High Schoolacademics

We found 96 articles

The puzzle pieces of an argument
When learning about argumentative writing, my students regularly freeze. The terms claim, reasoning, evidence, and explanation all appear to be the same. They are unsure where to start and where to end. So let’s break it down together.
How to prove the Pythagorean Theorem
The Pythagorean Theorem plays an essential role in many facets of math from Euclidean Geometry to complex numbers to trigonometry. Today we’ll explore one of its many proofs.
How to solve (almost) any math problem
Math is all about problems -- questions for which you don’t currently know the answer -- and problems can be really frustrating. That feeling of being stuck, for me, goes from a scattered confusion to a mind-numbing blankness. It’s really easy to shut down and give up, so the first step to solving any math problem is to persist! Don’t let the ...
5 weird moments in European history
Some people say “reality is stranger than fiction,” and throughout the course of human history, this has definitely been true. Here are just five of those moments that were as strange – or stranger – than something you would find in books or on tv:
How to study for Chinese dictation quizzes
听写 (dictations) have been used to evaluate how much effort students put into learning Chinese. Dictation often tests vocabulary memorization. How do you study/prepare for 听写 effectively? Do you spend hours of writing characters? Have you experienced cramming with flashcards, only found that you forget everything on the day of the quiz? 
How to ethically use WolframAlpha, Mathway, and Photomath
As a middle school and high school math teacher, I’ve seen my students try to get out of doing work in all sorts of ways. If you haven’t heard of WolframAlpha, Mathway, or Photomath, you may want to stop reading this article now - the temptation may ruin your hard-work ethic.
The dreaded “P” word
What’s the most dreaded letter that could appear on a transcript? I’ll wager that it’s not a “B,” or, gulp, a “C”, but a “P” as in “plagiarist.” In fact, if Hester Prynne were a 21st century student, instead of the protagonist of Nathaniel Hawthorne’s 19th century novel The Scarlet Letter, she’d probably be less concerned about having the letter ...
Suitcases and schedule scrapes: “packing” more punch into limited study time
In his book, Outliers, Malcolm Gladwell lays out criterion that in some ways has become the anecdotal darling of pop-academic culture. You’ve likely heard of it: the 10,000-hour rule. Mastery, Gladwell purports, is a matter of numbers. Put 10,000 hours of focused practice, and you can achieve mastery of a complex set of skills. Imagine the ...
Good writers start as good readers
Writing is a conversation. Whether you anticipate your audience to be a friend, a panel of scientists, a room full of legislators, the owner of a pizza shop, the divine universe, or oneself, to write is to put forth one’s wish to be heard. By extension, to read is to be in the position of the listener. Just as we learn to speak and to express ...
Where ideas come from
A lot of people who sit down to write a story are worried they don’t have any ideas. They think people who do have ideas are very special, or different in some way to people who don’t. It’s for this reason that authors are so often asked where they get their ideas from. The people asking think that the author will reveal the magical secret of ...
To ask or not to ask? That should NEVER be the question
My family often refers to me as “the questionnaire” because I am constantly peppering people with questions during all of our conversations. What can I say? I spent four years as both an English literature student at Bates College and a reporter/editor for my college newspaper. I simply always have questions to ask of myself and those around me. ...
How to use an outline to your advantage when you’re writing
How often do you start writing an essay with a great idea in mind, only to lose steam—or worse, lose track of your argument—well before you meet the length requirement? Have you ever reread a paper draft only to realize what you’re arguing on the first page isn’t quite the same thing you’re arguing on the last one? These sorts of problems are ...
Introduction to Functions
You’ve made it through algebra: now it is time to start talking about functions. While functions are often used to make upper-level mathematics easier to understand, they can be confusing at first. So – what is a function? How do functions relate to the algebraic equations we have used before? And how do they help us with mathematics and computer ...
Computer science buzzwords explained
Computer science can be intimidating! Especially when people use lingo you aren’t familiar with. The goal of this blog post is to help you start understanding some of the computer science buzzwords.
How to communicate better: unlocking language’s hidden meanings
We all know that language is a powerful tool for communication. Sometimes it can be surprising how much meaning is conveyed in the shortest of sentences. Language is composed not only of the direct meaning of the words used, but also of many additional layers of meaning that arise through prior knowledge, background information, word choice, and ...
