mainly due to me not reading social ques well which caused me to get used. I started getting so clingy to people, which caused people to become distant from me, which I didnt know was bad. I also had an emotional breakdown in front of my friend because I failed to admit that my crush didnt like me, which caused me to lose that friend. Recently, after a friend and I started growing distant, I started becoming so paranoid about how other people percieve me, which caused me to have a fear that people will laugh at me and betray me. During that time, I suddenly got stressed, and then went outside to be agressively social to someone I didnt know by cussing and emphasising logic to an extreme. I also noticed that it was harder for me to think, mainly due to the fact that I am so paranoid about others. But before that, I had an expierence where I got jealous, which caused me to suddenly want to get involved in a family friends personal business, by asking for their phone number via their parents, just so I can get invasive and make them feel uncomfy. I tend to want to have socially interactions, but I tend to fail at them due to how awkward I was.

INTP Argument Aux Ne and Tert Si argument:

I also noticed, that not only did I learn about many topics like history and science by watching videos. I also tend to make up my fictional World Wars, drawing maps based on those in the videos, and even coming up with new ways I believe the worlds problems could be fix. I tend to also find bizarre connections to things, such as me connecting Physics and Relationships, two things I somehow connected, even though they are not related to each other. I also tend to easily jump from topic to topic when talking to people about my ideas and even having normal conversations. Additionally, I seem to get really energized when brainstorming about all the possibilities, which to others can seem kinda quirky. I also tend to have a problem sticking to one possibility sometimes, due to the fact I can easily accept other possible theorys, even though it is not likely to happen. My Si shows up as me having vivid memories of things like dates. However my Si can be somewhat inconsistent due to the fact that somedays, I can be great with memories while on other days, I cant even remember where I sit in class. My Si kinda somewhat developed, thanks to my family member who is an ISTJ. She forced me to somewhat develop it because she tends to punish me for forgetting habits, routines, and chores by taking away my phone for 2 hours.

ISTP Argument Aux Se and Tert Ni

At the Age of 13, I suddenly was more active. I started playing tennis as a sport, and wanted to explore the world more by trying out new things around me. I also got less picky with food, and suddenly wanted to start trying things with a lot of topics despite me not liking those things in the past. I also started acting before thinking just for me to experience things. One time, I suddenly had a hunch that caused me to accuretly guess my friends birthday. I felt like I was in a Ti-Ni loop one time, where I was so obsessed about the future, that I slowed got less interested in staying present, and suddenly started worring more about the future.

-----------------------

Several problems with your submission:

- Overall, my impression is you don't have very deep knowledge of yourself. While some of this can be chalked up to youth, you also didn't follow the submission instructions properly, so you haven't done enough self-reflection. Remember, I'm only able to see what you're able to show, and you haven't shown enough, barely scratched the surface.

- Your descriptions of T and N overlap too much for comfort. I don't know if this is due to not understanding the difference conceptually, not being able to spot the difference in yourself, or a combination of both. Until you are able to disentangle the two cognitive processes, the dominant function remains unclear, which means it will be very difficult for the rest of the stack to snap into place.

- A lot of people, especially introverts, are socially awkward/inept but it doesn't mean they have inferior Fe - do not confuse the two. Until you are able to clarify the reasons for and/or explain the psychological mechanisms underlying your socializing issues, inferior Fe remains unproven. Additionally, there's a lot more to Fe than socializing. Until you have a better understanding of what Fe is and what exact role it plays in your mind in relation to the other functions, its stack position remains up in the air.

- The auxiliary and tertiary function descriptions were unhelpful due to lacking detailed examples and not providing exactly the information I asked for in the guide. ISTP seems unlikely, though.

Generally speaking, I need to reach >95% confidence before I'm willing to confirm or disconfirm a possibility. Unfortunately, since none of the stack positions are clear, your submission does not meet my threshold as sufficient proof of INTP, nor does it allow me to rule it out.

[class11maths]

NCERT Exercise 2.1 Chapter 2 Relations and Functions Class 11 Maths | MathYug

Expert Video Lecture by Ashish Sir – Relations and Functions (Class 11 Maths Chapter 1)

This video lecture provides a comprehensive explanation of the Cartesian Product, Ordered Pairs, and NCERT Exercise 2.1 from the chapter "Relations and Functions" in Class 11 Mathematics. The session is conducted by Ashish Sir, a subject expert known for in-depth and student-friendly teaching.

