UWorld math author back with a few more nuggets in advance of the February ACT. Just a reminder that I have included some question numbers that can be inserted in either Custom Test or the Search function in the menu on the left side of the app for some practice in these areas. See my previous post for more details on how that works.


Polynomials

One other area that we see some room for growth is quadratics and higher-order polynomials. One common formula that can save a lot of time on the ACT is factoring a difference of two squares. The ACT looooooooooves this formula, and it's fairly easy to remember.

It may also be helpful to memorize how to factor a sum of two cubes and a difference of two cubes. These aren't as common, but they do make an appearance from time to time, and they tend to be some of our lowest-performing questions as well. (questions 504003, 504050)

Finally, one thing to remember that the ACT uses in some tricky questions is that two polynomials are equal only if their constant terms and corresponding coefficients are equal. For example, if m and n are constants and 3x + 4 = mx + n, then m = 3 and n = 4. We know this because for the two polynomials to be equal the constant terms (4 and n) must be equal and the coefficients of the x-terms (3 and m) must also be equal. (504261, 504388)


I hope this has been helpful, and good luck on Saturday!