5 easy steps to good writing
Great chefs don’t cook wonderful meals on the first try. They’ve been in the kitchen for many sessions trying things out before they put a dish on the table. Writers need to do this too. Plan, practice, and prepare for the writing project you have in front of you. Break it into manageable chunks of about 2-3 hours each. These chunks need to be ...
Why I love teaching English
“I’m not good at writing.” “I don’t really like reading.” “I don’t think of myself as a writer.” “Why do I need to learn how to write? I’m going to study engineering!” 
Why I love teaching Spanish
In the spring of 2020, when we were all locked down due to the pandemic and feeling cooped up and anxious, I got an email that lifted my spirits. It was from a former student who wrote to thank me for writing him a letter of recommendation for an internship with his local congresswoman that led to a job after graduation. He revealed something that ...
What I love about psychology
I have always been fascinated by human emotions and behaviors, as well as the unique ways in which we interact with ourselves, others, and the world. I initially learned about a field that addresses these very phenomena—that is, the field of psychology —when I was in high school. However, I didn’t consider it as a possible career path until ...
What I love about history
It’s not uncommon for people to find history the most boring subject in school. It often gets a bad rap in popular culture, too. In Harry Potter, for example, the History of Magic teacher, Professor Binns, drones on and on and frequently puts his students to sleep with boring lectures about arcane material. When I tell people I study history, they ...
What I love about physics
What if I told you that there’s a way to describe the waves of the ocean, the winds in the skies, the motions of celestial bodies — almost everything around us — and harness that information to create great things? This tool does exist, and it’s a science so fundamental that its principles guide our understanding of everything from microbes to ...
How to streamline a draft
One way to make sure your writing is clear (beyond writing "good sentences") is to take a look at the content of your paragraphs. The technique I'm going to detail in this post is perfect for a first draft, but can be used for final drafts too. I like to use this method when I need to cut some words to make a paper shorter, or before and after a ...
How to plan and organize historical research
Designing and executing historical research for a short essay, seminar paper, or thesis can be daunting. How do you find a primary research question, and how do you know which sources will help you answer this question? How do you read and take notes on sources once you've found them?
Tips for studying biology
I am often asked the question, “Brooke how do you study for biology?” We know to use practice problems to study for physics, or pathway diagrams for chemistry, but biology is different: it is a lot of memorizations!
Working out your brain
My first day in the gym was intimidating. I always thought the gym wasn’t for me, and so I had tried to avoid it as much as I could. I remember feeling slightly embarrassed as I picked up the smallest weights in the gym with my slender arms. However, overtime I was able to pick up heavier weights and noticed that my arms were slowly filling up the ...
A language study routine that actually works
So you're studying a new language, and you've been told that you need to make time to review and study vocabulary regularly. That makes sense. You tell yourself you'll do it. You may even make some flashcards and spend time drilling them two or three times early in the semester when you are full of good intentions. But if you're like me, the ...
Reading is hard. But it doesn’t have to be.
There is no denying it. In the age of the attention economy, bright stimulating screens, and exhausting schedules it is very hard to sit down and read with focus. Whether we are talking about a novel for English class, a source for AP U.S. History, or that dense SAT Reading passage from the Federalist Papers, it is hard to truly dig in and read ...
What makes a good descriptor?
Cliche is natural; originality, not so much. Pre-packaged phrases like “bring to the table,” “at the end of the day,” or “read between the lines” are overused and now lack their meaning, becoming a kind of automatic thinking, according to George Orwell. But why? Because triggering automatic thinking in a listener is helpful to a speaker if he or ...
How to balance redox reactions in acidic and basic solutions
Balancing redox reactions is an essential skill for the Chemical and Physical Foundations section of the MCAT, the GRE Chemistry Subject Test, and the AP Chemistry Exam. Today, we will learn how to use the half-cell method for balancing redox reactions in acidic and basic solutions. We will first balance a redox reaction in acidic solution, then ...