Lecture Timeline:

00:00:01 Introduction to this lecture 

00:00:30 Why Relations And Functions is important for Class 12 Maths 

00:02:06 Practical Example related to Cartesian Product 

00:06:16 Cartesian Product and Ordered Pairs NCERT Exercise 2.1 

00:11:46 Question 1 

00:13:36 Question 3 

00:18:46 Question 2 

00:22:16 Question 6 

00:23:16 Question 9 

00:27:06 Question 5 

00:34:26 Question 10 

00:39:06 Brief revision of Cartesian Product 

00:44:26 Question 4 

00:47:46 Question 7 

00:52:06 Question 8

This session is ideal for students looking to strengthen their conceptual understanding and master the fundamentals of Cartesian Products and relations through detailed NCERT problem-solving.

To access the complete course, including all video lectures, notes, and assignments, visit: https://mathyug.com/class-11-maths

[inversetrigonometricfunctions]

00:00:00 Introduction for inverse trigonometry identities

00:03:34 Derivation of all inverse trigonometric identities

00:15:14 NCERT Solutions Exercise 2.2 Question 1

00:20:04 NCERT Solutions Exercise 2.2 Question 2

00:21:34 NCERT Solutions Exercise 2.2 Question 3

00:23:44 NCERT Solutions Exercise 2.2 Question 4

00:27:54 NCERT Solutions Exercise 2.2 Question 6

00:34:54 NCERT Solutions Exercise 2.2 Question 7

00:36:24 NCERT Solutions Exercise 2.2 Question 8

00:38:54 NCERT Solutions Exercise 2.2 Question 5

00:42:54 NCERT Solutions Exercise 2.2 Question 9

00:45:44 NCERT Solutions Exercise 2.2 Question 10

00:48:54 NCERT Solutions Exercise 2.2 Question 11

00:50:24 NCERT Solutions Exercise 2.2 Question 12

00:51:04 NCERT Solutions Exercise 2.2 Question 13

00:52:54 NCERT Solutions Exercise 2.2 Question 14

00:54:44 NCERT Solutions Exercise 2.2 Question 15

00:59:54 NCERT Solutions Exercise 2.2 Question 16

01:01:24 NCERT Solutions Exercise 2.2 Question 17

01:03:04 NCERT Solutions Exercise 2.2 Question 19

01:04:24 NCERT Solutions Exercise 2.2 Question 20

01:05:34 NCERT Solutions Exercise 2.2 Question 21

01:07:04 NCERT Solutions Exercise 2.2 Question 18

Detailed explanation of 'how to drive identities of Inverse Trigonometric Functions' and questions related to NCERT Solutions for Exercise 2.2 of Inverse Trigonometric Functions Class 12 Maths Chapter 2.

💎 Purchase the Class 12 Maths Membership for full access to video lectures, notes, and assignments: https://mathyug.com/class-12-maths

[sethiswiftlearn]

Class 12 Math | Basics of Relations and functions | JEE Mains, CUET Prep

Understanding the Basics of Relations and Functions is essential for building a strong mathematical foundation, especially for Class 12 students preparing for competitive exams like JEE Mains, CUET, and other entrance tests. In this comprehensive and engaging video tutorial by Sethi Swift Learn, we break down the key concepts of Relations and Functions in the most simplified way to ensure conceptual clarity and long-term retention.

This session introduces you to the core fundamentals including the definition of relations and functions, types of relations (reflexive, symmetric, transitive, equivalence), and various types of functions like one-one, onto, and many-one. We also cover domain, codomain, and range—which are crucial to understanding function mapping and their applications in higher-level math problems.

Whether you're just starting out or revising the topic, this video serves as a step-by-step guide. The concepts are explained with the help of visual examples and solved questions so that you can confidently tackle problems in your board exams as well as in JEE Mains and CUET.

Our expert-led teaching approach focuses on:

Conceptual clarity with real-time examples

NCERT and previous year-based questions

JEE-level problem-solving techniques

Tips and tricks to solve relation & function problems faster

By the end of this session, you'll be able to identify and differentiate various types of relations and functions and apply this knowledge in problem-solving efficiently.

