I'm supposed to write a 10-page paper on (fill in with your topic). How am I supposed to fill up 10 pages with (your topic)? How many points do I even need to make?
Assuming you're asked to type it up double-spaced, Font size 12 in Times New Roman, with 1-inch margins (etc., etc.)... A great rule of thumb for filling up that space is knowing that you can fit approximately two paragraphs to a page. So a 10-page paper equals about 20 paragraphs (give or take a paragraph). Still don't know what to do with those 20 paragraphs? Well, keep in mind that at a minimum, your paper will need an introduction and thesis (or main idea/argument), support for that thesis, and a conclusion. Depending on the type of paper you're writing (research paper? persuasive essay? narrative essay?) your introduction could take up anywhere from 1 to as much as 3 or 4 paragraphs depending on what needs to be said before stating the main idea in the paper. Your conclusion will also likely be 1 paragraph (or more depending on what you need to sum up, but usually try to keep it to 1 paragraph). So, at least 2 (or more) of about 20 paragraphs, or 1 in 10 pages, are taken care of. Addressing the rest will take some more creativity and a good understanding of both what you need to discuss and exactly how in-depth you need to go with each of your points. A good way to organize your thoughts and ensure your thoughts is to turn your rubric or prompt into an outline for your paper. Break down each line, sentence, or phrase into a question you need to address in your paper (hopefully in a paragraph or more). Ask yourself which parts of the prompt will take multiple paragraphs to answer. Breaking down the prompt should offer a good roadmap to stick to while writing your paper. If the prompt isn't so fleshed out, or your assignment didn't come with a formal prompt or rubric (and involves more open-ended exploration), that gives you a lot of freedom over what points to discuss. So if you have a main topic or thesis chosen, some additional ways to brainstorm supporting points include using tools like 1) a mind-map, 2) a Venn diagram (if your paper asks for comparing and contrasting), 3) flowcharts (to outline steps or cause-and-effect of your topic) 4) Point/Counterpoints (if you're writing an argumentative essay), or other organizational tools that fit your topic and assignment. The final step is turning each point you come up with into paragraphs, and knowing where to put each paragraph so your paper flows logically from one point to the next. Figuring that out does take practice and exposure to well-organized essays, but soon enough writing great essays of your own will be second nature.
Does it matter to score well on the PSAT, since it's just a practice test for the SAT? Do I even have to take it?
Those who aren't in-the-know might think that the PSAT doesn't matter, and even decide to skip the test altogether. But if they do, they're skipping out on decent practice for the real SAT. Plus, high-achieving students who care about their chances for admission to top universities would be missing on a great opportunity to get a competitive advantage in applying to schools, and possibly on scholarship money too. The PSAT is not just the Preliminary SAT-- it's also the National Merit Scholarship Qualifying Test (NMSQT). Students who take the PSAT in the Fall of their junior year (or in the Fall the year before they apply to college) will automatically be considered for the National Merit Scholarship competition. Only the top 3% or 50,000 of the more than 1 million students who take the PSAT/NMSQT each Fall receive recognition from the program. Only 1 in 3 of those students will move forward with the scholarship competition as Semifinalists, then Finalists and Winners, which involves submitting resumes, academic records, a recommendation from a school official, and a personal essay. About 7,000 students a year find out the Spring of their senior year that they've won $2500 from the National Merit Scholarship Corporation. The other 2/3 of the 50,000 recognized students become "National Merit Commended Students" which, despite not leading to a National Merit scholarship, gets your name and achievement publicized to top universities that will give you preference for admission. You may also still qualify for scholarships sponsored directly by universities, businesses and other organizations. The same applies for Semifinalists and Finalists, regardless of whether they're awarded the NMSC scholarship. What might this mean for you if you become a Commended Student, Semifinalist, Finalist or Winner? If it's anything like what happened for me, you'll start receiving a deluge of mail in your junior and senior year from a variety of universities, some of which you may not have known about or considered otherwise. Some of these mailings will come with bonuses, ranging from free gear (I still have a scarf from University of Chicago) to application fee waivers to encourage you to apply. When looking into the costs and financial aid of the schools you're interested in, you'll notice that many offer university scholarships and grants for Commended Students and above. In my case, at least three of the schools I got into offered scholarships of at least $10,000 for up to four years (and one top tier school offered me a FULL RIDE scholarship, even though I was a Commended Student). So ultimately, the PSAT could offer a huge advantage if you're a high-achieving student. But at the very least? Even if you don't qualify for the competition, it's still great practice for the SAT-- and colleges will certainly be looking at that.
How do you find f(4) - f(2) if f(x) = 8x^2?
To find f(4) - f(2), you must find the values of f(x) when x=4, and x=2, which you find by substituting 4, then 2, into the function for x. Given that f(x) = 8x^2, f(4) = 8(4)^2 = 8(16) = 128 f(2) = 8(2)^2 = 8(4) = 32 Now that we've found f(4) = 128 and f(2) = 32, we can substitute those values into the equation to get the final answer. f(4) - f(2) = 128 - 32 = 96