Top grammar errors to avoid
Throughout the years I’ve spent reading and writing, I’ve seen my fair share of grammar errors. But few are peskier, or more pervasive, than the two I’ll discuss in this post. So common are these two grammar errors that I regularly encounter them in professional writing — sometimes even in articles by full-blown professors! These two errors often ...
How to use root words to learn vocabulary
Retaining new English vocabulary is challenging, whether you’re learning English for the first time or studying for standardized tests like the SAT or GRE. The challenge arises, in part, from the sheer volume of words in English. English’s massive lexicon comes from words in several other languages, and learning some of these words—more often ...
The Intermediate Value Theorem explained by everyday life
Calculus can be tough stuff. Calc AB was the first AP class I ever took in high school, and though I love the subject now, I certainly didn’t love it when I was first struggling with limits or with the chain rule for derivatives.
What I learned about the writing process from bread baking
Working from home means I can adapt myself to the capricious schedule of bread making. Dough waits for no one (and it will not rise more quickly if prodded!). I’ve loved baking since childhood, but I discovered bread more recently.
S’more fun: simplifying limiting reactants using chocolate
Stoichiometry: it’s the bane of many chemistry students’ studies. It’s so easy to get tangled up in a jumble of numbers without any idea of what’s actually going on.
How to make sure you don’t fall behind during distance learning
Let’s be real: it’s hard to focus on school at home. And as COVID-19 cases persist and online learning remains part of our lives, it is important to not fall behind. Here are some tips to help you stay on top of your work while learning from home:
Explaining eight common Chinese idioms (“chéngyǔ”)
“Chéngyǔ” (成语) are Chinese idioms that usually occur in groups of four characters and often originate from old fables in classical Chinese writing. As a testament to China’s long history and rich culture, chéngyǔ have persisted as a fundamental component of modern Chinese language in both formal writing and in everyday language. There are over ...
Six ways to brainstorm more effectively
At its core, writing is about discovering relationships between words and ideas. Your brainstorming process can and should reflect that central goal from the very beginning of the writing process. Here are a series of investigative approaches to help you expose and explore these relationships:
A beginner’s guide to analyzing historical documents
Most high school and college-level history courses will require that you read, interpret, and analyze a document or set of documents from the past—otherwise known as primary sources. In this post, I will provide five basic questions that you should ask about your document(s) that will kickstart your thinking about the past and serve as a starting ...
Introductory statistics: are my data normal?
Statistics is fun, I promise! But before we can start having all the fun, it is important to describe the distribution of our data. We will need to handle problems differently depending on the distribution.
Studying at home: how to keep up with work while learning online
In the early stages of the COVID-19 pandemic, most of us had to deal with the sudden reality that we could not go to school physically. We might have had have school content posted online or packets of work to complete, but we were likely not allowed to physically be at school with our teachers and classmates. We were, essentially, homeschooling.
Where do Taylor series come from and why do we learn about them?
Taylor series can often seem a bit mysterious the first time that we learn about them. The formula for the Taylor series of a function f(x) around a point x=a is given by
But what is “dx” really? Calculus terms explained
The symbol “dx” comes up everywhere in calculus. For example:
Two common grammatical mistakes to avoid in polished writing
There are no hard and fast rules in writing. But even if an experimental poet or an avant-garde novelist has dispensed with capitalization or written an entire novel without the letter E (yes, a novel like this really exists!), this does not mean that you need to follow suit. Your personal statement, for example, is not the place to defy the ...
The music of Mandarin: learning the five tones of the language
Learning Chinese is challenging but fun! Even the parts that require repetitive practice can be enjoyable with the right framework and point-of-view.
Homonyms
English is one of the languages in which spelling is a big deal. Spelling bees were created in English, and the concept is not present in other languages in which words are more often pronounced just like they look. In English, we have words that are pronounced the same but have different meanings and spellings (homophones). We also have a lot of ...
Grammar: one to 1
When learning a new language, students almost always begin with the alphabet and numbers. We use letters, of course, to form words, which form sentences that express ideas of varying complexity in a form that people who read this written language can understand. Numbers designate a different kind of language, one that conveys equations and ...
Betwixt and between: difficult grammar rules explained
English is not the easiest language to learn. This may be because of the many exceptions to its rules or because the same combinations of letters can be pronounced in many different ways. English also has one of the largest vocabularies of any recorded language, which means English speakers can say what they mean in a lot of different ways, but ...
