What’s slope anyway? Well, kind of intuitively, it’s just a way to measure how tilted a line is. We could say “oh, this one is kinda tilted just a little bit, and this other one is titled a lot, but in the other direction, and this one is tilted more than that one.” But that’s a whole lot of words and ain’t nobody got time for that. We want to attach a number to measure how tilted a line is, so we use the formula for slope:

Where all the x’s and y’s are coordinates of two particular points: (*x*_{1},*y*_{1}) and (*x*_{2},*y*_{2}). Here’s the trick you might not know though…

IT DOESN’T MATTER WHICH TWO POINTS YOU USE.

That’s the beauty of slope, if they give you a graph and ask you to find the slope, you can pick any two points on the line, and those can be your (*x*_{1},*y*_{1}) and (*x*_{2},*y*_{2}). So pick a couple that make your life easy. Pick points that are definitely whole numbers!

That’s all for now Brightstormers, beware the slippery slope!

]]>You may not recognize it by name, but subject-verb agreement is something you do in every sentence. In fact, it’s the foundation of every sentence and when there’s disagreement between the two, the sentence sounds strange.

You probably don’t need a reminder of what roles subjects and verbs play in a sentence, but just so that we’re all on the same page, here’s a brief overview. Take the following sentence for example:

**Christopher likes ice cream.**

As you probably guessed by now, the subject in the sentence above is “Christopher” and the verb is “like.” Most native English speakers know this intuitively, but many don’t know why. Here are the basics.

The test is easy.

The tests are difficult.

Garden of roses

The subject in the phrase above is “garden” not “roses” which means it’s singular. Therefore, a sentence that uses the phrase above should also be singular.

**The garden of roses smells good.**

If we were just talking about roses then we would say “The roses smell good.” The difference between “smells” and “smells” completely depends on the subject.

Either Rick or John hates cotton candy.

Pizza, soda, and ice cream make a perfect meal.

Now that you have the basics down, you should have no problem figuring out what type of verb to use in a sentence. Good luck!

]]>Life can change in an instant – a birth, a death, an accident, a chance meeting with someone, exposure to an idea, an acceptance, a denial, etc. No amount of planning can ever fully prepare you for what lies ahead or predict an outcome. Life is full of twists and turns and as a result so is success. This does not mean that one should sit back and just let life happen and hope for success. Rather it is important that people be receptive to the detours that may present themselves. So if you are a high school senior that has recently accepted an offer of admission or decided on your next step, or a high schooler graduating in the future, here are some tips to help you be prepared for the windy path to your dreams.

- It is important to have goals. Sure these goals may change gradually over time or perhaps even every other day, but setting goals is an important skill that you must have in life. Goals give you something to aspire to and give you direction when you at times feel aimless. Goals help you to take that next step. If you are entering college next year and feel a little lost about what you want to study, spend some time this summer exploring different subjects and careers. You may not find your dream career, but you can see how the real world operates and learn what paths other people took. If you will still be in high school next year, the advice is actually the same. Summer time is a great time to explore. This will help you make some decision about things you want to do in high school and also give you some direction for when you apply to college.
- Get a mentor or two. Other than your parents, teachers, and close family members, it is a great idea to have a mentor or two that you respect and feel comfortable talking to. If you have a given career in mind, try to find a mentor in that field – someone who can help guide you. These mentors can not only serve as a great sounding board, they can also potentially connect you to other people and opportunities. They can also share with you their experiences, their learnings, their successes, and their failures.
- Don’t get stuck. Too often students get stuck on a path and then feel overcommitted. One of my students several years ago swore her commitment to medicine for a solid three years of high school. During her first semester of college, she changed her mind and wanted to study math and then eventually finance. It was because of her receptiveness to new fields that she was able to make the switch over more easily. Another student did not want to deter from his original goal of becoming a computer scientist. Unfortunately, he realized early in college that computer science was not for him. But he did not want to disappoint his parents and truly could not imagine any other career as suitable. He stuck it out with computer science and graduated with a 1.5 GPA. He also struggled for two years to find a job. He eventually switched over to a different field that suited his interests and skills better. Had he made the switch earlier he might have had a more successful and happy college career as well as an easier time finding a job.
- Allow yourself to get caught up in new experiences. Throughout your life, you will see so many new things, hear new ideas, meet new people. Immerse yourself in these moments because they may lead you to dreams you did not know were possible.

