So, my high school has five years of schooling. For 3 of those years, you are essentially forced to take a certain math course (unless you took a placement test for a higher level of math earlier, but that’s irrelevant), and as a Sophomore, next year will be the point at which people break off into three other areas of math: Calculus, Advanced Topics, and Statistics. However, if you’re interested in doing Calculus, you need to take an assessment test which is included in the first-semester math final.
I want to take Calculus! However, I have received a B in every math course so far, and I’m looking at turning this quarter’s grade into an A, as well as passing the placement test for Calculus. What was described as being on the assessment test is “all of the skills you have learned thus far,” basically meaning everything from Algebra I, Geometry, and AlgebraII/Trig.
My question is, how should I go about studying all of these topics? Like I said, I didn’t do amazing in each course, but that was in part due to my own laziness as a Freshman and an 8th grader. I’ll have to play catch up, but I appreciate any book recommendations, advice on where to start, or studying methods. Feel free to include input about you learned math, since it’s probably my worst subject in school.
You will certainly need to know algebra and trig. While calculus will teach you derivation and integration, you won’t be able to manipulate the problems they provided without good algebra and trig skills. Know trig identities back and forth and study exponential functions and how they are manipulated in algebra.
And remember, calculus is a new topic for you so don’t get discouraged. It is a very useful skill to learn and I expect that you will continue to take calculus classes into college as well. Good luck!
Start on pre-calculus modules in your favorite online source. I’ve heard great things about Khan Academy, but it came along well after I was in school. Another source I like is purplemath.com - if it’s still there (been a few years since I visited). I agree with good practice in algebra and trig. The binomial theorem is crucial for calculus.
One area that often crops up when studying calculus and, more generally, appears throughout high school and early college math, is trigonometry. You can’t go wrong by learning it and, ultimately, mastering it.
So, for your purposes at present, I suggest going over basic trig - be certain to have all the identities down pat and be prepared for some ‘second level’ questions based on the more fundamental stuff, e.g. sine (A+B).
I had a lot of trouble in calculus, so I’m probably not a good example. But what helped me was buying a calculus textbook with an answer key where the answers were worked out, that way you can do problems and figure out how they were done. If you are stuck in calculus, you are stuck. And if you don’t have a tutor or AI to help, you can stay stuck. Doing that helps educate you on what to do to get better.
Also Khan Academy has various calculus videos that may help.
The only way to get good in high school math is practice, practice, practice. Open your textbooks and do every single exercise, then find some more textbooks and do those too.
Trust me - I learned this the hard way. I thought I understood the material, so I didn’t have to do my homework. I was very, very wrong.
All I can say is that Calculus was my favorite math class ever. I was generally a mediocre/struggling math student until Calculus and I might have gone through life always thinking math was a terrible agony, if I hadn’t had the chance to take it.
(If you are wondering why I was in Calculus at all, my HS required 4 years of in-residence math classes, and I arrived a year accelerated based on my junior high curriculum. Before you conclude I wasn’t really mediocre or struggling because I was accelerated, about 75% of students arrived at my hs “accelerated” by at least one year. The actually good students were two and even three years accelerated.
I found calculus to be easier than algebra. High school calculus is actually a pretty small subject. It’s basically about four things. By contrast, you’ve now spent half your school life learning algebra.
The most important thing is to be rock-solid in your algebra and trig skills. If you have any weaknesses, address them now and work lots of practice problems until you can do algebra as easily as you can multiply.
Calculus was invented by Sir Issac Newton, a man who spent so much time thinking that he never had sex in his whole life. This is why calculus is foisted upon nerdy high school students, so they will never have sex.
Ah, yes, this old blast from the past: I violently hate calculus and physics. Interesting to see how your attitudes changed over the course of that thread.
I forgot to mention Schaum’s Outlines. It’s a great supplement to a class or textbook. Schaum’s Outlines have breif, but very clear!, explanations of each topic under a subject, and then a bunch of worked problems. They are also very affordable. Here’s the Amazon link for Schaum’s Outline of Calculus, but other books from them might be more helpful to you at this point: http://www.amazon.com/Schaums-Outline-Calculus-Fourth-Edition/dp/0070419736
After struggling in high school calculus, when I went to college I took a semester to re-take a basic algebra course to refresh myself on all of those basics. Having done that is the only reason I survived two semesters of college calculus.
So you are in Alg II this year and taking the placement test at the end of the year? Go to your teachers for help. It doesn’t have to be this year’s teacher, if earlier teachers will work with you and you get along with them better. Take your homework in for them to look over before you turn it in, and when something is wrong, show them how you worked the problem and let them point out your mistakes (this is worth a lot more than just having them show you the right way). When you get a test or quiz back, go over the ones you missed, rework them, and then take them in to the teacher and ask if you got them correct. If not, have them show you where you went wrong. Develop an awareness of the types of mistakes you make, the places where you tend to get confused.
This will have two advantages: one, mastering Alg II inside and out will prepare you for the test. Two, if you are borderline on the test ( and you likely will be), you want the teachers that can make the call to be say “I would have said ‘hell no!’ back in November, but man, oh, man has she come on strong. She really, really wants this and will do the work to make it happen.’”.
Math teachers, more than any others, IME, appreciate hard work–not just doing your homework, but doing the hard work of struggling when you are stuck, of figuring it out. Because math, more than any other course, really rewards that kind of work. The vast majority of kids can be successful at math if they put the time in–but the time required can be substantial. Show them you will give them that time and that work, and they will take you.
Especially if you can find an Algebra text that covers it in detail.
As far as I know, typical algebra classes and textbooks give only a brief and superficial treatment of inequalities. If you can find any resource that teaches inequalities in depth, go for it!
In particular, see if you can find a resource that teaches how to prove unconditional inequalities. This is typically not taught at all. But I have an old college-level algebra textbook (published in 1948 I think) with an entire chapter on it. I studied that, on my own, before studying Calculus and I think I was vastly better off for it.
It turns out that Calculus is mostly just a whole lot of algebra, with just one or two basically new concepts added: Limits and derivitaves. BUT, it happesn, those few new concepts are fundamental to Calculus and are used extensively, through and though.(Integration is just another application of limits.) And it turns out, that if you understand the logic of inequalities, you will be very well-positioned to understand the logic of limits.
I think it will also be helpful if you intensively review all the algebra you’ve already learned, and bring your skills up from whatever level you had to A+++ level.
Here’s a fact about all math education: It’s extensively progressive. That means, everything (just about) that you learn, you will continue to need and use thereafter.
This is in contrast to, say, History. In a History class, you can generally forget most of each chapter right after the exam (but you’ll have to review for the final). And, wherever I’ve looked at the course requirements, you can generally take U.S. History I (colonial days through Civil War) and U. S. History II (Reconstruction to present) in either order! – You don’t need History I before taking History II.
You wouldn’t dare try a stunt like that with math. Every topic you study, you will continue to need thereafter. And even if you don’t see a topic for several years, it all comes back in Calculus. It’s ALL there – Special products and factoring; quadratics; half-angle and double-angle formulas; conic sections; the works.
I claim that if you miss anything in ANY level of math class, that will put a limit on what you can learn in later classes. Typically, you are expected to master 90% of the material to get an A. If you only master 81%, you get a B. BUT, if that happens, the 19% you missed will limit you in the later classes. If you learn 71% of the material and get a C, that will limit you even more in later classes. If you can learn 99% of the material in every class at every level, and retain it then you will be best equipped to learn 99% in your later classes too.