Checking your answers in physics
Having worked through a long physics problem, you finally have an answer. How do you know if it’s right and all that work wasn’t for naught? In this post, I will cover a few quick strategies that can help rule out wrong answers.
An application of calculus: finding optimal road networks
Suppose that we have many towns spread across the country and we are trying to connect them with a network of roads. If we would like to do so by laying as little road as possible, how do we do it? In this blog post, we will use Calculus to tackle a special case of this optimization problem.
Understanding elasticity of demand in economics
You may have heard in your econ class about a good’s elasticity of demand, or about “elastic” or “inelastic” goods. Consumers’ elasticity of demand is just a fancy way economists talk about how sensitive people are to changes in a good’s price.
High school chemistry: What is it? Can I be good at it?
The word “chemistry” inspires so many emotions. To some, it brings about the excitement of mixing together glowing liquids and crafting the perfect radioactive potion that, when consumed, will turn you into the Incredible Hulk. To others, it’s discombobulated numbers and letters on a piece a paper in a classroom, a concatenation that strikes fear ...
What physics equation sheets can do for you, and what they  can’t
In your time taking physics courses, you will likely run into one that deals with equation sheets. These can be note cards or an entire sheet of paper, and anything that can fit on it is fair game and can be brought into a test. The natural reaction might be to try to cram and squeeze an entire textbook on those sheets using really, really tiny ...
5 tips to improve your writing
I was recently helping someone with a comparative essay they had to write for school. This person did not like writing—a common enough state of affairs. They felt that they had no talent for it. The process frustrated them. I could see that they were struggling in part because they were trying to do everything at once (come up with ideas, write ...
The key to mastering mathematics? Quit memorizing.
There are many misconceptions when it comes to the subject of mathematics.  One of the most common myths I encounter is related to the way one approaches learning math. 
What is a thesis statement?
Every paper you write in college should have it. Sometimes professors call this a “thesis statement,” sometimes a “claim,” and sometimes they don’t really specify what it is. But it’s essential — and sometime elusive. But it shouldn’t be! 
A guide to limiting reactant problems... using sandwiches
An everyday limiting reactant problem You’re expecting company and totally forgot to go grocery shopping. What on earth will you feed your guests? Sandwiches! You have some ingredients to whip up some sandwiches. So, let’s assume you are going to go through with making these sandwiches. You need 2 slices of bread, 3 slices of meat (can’t be ...
Electron configurations: a must know hack
Imagine this...you’re taking your general chemistry midterm and you’ve decided to shuffle through the exam and complete all the hard things first. You’ve totally underestimated how much time those problems were going to take you and now you have three minutes left to write the electron configuration of 10 elements. Untimed, this would be easy to ...
Formal charge: what they didn’t tell you in your chemistry class
Formal charge is the charge that a bonded atom would have if its bonding electrons were shared equally. Note:
Tips for writing an exam essay in 80 minutes
We've all been there.  The teacher is at the front of the classroom with a pile of blue books.  She begins handing them out.  You scrawl the name and date on the front and wait for her to start the timer.  As you open the first page, an overwhelming white page stares back at you.  And you panic. Luckily, there are ways to prepare for essay exams ...
3 ways to better analyze poetry
“Cikgu Tess!” “Pagi.” “Miss. Look lah.” “Alyaa—why?” “Girl’s bathroom,” she says. “Cikgu, you touch?” Our state has the highest concentration of venomous snakes in the region. “Is it poisonous?” I mime the action of being bitten (by my hand) and then dying. “Mm, don’t know.” In 2017, I taught ESL, literature, and political science at a rural ...
An introduction to supply and demand
What is supply and demand? In economics, supply and demand is the relationship between the quantity of a commodity that producers wish to sell at various prices and the quantity that consumers wish to buy.  Though it is a seemingly straightforward relationship, in practical application it can become quite complicated.  In this blog, we will use an ...
How to make introductory physics exciting (when you're bored out of your mind)
Why do many students find physics so boring?  Cutting-edge physics research gets to address amazing, deep questions: "What is all the stuff in the Universe fundamentally made of?” and “Where did all this stuff come from anyway?” Yet college-level introductory physics courses on Newtonian mechanics can feel quite...mechanical. Why does introductory ...
