When it comes to deciding which major to choose when applying to colleges, there are two major questions that you should ask yourself:

The answer to the first question should be reflected in your grades. If you believe that you’re good at math, then hopefully you’ve received good math grades throughout high school. If not, you may want to rethink choosing any math-related major when applying to colleges.

Once you figure out what you’re good at, you can start thinking about all the different jobs and careers that require those skills. When you narrow down your list to a handful of jobs you can see yourself doing, choose a major that will prepare you for that position.

Whatever you do, **don’t stress out about choosing a major**. Most universities will let you switch majors within your first two years. If you really can’t decide, it’s always okay to select “undecided” as your major. You can use your first year or two at college to make a better decision.

However, if you do choose a major, make sure that it makes sense with the rest of your application. Don’t choose an easy major just to get in to your college of choice and don’t choose a major that doesn’t match your grades in high school.

Keep in mind that each university is unique and some colleges have impacted majors. Do your research before applying to make the best decision possible. For more information about applying to college, visit Brightstorm College Counseling.

]]>Lots of times you’re going to have to do this crazy thing called “combining like terms.” I know it might seem like some arbitrary procedure invented by mathematicians to make you want to pull you hair out, but it’s actually super easy.

Remember our old friend the distributive law? For all numbers a, b, and c, the following is true: a(b+c)=ab+ac? Of course you do. Combining like terms is just the application of the distributive law. say we’ve got this problem, and the instructions are to “simplify”.

2x^{2}+3x^{2}

We use the distributive law, with x^{2} playing the role of “a”, 2 playing the role of “b” and 3 playing the role of “c”.

2x^{2}+3x^{2}=(2+3)x^{2}

And you know what 2+3 is, right? Right.

2x^{2}+3x^{2}=(2+3)x^{2}=5x^{2}

How many x squareds do we have? 5! Easy peasy.

If you have a problem that’s a little more complicated, the same method applies.

2x^{2}+3x+4x^{2}+5x

First we rearrange terms using the commutative law of addition, so all the x squareds are with the x squareds and all the x’s are with all the x’s:

2x^{2}+3x+4x^{2}+5x

=2x^{2}+4x^{2}+3x+5x

Now do the same distributive law magic we did before:

2x^{2}+3x+4x^{2}+5x

=2x^{2}+4x^{2}+3x+5x

=(2+4)x^{2}+(3+5)x

Now add!

=6x^{2}+8x

We can take a shortcut too… if you don’t want to write out all those steps, that’s okay. If we have a look at 2x^{2}+3x+4x^{2}+5x again, paying attention to coefficients (that’s the numbers in front of x^{2} or x), you can see that the coefficients of x^{2} are 2 and 4, so add ‘em. That’s your new coefficient for x^{2}. The coefficients of x are 3 and 5, we add those and get 8, that’s our new coefficient of x. So our new expression, after combining like terms, is =6x^{2}+8x, just like before.

PROTIP: x^{2} and x ARE NOT like terms. The exponent on the variable has to match to have like terms. We can’t combine 2x^{2}+3x into 5x^{2} or 5x^{3} or whatever. Don’t do it. You’ll make me cry.

Check out this video for more combining like terms goodness.

http://www.brightstorm.com/math/algebra/pre-algebra/simplifying-expressions-and-combining-like-terms-problem-1/

]]>Before you sit down to start your college application, make sure that you have everything you need. You’ll get less frustrated along the way and even save a lot of time. Here are 8 things you should have in front of you before starting your application:

**Transcripts**— Have a copy of all the grades you’ve received in high school.**Test scores**— This includes the SAT, ACT, and all AP test scores.**High school info**— The name, address, and school code are what you’ll need.**Parents’ info**— This includes full names, occupations, education, etc…**Extracurricular**— List all your activities and awards received in high school.**Relative info**— List your relatives who attended the schools you’re applying to.**Location**— List all the places you’ve lived since birth.**SSN**— Have your social security number handy.

College applications ask for a lot of information, but these are some of the most important pieces of information that you’ll need. Have it all organized before you start your application and you may save yourself a headache or two.

For more information about applying to college, check out Brightstorm College Counseling.

