Back to the original problem, in case someone is reading this that doesn’t get the other explanations, (this is like #4) imo this is the simplest way for people who aren’t so great at math: I would let x = 1, then you have 4 + 4 + 4 +4 = 16. Sixteen is four squared (4^2). You started with 4^1, x=1, so 4^x+1 = 4^1+1 = 4^2, which is 16. Really, it comes down to knowing that 4^2 = 4+4+4+4 = 16, and that 1+1=2 (and a little bit about how exponents work).
Lol…I never knew that one question that I post could result in such a huge debate! I understood the original question and thanks to atomom for bringing the original question back up. Looking through the thread, just in a simple answer, should I use the plug-in method or concrete algebra on the math sections for the SAT?
@Desi4life If you consider yourself fluent with HS algebra, then solving these problems directly will often save you time, and you can solve more accurately.
If you are not very confident with your algebra skills, plugging in is not a bad idea for most cases. Even if you are very good with HS algebra, plugging in random numbers can sometimes help, especially if you want to check an answer.
I think it will depend if someone is taking the old SAT or the new one. For the current test I’d say there is often a shortcut that, if you see it, will make the problem easy and save time. Plug ins are what make a lot of the shortcuts possible. Recognizing the shortcuts is something you get better at the more you practice the types of problems on the test.
If you are taking the new test next year, it will be different. Has anyone done the new PSAT practice test on CB website? I did the math section recently and it seems much more like the ACT. IMO, harder math, not so “tricky,” more time pressured, and more calculator dependent. More like school math. Just my impression of that first new practice test. I’m wondering what others think of it. . .
@atomom First off, nice timing to post the comment…9:11! I’m the last graduating class to be taking the 2400 SAT so I haven’t looked at the new format. I’ve been using a mix of plugging-in and using concrete algebra. Both work perfectly, but the only flaws are in my understanding. When you read an SAT math question, how do you break it down?
Time zones…I see 10:11.
@Desi4life It will vary among students with different math backgrounds, but here is how I usually approached SAT math problems:
- The early and middle problems are generally pretty straightforward; any "reasonable" approach should eventually lead to a correct solution. Most important thing is to read carefully and answer exactly what is asked.
- Out of the harder ones (e.g. level 4-5), some can turn out to be very easy if you can find a clever way around it (I can pull up a few example problems).
However that is usually not the case; I usually just break up the problem sentence by sentence, or phrase by phrase, so that I understand exactly what it’s asking for. I usually prefer to just solve it directly, rather than plugging in random numbers or answer choices, although I occasionally did the latter method in case I wanted to check that my answer was correct. In any case, even the level 5 questions can be solved in under a minute with a good approach.