Introduction to physics: the language of the universe
 In elementary and middle school, we learn mathematics for the sake of mathematics, we are never told what mathematics can ultimately be used for or why mathematics is useful other than the fact that it can help us make change and do our taxes one day. What they should be telling you is that the laws of the universe are written in a language that ...
How to write a killer essay in 3 easy steps
We’ve all been there: staring at a blank document, practically able to feel the creeping imminence of our paper’s deadline. For so many of us, it’s really hard to sit down and actually channel our thoughts into a coherent form, let alone one that’s structured and based on an argument worthy of praise.
Solving the “I’m not good at math” problem
You’ve heard it before. Or you’ve said it. I’m not good at math. I hear it from seventh graders struggling with fractions, high school students preparing to take the SAT, friends at a restaurant when splitting a check, and even from parents assuring me that their child’s own difficulties are in fact genetic. And while I’ve heard it countless ...
The top 3 reasons you should study Latin
There comes a moment in the careers of most middle- and high-schoolers learning Latin, and also among some college students considering it as a possibility when picking classes; a moment when they ask themselves (or their parents, or their teachers), “Why do I need to study this?”  After all, Latin is a dead language; unless you plan to become a ...
How to solve kinematics problems: a guide to vectors
This article is the third chapter in a series on how to understand and approach kinematics problems. The first chapter covered position, velocity, and acceleration. The second chapter covered solving kinematics in one dimension Now we are going to take a quick detour into vectorland so that we’re ready to approach kinematics in two (and even ...
What is the phospholipid bilayer and what determines its fluidity?
All cells are surrounded by a cell membrane that forms a barrier between the cell and its surroundings. This membrane is often referred to as the phospholipid bilayer. As you can probably tell from the name, a phospholipid bilayer is made up of two layers of lipids. The fluidity of this membrane must be maintained within a certain range for the ...
An introduction to blood types: genotype, phenotype, inheritance, transfusion, and more!
What determines blood type? Contained within their cell membranes, some red blood cells have special glycolipids called A and B glycolipids. People with blood type A have the A glycolipid in their cell membranes, people with blood type B have the B glycolipid in their cell membranes, and people with blood type AB, have both glycolipids in their ...
Why does English borrow so many words from other languages?
The Canadian blogger and free-lance reviewer James Nicoll created the following epigram on the English language: "English doesn't borrow from other languages. English follows other languages down dark alleys, knocks them over and goes through their pockets for loose grammar."
How to sketch any graph by eye
Equations in math are useful but they’re also kind of inefficient – for each x value, you have to do a separate calculation to figure out what y is. Graphs take that equation and turn it into a visual, something you can look at and immediately see what happens at different values of x, how the function changes, and more!
What is moment and how do you calculate it?
When I tutor my physics students, I want them to understand the fundamentals of the concept, not just how to plug in numbers into an equation. I wished when I was learning physics, my teachers drew upon real life applications more, things we already understand about the world to help us really get it.
5 key differences between American and British spelling conventions
Before America became a nation, the colonists who arrived to establish the country spoke English. From England. As there was not yet an authoritative source for how to spell words correctly in English, the colonists spoke English they were used to back home and wrote much the same way, using the way language was written in English literature as a ...
How to write an excellent history paper
I love the film Bill and Ted's Excellent Adventure and I've seen it more times than I can count. It is about two teenagers on the brink of failing high school, unless they ace their final history exam. The Hollywood twist? The protagonists acquire a time machine that allows them to travel through different eras of history. Throughout the film, ...
Four mathematicians you should know
Math has changed a lot over the years. When most people think of math, they likely think of someone sitting quietly at a desk with a book or some paper. It’s an unmoving image. When we think of people who are good at math, we conjure up people who blaze through problems quickly and alone. They follow the rules in math and in life. But this is a ...
How to solve kinematics problems, part 2
This article is the second chapter in a series on how to understand and approach kinematics problems. The first chapter covered position, velocity, and acceleration. Now that we understand these quantities, we are going to use them to solve problems in one dimension. 
