Why Do Some Students Excel in Calculus but Struggle in Pre-Calculus?

[Zill1]

Sorry... long read.

So firstly, I am quite possibly the worst student in the history of students. I entered my first year of university as a Political Science major (because all the courses I liked required some math prerequisites, and I and hated math) and ended up despising every moment of it. End of first term I had failed one course and dropped one course. Second semester I decided to take pre-calculus and hated it. Just hated it. So what did I do? I failed it. Also dropped another course. So at the end of my first year I had dropped two courses, failed two, and had 6 elective courses that count towards nothing.

At the beginning of April I actually picked up my pre-calc book (something I never did) and worked my way up to the unit circle and trig functions. I really enjoyed doing it myself. I enrolled in the same pre-calc course with a different teacher and here I am today. My problem is that I am still not doing well. I got 62% on my first test and by the looks of this one I just took... I did terrible. I did all the work correctly, but when it came to the answer I did something wrong at the last steps. So now I am sitting here relying on my final exam which will be shifted to 100% assuming I do better on it than I did on the tests (just his marking scheme).

It's really frustrating me because I also picked up a calculus textbook and I am able to understand and do questions with the maclauren (spelling?) and taylor series, and I really enjoy linear algebra... I just keep screwing up on pre-calc and it's so important for me; I can't do anything I want to until I get this done. My plan is to get this done, get my GPA up, and switch into my sciences faculty and possibly do statistics with a minor in maybe economics. I enjoy business but also math so I think it's a good middle ground. Now that I have ranted I just have a few questions...

Is there any specific way I should be studying? Just repetition, repetition, repetition? This is my first time trying to take math seriously in my LIFE. Are there any outside books I should pick up?

Is it normal for me to be much better at calc than pre-calc? What gives?

I'm sorry for the long rant.

 

[rootX]

Solve many problems.

 

[iamthegelo]

Assuming that you are having troubles with trig. I would like to suggest that you memorize these things:

1.) (sin a)^2 + (cos a)^2 = 1, from here you can manipulate this to tangents, secants, etc. (ex. divide through with sin a).

2.) Formula for sin (a+b) from here you can get the other formulas say, set a=pi or set b=a. Same for cos (a+b).

3.) The values for the sines and cosines of 45, 60, 30 and 90 degrees.

I don't think these are a lot to ask, but please realize that these are not the be all and end all of trig. just something that would help you pass pre-calc.

I need to learn LATEX, sorry.

 

[Feldoh]

Well let's start with your test that you have all ready taken. Do you know what you did wrong and how to correctly answer those problems now?

Second are you certain you understand the material. This goes back to rootX's comment. Anyone can read something and THINK that they understand but until you actually apply the knowledge then how do you know?

If you are not doing well on tests I can think of two particular problems from how you describe it:

1.) You don't fully understand material which leads to incorrect answers and faulty logic. If this is the case I urge you to go back and re-read the parts you have missed on your tests, and make sure that you understand what the book is saying, don't just simply follow along ask yourself why the author does such-and-such. This is the first step to fixing the problem.

2.) You are making easy mistakes on tests. Check through your work, don't be sloppy. you make get partial credit in a class but in the real world there is no partial credit -- you're either wrong or right and because of such you must be smart about how you solve problems. In pre-calc there are multiple ways or solving problems, try to solve the same problem in a different way if the answers match then you know you've got the right answer. Also there is no set strategy for coming up with different ways to check your answers. The more experience you get with problem solving the more you understand a particular concept helps to construct different ways of seeing a problem which can be used to figure out ways to check answers.

 

[anubis01]

Is it normal for me to be much better at calc than pre-calc? What gives?

It happens; I got a D in Calc I but got a B in Calc II. However, I do remember putting a lot more work into Cal II than I did Cal I.

As for studying tips, the best thing you can do is at a minimum start studying 2 weeks before your midterm and exam and go over every problem that you believe might be on the exam. The longer you spread out your studying the better your retention rate will be. Also if you’re having trouble in the final steps of a problem (something I struggled with for a long time) it means you don’t fully understand the material.

For myself I got over this by putting lots of man hours into making sure I knew the material and when I was still nervous, I got up early morning before my exam and did problems until it was time to write the exam. These studying habits helped me salvage my Calculus mark (failed first midterm with a 37% but got 80% on my second midterm & exam) and I avoided probation.

