#Learn Inequalities JEE

[9nid]

🎯 Master the Graphical Method to Solve Inequalities for JEE | JEE Series Part-10 | 9nid

📖 Introduction: Solving inequalities is one of the most important concepts in JEE Mathematics, and if you’re preparing seriously, then the Graphical Method is a tool you must master. In Part-10 of the JEE Series by 9nid, we dive deep into the Graphical Approach to Inequalities, explaining how to visualize and solve even the trickiest algebraic inequalities with confidence. This session is…

[edusquaremaths]

🎯 Master the Graphical Method to Solve Inequalities for JEE | JEE Series Part-10 | 9nid

📖 Introduction: Solving inequalities is one of the most important concepts in JEE Mathematics, and if you’re preparing seriously, then the Graphical Method is a tool you must master. In Part-10 of the JEE Series by 9nid, we dive deep into the Graphical Approach to Inequalities, explaining how to visualize and solve even the trickiest algebraic inequalities with confidence. This session is…

[acamind]

CBSE Class 11 Science: A Comprehensive Guide

The CBSE (Central Board of Secondary Education) curriculum for Class 11 Science is an essential stepping stone for students aiming to build a strong foundation in various scientific fields. It is a crucial phase where students transition from basic concepts learned in previous classes to more advanced topics that lay the groundwork for future studies in fields like engineering, medicine, pure sciences, and more. The Class 11 Science curriculum under the CBSE board is designed to challenge students, promote critical thinking, and encourage a deeper understanding of the subjects.

Whether you are aspiring to crack competitive exams such as NEET, JEE, or other entrance tests, or simply looking to solidify your knowledge for higher studies, CBSE Class 11 Science offers a thorough academic experience.

Subjects Offered in CBSE Class 11 Science

In CBSE Class 11 Science, students typically have the option to choose between two streams—Medical (PCB) and Non-Medical (PCM). Both streams offer core subjects with slight variations based on the student's career aspirations.

1. Physics

Physics is a core subject in the Science stream for both medical and non-medical students. It covers topics such as Mechanics, Thermodynamics, Waves, Electromagnetic Induction, and Modern Physics. The concepts taught in Class 11 Physics help students understand the physical laws of nature, which are foundational for higher studies in science, technology, and engineering.

Key topics include:

Units and Measurements

Kinematics

Laws of Motion

Work, Energy, and Power

Gravitation

Properties of Matter

Thermodynamics

Oscillations and Waves

2. Chemistry

Chemistry is another vital subject in the Science stream that deals with the composition, structure, properties, and reactions of matter. It is divided into Physical Chemistry, Organic Chemistry, and Inorganic Chemistry, giving students a broad understanding of how different elements and compounds interact.

Key topics include:

Some Basic Concepts of Chemistry

Atomic Structure

Chemical Bonding and Molecular Structure

Thermodynamics

Equilibrium

Redox Reactions

Organic Chemistry – Some Basic Principles

Hydrocarbons

3. Biology (PCB Stream Only)

For students opting for the Medical (PCB) stream, Biology is a major subject that covers a wide range of topics related to living organisms. This subject is essential for students aspiring to pursue careers in medicine, biotechnology, pharmacy, and related fields.

Key topics include:

Diversity of Living Organisms

Cell Structure and Function

Plant Physiology

Human Physiology

Biomolecules

Ecology and Environment

4. Mathematics (PCM Stream Only)

For students in the Non-Medical (PCM) stream, Mathematics is a critical subject. The concepts taught in Class 11 Mathematics are essential for students aspiring to pursue engineering, computer science, and pure mathematics. This subject helps students develop problem-solving skills and logical thinking.

Key topics include:

Sets and Functions

Trigonometry

Calculus

Probability

Statistics

Linear Inequalities

Permutations and Combinations

Coordinate Geometry

5. English

English is a compulsory subject for all students, regardless of the stream. The focus is on improving communication skills, reading comprehension, and writing abilities. The subject also helps students build a strong command of the language, which is essential for both academic and professional success.

6. Optional Subjects

Students can also opt for optional subjects like Computer Science, Physical Education, or Economics to complement their core Science subjects. These optional subjects provide additional knowledge that can be useful for students in their future careers.

Importance of CBSE Class 11 Science

Foundation for Competitive Exams For students aiming to crack competitive exams like JEE (for engineering) or NEET (for medical), CBSE Class 11 Science plays a pivotal role. Many questions in these exams are directly based on concepts from the Class 11 syllabus. Hence, mastering these subjects early can give students a significant advantage.

