# Calculus for a 9th grader?

1. Dec 18, 2011

### Willis666

Are there any websites that can help a 9th grader learn basic calculus? I'm almost done with Algebra 1, but its way too easy.

I wanna learn some fundamental rules and such, and do own a few graphing/scientific calculators (TI-82, and I bought one for my phone.)

I dont really want to do anything fancy, I just want to get the basic jist when I read formulas in some of my books.

Thanks guys for any help. I've searched all over the internet, and found a good PDF that im reading right now. Just wondering if there's any full websites.

2. Dec 18, 2011

### DivisionByZro

I believe your best bet is Khan academy. The difficulty and breadth of material covered ranges from very elementary to mid-undergraduate level I'd say. I trust you'll find everything you want there.

Check our the Youtube channel for Khan Academy. Good luck with your studying. Remember that if you have any questions, many people will be more thna happy to help you with them on here. Just post away.

3. Dec 18, 2011

### Highway

^ i hear the place above is great for online lectures, and ive used this site a lot for theorems / example problems to help my understanding more:

http://tutorial.math.lamar.edu/

4. Dec 18, 2011

I'm not sure what your algebra course covers, but the standard "algebra I" course in high school usually is not enough to prepare someone for calculus. If you would like to self-study Intermediate Algebra, College Algebra, and get an introduction to trigonometry, then you will have the appropriate tools.

That said, there isn't really anything preventing you from learning how to evaluate limits, take derivatives, and learn integration techniques, but your ability to finish problems that involve these concepts will be hindered, if not completely halted, without a solid foundation in algebra. I only mention this because it might save you a great deal of frustration.

If you're finding that your current course is too easy, work ahead a little bit. However, I do not recommend skipping any courses; calculus is hard enough with a solid foundation.

5. Dec 18, 2011

### Willis666

http://www.stat.wisc.edu/~ifischer/calculus.pdf
I read up to section 3, and understand it a bit.
I kind of just want to slowly work on it so its not in my face when I finally get to actually doing it in school.

6. Dec 18, 2011

Nice. Ambition is good! Just don't get too discouraged if you come to something you can't follow; you still have some more tools to acquire. Come here and we'll be happy to help.

7. Dec 18, 2011

### brocks

I would go further than the other posters in warning you about trying to tackle calculus without a solid foundation in at least trigonometry and analytic geometry, and preferably plane geometry and advanced algebra.
You simply won't understand what is going on. You can memorize some of the formulas, but more than half of solving even freshman calculus problems is setting up the problem so that you can apply the formula, and you can't do that without geometry and trig.

If you found first-year algebra easy, that's great, but compared to the above, it's supposed to be easy. Calculus is typically not easy except for the gifted, even when they have taken the normal sequence of prerequisites.

If you do feel that you are gifted in math, then you should download a free precalculus text, or buy a used one on Amazon or Ebay. Most of the popular calculus text authors, like Stewart and Larson, also have precalculus texts. It would take a very advanced ninth grader to work his way through one of those books in a year, and I wouldn't even consider calculus until you've done that.

8. Dec 18, 2011

### JustAnotherGu

I agree with brocks.

You definetely shouldn't get ahead of yourself by trying to jump straight from Algebra 1 to Calculus.
Before you can properly understand Calculus (as opposed to memorizing algorithms that can help you solve problems), you need a solid grounding in Geometry, Algebra 2, and precalculus/trigonometry.

It's great that you're doing well in Algebra, and I think it's awesome that you want to do more math outside of school.

sparknotes has a lot of great recources for all of this stuff. They also have review tests.

http://www.sparknotes.com/math/

9. Dec 18, 2011

### DivisionByZro

While this is sound advice, do not discredit reading through some calculus. It is very helpful to get acquainted with the topics before you cover them in class. You won't get shocked when you're introduced to limits or integrals (At least, not as much). I would recommend you pick up Serge Lang's Basic Mathematics. Try to tackle some problems. It's probably far over your head right now, but get some help from teachers or peers. It is, in my opinion, a very solid foundation for everything pure math.

Last edited: Dec 18, 2011
10. Dec 18, 2011

### Willis666

Thanks for the advice guys. I'll have my stepdad help get a little further, hes really good at math.

11. Dec 18, 2011

### BloodyFrozen

I wouldn't say a student needs ONE whole year on precalculus if he/she is determined. I personally learned it in 2 months and I'm not especially gifted in mathematics. However, I still would highly recommend learning Algebra II and Percalculus before starting Calculus.