This video is ideal for:

Class 12 Students (CBSE & State Boards)

JEE Mains Aspirants

CUET and Other Competitive Exam Candidates

Don't forget to like, share, and subscribe to our channel for more such subject-wise breakdowns and in-depth lessons. Start mastering Relations and Functions with confidence today!

📌 Subscribe for more: Sethi Swift Learn 📌 Watch the full video here: https://youtu.be/yaNC_1ZcwwE?si=JHLJ6RQRSv_fxw94

Let me know if you want short captions, tags, or thumbnail ideas for this video too! 🎓📘

[ashishkumarletslearn]

Training Teachers to Teach Class 12 Maths — MathYug

In the ever-evolving landscape of education, having access to high-quality learning resources can make a world of difference. For Class 12 students, mastering mathematics is crucial, not only for academic success but also for future endeavors in various fields. At MathYug, we understand this importance and have dedicated ourselves to providing top-tier educational materials. Today, we’re excited to introduce our training program designed specifically for teachers who aspire to elevate their teaching skills and make a significant impact on their students’ learning journey.

Sample Videos: A Glimpse into Quality Education

To give you a taste of what MathYug has to offer, we are sharing a selection of sample videos from our Class 12 Maths tutorials. These videos exemplify the high-quality, in-depth teaching style that Ashish Kumar, affectionately known as Agam Sir, is known for.

Relations and Functions

2. One to One and Onto Functions

3. Inverse Trigonometric Functions

4. Continuity and Differentiability

5. Applications of Derivatives

6. Integrals

7. Inverse Trigonometric Functions

8. Basics of Logarithms, Log Table and Antilog Table

Why Choose MathYug for Teacher Training?

MathYug stands out as a premier platform for learning and teaching mathematics, especially for Class 12 students. Our resources are meticulously designed to cater to the diverse needs of both learners and educators, ensuring that each student can grasp complex mathematical concepts with ease. Here’s why MathYug is the best choice for your teaching journey:

Expert Guidance

All our content is created by Ashish Kumar (Agam Sir), a renowned educator with years of experience in teaching mathematics. His unique teaching style simplifies complex topics, making them easily understandable. By training with MathYug, teachers can learn how to effectively convey these methods to their students.

Comprehensive Coverage

Our tutorials cover the entire Class 12 Maths syllabus, aligned with the NCERT guidelines. This ensures that students are well-prepared for their board exams and other competitive exams. Teachers trained with MathYug will be equipped to offer their students a thorough and well-rounded mathematical education.

Interactive Learning

We believe in making learning engaging and interactive. Our video lessons are complemented by practical exercises, assignments, and downloadable PDFs to reinforce learning. Teachers will be trained to use these resources to create a dynamic and interactive classroom environment.

Elevate Your Teaching Experience with MathYug

At MathYug, we are committed to providing the best possible educational resources to help both students and teachers excel in mathematics. Our Class 12 Maths tutorials are designed to build confidence, enhance understanding, and foster a love for learning. By sharing these sample videos, we hope to give teachers a glimpse of the quality education that awaits them on our platform.

Join MathYug Today!

Experience the difference with MathYug and take your teaching skills to new heights. Subscribe to our Class 12 Maths membership and gain access to a comprehensive collection of video lessons, study materials, and expert guidance from Ashish Sir. Let’s embark on this journey of academic excellence together!

Visit MathYug now and start your journey towards mastering Class 12 Maths with ease and confidence.

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Learn to Bake! Kids & Teens Classes (10-18) | 9448925759 - A detailed guide!

Children's baking classes provide a high and interactive method of teaching them necessary skills while exposing them to the culinary arts. These classes teach children much more than the ways of baking cookies or cakes; they teach a diverse range of lessons that can be applied in many areas of their lives.

·        Creativity and Imagination: Baking provides opportunities for children to be creative. They can test out various ingredients, colors, and shapes to come up with their own individual designs. From frosting cupcakes in bright colors to creating intricate cakes, children learn how to execute their imaginative creations. This learning experience promotes creativity, which can spill over from the kitchen to other aspects of life, such as art, problem-solving, and even fiction.

·        Following Instructions and Patience: Baking is a process that demands meticulous attention to detail and step-by-step following of instructions. In a baking class, children learn to follow recipes, measure ingredients, and time their work correctly. This instills patience in them and makes them realize the value of sequential steps to get a desired outcome. It also makes them learn to concentrate on the task at hand and enhances their listening skills.