Critical Thinking and Problem-Solving Skills The syllabus is designed to enhance students' critical thinking and analytical skills. Physics and Mathematics, in particular, require problem-solving abilities, while Chemistry and Biology test students' understanding of fundamental concepts. This comprehensive approach ensures that students are well-prepared for the academic challenges that lie ahead.

Preparation for Higher Education Whether a student chooses to pursue engineering, medicine, or pure sciences, CBSE Class 11 Science prepares them for the rigors of higher education. The topics covered form the base for Class 12, which is equally significant, and for college-level studies.

Practical Application of Knowledge In addition to theory, students also engage in practicals in Physics, Chemistry, and Biology. These practicals give students hands-on experience, helping them understand how scientific principles are applied in real-life scenarios. This knowledge is invaluable, especially for those pursuing careers in research or technical fields.

Tips to Excel in CBSE Class 11 Science

Consistent Study Schedule Given the vast syllabus, it's important to have a consistent study schedule. Break down each subject into manageable sections and dedicate time each day to review and practice problems.

Focus on Understanding Concepts Instead of rote learning, focus on understanding the underlying concepts in each subject. This is especially important in Physics and Chemistry, where application of knowledge is key to solving problems.

Practice Regularly For subjects like Mathematics and Physics, regular practice is essential. Solve as many problems as possible to build your confidence and speed. For Biology, make sure to memorize important terms and processes.

Revise Frequently Since the syllabus is extensive, regular revision is necessary to retain information. Make summary notes and revise them frequently to ensure you're prepared for exams.

Seek Help When Needed If you're struggling with a particular topic, don't hesitate to seek help from teachers, peers, or online resources. Addressing doubts early on will help you avoid confusion later.

Conclusion

CBSE Class 11 Science is a challenging yet rewarding phase in a student’s academic journey. With its emphasis on critical thinking, practical application, and foundational knowledge, this curriculum prepares students for a wide range of career options in science and technology. By focusing on understanding key concepts, practicing regularly, and staying consistent with your studies, you can excel in Class 11 and build a solid foundation for the future.

Whether you're aiming for top ranks in competitive exams or simply looking to pursue higher education in a scientific field, mastering the CBSE Class 11 Science syllabus will set you on the path to success.

[class11maths]

Linear Inequalities — Class 11 Maths Course by Mathyug

Understanding Linear Inequalities is a fundamental aspect of Class 11 Maths, laying the groundwork for various advanced topics in algebra and calculus. Mathyug’s course on Linear Inequalities is designed to make this topic engaging and easy to grasp, ensuring students not only master the concepts but also apply them effectively in problem-solving scenarios.

Why Choose Mathyug for Linear Inequalities?

Mathyug stands out for its structured approach and comprehensive coverage of topics. The Linear Inequalities module is no exception. Here’s what makes it unique:

High-Quality Video Lectures: Each concept is explained in detail, breaking down complex ideas into simple, understandable steps. The use of real-life examples helps in visualizing abstract mathematical concepts, making the learning process intuitive and engaging.

Detailed Notes: Mathyug provides meticulously crafted notes that complement the video lectures. These notes cover all the theoretical aspects, important formulas, and shortcuts, ensuring a solid understanding of the topic.

Assignments for Practice: The course includes a variety of assignments for linear inequalities that challenge students to apply what they’ve learned. These assignments are curated to cover a broad spectrum of problems, from basic to advanced levels, fostering a deeper understanding and preparing students for exams.

Conceptual Clarity: The focus is on building a strong conceptual foundation. This is crucial as Linear Inequalities form the basis for several other topics in mathematics, including linear programming and calculus.

Course Highlights

Comprehensive Coverage: The course covers all NCERT topics as well as additional concepts required for competitive exams like JEE.

Interactive Learning: The lectures are interactive, encouraging students to think critically and solve problems in real-time.

Regular Updates: Mathyug ensures the content is up-to-date, incorporating the latest syllabus changes and best teaching practices.

Sample Video Showcase

To give you a glimpse of the quality and style of teaching, here’s a sample video from the Linear Inequalities course. This video demonstrates Mathyug’s approach to making complex topics accessible and interesting. It’s a must-watch for anyone looking to excel in Class 11 Mathematics.