 

[Zill1]

I thought I would update... I ended up getting a B in pre-calculus. I am currently enrolled in Calculus I and it is going far better than pre-calc did. I have trouble with the proofs but from what I understand I only need to memorize the rules in CalcI. Thanks for the kind words and advice. By the end of this school year I will hopefully have completed up to Calculus III and Linear Algebra II!

 

[anubis01]

Well that's great news. Best of luck in Calc I

 

[206PiruBlood]

I believe it's fairly common for individuals to struggle with precalc and then find calculus more manageable.

 

[Troponin]

I took Calc II and Calc III at the same time and got a better grade in Calc III. I felt like I understood differential equations as well as I could understand any subject after one course and I got a B+. I felt confused throughout the entire semester of Linear Algebra and got an A with a 105% on the final.
I was certain I was the dumbest human alive in proofs and I got an A.
That's just how it goes sometimes.

For the most part, there is a pretty linear relation between number of problems solved at home and percentage correct on a test, so solve as many as you possibly can.
I got so frustrated in Calc II that I started referencing other texts, and solved the problems over and over again so many times that I could no longer remain objective because I knew the answer as soon as I saw the problem...because I had already solved it a dozen times.
And, like I said at the start, I scored lower in Calc II than I did in Calc III...despite taking them at the same time...and rarely even looking at the Calc III material.

Just keep plugging along. Your college career isn't one class. You'll get through this and love your Calc I class...and then maybe hate Calc II...but love linear Algebra, etc., etc. lol

 

[Pattonias]

I can definitely help you out here.
I am studying to become a mechanical engineer and am still taking my core math classes.
Last semester I took Chem 2 and Pre-Cal.
God decided to shine his light on me and gave me the most undeserving C in Chem 2 I have ever received. I mean seriously the teacher must have liked me. I talked to him maybe three times the entire semester and he gave me a passing grade. (I actually talked to my adviser about Pre-Law, but that is neither here nor there.)
The down side is I made a D in Pre-Cal. I spent so much time studying in Chem 2 that I let my Pre-Cal go because I thought It should come easily to me. I didn't do my homework reliably (huge mistake 1) and I didn't make sure that I understood what I was doing beyond the process of working the problem (huge mistake 2).
I took Cal 1 during the summer and was surprised at the fast pace and crash course style of teaching that we were put through. Our teacher had a funny accent, but he was good hearted and was really willing to work with us. From the start I knew that If I didn't do well in this class I would probably need to start looking at other college major choices.
I did several things:
1. I made sure that I understood the "Why does this work like this" principle in what we were learning.
I didn't just learn the mechanism by which you reach the answer, but I tried to understand how and why it worked. In Cal 1 I made sure that no matter what we were doing, I could visualize/draw it on a graph. Drawing all the problems out on a graph is hard at first, but after a while you get to where you can do it for any problem.
2. I did my homework religiously.
I didn't just stop when I finished I worked the problems over and over until I knew what was happening each step of the way. It was also really helpful to work out the written problems in the textbook. It is very satisfying to be able to fill in those crucial little steps in the example that the "God of Colleges" assumed you already knew in the example problems. (I'll add that once you understand what your doing and if you keep up with it, you will not spend all your time doing homework. After a while I could do mine in under two hours If I did it every day.)
3. I actually learned to enjoy the subject.
This comes from following the other two steps. Think of the class as a personal challenge. I saw that class this summer as my obstacle to fulfilling my dream. I wanted to do well in it more than anything. Once you can sit in class and actually follow along with the teacher and answer the questions he asks you will start to enjoy the subject.

I made a high B in the class once it was over. I feel that I have seen what I have to do in order to do well. Math does not come naturally to me, but I know that if I make the changes to myself that I KNOW I NEED TO. Then I will pass the class. I probably could have made an A, but that would have required even more study time, possibly a tutor. I would recommend a tutor if you feel you need it. You can ask in a single question what would take you an hour or so to find out yourself. Just make sure your tutor is teaching you how and why, not just answering your questions.

I think that If you want it you can do it. I also think that YOU know what needs to be done.
Every bad grade I have made I have earned. I know that I hate to admit that but killing characters in Halo 3 and rugby practice don't make me any better at graphing the A'.