·        Basic Math Skills: Baking requires a significant amount of math, from measuring ingredients to scaling recipe quantities. Kids can develop their math skills by learning to measure with cups and spoons, read fractions (like half a cup or a quarter teaspoon), and scale recipes up or down. These real-world applications of math make the concepts more concrete and accessible, giving kids more confidence in the subject.

Science and Experimentation: Baking classes for teensintroduces young people to fundamental science principles like the way in which heat induces chemical reactions (e.g., how yeast makes dough rise) or the way ingredients relate to each other (such as the manner in which baking soda causes cakes to rise). The hands-on nature of thesebaking classes for 10 year oldsmake science enjoyable and accessible. They also get to understand the principle of trial and error, where they can try various ingredients and methods to observe the impact of minor variations in the result.

·        Teamwork and Social Skills: Numerous children's baking classes allow group work where the kids join forces to work on a recipe. This inspires teamwork and camaraderie while educating them how to divide jobs, communicate openly, and reach a shared end goal. The ability to be social and effectively function in team-based environments plays an important part in developing human relationships and professional workplaces.

·        Life Skills and Independence: Not only does learning to bake give children the skill to make tasty treats, but it also teaches them life skills like responsibility and independence. They become more confident by learning new skills, making choices about flavors or decorations, and being responsible for the baking process from beginning to end. Baking classes for 12 year oldscan enhance self-esteem and provide a sense of achievement.

·        Health and Nutrition Awareness: Baking classes can provide a platform for kids to learn about nutrition. They can be educated on the advantages of healthy ingredients such as fruits, whole grains, and natural sweeteners, and how to choose healthier options while baking. Knowledge of the balance between indulgence and healthy options gives children the power to make smart choices regarding what they consume.

·        Emotional Benefits: Baking can also be a therapeutic experience for children. The concentration needed and the feeling of accomplishment when they finish a recipe can give them emotional fulfillment and a mental boost. Moreover, getting to share the goodies they've prepared with family or friends gives them a sense of belonging and connection.

In summary, children's baking classes provide a well-rounded learning experience. Not only do they help children learn the craft of baking, but they also impart useful lessons in creativity, patience, math, science, teamwork, life skills, and emotional well-being. Learning these things through baking classes helps kids acquire valuable tools that will benefit them in so many ways, while doing something fun in the kitchen.URL: https://anjalicookingschool.com/

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Master 12th Math with the Best Tuition in Chandigarh

Master 12th Math with the Best Tuition in Chandigarh Mathematics in Class 12 is important in determining the academic life of a student. Whether you want to pursue engineering, commerce, or competitive exams, math literacy is crucial. The proper math tuition in Chandigarh can turn the tables and help you understand tricky concepts, enhance problem-solving ability, and increase confidence.

Why 12th Math Tuition in Chandigarh? Chandigarh boasts some of the top coaching centers offering professional guidance for Class 12 math preparation. Here's why professional tuition can be a game-changer: Personalized Learning Approach – Limited batch sizes allow students to receive personal attention, enabling them to clear doubts easily. Expert Faculty – Highly qualified teachers apply modern teaching methods to make difficult mathematical concepts easier. Regular Practice and Tests – Ongoing tests and assignments aid in monitoring progress and consolidating learning. Exam-Focused Preparation – A well-designed curriculum emphasizes crucial topics, past question papers, and competitive exam trends.

Major Topics Covered in 12th Math Tuition

A well-designed tuition course covers all the major Class 12 math topics as mandated by the CBSE and other boards. Some of the major areas are: Calculus – Differentiation, Integration, and Application of Derivatives Algebra – Matrices, Determinants, and Linear Programming Probability & Statistics – Conditional Probability, Mean, Median, and Standard Deviation Coordinate Geometry – Three-Dimensional Geometry and Vectors Relations & Functions – Inverse Trigonometric Functions and Continuity

How to Select the Best Math Tuition in Chandigarh?

Getting the most appropriate tuition center is a thoughtful decision based on numerous factors: Faculty Experience – Inspect the education and experience of teachers. Student Reviews and Success Rate – Check previous outcomes and students' reviews. Flexible Batch Timings – Make sure the class timing is compatible with your study schedule. Doubt-Solving Sessions – Provision of additional classes for resolving doubts.