Why Linear Inequalities Matter

Linear Inequalities are more than just an academic requirement. They are essential in understanding and solving real-world problems involving constraints and optimization. Whether you’re calculating budget limits, analyzing business profit margins, or simply planning your daily schedule, the principles of inequalities are at play.

Conclusion

Mathyug’s Linear Inequalities course for Class 11 is an excellent resource for students aiming to master this topic. The combination of engaging video lectures, comprehensive notes, and challenging assignments makes it an ideal choice for both regular curriculum studies and competitive exam preparation.

If you’re looking to strengthen your grasp of Linear Inequalities and ace your exams, Mathyug’s course is the perfect companion on your learning journey.

[punejago]

Benefits of IOQM

Indian Olympiad Qualifier in Mathematics (IOQM) will be a three-hour examination and will be jointly organised by the Mathematics Teachers Association of India (MTAI), Indian Association of Physics Teachers (IAPT) and Homi Bhabha Centre for Science Education (Tata Institute of Fundamental Research) – HBCSE (TIFR).

Indian Olympiad Qualifier in Mathematics (IOQM) is the first stage of the Mathematical Olympiad Programme in India. Only those students who qualify IOQM are eligible to appear for the INMO, the second stage of the International Mathematical Olympiad (IMO).

IOQM Syllabus & Test Pattern

Basis a detailed year-wise analysis of PRMO, RMO, and IOQM papers, it has been suggested that the main units covered in the IOQM syllabus are:

1. Algebra

2. Combinatorics

3. Geometry

4. Number Theory

Topics include: arithmetic of integers, geometry, quadratic equations and expressions, trigonometry, co-ordinate geometry, the system of linear equations, permutations and combination, factorization of polynomials, inequalities, elementary Combinatorics, probability theory and number theory, finite series, complex numbers, and elementary graph theory, etc. The difficulty level increases from one stage to another.

Benefits of IOQM

• The IOQM is a platform for students of school level to showcase their skills and talent in mathematics.

• It helps them to understand deep knowledge about subjects and sharpens their mind for aptitude and competitive exams.

• IOQM helps students to solve complex problems in no time.

• One can strengthen the fundamentals of Maths, which not only help in cracking IOQM but also help in getting good scores in school-based exams.

• Appearing for IOQM gives self-confidence in students and helps them work hard to achieve their goals.

• Subjects become interesting to learn when students challenge themselves to come out of their comfort zone and have a desire to learn more and master themselves.

• Olympiads give motivation to students to push themselves forward and do brainstorming.

• Olympiad exams are extremely useful for all classes from class 1 to class 10. These exams help students from different schools and different boards on the same platform. It promotes learning in the same subjects that are taught in class. It also helps to identify their strengths and weaknesses.

Check out the 2022-23 Question Paper and Answers here:

IOQM 2022 Answer Key - Pune Jago IIT JEE for Main and Advanced, KVPY, MHT CET

[adventuresincuriosity]

An education

Over the past couple of weeks, my Facebook feed has been inundated with graduation status updates and photographs from family and friends.

As someone who has already graduated — and who will do it again soon, albeit with a Master’s degree this time — it made me think: what was going on in these young students’s minds? What were they thinking, as they stood in cap and gown, confronting the threshold of a new beginning? Were they excited, terrified or clueless at the prospect of what lay ahead?

The real world sneaks up on you

I remember feeling all three on my graduation day. As I walked down the aisle to receive my degree, I remember feeling cheated. I was startled to discover that the ‘real world’ (a phrase I have since come to despise and use only begrudgingly) had somehow snuck up on me.

Education was my safety blanket, a comforting shelter which had dictated the purpose and the rhythm of my life. For eighteen years, school had given me structure: it filled my days with classes, it gave me homework on the weekends, it gave me exams and summer vacations. It was a comfortable, familiar pattern that repeated over and over for nearly two decades.

And then suddenly, at 21, you find that the pattern is broken. You’re on your own. Have fun figuring out what the hell to do with you life. Good luck!

John Lennon cheekily summed it up in his song ‘Working Class Hero’:

When they’ve tortured and scared you for 20 odd years then they expect you to pick a career.

Lennon may have been tongue-in-cheek with that lyric, but it hides a grain of truth. And the truth is that we see education as a linear process — a cut-and-dried path with a career as the goal in the end.

