When someone reads your essay, they shouldn’t just be reading your words, they should also be feeling them. The mark of every great writer is their ability to evoke emotion from the reader. Every word you use and every sentence you compose should convey some type of feeling.

- Choose a topic that you’re actually excited about.
- Use strong adjectives to describe how you feel.
- Avoid using cliches or overused expressions.

Whether it’s happiness, sadness, regret, or pride, emotions help your reader connect with you on a personal level. The more passionate you are about describing your experience, the more entertaining it will be to read your essay!

For more tips on how to write your best college essay, read part 6 of this series and check out Brightstorm College Advice.

]]>The log function is just the inverse of the exponential function. That’s all there is to it. Peace out yo, check ya laterz.

Just kidding.

Before we get started go read my last post for a refresher on inverse functions if you haven’t read it yet.

An exponential function is a function *f* of the form *f*(*x*)=*a ^{x }*where

Turns out that *f* is a 1 to 1 function… that means *f* has to have an inverse. But what could the inverse of *f* possibly be? If we try to do the same thing we did before, “solve for *x*” we get a whole bunch of nonsense. How can I take the *x*th root of both sides, anyway? I can’t! The *x*th root doesn’t make any sense. So we can’t do what we did before.

Let’s pause for a moment and I’m going to let you in on a little secret of doing math. The secret is, if you don’t know what something is, you give it a name. Then we can talk about it. Sneaky sneaky! We know the exponential function *f *has to have an inverse because *f* is 1 to 1. We don’t know what that inverse might be, so let’s say it’s this

*f*^{-1}(*x*) = log_{2}*x*

I know it looks funny, but why not? We read that as “f inverse is log base *a* of *x.”* And what this function *f*^{-1}(*x*) does is, is it takes an output of *f*(*x*)=*a ^{x }*and tells us what input we had to use to get that output. So for example, suppose

Then what *f*^{-1} does is, it takes 8, and it’ll spit out 3, like: this *f*^{-1}(8) = log_{2}8 = 3*. *So what we’re really asking when we talk about the log function, is “to what power do I have to take my base to get this number?” Looking at *f*^{-1}(*8*) = log_{2}*8*, we think “to what power do I have to raise 2 to get 8?” We know *2 ^{3}*= 8, therefore

Now go forth, and never fear logs again!

]]>College decisions are rolling out almost daily. Students are checking their email accounts, college portals, and mailboxes almost every hour in hopes of an acceptance rolling in. The excitement of this time also brings with it great disappointment. A denial is certainly disappointing. But this is a disappointment that students are prepared to handle. They realize that denials are a part of the admissions process. But the surge in waitlist offers brings with it a level of ambiguity that can actually cause more confusion and stress – this is heavily influenced by the fact that students and parents don’t really understand what a waitlist position truly means.

These days many colleges are placing students on waitlists because the number of qualified students greatly surpasses the number of seats a college has available. Since students are applying to more colleges than ever, it has become more difficult for these schools to predict their yield – the percentage of students that will accept their offers of admission. If the school offers too few spots, they will have empty seats, and as a result a potential loss in revenue. If the school offers too many acceptances, then they risk not having enough seats in the classroom or beds in a dorm. A too large class can also change the dynamic and student body that the college is aiming to create. It can also unfortunately impact the school’s college ranking. As a result, the waitlist has become a very popular enrollment management tool. So now we know what it means to the college to have a waitlist. But what does it mean to you?

Well, a waitlist essentially means that the admissions officers think that you are a great candidate for the university and believe that you deserve to be admitted, but as of right now there is not a definitive space. Once the schools have heard back from all of its admitted students, the admissions officers will again revisit the list of waitlisted students and handpick students to fill in the remaining seats. Most waitlists are not ranked meaning that you will not know if you are the school’s next in line. The reason is that colleges are still trying to build a balanced class and will look at multiple different factors when choosing which students to pull off the list. The reality is that the school may not even take any students off the waitlist. As a result, you cannot make any assumptions about these decisions.

Many colleges will not make final waitlist decision until well after the May 1 national signing deadline. By that day, students must submit their Intent to Register and deposit to a given school. Colleges then go through the arduous task of tallying their yield, sorting through the waitlist, and making additional offers if the space allows it. Typically a college will send out waitlist offers in waves, meaning that a student may not get a final decision until late June even July. At this point, colleges close their lists.

So what is a student to do? Well the first thing you have to do is decide if you want to stay on the waitlist. It may be tempting to accept every waitlist offer you have – just to see what happens. But don’t fall into that trap. Only accept the waitlist offers for schools you would actually consider. The stress of waiting is just not worth it otherwise. If you decide to stay on the waitlist, accept it and then move on to making a final decision about your other options. You must work under the assumption that the waitlist will not come through. You will by May 1^{st} have to choose an offer from another school. If you don’t, you run the risk of not having a college to attend.