The crazy, twisty, unpredictable journey that is life should be unique for every person. Don’t follow someone else’s path. Create your own. Don’t worry if it does not seem to follow the common trail.

]]>With a slew of new changes hitting the SAT next spring, high school students across the country have been trying to decipher what these changes mean for them. So let’s break it down.

These changes are going to have the most impact on current freshman and sophomores. Current juniors will have completed all of their testing by this upcoming December. Freshman and sophomores will have the option of taking either the current SAT, the ACT, or the new SAT. While sometimes too many options can be overwhelming, this is actually a really great opportunity for students to find the test that best suits their style and capabilities. The best way to get a sense of that is to do diagnostic tests for each exam. These are readily available in prep books, online, and on Brightstorm.

After doing diagnostics, you want to get a sense of which test felt the most comfortable and which one garnered the highest baseline score. Accordingly, you want to look at the testing schedule and plan out your prep schedule, when you will take your first exam, and what will be your backup option. If you decide that you will be taking the current SAT, there will only be four more options during the next academic year: October, November, December, and January. Ideally students should plan to take the test as early in the Fall as possible so as to have ample time to retake it if needed. More importantly, students can do their prep over the summer and take the test while they are still in the zone. After January, the current SAT will be unavailable. At that point, students will only have the option of the new SAT or the ACT.

The ACT has proven to be a great alternative to the SAT. In recent years, it has actually become a more popular exam. Students appreciate that it is a slightly shorter exam, but more importantly that it feels less tricky. Just because some students have found greater success with this test does not mean that it is the better exam for all students. Before jumping on the ACT bandwagon, make sure you are comfortable with the test. This test can be taken multiple times throughout the year.

For those that want to try the new SAT, it will be available March 2016. Students should only wait for this test if they are positive that the current SAT does not suit them. Remember that you cannot go back to the current SAT after January 2016. The new exam is not a slightly modified version of the current test; it is a brand new exam. The scores from the first exam will also likely not be available until May or June; typically scores are available in less than three weeks. This can make strategizing tricky for soon to be seniors that are trying to finalize testing and their college lists.

This is really a personal choice. Many students like classes because they offer structure and students have a particular timeline to follow. Others prefer one-on-one tutoring because their time is limited and they can focus on the areas where they are the weakest. Some want to study on their own because they are self-disciplined and will make the time to prepare diligently. Whichever way you choose, it is important that you plan ahead. Many students are able to effectively study and master the strategies after just a few weeks, but then need to continue practicing these strategies until test day.

Standardized testing is meant to give admissions officers a way to compare students across many different factors including schools and opportunities. A new exam always throws a wrench in this type of comparison as they try to understand how the new exam will be a predictor for success. Students in the Class of 2017 and 2018 (those most affected by the exam changes) will get the most leniency. Admissions officers will accept all three exams and use the highest reported score for admissions purposes.

Remember that testing is simply one piece of the admissions process. Once you have chosen the test you will take, move on to the many other things that high school and life have to offer. Life and you are much more than a test score.

]]>I know it seems like there’s a million different things you have to memorize for math class and the distance formula is just another one. Here’s the secret about the distance formula though… it’s not some new thing to learn… you already know it! Don’t believe me? Check this out.