The promise of a career

This eighteen year old journey is marked by checkpoints and milestones scattered across its path— GPAs and SAT scores, JEE marks and nationwide ranks, volunteer experience and extracurricular activities — all demarcated, always, with the explicit purpose of moving your educational career forward. Get good grades to get into a good college. Volunteer on weekends to make your application shine as a well-rounded student. Join the debate team.

You do one thing to move on to the next, and the summation of all your effort is leading up to one ultimate goal. The fabulous prize of a comfortable salary package. Perks and fancy job titles and corporate leases. Gym memberships and dental insurance and yoga classes. The rewards for all your hard work.

The promise of a career.

To be honest, it’s an alluring promise — a tempting prospect. Except when it’s not. Except when graduates, armed with their hard-earned degrees in hand, cannot find jobs. When young people barely starting into their adult lives are weighed down by monstrous amounts of debt.

An education

A degree is the stamp of approval of a student’s ability — a validation of their potential. This validation is their ticket into the workforce. And to be sure, it seems like a pretty fair deal. But we know that that’s not the whole equation. ‘It’s not what you know, it’s who you know’ is thrown around heavily in and out of business school classrooms. A degree doesn’t account for the state of the economy, or the changing state of industry, or the inequalities in the backgrounds and disparity of opportunities between students of different classes.

And most of all, a degree doesn’t account for an education, and an education doesn’t account for a career.

What we think of as a linear, one-track process as a means to an end, is anything but that. Education doesn’t begin in kindergarten and end in college. It is a continuous and life-long process, often times meandering and wavering and with a lot of back-and-forth.

Education is the unleashing of curiosity. It is tinkering, wondering out loud, and looking at the whole world, in all its myriad possibilities, as your blank slate. You can draw on it whatever you want — whatever interests you and sparks you intellectual curiosity — physics, literature, history, linguistics, anthropology, computer science, philosophy, history, mathematics, marketing, theater, engineering, psychology, artificial intelligence, graphic design, medicine. All is yours to learn and question and master and use.

Ultimately, a career does not begin where an education ends. They are undeniably fused and feed into each other. A solid education can — and should — help you begin your career. It is important to remember, however, that you dictate what that career will be. And a career is much more than just a 9–to-5 job. It is the collective progression of your professional and personal learning, experience and achievement. It is your life’s work. ‘Do what you love’ is a staple of commencement speeches, now almost an empty cliché that mocks young graduates in the face of what awaits them. Many are lucky to have a job at all, let alone a job doing what they love.

But an education can help us do just that — do what we love. It is our responsibility to stay determined and steadfast in the face of challenges. To go in pursuit of what it is you want do and pursue it, fearlessly and intensely. To master it, rethink it, reshape it. You studied journalism or publishing or or English literature in school. Don’t let others tell you that you picked the wrong major. There is no question that your industry maybe undergoing an upheaval of change, in some cases even struggling to stay afloat. That just means it is an industry ripe for a revolution. And revolutions are happening around us, if we care to notice. Look at Medium, for example. How can it change — and is changing — publishing? How does journalism fare in the age of Twitter and Facebook Instant Articles — and how can we make it better?

Be resourceful. Channel your passion into inventiveness. That’s the real goal of your education. To keep you on your toes and equip you with the faculty and tools to solve problems. Ultimately:

It is up to you to do with your education what you will.

My favorite advice regarding how to find your life’s purpose comes from John Green. Answering the question ‘What the hell should I do with my life?’ from a college freshman in a reddit AMA, John goes on to say:

You are always figuring out what the hell to do with your life, and then the decisions you’ve made are always be changed by circumstance: Your wife gets a job in Kuala Lumpur or there’s no one to take over your dead uncle’s junkyard or in your mid-30s you develop an intense love of astrophysics that sends you back to school.

So don’t put quite so much pressure on yourself. Study as broadly as you can; think practically but with the understanding that what you do as a job need not be the only thing you do (or even the only thing you do to make money).

In the end, a lot of what the hell you do with your life isn’t even about what you do for a job but whom you love, whom you marry, whether you have kids, and whether you find passions and have the ability to pursue them. College is part of that process, for sure, but it’s not the end of the line.

So when you walk and smile for the camera and receive your diploma, remember that it’s okay to feel afraid. It’s okay to feel lost at the prospect of a long dark road ahead. But we can all take comfort in the fact that you can decide what road to go by, that you have the power to shape it, take detours and combine different ones, and — if need be — even change the road you’re on. You are allowed to stumble, get up, and make your way through.