Don't actually 'break a leg': common English idioms explained
One of the recent lessons I gave to my English Language Learners involved English idioms and their origins. An idiom is a saying that does not mean what the words literally express, but rather it has some representative meaning behind the words. Often, the reasons for the meanings of idioms are obscure; in this post, I will try to bring to light a ...
Breaking down nephron functioning into six easy steps!
The nephron is the kidney’s smallest functional unit. It works to ensure that the urine you excrete leaves your body in the correct volume and concentration. This is a complicated process, but once you master it, it is exciting to understand this important function of the human body!
What is kinematics? Physics answers made simple
How to use this guide This blog post is the first in a series on how to understand and approach kinematics problems. It is meant to supplement your class and textbook. I will focus on practical applications, how to solve problems, and common mistakes that students make. If you want to learn the basics of kinematics, I recommend a textbook, but if ...
Tips and mnemonics for memorizing amino acid structures
Learning amino acid structures is a challenging part of biology and biochemistry coursework. Many students feel totally overwhelmed by the task. The best way to master this skill is lots of repetition (here is a link to a Sporcle quiz that may help you with the repetition part) but it can be helpful to have tricks and mnemonics to get you started. ...
Revolving curves to make solids
Have you ever wondered where the formulas for volumes that you studied way back in geometry come from?
What is the subjunctive tense in English?
One grammar category that seems to be widely untaught is the names and functions of various verb tenses. For those who have studied a foreign language, the existence of these constructions is not so foreign, but native English speakers rarely learn what the subjunctive – in English – even is, let alone how to use it correctly. The same goes for ...
A list of common homophones and their differences
What is a Homophone? There are many more words in the English language than one might expect, given how similar their pronunciation and spelling can be. They're usually nouns and adjectives, except for those that function as conjunctions or contractions. Once you accept that English contains many pairs or groups of deceptively similar words with ...
4 tricks for solving any physics problem
Physics can be intimidating—all those pulleys and protons and projectile motion. If you approach it with the right mindset, however, even the hardest problems are usually easier than you think. When you come up against a tough question, don’t panic. Instead, start with these short, easy tricks to help you work through the problem. 
The most common English prefixes and their meanings
The English language comprises a plethora of words that can change meanings with the addition of a prefix or a suffix. For example, the prefix re signifies that the base word to which it attaches is happening again, as in "do" and "redo". In theory, one could add re an infinite number of times to the front of a word, and the effect would continue ...
Three essential things to remember when citing parenthetically
For a lot of students, parenthetical citations may seem like the bane of their existence. You've just written a ten-page essay, you're happy with your argument and the conclusion you thought of in the middle of the night before it was due to submit, but you still have to check all the quotes. Especially in today's digital age, in which reading and ...
Physics: learn, don’t memorize!
Intro to Physics Blues    As a high school student, I took physics my junior year and struggled to stay afloat in the class. While I was interested in understanding and applying the theories I learned, it was difficult to make sense of them in my head. As a result, I began my first collegiate physics course with a lot of excitement, yet some ...
How to use logarithms to simplify Arrhenius temperature dependence
  Learning about logarithms is one of those times in math class where you wonder if this will ever be useful in any way. I see lots of students struggle with topics like logs, since they can seem abstract and they aren’t obviously useful. But I’m here to explain why they are actually incredibly important and describe so much of the world we live ...
How to study for AP Biology
When I was in high school, it was actually my AP Calculus teacher who gave me this AP Bio study tip. I used it with great success that year in AP Bio, and it continued to serve me well throughout college as I majored in molecular biology.
Choosing between AP and IB: an in-depth guide
I went to the International Academy (IA), which, for two years, was ranked the number one public high school in America by USA Today. As a metric, they used the number of IB or AP tests each student took.  My high school was an all IB school, one of the first in the country, and as an IB school, it required every student to take 6 IBs.
Five ways to reduce procrastination while studying or writing papers
  The night before every exam or paper deadline is always the same for me: Me: Why did I spend the last two weeks working on the opening sentence?! Roommate: Didn’t you also watch the entire first season of Game of Thrones? Me: For inspiration! Roommate: [Raises eyebrows] On rodent neurogenesis? Me: It’s ok—I have the rest of the night to work on ...
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