Remember the Pythagorean Theorem? Of course you do! Hmmmm. Okay maybe you don’t. Here it is: in any right triangle with legs of length *a*, *b* and hypotenuse *c*, a^{2 }+ b^{2 }= c^{2}. Okay, now if we solve this equation for *c*, we get

Right? Right. Okay, now think about this here triangle for a sec:

The length of the hypotenuse is d, which is also the distance between the points (x1,y1) and (x2,y2). The length of the legs of this triangle are x2-x1 and y2-y1. So let’s use this information and substitute these values into the Pythagorean Theorem. The hypotenuse is d=c, and the legs are a=x2-x1 and b=y2-y1.

Oh my goodness! It’s amazing! As you can see, the distance formula is just the Pythagorean Theorem in disguise! So go ahead and fall in love… all over again.

For more help, check out our study video for the distance formula.

]]>Clowns to the left of me, jokers to the right. Here I am, stuck at the midpoint with you…

At some point they’re going to give you a line segment on the coordinate plane and ask you to find the midpoint. You could just memorize the formula. Which would be fine, except you’ve got eight million other formulas memorized and when test time comes they’re all jumbled up in your noggin and you pick the wrong one. If you understand where the midpoint formula comes from though, you don’t need to memorize anything because you’ll know it. So here’s the deal.

Let’s say your line segment has endpoints A(*x*_{1},*y*_{1}) and B(*x*_{2},*y*_{2}) and you have to find the midpoint M of line segment AB. And let’s say you make a right triangle with AB as the hypotenuse and one of legs is parallel to the *x* axis and the other one to the *y* axis, like this:

Can you figure out what the coordinates of point C should be? It’s a little tricky, I’ll walk you through it. C lies on the same vertical line as point A, so it has the same x-coordinate as point A: *x*_{1}. C is on the same horizontal line as point B, so C has to have the same y-coordinate that B does: *y*_{2}. Cool, so now we know point C has coordinates (*x*_{1},*y*_{2}). Right on, right on.

What’s the x coordinate of the point halfway between B and C? It’s halfway between *x*_{1 }and *x*_{2}, so it’s *x*_{1 }+ *x*_{2 }divided by 2. And what’s the y coordinate of the point halfway between A and C? Same story, it’s halfway between *y*_{1 }and *y*_{2}, so the y coordinate of the point halfway between A and C is *y*_{1 }+ *y*_{2 }divided by 2. Now let’s draw a horizontal and a vertical line connecting these two points to AC… and where those lines intersect… that’s the midpoint!

So to find the midpoint of a line segment, you pretty much take the average of your points’ x-coordinates to find the x-coordinate of the midpoint, then do the same thing for the y-coordinate. Now go forth, and find the midpoint like a boss!

If you need more help with the midpoint formula, be sure to check out our study videos on the topic and much more!

]]>If you’re like most people, quotation marks can often be a source of frustration. It seems simple enough: All you have to do is put the quoted material inside two quotation marks and you’re done, right? Wrong. There’s a lot more that goes in to quotation marks and you’ll find all the rules below.

Correct: We were listening to music in the car when John said, “**This** is the best song ever.”

Incorrect: We were listening to music in the car when John said, “**this** is the best song ever.”

Correct: Mom said we can continue listening to music as long as we “**keep** the volume reasonable.”

Incorrect: Mom said we can continue listening to music as long as we “**Keep** the volume reasonable.”

Correct: My dad always said, “Hard work pays off**.**”

Incorrect: My dad always said, “Hard work pays off”**.**

Correct: After they scored their first touchdown, Johnny yelled “Go Raiders**!**”

Incorrect: After they scored their first touchdown, Johnny yelled “Go Raiders”**!**

Correct: Would you say that your favorite Taylor Swift song is “Shake It Off”**?**

Incorrect: Would you say that your favorite Taylor Swift song is “Shake It Off**?**”

Correct: In the prologue to his new book, the author states, “**Their [sic]** were many things to consider.”

Incorrect: In the prologue to his new book, the author states, “**Their** were many things to consider.”