Good luck!

[9nid]

🎥 JEE Series Part-08 (Solving Inequalities - 02)

📘 JEE Series Part-08: Quadratic Inequalities Made Easy | 9nid Hinglish JEE Maths In this part of the 9nid JEE Series, we explore how to solve Quadratic Inequalities, a crucial topic in the Algebra section of JEE Maths. You’ll learn: What makes quadratic inequalities different from linear ones How to solve them using factorization and sign analysis Common mistakes students make in…

[edusquaremaths]

🎥 JEE Series Part-08 (Solving Inequalities - 02)

📘 JEE Series Part-08: Quadratic Inequalities Made Easy | 9nid Hinglish JEE Maths In this part of the 9nid JEE Series, we explore how to solve Quadratic Inequalities, a crucial topic in the Algebra section of JEE Maths. You’ll learn: What makes quadratic inequalities different from linear ones How to solve them using factorization and sign analysis Common mistakes students make in…

[9nid]

JEE Series Part-09 | Solving Inequalities – 03 | Compound Inequalities | JEE Maths in Hinglish | @9nid

Welcome back to the JEE Series by 9nid!In Part-09, we’re diving into an important concept: Compound Inequalities — a must-know for scoring in JEE Mains & Advanced. 🧠 What You’ll Learn in This Video: What are compound inequalities Solving AND & OR inequalities Number line visualization for compound solutions Shortcut methods to handle multi-inequality expressions Real JEE-level examples –…

[edusquaremaths]

JEE Series Part-09 | Solving Inequalities – 03 | Compound Inequalities | JEE Maths in Hinglish | @9nid

Welcome back to the JEE Series by 9nid!In Part-09, we’re diving into an important concept: Compound Inequalities — a must-know for scoring in JEE Mains & Advanced. 🧠 What You’ll Learn in This Video: What are compound inequalities Solving AND & OR inequalities Number line visualization for compound solutions Shortcut methods to handle multi-inequality expressions Real JEE-level examples –…

[9nid]

📘 JEE Series Part-07: Solving Inequalities – 01

In this latest episode of the 9nid JEE Maths Series, we’re diving into the world of linear inequalities! 🧠 This video is perfect for JEE aspirants who want to: Master solving inequalities from scratch Understand graph-based solutions Tackle JEE-style problems with clarity Learn in Hinglish for better understanding and comfort Whether you’re starting out or reviewing for JEE 2025, this…

[edusquaremaths]

📘 JEE Series Part-07: Solving Inequalities – 01

In this latest episode of the 9nid JEE Maths Series, we’re diving into the world of linear inequalities! 🧠 This video is perfect for JEE aspirants who want to: Master solving inequalities from scratch Understand graph-based solutions Tackle JEE-style problems with clarity Learn in Hinglish for better understanding and comfort Whether you’re starting out or reviewing for JEE 2025, this…

[adventuresincuriosity]

An Education

Over the past couple of weeks, my Facebook feed has been inundated with graduation status updates and photographs from family and friends.

As someone who has already graduated — and who will do it again soon, albeit with a Master’s degree this time — it made me think: what was going on in these young students’s minds? What were they thinking, as they stood in cap and gown, confronting the threshold of a new beginning? Were they excited, terrified or clueless at the prospect of what lay ahead?

The real world sneaks up on you

I remember feeling all three on my graduation day. As I walked down the aisle to receive my degree, I remember feeling cheated. I was startled to discover that the ‘real world’ (a phrase I have since come to despise and use only begrudgingly) had somehow snuck up on me.

Education was my safety blanket, a comforting shelter which had dictated the purpose and the rhythm of my life. For eighteen years, school had given me structure: it filled my days with classes, it gave me homework on the weekends, it gave me exams and summer vacations. It was a comfortable, familiar pattern that repeated over and over for nearly two decades.

And then suddenly, at 21, you find that the pattern is broken. You’re on your own. Have fun figuring out what the hell to do with you life. Good luck!

John Lennon cheekily summed it up in his song ‘Working Class Hero’:

When they’ve tortured and scared you for 20 odd years then they expect you to pick a career.

Lennon may have been tongue-in-cheek with that lyric, but it hides a grain of truth. And the truth is that we see education as a linear process — a cut-and-dried path with a career as the goal in the end.