]]>Solving exponential equations with different bases can be a little trickier than solving exponential equations with the same base. Let’s have a look at this equation:

3^{x}=2^{x-1}

Not only are the bases, 3 and 2, not the same, we can’t even rewrite them to be the same base, like we could of this was our equation:

4^{x}=2^{x-1}

2^{2x}=2^{x-1}

So what’s a poor Brightstormer to do? Well I’ll tell ya. First, we have to get every base with an x in the exponent on one side of the equation, and everything else on the other side. We split apart the crazy stuff in the exponent of 2 using the rule

Like this:

Now we can multiply both sides by 2, and get this equation:

Then divide both sides by 3^{x}:

Whew. That was a alot. But we’re in really good shape now. Remember this rule of exponents?

Let’s apply it to the left hand side of our equation. We get

Suh-weet! Now we can take the natural log of both sides of the equation (or you can use log base 10 AKA the standard logarithm… it’s your choice!)

Use the power rule for logarithms to pull the x out front…

Divide both sides by ln(2/3) to get x all by itself…

And we’re done! Ta-da! You can put the left hand side of the above equation into your calculator if you need to get an actual number for some reason. If you’re still having trouble with solving exponential equations with different bases, check out these Brightstorm videos

http://www.brightstorm.com/math/precalculus/exponential-and-logarithmic-functions/solving-exponential-equations-with-the-different-bases/

]]>If you’re reading this, you’re probably planning on going to college, which means your probably going to take out student loans, which probably means you should know a thing or two about how interest works. You know, interest, as in the extra money you have to pay the bank on the money you borrow, interest as in how much more than you actually spent that you owe your credit card company.

There’s three main kinds of interest: simple, compound and continuously compounded. Say you decide to put your spring break trip on your credit card… with airfare, hotel, food and whatever else, your tip total is $3000 (must’ve been a fun week!). You can’t start paying that off until you get a real job, so you be accumulating interest for (say) three years. Let’s see how much you’ll actually end up paying for your trip at 12.99% interest using simple annual interest, annually compound interest, and continuously compounded interest.

First we’ll do simple interest:

So with simple interest you’d owe $4169.10 on the $3000 you spent on your trip. Now let’s calculate annually compounded interest.

As you can see, annually compounded interest is a little bit more, you’d owe $4327.54 on the $3000 you spent on your trip. Here’s how we figure out continuously compounded interest:

The grand total using continuously compounded interest is $4429.61. What does all this math tell us anyway? Continuously compounded interest is bad! (well, it’s bad if its money you have to pay back, good if it’s in your savings account!). The moral of the story? Interest adds up quick so be careful!

Check out this video to learn more about compound interest:

]]>The difference between getting a good letter of recommendation and getting a great one is how you approach it. Follow these four steps to make sure your teacher or counselor writes the best letter of recommendation possible.

- The latest you should ask someone to write a letter of recommendation for you is the beginning of the fall semester that you’re applying to college. If you can ask them the semester before, that’s even better. The more time they have, the better the letter of recommendation will be.
- Before your recommender begins writing the letter, spend some time with them to go over the different things that you would like them to emphasize. Remind them of your most recent academic achievements and other important details that they can include in the letter.
- Share your college essay and application with your recommender so they have a better idea of who you are and what you care about. It will help them to write a letter of recommendation that complements your application.
- Tell your recommenders about the other teachers and counselors that you asked to write letters for you as well. Also, don’t forget to treat your recommenders like real people and not just a means for getting your letter.

If you can follow these four steps, you’re sure to get letters of recommendation that will really highlight your application. If you’re interested in learning more great strategies about getting great letter of recommendation, read the two other posts in this series and check out Brightstorm College Counseling.

]]>Deciding who to ask to write your letter of recommendation can be a tough decision. After investing so much time and energy into your college application, you want to make sure that whoever you ask to write you a recommendation will help make your application stronger, not weaker.

Equally difficult is deciding among all the teachers that you’ve had in high school. There are the teachers that you really get along well with and there are the teachers of important subjects that you’re thinking about majoring in. Sometime they’re the same, but sometimes they’re not. So how do you choose?

For starters, you definitely want to choose a teacher who knows you well. Otherwise, they won’t be able to provide meaningful insights into who you are which is the core purpose of a recommendation.

Secondly, you should aim towards asking an 11th or 12th grade teacher since those classes usually require more academic rigor and your performance as a student is still fresh in their minds.

If you’re applying as a STEM major, you should really get at least one letter of recommendation from a math or science teacher and then one from a humanities or social science teacher. It’ll show that you’re a well-balanced student.

You don’t always have to choose teachers for classes where you got the highest grades. Usually, it’s more important to choose teachers who know you well and will speak highly of all your achievements. Doing so will surely result in a great letter of recommendation.

If you’d like to learn more about how to get your teachers to write the best letters of recommendation, read part 3 of this series and check out Brightstorm College Counseling.

