<p>From the Blue Book 2nd Ed. on page 422 number 8.</p>
<ol>
<li>If x and y are positive integers and (3^2x)(3^2y)=81, what is the value of x+y?</li>
</ol>
<p>I looked at the college board explanation but I got lost. There explanation was a bunch of complicated steps that I probably wouldn't think to conduct in such a crammed time frame. If someone can give me tips to solve this problem in lay-man's terms, I'd appreciate it. I'm good at math generally, but sometimes I'm like... Duh, huh what derr.</p>
<p>Ah of course. Thanks Sikorsky. I looked at the first step of your explanation and it clicked. I looked at college board’s explanation and I just got lost on one of the steps so thankyou very much. It seems like an easy problem now.</p>
<p>Seriously, sometimes I feel as if using algebra is cheating! It’s like I know there should be a clever work-around, but I can’t always find it. When I use algebra in my SAT class, I always apologize in advance. And sometimes, my students interrupt and announce the work-around that they found.</p>
<p>So in this case, you could also play with numbers and see what happens. I bet that x=1 and y=1 would be one of the first cases that you tried.</p>
<p>Yeah well I blame geometry for making me forget my algebra. I’m a freshman now in geometry Pre-Ap and I feel like I forgot half what I learned last year. Last year in my algebra class my teacher thought I was a genius I worked ahead of the class and she would come to me and give me really hard problems, sometimes ones she wasn’t even sure about. Yeah but I forgot that all and when I do some problems I feel like “Wow I could’ve done that last year” haha. I forget a lot over the summer :D</p>
<p>well, i’d immediately look at that first and go “okay, 9x9=81…” and realize that 3^2 x 3^2= 81. That means x and y are both 1, so x+y=2. Seriously, they aren’t going to give a problem where the algebraic solution conflicts with numbers you get from plugging into the equation, so you might as well try it if you’re working with nice numbers like this problem does.</p>
<p>“Seriously, they aren’t going to give a problem where the algebraic solution conflicts with numbers you get from plugging into the equation”</p>
<p>…because they CAN’T! There’s no such thing. If an algebraic solution is correct, it will always apply to specific numbers as well. That’s the reason plugging in numbers works so often as an algebra evasion technique!</p>
<p>I find this discussion interesting. As a math teacher, I think there’s a rather short list of basic math facts that students at this level ought to know cold, and they’re hurting themselves if they don’t know them. IMO, students ought to know:</p>
<p>primes less than 100;
powers of 2 up to and including 2^10;
powers of 3 up to and including 3^4;
powers of 5 up to and including 5^4;
pi is approximately 3.14;
square root of 2 is approximately 1.414, and square root of 2 over 2 is approximately 0.707;
square root of 3 is approximately 1.732, and square root of 3 over 2 is approximately 0.866; e is approximately 2.718;
a few primitive Pythagorean triples: 3-4-5, 5-12-13, 8-15-17, and maybe 7-24-25.</p>
<p>In this problem, if you know that 81 = 3^4, then the rest of the problem is trivial and quick. If you don’t know this fact, and other basic facts like it, you’re going to spend a lot of time on some SAT questions that could be easy.</p>
<p>I am not, however, the kind of enthusiastic SAT-watcher that many other CC posters are. I wonder whether anybody has other essential facts to add to the list.</p>
<p>Coach Monk’s ‘Mathcounts’ Playbook! It’s more or less a list of things you need to know to do well in Mathcounts (a middle school math competition). SAT questions are quite a bit easier than Mathcounts ones, so if you can learn everything in that file you’re set.</p>
<p>Nice link, conqueror. I agree that it’s more than you need for SAT, but I can see it does include some things I left out of my top-of-my-head list above: squares of natural numbers up to 20, and decimal equivalents of common fractions were two important ones.</p>
<p>I agree with the sentiment. And yes, there are things on the lists that are definitely more for math competitions than for the SAT. For example, for the SAT there is no reason to know prime number – but you better know that 2 is prime. Also, calculators make it unnecessary to know divisibility rules.</p>
<p>But I absolutely agree that top scorers should be able to rattle off decimal equivalents of fractions even though a calculator will do it for you. And in general, it’s good to have “number sense” – you see where a question is going by the numbers that are in it. On the other hand, for people who don’t have this, it’s hard to cram.</p>
<p>Hmm. I definitely wouldn’t know much of those criteria instantly off the top of my head. I’d like to share an anecdote about how our math system here is so lackluster. </p>
<p>So, personally, I made some stupid decisions in middle school that account for why I’m only in Geometry Pre AP as a freshman. In sixth grade, we were on self study and as soon as I finished the 6th grade book and moved on to pre-algebra I was lost and I didn’t really have anyone to ask. I actually passed the test to skip Pre-Algebra but made the immature decision to stick with my friends. No one objected. </p>
<p>So in 7th grade, I had an idiot as a math teacher whom had nauseatingly awful teaching methods. The crappy math at my school in 6th and 7th grade led to math changing from something that was my favorite subject and that I was fascinated by to something that could barely keep me awake in class. In 7th grade my teacher taught exclusively from this one TERRIBLE notetaking guide. When she did it, she would use this terrible invention called a “smart board” that was a waste of 3,000 dollars per class. The board didn’t live up to it’s name and I couldn’t read anything she wrote despite my perfectly normal vision. I found it hard to even stay awake in her class because I thought she was so unintelligent and her teaching methods were so mechanical and trite. I learned pre-algebra at home from my Dad that year. And when 8th grade regular algebra came I already knew it all and was equally bored. </p>
<p>So anyways I digress. I thought I’d put this out there because we’re discussing all this stuff. Just had to vent because I’ve been so dissappointed in myself and my middle school math curricula. This year math is pretty good though. I mean, I’ve always had perfect test scores and good grades in math, but I just feel like I wasted my potential and now I’m stuck a year behind in math than I could have been. I will even note that my passion went from math to politics and speaking because of all this crap. Man… middle school really sucked. I’m a freshman btw I just was taking an SAT for fun.</p>
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