The promise of a career

This eighteen year old journey is marked by checkpoints and milestones scattered across its path— GPAs and SAT scores, JEE marks and nationwide ranks, volunteer experience and extracurricular activities — all demarcated, always, with the explicit purpose of moving your educational career forward. Get good grades to get into a good college. Volunteer on weekends to make your application shine as a well-rounded student. Join the debate team.

You do one thing to move on to the next, and the summation of all your effort is leading up to one ultimate goal. The fabulous prize of a comfortable salary package. Perks and fancy job titles and corporate leases. Gym memberships and dental insurance and yoga classes. The rewards for all your hard work.

The promise of a career.

To be honest, it’s an alluring promise — a tempting prospect. Except when it’s not. Except when graduates, armed with their hard-earned degrees in hand, cannot find jobs. When young people barely starting into their adult lives are weighed down by monstrous amounts of debt.

An education

A degree is the stamp of approval of a student’s ability — a validation of their potential. This validation is their ticket into the workforce. And to be sure, it seems like a pretty fair deal. But we know that that’s not the whole equation. ‘It’s not what you know, it’s who you know’ is thrown around heavily in and out of business school classrooms. A degree doesn’t account for the state of the economy, or the changing state of industry, or the inequalities in the backgrounds and disparity of opportunities between students of different classes.

And most of all, a degree doesn’t account for an education, and an education doesn’t account for a career.

What we think of as a linear, one-track process as a means to an end, is anything but that. Education doesn’t begin in kindergarten and end in college. It is a continuous and life-long process, often times meandering and wavering and with a lot of back-and-forth.

Education is the unleashing of curiosity. It is tinkering, wondering out loud, and looking at the whole world, in all its myriad possibilities, as your blank slate. You can draw on it whatever you want — whatever interests you and sparks you intellectual curiosity — physics, literature, history, linguistics, anthropology, computer science, philosophy, history, mathematics, marketing, theater, engineering, psychology, artificial intelligence, graphic design, medicine. All is yours to learn and question and master and use.

Ultimately, a career does not begin where an education ends. They are undeniably fused and feed into each other. A solid education can — and should — help you begin your career. It is important to remember, however, that you dictate what that career will be. And a career is much more than just a 9–to-5 job. It is the collective progression of your professional and personal learning, experience and achievement. It is your life’s work. ‘Do what you love’ is a staple of commencement speeches, now almost an empty cliché that mocks young graduates in the face of what awaits them. Many are lucky to have a job at all, let alone a job doing what they love.

But an education can help us do just that — do what we love. It is our responsibility to stay determined and steadfast in the face of challenges. To go in pursuit of what it is you want do and pursue it, fearlessly and intensely. To master it, rethink it, reshape it. You studied journalism or publishing or or English literature in school. Don’t let others tell you that you picked the wrong major. There is no question that your industry maybe undergoing an upheaval of change, in some cases even struggling to stay afloat. That just means it is an industry ripe for a revolution. And revolutions are happening around us, if we care to notice. Look at Medium, for example. How can it change — and is changing — publishing? How does journalism fare in the age of Twitter and Facebook Instant Articles — and how can we make it better?

Be resourceful. Channel your passion into inventiveness. That’s the real goal of your education. To keep you on your toes and equip you with the faculty and tools to solve problems. Ultimately:

It is up to you to do with your education what you will.

My favorite advice regarding how to find your life’s purpose comes from John Green. Answering the question ‘What the hell should I do with my life?’ from a college freshman in a reddit AMA, John goes on to say:

You are always figuring out what the hell to do with your life, and then the decisions you’ve made are always be changed by circumstance: Your wife gets a job in Kuala Lumpur or there’s no one to take over your dead uncle’s junkyard or in your mid-30s you develop an intense love of astrophysics that sends you back to school.

So don’t put quite so much pressure on yourself. Study as broadly as you can; think practically but with the understanding that what you do as a job need not be the only thing you do (or even the only thing you do to make money).

In the end, a lot of what the hell you do with your life isn’t even about what you do for a job but whom you love, whom you marry, whether you have kids, and whether you find passions and have the ability to pursue them. College is part of that process, for sure, but it’s not the end of the line.

So when you walk and smile for the camera and receive your diploma, remember that it’s okay to feel afraid. It’s okay to feel lost at the prospect of a long dark road ahead. But we can all take comfort in the fact that you can decide what road to go by, that you have the power to shape it, take detours and combine different ones, and — if need be — even change the road you’re on. You are allowed to stumble, get up, and make your way through.

Good luck!