]]>Colleges are looking for students who not only perform well academically, but are also unique in their personalities and extracurricular activities. Your personal statement is often the best way to show admissions officers what characteristics set you apart from the rest of the applicants.

However, students often complain that the word limits for personal statements prevent them from fully expressing who they are. What students don’t always realize, however, is that there is another way to make admissions officers aware of your special qualities and, best of all, you don’t have to write a word. How? With letters of recommendation!

Letters of recommendation are the perfect way to inform colleges of your special traits apart from your personal statement. Here are a few ways letters of recommendation can strengthen your college applications:

**Give admissions officers a different perspective of who you are**

**Show strengths in areas not visible elsewhere on your application**

**Show your passions and interests from a different point of view**

Overall, your letter of recommendation should complement your application. It shouldn’t repeat what’s already demonstrated on your application, it should add to it with new and insightful information. Ideally, it should talk about your personality as well as your academic achievements. Cover all these bases and you’ll have a well-rounded application that’s sure to stand out.

If you’re interested in learning who you should ask for recommendations or how to help your recommenders write phenomenal letters, read part 2 of this series and check out Brightstorm College Counseling.

]]>Business calculus students know this problem all too well… how much of some thingamabob should I make to make the most money? I love me some dolla dolla bills as much as you do, so here’s how to maximize your profit.

Let’s say your cost in C dollars of making n thingamabobs is given by the function C(n)=100n+.05n^{2}+150. And let’s say we’re going to sell them for a hundred bucks a piece, so our revenue function is R(n)=100n. Then our profit function is our revenue minus our cost:

P(n) = R(n) – C(n) = 100n – (100n+.05n^{2}+150) = -.05n^{2}+90n-150

or P(n) = -.05n^{2}+90n-150. The graph of our profit function looks like this:

You see that big blue dot at the top? That’s our maximum profit! So how do we find out what n is at that point? Well check this out. You see this big green line that’s tangent to the function at the max? What do you think is the slope of that line?

It’s zero! And, dear readers, what’s another way to say “slope of a tangent line”? The derivative of course! And it just so happens that where the derivative is equal to zero is exactly where we get our max profit. So to find the number of thingamabobs we should make, we’ll take the derivative of P(n), set it equal to zero, then solve for n.

P(n) = -.05n^{2}+90n-150

P'(n) = -.1n+90

-.1n+90 = 0

n = 900

This tells us we need to make 900 thingamabobs to get the most profit. (Caution! Make sure the n you find is a max, not a min! The derivative is equal to zero at minimums too!)

Okay, to sum up. To maximize profit, take the derivative of the profit function, set it equal to zero, then solve for your variable. Now go forth Brightstormers and make some bank! I accept royalties in the form of pints of ice cream.

]]>Deciding how to express numbers in your writing can be confusing. Especially since there’s no consensus on what’s right and what’s wrong. There are some basic rules that are fairly universal, but there are others that many writers disagree on.

The best way to express numbers in your writing is to stick to the basic rules, use your own personal logic, and remain consistent in all your writings. With that being said, here are some basic rules for deciding when to use numeral and when to write the numbers out.

Some people will tell you to write out numbers all the way up to 100. However, it’s not necessary. I prefer to write out numbers only up to twenty. Numbers that are less than 21 are easy to write because you don’t have to use hyphens. Who would prefer to write eighty-seven when 87 is so much easier? Not me!

Numerals are the symbols that we use for number (e.g., 7, 61, 103). You should never start a sentence with a numeral. This may contradict the previous rule, but it’s necessary. Instead of starting your sentence with “35 people won the lottery” you should say “Thirty-five people won the lottery.”

Instead of saying the 60’s or the 20th century you should write it out. For example, “The sixties was known for rock-n-roll” or “The twentieth century made huge technological advances.”

Let’s say you decide to use numeral starting at 21. That means you’ll always use numerals for numbers like 99, 515, 800, 1,600, 73,000, and 429,000. That’s fine. But when you start getting into the millions and billions, it’s much better to write 80 million instead of 80,000,000.

This rule has more to do with the reader than it does with the writer. In order to make your writing easier to understand, avoid putting to separate numbers next to each other. For example, “35 15-year-old students are on the bus” is better expressed as “thirty-five 15-year-old students…”

These are just some of the many rules there are to writing numbers. The most important thing to remember is that once you pick a style, try to stick with it throughout the entirety of your writing. It’ll make things a lot easier for you and the reader.

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