There is quite a bit of talk around the impact of high school on college admissions and let me definitely say that the high school you go to makes a difference in college admissions. But this is where it starts to get fuzzy – that impact can be positive or negative depending on so many factors including but not limited to: your performance relative to your peers, the opportunities that you are afforded or denied, the way in which your peer group can influence you, the socioeconomic status of most students, location, and perception of the school in the eyes of admissions officers. Now this is not a mandate to change your high school or to blame your limited college offers on the name of your high school. Rather it is simply an opportunity to understand the process more holistically and deeply.

People often believe that attending the most competitive (or perceived as competitive) high schools will get them into the best colleges – and please remember that the definition of “best” is subjective. But let’s break this down. Competitive high schools are often filled with highly driven students that succeed academically, potentially driving up curves and average GPAs. Students might come from families that are also highly educated and provide opportunities for great learning outside of the classroom setting. Students might have the resources to pay for standardized test prep and as a result scores go sky high. If the high schools are in affluent areas, there is also a great chance that the extracurricular opportunities will be great in terms of sheer number and quality. Sounds like everyone should go to one of these schools, right? Wrong! Not all students thrive in highly competitive environments. In fact, many struggle and the environment that is fostered actually causes them to retreat rather than excel. And not everyone can be at the top of the totem pole at these schools so the competition to get into the same colleges becomes fierce with students separating themselves with the smallest nuances. Remember that no college wants to admit multiple students from any given high school, especially when they are pulling applicants from all over the world.

In an effort to avoid these schools and give their children the best chance of “standing out”, parents often move their kids to less competitive schools. The belief there is that their kids will have the opportunity to rise to the top of the class and thereby prove to colleges that they are the best applicants from that given high school. But these schools may offer fewer accelerated courses, fewer extracurricular opportunities, and fewer resources dedicated to working with students. The reality is also that kids often perform at the same level regardless of high school, meaning that students that are going to settle into the middle of the pack will do so at the highly competitive and less competitive high schools. In that case, better to be at the highly competitive school. Also, not all students are comfortable stretching beyond the boundaries of what their schools offer and then will only take advantage of what is easily accessible.

All this simply means that all high schools are not created equal. If you are a senior struggling to make sense of your admissions offers, it is likely that your school played one role in the process. But if you are student that excelled at a highly competitive school but you feel that you fell shy of your college dreams, remember that you have learned a set of skills that will benefit you throughout life. If you are a student that feels that a lack of opportunities at your school prevented you from reaching your goals, take this lesson to heart and remember that you are not limited by what is in front of you directly. Learn to take initiative and make opportunities for yourself. So yes, your school is one factor in a long list of factors that impact your admissions.

]]>The Pythagorean Theorem is one of the most important theorems that you’ll come across in geometry. However, before we delve into it, first let’s look at the definition of a right triangle.

The Pythagorean Theorem states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum f the square of both sides. It’s mathematically expressed as a² + b² = c². The letters represent the side lengths of a right triangle. The *c* is the length of the hypotenuse and the *a *and *b* are the lengths of the other two sides or legs.

The Pythagorean Theorem should always be the first thing you think of when you see a right triangle! Remember, the Pythagorean theorem ONLY applies to right triangles. It does NOT apply to triangles that don’t have right angles.

Read Part 3 of this series to see how Pythagorean Triples will make your life easier when dealing with right triangles. For additional help, check out Brightstorm geometry.

]]>All right triangles are Pythagorean Triples. The most common triples, however, are {3,4,5} and {5,12,13}. What does this mean? Any right triangles with side lengths that are positive-integer multiples of these triples are also right triangles. Here’s the formal definition of Pythagorean triples.

For example, if you see a right triangle that has leg lengths of 6 and 8, then the hypotenuse has to be 10 because that’s a positive-integer multiple of the Pythagorean Triple {3,4,5}. In other words, if you multiply the positive integer 2 with {3,4,5}, you’ll get {6,8,10}, therefore saving you from using the Pythagorean Theorem!

Memorize the two most common Pythagorean Triples, {3,4,5} and {5,12,13}, to save yourself time while doing geometry homework and tests. For more help with geometry, read the rest of this series and check out Brightstorm geometry.

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