12. Dec 18, 2011

### eumyang

This may be a dumb question, but if Algebra 1 is "way too easy," why didn't you take it sooner? Some students take it in the 8th grade, and some even take it in the 7th grade.

13. Dec 18, 2011

### mathwonk

If instead of a calculus "course", you want to actually understand the ideas, namely limits and the interplay between rates of change and areas and volumes, I recommend my epsilon camp notes on Euclidean geometry, #10, from the bottom of my web page:

http://www.math.uga.edu/~roy/

the last 4-5 pages of these notes explain the transition to calculus methods to handle volume problems, in 3 and even 4 dimensions. The earlier parts explain the geometry that lies behind the calculus problems. On the other hand if you just want a nice clear explanation of standard calculus ideas and techniques without this background of what it is all for, khan academy is fine.

14. Dec 18, 2011

### BloodyFrozen

Exactly, there may be more than what you are currently learning that is "way too easy". Do you know how to do some of the more advanced things in Alg I?

Can you solve a system of equations?
Ie. Find the values of x and y

$$-2x + 3y = 8$$
$$3x - y = -5$$

Can you find these with relative ease? A student entering Calculus should be able to solve this.

15. Dec 18, 2011

### Willis666

I was in Algebra 1, but I went to a private montessori school from preschool to 8th grade, and we didn't finish the book (There were 2 people, me and my like best friend, but my friend forgot his homework a lot.) So I had to restart it the next year.

16. Dec 18, 2011

### iRaid

You should learn trig before calculus.. Atleast the basics..

I.E.
$cos^{2}+sin^{2}=1$
etc..

And yeah I took alg 1 in 8th grade.

17. Dec 18, 2011

### PAllen

It's too long ago for me to remember what my real (rather than official) background was, but right after 9th grade I looked at calculus sequence books in the library to find one that read well for self study (I'm sure the one I liked is no longer in print). Over the next year, I did the whole sequence including all exercises. It is possible, but ambitious.

Actually, I remember something. I had completed algebra and geometry by 9th grade, and was taking trig contemporaneously with the calc self study. I also asked my parents to buy a separate trig book along with the calc (trig book also selected for self study effectiveness) so I could do that independent of the class rate. So I guess I actually agree with what everyone said about background.

18. Dec 18, 2011

### Willis666

Last edited: Dec 18, 2011
19. Dec 18, 2011

### PAllen

20. Dec 18, 2011

### brocks

Sorry, no. And I don't want to discourage you, but your answer makes it clear that you need more algebra, as well as the other subjects we've discussed.

Your first answer doesn't work at all; I don't know what you did to get it. The second answer does solve the second equation, but you should be able to see that there are an infinite number of correct values for x and y. If you give me ANY value of x, I can give you a value of y that will solve the equation. The fact that you didn't notice this indicates that even your basic algebra is shaky.

The same goes for the first equation, or for any other linear (the variables are all in the first power) equation in two unknowns. Using your values for the first equation, if x = -4, then y = 0. If y = 12, then x = 14.

So why did the poster act as if there were only one answer? Because the problem is to solve BOTH equations with the same x and y, "simultaneously." Only one set of values (x, y) will solve both equations at once.

One way to solve them is to multiply the second equation by 3. You can then add the equations together, the y's will cancel out, and you end up with 7x = -7, which means x = -1. You can then plug this into either equation to get y = 2. So the answer is x=-1, y = 2.

When you learn analytic geometry, you will see that each equation is the equation of a line in the x-y plane (which is why they are called linear). Every point on each line is an x-y pair that solves the equation, hence there are an infinite number of solutions. But the single x-y pair that solves both equations is the point where the two lines intersect, so for non-parallel lines, there is exactly one such point, hence one x-y pair.

Slopes of lines are usually the very first thing that calculus deals with, and it gets tougher from there. You really, really need to learn analytic geometry to understand calculus.

This is not a knock on you; everybody makes mistakes in algebra. But if you don't even understand the questions, then it's obvious that you need to learn more before tackling calculus. That is why every school in the country has you take something along the lines of two years of algebra, a year each of geometry and trig, and then a semester or two of precalculus before you learn calculus. With talent and hard work, you can shorten the process, but you can't skip it entirely.

Last edited: Dec 18, 2011