Conclusion Excelling in Class 12 mathematics requires the right guidance, consistent practice, and strategic preparation. Enrolling in the best math tuition in Chandigarh can help you build a strong foundation and secure excellent marks in your board exams. With expert coaching, a structured curriculum, and personalized attention, you can overcome challenges and master every concept with ease. Start your journey today and make math your strength!

[3dprintinginedushaikhsamreen]

Application of 3D Printing in STEM Education

3D printing has revolutionized various fields, and its application in STEM (Science, Technology, Engineering, and Mathematics) education is particularly significant. By providing hands-on learning experiences, 3D printing enhances students’ understanding of complex concepts and encourages creativity and innovation. Here are some examples of how 3D printing is being utilized in STEM education.

 1.Engineering Prototyping

In engineering courses, students can design and print prototypes of their projects. mechanical engineering students can create working models of machines or mechanisms, allowing them to test and examine their designs quickly. This hands-on experience solidifies theoretical knowledge and develop problem-solving skills.

2. Biology and Anatomy Models

3D printing is extensively used in biology classes to create models of cells, organs, and organisms. Students can print detailed models of the human heart or brain, which helps them understand anatomy in a easier way.

3.Mathematics Visualization

Students can create geometric shapes and complex mathematical surfaces, allowing them to explore properties such as volume and surface area. This practical application helps fill the gap between theoretical math and real-world applications.4

4. Robotics and Coding

Students can design and print custom parts for their robots, coding them to specific functions. This process integrates coding with mechanical design, providing a comprehensive learning experience that enhances both programming and engineering skills.

5.Environmental Science Projects

Students can use 3D printing to create models that simulate ecological systems or showcase the impact of human activities on environments. For instance, they might design models of habitats to study biodiversity or print pollution models to visualize and analyze data. These projects foster awareness and understanding of environmental issues.

 6.Art and Design Integration

In STEM courses, students can design artistic sculptures or functional items, . This integration encourages innovation and creative problem-solving, essential skills in both STEM and the arts.

7. Space Exploration Stimulation 

With the growing interest in space exploration, students can engage in projects that involve 3D printing to design and create models of spacecraft or Martian habitats. This not only enhances their understanding of aerospace engineering but also inspires interest in STEM fields related to space science.

8. Accessibility and Customization

3D printing also allows for the customization of educational tools and resources. For example, students with disabilities can have assistive devices tailored to their needs, fostering inclusivity in STEM education. This adaptability makes learning more accessible and engaging for all students.

9. Chemistry Molecular Models

In chemistry classes, students can use 3D printing to create models of molecules and chemical compounds. By printing these structures, students gain a better understanding of molecular geometry, bonding, and chemical reactions, which can be challenging to visualize through diagrams alone.

10. Physics Experiments

Physics students can design and print custom apparatus for experiments. For example, they might create resonance or simple machines to study forces, motion, and energy transfer. This hands-on approach helps to understand theoretical principles through practical application.

 11.Historical Artifacts in Social Studies

In social studies or history classes, students can print replicas of historical artifacts, such as ancient tools or architectural features. This experience enhance their understanding of historical contexts making learning more engaging.

 12.Renewable Energy Models

Students studying renewable energy technologies can design and print models of solar panels, wind turbines, or hydroelectric systems. These projects can be used to simulate energy production and understand the principles of sustainability, engineering, and environmental science.

13. Customized Tools and Gadgets

In technology and design courses, students can create customized tools or gadgets tailored to specific tasks or problems. For example, they could design ergonomic tools for specific user needs, promoting innovation and practical application of design thinking.

14. Architectural Models

Architecture students can use 3D printing to create detailed scale models of their designs. This allows them to visualize relationships and aesthetics, providing insights into both structural integrity and design principles.

15.Game Design and Development

In computer science and game design programs, students can print 3D models of characters or environments they create. This integration of physical and digital design fosters creativity and helps students understand the complexities of game development.

 16. Assistive Technology Projects

Students can engage in projects that focus on designing assistive technologies, such as prosthetic limbs or adaptive devices. By creating functional prototypes, students learn about engineering design, user-centered design, and the impact of technology on accessibility.

17. Personalized Learning Tools

Teachers can use 3D printing to create customized learning tools, such as tactile math manipulatives for younger students or specialized equipment for science labs. This tailored approach supports diverse learning styles and needs within the classroom.

