<p>So Im going to be a senior, and took precal last school year. This year Im taking BC Calc. I signed up for Math Level 1 and 2 for October and I looked at the Math Level 2 practice questions and I legit know nothing! Im going to get a review book, so if I study for an hour every day do you think I will know these funky concepts by October and score in the 700s? Im really good at math,but I have never done this types of problems (limits, complex functions,etc)</p>
<p>Thanks!!</p>
<p>Anything is possible. Although, I suggest that you don’t take math1 if you are going to take math 2 because most colleges don’t consided math 1</p>
<p>Have you taken pre-calculus?</p>
<p>Limits on math II are super easy since they don’t require any knowledge of calculus. Usually the answer is obtained by plugging in the number that x is approaching.</p>
<p>^Or just plugging it into the graphing calculator.</p>
<p>Yeah, but I believe only CAS calculators can evaluate limits.</p>
<p>^you just plug in the equation in the graphing mode and look at the table of values as have values that get arbitrarily close to the limit on either side. That way, you can also easily tell when the limit is infinite without going through dividing through by the largest exponent in the denominator.</p>
<p>Ah okay. But you don’t really need to do that, if it asks you the limit as x approaches infinity of some rational function, say (x^4 + 3x + 1)/(5x^3 - 2x^2 + 4), you just compare the degree of the numerator and denominator…clearly that one diverges.</p>
<p>No, I mean when your limit itself is infinity. Like a vertical asymptote as x approaches a real number.</p>
<p>Yes, I took honors precal last year but we didn’t really do limits. Like we did the basic ones, but these confuse me! So can someone explain how you do them, and like how you get to the tables of values once you put it in your graphing calc?</p>
<p>Thanks for the responses!</p>
<p>For a continuous function, the limit as x approaches a <em>is</em> the value of the function at x = a. For example, lim(x->3) x^3 + 1 = 3^3 + 1 = 28.</p>
<p>There are other functions where they ask you to find the limit as x approaches infinity. SAT doesn’t test anything on L’Hopital’s rule, and usually they give you some rational function like the one I stated above. In general, if p(x) and q(x) are polynomials, then</p>
<p>lim(x->infinity) p(x)/q(x) = ±∞ if the degree of p(x) is greater than the degree of q(x)</p>
<p>lim(x->infinity) p(x)/q(x) = ratio of leading coefficients if the degrees of p(x) and q(x) are the same,</p>
<p>lim(x->infinity) p(x)/q(x) = 0 if the degree of p(x) is less than the degree of q(x).</p>
<p>You will also have the case of the limit being infinity (aka does not exist). So when you plug in arbitrarily close values of x to a as x approaches a, you just get increasingly large numbers. On a TI84, you just go to the graphing menu, enter the equation and type “2nd” then “graph”. You can change the change of x and therefore find out infinite limits</p>
<p>Yes, be prepared for limits involving asymptotes. For example,</p>
<p>lim(x->3) (x^2 + 6x + 5)/(x-3) clearly does not exist.</p>
<p>However, lim(x->3) (x^2 - 2x - 3)/(x-3) does exist and is equal to 4.</p>
<p>Both of these can easily be solved without use of a calculator. By the end of Calculus BC, you should definitely know how to evaluate limits.</p>
<p>Thanks for the info! And just wondering, what is the diff between the first and the second one? I understand the numerator is different but wouldn’t the second one cancel out to zero at x=3?</p>
<p>and building on the rule if the powers are the same then the limit is the ratio of the coefficants so if it is 3x^3+2x^2+6x+7/5x^3+4x^2+5x+2, then its limit is 3/5?</p>
<p>No, you can factor x-3 out of both top and bottom. So you have a removable discontinuity (hole) and the function still approaches the same value from both sides. Note that the definition of a limit only stipulates that the y values approach some number as x approaches a BUT not necessarily at a.</p>
<p>The second one can be factored as (x-3)(x+1)/(x-3). The x-3 terms cancel, and you are left with x+1. Plug in 3 for x, and the limit is 4.</p>
<p>For limits, what I just do is plug the value of x into the equation on my calculator. The answer you’ll get will be very close to one of the answers. If it asks for what value results as x approaches 3, do 2.999. For approaching infinity, I just choose a large number, like 10000. That’s usually big enough (if you get a very large number, then the answer is infinity as well). </p>
<p>You should look at complex numbers, but the SAT II doesn’t go TOO indepth into it. It’s mostly different types of algebra, not too much precalc.</p>
<p>And if you’re taking math II, go full on and don’t consider math I b/c colleges want at least 2 subject tests in different areas (math, science). Math II is much easier to score an 800 in anyway.</p>
<h2>No, you can factor x-3 out of both top and bottom. So you have a removable discontinuity (hole) and the function still approaches the same value from both sides. Note that the definition of a limit only stipulates that the y values approach some number as x approaches a BUT not necessarily at a.</h2>
<p>so it rougly goes to 5/3? And thanks so much guys! I have to study up! And I got the Barrons book at B&N today! Do I need to know alot about like trig identities and such? and like the double angle formulas and those things?</p>
<p>I want to major in mechanical engineering and I got a 790 on the Us history subject test (to prove im also good at history) but I still need to take this math one!</p>
<p>Don’t worry about trig identities or double angle formulas at all, they like never show up on the test. Just remember that sin^2+cos^2=1. That one appears on the test sometimes. </p>
<p>Mechanical engineering → physics?</p>
<p>At my school, you can’t fit AP sciences into your course load until senior year, and even senior year Im in too many APs to even fit in AP physics so Im taking honors 
Therefore it’s like impossible for me to take subject tests in the science field #justmyluck</p>
<p>And you know how collegeboard has the practice problems on the website? Are those similar to the test or harder/easier? :)</p>
<p>Basically, if you evaluate a limit and get something like 5/0, the limit is infinity/doesn’t exist. If you get 0/0, you cannot conclude whether or not the limit exists, because 0/0 is indeterminate.</p>
<p>I’m also thinking about mechanical engineering…I took Math II and Physics the October of my senior year.</p>