I realize that a waitlist can prolong the agony of college admissions, but try not to let it. Focus on the amazing options that you have in front of you.

]]>Throughout high school and college, you’re going to be doing a lot of writing. Even if you major in math or science, you’ll still have to take plenty of humanities courses which will require you to write essays. If you love to write, then you have nothing to worry about. But if writing doesn’t come naturally to you, here are some tips to help you along.

Fiction, as you know, is anything that isn’t based on reality. It can range anywhere from a made-up story of your childhood to an advanced civilization in a far-off galaxy. The key to writing good fiction is to **be as creative as possible**. Since it’s not based on facts, feel free to invent whatever you like.

If creativity isn’t your strong point, another way to get motivated about writing fiction is absurdity. Don’t think about writing the next best-seller, instead think of something that you would consider absurd if it existed/happened.

For example, if you love chemistry but hate writing, create a story about the mutation of an organism that made humans incapable of writing fiction. The more absurd you make it, the more fun you’ll have with it which will most likely result in a better grade.

Non-fiction, of course, is the opposite of fiction and only allows for facts based on reality. **The key to writing great non-fiction is detail. **In a history paper, for example, details might come in the form of names and dates. You want to describe as many details as possible in order to support your argument.

In a personal essay, however, details are less about facts and more about description. These types of details help the reader enjoy and imagine the story you’re sharing. For example, instead of simply saying that you had a childhood friend who would always make you laugh, you could add detail the sentence to stretch it out to a paragraph.

“Samantha and I have know each other since kindergarten. She had long, orange hair that came down to her waist and freckles that formed tiny constellations on her face. She always knew how to make me laugh by tying her hair into ponytails and pretending she was Pippi Longstocking.”

Writing can be fun and easy as long as you don’t take it too seriously. Instead of feeling down next time you’re given a writing assignment, use some of these strategies to make things more exciting.

]]>Inverse functions give students a lot of trouble, so here’s a quick run down of what an inverse function is, and how to find it.

Say you’ve got some function called *f* such that *f*(*x*) = 2*x*-3. This says that if I stick some number *x* into the function *f*, what’s going to pop out is 2*x*-3. I stick in, say, *x*=2, what pops out is *f*(2)=2(2)-3=4-3=1. That is, *f*(2)=1. (you still with me? If not, read that again. Don’t worry, I’ll wait for you.)

What we’re trying to do when we look for an inverse of *f*, is to find some other function, let’s call it *g*, that when we stick one of *f*‘s outputs into *g*, we get back *f*‘s input. In *f*(2)=1, 2 is the input, and 1 is the output. So for *g* to be *f*‘s inverse, we want *g*(1)=2. We want *g* to work this way no matter what input for *f* we’re talking about. The input of *f* could be *x*=2, or *x*=π or *x*=100,000,003. We want *g* to be a function that basically does the opposite of whatever *f* does. Cool?

CAUTION: For a function to have an inverse, the function has to be 1 to 1. That means every output only has one input. You can tell from the graph of a function if it’s 1 to 1 by using the horizontal line test.

Here’s how to figure out what *g* should be… we’re going to take *f*(*x*) = 2*x*-3 and solve for *x*, like this:

This means that given some output of *f*, this tells us that to figure out what the input was we have to add 3 then we divide the whole thing by 2. That means that the inverse of *f*, the function *g*, has to be

Sometimes the inverse of *f* is written like this instead:

No big deal.

So that’s it, that’s how to find a function’s inverse! You have some questions? Leave a comment!

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9 out of 10 grammar fanatics will probably tell you that this is the most annoying grammatical mistake ever. There is no excuse for confusing “then” and “than”. Yes, the two words share three out of four letters in common, but that doesn’t mean you can use them interchangeably.

It’s pretty easy to know when you’re using “than” correctly. If you’re comparing two things then you need to use “than.” If not, you’re using the wrong word. Here a few examples to illustrate.

Correct: I am taller than you.

Correct: You make more money than me.

Incorrect: I’m going home than cooking dinner.

When you’re talking about an action taking place within a sequence of events, your go-to word is “then.” Another easy to remember if you’re using “then” correctly is to ask yourself “am I comparing two things?” If the answer is no, then you’re using “then” correctly.

Also, whenever you make an “if” statement, you will most likely always be using “then” to follow up. Here’s an example.

Correct: If it rains today, then I will stay home.

Correct: He fell asleep and then started snoring.

Incorrect: If I get good grades, than I’ll go to college.

The key thing to remember is whether or not you’re comparing two things. If you are, then you must use “than” with an “a.” In every other instance, you want to use “then.” There’s only a small difference between the two words, but they can make a world of difference in your writing.