 18. Bioengineering Simulations

In bioengineering programs, students can print models of biological systems or tissues to study concepts like tissue engineering and regenerative medicine. This application enhances understanding of complex biological processes and fosters innovation in medical technology.

 19. Virtual Reality Integration

Combining 3D printing with virtual reality (VR) allows students to create physical models that can be used alongside VR simulations. This integration provides a multidimensional learning experience, enabling students to explore concepts in both physical and digital spaces.

20.Student Competitions and Challenges

Many educational institutions host competitions that encourage students to solve real-world problems using 3D printing. For instance, challenges might involve designing and building sustainable housing models or innovative transportation solutions, fostering collaboration and creativity.

 Conclusion

These examples illustrate the diverse applications of 3D printing in STEM education, highlighting its potential to enhance learning experiences, encourage innovation, and prepare students for future careers in technology and engineering fields. As educators continue to explore and implement 3D printing in their curriculum.

[shiva10010]

JEE Main 2025! Prep Your Math Strategy with the Latest Syllabus

The Joint Entrance Examination (JEE) Main is a critical gateway for aspiring engineers in India. While the official syllabus for JEE Main 2025 will likely be released by the National Testing Agency (NTA) in November 2024, you can get a head start on your preparation using the previous year's syllabus as a guide.

This article focuses on the Mathematics section of the JEE Main 2025 exam.

Key Elements of the JEE Main 2025 Maths Syllabus

The JEE Main Maths syllabus covers a wide range of topics from Class 11 and 12 NCERT textbooks. Here's a quick glimpse of the major areas you'll encounter:

Algebra: Sets, relations and functions, complex numbers, matrices and determinants, mathematical induction, binomial theorem, sequence and series.

Calculus: Limit, continuity and differentiability, integral calculus, differential equations.

Geometry: Coordinate geometry, three-dimensional geometry, vector algebra.

Other Quantitative Techniques: Statistics and probability, trigonometry, mathematical reasoning.

Why eSaral is Your Perfect JEE Main 2025 Maths Companion

While the syllabus provides a roadmap, in-depth preparation is essential for success. This is where eSaral steps in:

Complete Syllabus Coverage: eSaral ensures you cover all the essential JEE Main Maths topics.

Detailed Learning Material: Access a treasure trove of resources, including crisp explanations, illustrative examples, and topic-wise revision notes [refer to JEE Main 2025 Maths Revision Notes on eSaral for details].

Catered Learning Styles: Whether you prefer short and focused content or a deep dive into concepts, eSaral offers options to match your learning style.

Practice Makes Perfect: Sharpen your skills with ample practice problems available on the platform.

Additional Tips to Conquer JEE Main 2025 Maths

Focus on NCERT Textbooks: They form the foundation for the entire syllabus.

Regular Practice: Solve problems consistently to build speed, accuracy, and exam temperament.

Mock Tests: Take regular mock tests to simulate the exam environment and identify areas for improvement.

Clear Your Doubts: Don't hesitate to seek clarification from teachers or online forums.

Conclusion

JEE Main 2025 Maths can be aced with the right approach and resources. By leveraging the detailed syllabus and comprehensive learning materials offered by eSaral, you can approach the exam with confidence and a strategic plan. Remember, consistent effort and focused practice are key to achieving your engineering dreams.

[mpboardsolutions-blog]

