Note: Below are posts transferred from my previous blog.
Restarted Khan Academy's Calculus AB course. (Attempted it a long time ago but didn't get very far.) Took quizzes 1 and 2 in the limits and continuity section. Some stuff I remembered, but some stuff had me lost. Fortunately there were in-depth explanations for every question. Definitely need to review a lot of concepts, but now I know what I don't know.
Practiced completing the square with Wolfram Problem Generator. Did three beginner questions, six intermediate, and one advanced. Got all 10 correct, but I think I made the last question way too complicated. The fraction in the constant term threw me off. But it felt good to work through my confusion instead of giving up immediately.
Did some practice problems using Wolfram Problem Generator. Tried completing the square, just because I felt like it. Didn't even need to review to successfully answer 10 questions. Almost forgot what to do when the leading coefficient isn't 1, but I figured it out on my own eventually.
One thing that keeps me slow is not having memorized enough squares. I only know up to 12 x 12. I should work on improving my mental math skills.
Read the entirety of 5.1: The Complex Number System, from the LibreTexts book I found yesterday (Sundstrom & Schlicker's Trigonometry). Yesterday that section taught me how to get the norm, or modulus, of a complex number. Today it taught me the formula to use to find the quotient of two complex numbers.
Read the Purplemath lesson on complex numbers to refresh my memory, then did a few practice problems using Wolfram Problem Generator. Did a couple of beginner problems and a few intermediate ones.
One of the intermediate problems wanted me to find the norm of something. Didn't know what that was, so I looked it up and found an article from a LibreTexts book, which explained the concept pretty well. Now I'm interested in LibreTexts, which looks like a collection of free online textbooks in a variety of subjects.
Did some practice problems using Wolfram Problem Generator. Binomial expansion again. Did two beginner questions as warm-ups and four intermediate questions. I've been practicing this topic for the past few days and it's not a challenge anymore, so I gotta move on now. Not sure what to try next.
Read the Purplemath lesson on the binomial theorem. It was a lot to review, especially because I barely remembered permutations, combinations, or summations. Remembered factorials, though.
Did some practice problems using Wolfram Problem Generator. Did five binomial expansion questions at beginner level. Surprisingly wasn't that hard. Pascal's triangle made everything a breeze. Tomorrow I'll try the intermediate level.
Practiced factoring polynomials with Wolfram Problem Generator. Five questions at beginner level (quadratic polynomials), five at intermediate (cubic polynomials), and one at advanced (a fifth-degree polynomial). The advanced question took almost the same amount of time as the previous ten questions combined. But I feel like I can move on from this topic now.
Did some more practice problems using Wolfram Problem Generator. Spent 15 minutes factoring polynomials. Three beginner questions to warm up, then five intermediate questions. Much faster than yesterday. Might practice binomial expansion tomorrow because I have absolutely no memory of how to do that.
Practiced some math with Wolfram Problem Generator, which generates math problems instantly. It offers 3 difficulty levels and 6 main topics: arithmetic, number theory, algebra, calculus, linear algebra, and statistics. Considered jumping back into calculus, but decided to do algebra instead. Something easier so I don't get too discouraged.
Tried factoring polynomials at the beginner level. Answered five questions in 10 minutes, with no review beforehand. Pretty good, just slow.
Moved on to the intermediate level and immediately got stuck. Visited Purplemath, a website that explains algebra topics, to review synthetic division and the rational roots test. Went back to Wolfram and did five questions successfully in 35 minutes. Definitely need to practice more tomorrow.