]]>Proving trigonometry identities can be a pain. Sometimes they’re straight forward, other times they make you want to tear your hair out. Before you tear your hair out try these:

1. Recognize difference of squares. For all numbers a and b, a^2-b^2 = (a+b)(a-b). So for example

(cosx)^2-(sinx)^2 = (cosx+sinx)(cosx-sinx)

If you have a rational expression, factoring the top or bottom using difference of squares sometimes makes things cancel out.

2. Work from both ends. You don’t have to start on one side of the equation and plow your way forward, you can work both ends then meet someplace in the middle.

3. Go all sine and cosine. Turn tan and sec and cot and csc all into sin and cos. Like difference of squares, sometimes things cancel out. Only use this trick as a last resort though… things can get messy quickly.

4. And the sneakiest of all the sneak McSneakerson tricks is anywhere you see a 1, substitute (sinx)^2+(cosx)^2. We’re so used to seeing (sinx)^2+(cosx)^2 then substituting a 1, we forget that the equals sign goes both ways.

That’s all the tricks for now, have fun kiddos!

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The two most confused words in all of English history are lie and lay. Okay, maybe that’s a bit dramatic, but it’s true that many native English speakers—even those who are good writers—confuse these two words.

There’s really no easy way to remembering which is which—other than repeating the rules to yourself over and over again—but here are a few tricks that might help.

This is the word you want to use whenever you’re describing yourself going to bed or relaxing on a sofa.

**You NEVER say “I’m going to lay down on the bed.”**

**The correct way is “I’m going to lie down on the bed.”**

It may sound weird because a lot of your friends don’t talk like this, but it’s the right way to say it. Next time you hear someone say “I’m going to lay down for a second,” correct them by saying “lie down!”

Whenever you use “lay” make sure that the action is being performed on something. The technical term is direct object, but all that means is that you’re “laying” something down somewhere. For example:

**“I’m going to lay down this book on the table.”**

Most people know how to use “lay” correctly when it comes to describing other things. The problem is that that they often confuse it for “lie” when they don’t have a direct object to use it with. Now comes the tricky part.

Here’s the strangest thing about this topic: **The past tense of “lie” is “lay.”** I know, it doesn’t make sense but that’s just how English works. Here’s an example:

Present: I’m going to **lie** down on the bed.

Past tense: I **lay** down on the bed yesterday.

It may not sound correct and you would probably much rather say “lied down” or “laid down,” but both of those would be incorrect in this instance. You don’t have to agree with these rules, you just have to know that the past tense of “lie” is “lay.”

The past tense of “lay” on the other hand is a little more logical; it’s “laid.” Here’s an example.

Present: I’m going to **lay** down this book on the table.

Past tense: I **laid** down the book on the table yesterday.

Don’t get too overwhelmed. If you can simply remember that you never “lay down on a bed” but instead “lie down” then you’ll be one step ahead of the curve. If you’re interested in learning more writing tips, check out Brightstorm Grammar.

]]>What up Brightstormers. Long time no see. This one’s going to be super short. I see people get confused all the time though, so just a quick heads up. When you have

2^3 • 2^2

You add the exponents. DON’T MULTIPLY THEM.

Here’s why:

2^3 • 2^2 = 2 • 2 • 2 • 2 • 2 = 2^5

3+2=5, in case you forgot.

If you have

(2^3)^2

Then you multiply the exponents because

(2^3)^2 = (2 • 2 • 2)^2 = (2 • 2 • 2)(2 • 2 • 2) = 2 • 2 • 2 • 2 • 2 • 2 = 2^6

Okay that’s all. You can go back to watching youtube now.

]]>Everyone loves a great story and the key to great storytelling is description. The more real you’re able to make an experience feel, the easier it will be for readers to become totally consumed by it, which is exactly what you want.

Read the two examples below¹ and notice how the second paragraph uses description to bring the moment to life. Try to apply this technique to your own writing.

I hit a home run yesterday. I’ve never felt so good in my life. My teammates finally appreciated me, because it won the game, and I’m glad all the hard work paid off. I realized what it meant to succeed.

We were tied, 4-4, in the ninth inning with barely enough sun- light for another at-bat. I looked at a strike. On the next pitch, I tightened my core, swung the bat low, and felt it make contact in the middle of the ball. I was almost to second base by the time it crashed into the scoreboard beyond the right-field fence. My teammates greeted me at home plate with the obligatory dogpile.

Do you see how the “show” version is more exciting to read? Use this technique in your own college essay and you’ll definitely hit a home run with the college admissions officers.

For more tips on how to write your best college essay, read part 5 of this series and check out Brightstorm College Advice.