MP Board Class 12th Maths Book Solutions in English Medium

MP Board Class 12th Maths Chapter 1 Relations and Functions

Chapter 1 Relations and Functions Ex 1.1

Chapter 1 Relations and Functions Ex 1.2

Chapter 1 Relations and Functions Ex 1.3

Chapter 1 Relations and Functions Ex 1.4

Chapter 1 Relations and Functions Miscellaneous Exercise

MP Board Class 12th Maths Chapter 2 Inverse Trigonometric Functions

Chapter 2 Inverse Trigonometric Functions Ex 2.1

Chapter 2 Inverse Trigonometric Functions Ex 2.2

Chapter 2 Inverse Trigonometric Functions Miscellaneous Exercise

MP Board Class 12th Maths Chapter 3 Matrices

Chapter 3 Matrices Ex 3.1

Chapter 3 Matrices Ex 3.2

Chapter 3 Matrices Ex 3.3

Chapter 3 Matrices Ex 3.4

Chapter 3 Matrices Miscellaneous Exercise

MP Board Class 12th Maths Chapter 4 Determinants

Chapter 4 Determinants Ex 4.1

Chapter 4 Determinants Ex 4.2

Chapter 4 Determinants Ex 4.3

Chapter 4 Determinants Ex 4.4

Chapter 4 Determinants Ex 4.5

Chapter 4 Determinants Ex 4.6

Chapter 4 Determinants Miscellaneous Exercise

MP Board Class 12th Maths Chapter 5 Continuity and Differentiability

Chapter 5 Continuity and Differentiability Ex 5.1

Chapter 5 Continuity and Differentiability Ex 5.2

Chapter 5 Continuity and Differentiability Ex 5.3

Chapter 5 Continuity and Differentiability Ex 5.4

Chapter 5 Continuity and Differentiability Ex 5.5

Chapter 5 Continuity and Differentiability Ex 5.6

Chapter 5 Continuity and Differentiability Ex 5.7

Chapter 5 Continuity and Differentiability Ex 5.8

Chapter 5 Continuity and Differentiability Miscellaneous Exercise

MP Board Class 12th Maths Chapter 6 Application of Derivatives

Chapter 6 Application of Derivatives Ex 6.1

Chapter 6 Application of Derivatives Ex 6.2

Chapter 6 Application of Derivatives Ex 6.3

Chapter 6 Application of Derivatives Ex 6.4

Chapter 6 Application of Derivatives Ex 6.5

Chapter 6 Application of Derivatives Miscellaneous Exercise

MP Board Class 12th Maths Chapter 7 Integrals

Chapter 7 Integrals Ex 7.1

Chapter 7 Integrals Ex 7.2

Chapter 7 Integrals Ex 7.3

Chapter 7 Integrals Ex 7.4

Chapter 7 Integrals Ex 7.5

Chapter 7 Integrals Ex 7.6

Chapter 7 Integrals Ex 7.7

Chapter 7 Integrals Ex 7.8

Chapter 7 Integrals Ex 7.9

Chapter 7 Integrals Ex 7.10

Chapter 7 Integrals Ex 7.11

Chapter 7 Integrals Miscellaneous Exercise

MP Board Class 12th Maths Chapter 8 Application of Integrals

Chapter 8 Application of Integrals Ex 8.1

Chapter 8 Application of Integrals Ex 8.2

Chapter 8 Application of Integrals Miscellaneous Exercise

MP Board Class 12th Maths Chapter 9 Differential Equations

Chapter 9 Differential Equations Ex 9.1

Chapter 9 Differential Equations Ex 9.2

Chapter 9 Differential Equations Ex 9.3

Chapter 9 Differential Equations Ex 9.4

Chapter 9 Differential Equations Ex 9.5

Chapter 9 Differential Equations Ex 9.6

Chapter 9 Differential Equations Miscellaneous Exercise

MP Board Class 12th Maths Chapter 10 Vector Algebra

Chapter 10 Vector Algebra Ex 10.1

Chapter 10 Vector Algebra Ex 10.2

Chapter 10 Vector Algebra Ex 10.3

Chapter 10 Vector Algebra Ex 10.4

Chapter 10 Vector Algebra Miscellaneous Exercise

MP Board Class 12th Maths Chapter 11 Three Dimensional Geometry

Chapter 11 Three Dimensional Geometry Ex 11.1

Chapter 11 Three Dimensional Geometry Ex 11.2

Chapter 11 Three Dimensional Geometry Ex 11.3

Chapter 11 Three Dimensional Geometry Miscellaneous Exercise

MP Board Class 12th Maths Chapter 12 Linear Programming

Chapter 12 Linear Programming Ex 12.1

Chapter 12 Linear Programming Ex 12.2

Chapter 12 Linear Programming Miscellaneous Exercise

MP Board Class 12th Maths Chapter 13 Probability

Chapter 13 Probability Ex 13.1

Chapter 13 Probability Ex 13.2

Chapter 13 Probability Ex 13.3

Chapter 13 Probability Ex 13.4

Chapter 13 Probability Ex 13.5

Chapter 13 Probability Miscellaneous Exercise

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Relations and Functions Class 12 Notes Maths Chapter 1