Is It Possible for a 9th Grader to Learn Calculus?

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

I don't 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 I am reading right now. Just wondering if there's any full websites.

 

[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.

 

[Highway]

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

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

 

[Dembadon]

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.

 

[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.

 

[Dembadon]

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.

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.

 

[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.

 

[JustAnotherGu]

I agree with brocks.

You definitely 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/

 

[DivisionByZro]

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.

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.

 

[Willis666]

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

 

[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.

 

[eumyang]

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.

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.

 

[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.

 

[BloodyFrozen]

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.

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.

 

[Willis666]

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.

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.

 

[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.

 

[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.

 

[Willis666]

Oh, i just saw those two questions.

1. x = -4
y = 12

2. x = 1
y = 8

Is that right?

http://www.fmaths.com/trigonometry2/lesson.php?PHPSESSID=817d295b9b517322070f49ea7b540680
Reading over this one now.

 

[PAllen]

Oh, i just saw those two questions.

1. x = -4
y = 12

2. x = 1
y = 8

Is that right?

http://www.fmaths.com/trigonometry2/lesson.php?PHPSESSID=817d295b9b517322070f49ea7b540680
Reading over this one now.

No, that's not correct. if you're referring to the system of equations BloodyFrozen gave.

 

[brocks]

Oh, i just saw those two questions.

1. x = -4
y = 12

2. x = 1
y = 8

Is that right?

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.

 

[Willis666]

Thanks. What is that called so I can look it up in my book to study?

 

[brocks]

Most pre-calc books would call it "Systems of Equations." But in most pre-calc books I'm familiar with, that chapter follows the chapters on trig and analytic geometry, so they probably assume you know those subjects.

 

[Willis666]

I'll look it up in my book.

 

[Thundagere]

This is coming from a student and what I'm doing now.
As a middle schooler, I'll tell you that I studied Alg 1 in 7th, and Geometry in 8th. In 8th grade, I did feel bored in math class, so I started studying very basic calculus about that time.
I'll tell you it's definitely possible for a 9th grader to study BASIC calculus. I did it myself, self studying from several advanced textbooks from Singapore. I could, at least, solve the problems as well as my currently 12th grade sister.
But I did make sure to have a strong foundation. If I didn't understand one lesson, I would spend as much as a month on it. When you self study, you need to make sure you have a very strong foundation, as there's no one to correct you when you're wrong. Just remember that.

 

[ander]

For whatever it's worth, my recommendation is to relearn algebra, geometry, and trig so that you attain a whole new and more profound understanding of mathematics. I found myself in a similar situation, and I ended up using the khan academy and some textbooks to relearn math from 1 + 1 = 2 through trig. Math is usually taught terribly in primary school, so chances are that your knowledge base is full of holes. I took mathematics through Calculus BC without understanding probability, for example. You could even read up on some basic number theory to understand the logic behind some of the basic calculus concepts like limits and continuity. I found that giving my mind a break from mindless exercises gave me a fesh understanding and greater appreciation of math as something more than a rung on a ladder to nowhere in particular. Just a thought.

 

[PAllen]

For whatever it's worth, my recommendation is to relearn algebra, geometry, and trig so that you attain a whole new and more profound understanding of mathematics. I found myself in a similar situation, and I ended up using the khan academy and some textbooks to relearn math from 1 + 1 = 2 through trig. Math is usually taught terribly in primary school, so chances are that your knowledge base is full of holes. I took mathematics through Calculus BC without understanding probability, for example. You could even read up on some basic number theory to understand the logic behind some of the basic calculus concepts like limits and continuity. I found that giving my mind a break from mindless exercises gave me a fesh understanding and greater appreciation of math as something more than a rung on a ladder to nowhere in particular. Just a thought.

I agree with the gist of this. The outside book I found for trig and pre-calc happened to have a thorough chapter or two combinatorics and probability. It was immensely useful later that I did this at the beginning of high school. It's out of print, but this is the the precalc book I used for self study (before calc self study):

Integrated Algebra and Trigonometry, with Analytic Geometry [Hardcover]
Robert Charles; Ziebur, Allen D. Fisher (Author)

As noted, it addition to the algebra II and trig, and analytic geometry, it included thorough intro to combinatorics and probability. I have no idea if there is any similar book in print now. It was a joy for self study.

 

[nickadams]

maybe study more advanced books that cover topics before calculus.

I have seen knowledgeable posters here recommend

principles of mathematics by allendoerfer, and..
method of coordinates, functions and graphs, algebra, and trigonometry by gelfand as challenging high school math books (before calc)

 

[DivisionByZro]

I liked Algebra by Gelfand as well as Trigonometry by Gelfand; bot cover a lot of material and the exercises are challenging and interesting. However, I found that Method of Coordinates was lacking in content and kind of disappointing considering the amount of money it is worth ($35 CAD for 84 pages).

 

[alexhenderson]

Hey Willis,

This is coming from a ninth grader as well, but don't take my word. I began taking Algebra I in the 7th grade, and then taking geometry in the 8th grade. And I can say understanding basic calculus was tangible for me near the end of the 8th grade. I used resources such as ocw.mit.edu, khan academy, I even bought my own calculus textbook.

When I began to look at differentiation I noticed I lacked some very fundamental algebra skills, like how to multiply (a+h)^4, so I learned how to do that and it was a long process and it took me time. Then I learned the binomial theorem, and how is was derived. So, yes, I think it would be perfectly graspable for a ninth grader to learn basic calculus coming from my own experience. My method was learning necessary algebra skills I wasn't great at "on the fly."

What I have found from my high school experience is that teachers will not teach you how certain mathematical mechanisms are derived, for example reduced row echelon form or the quadratic formula. I would suggest learning why things work in math as well, apart from just learning calculus. Good Luck!

 

[mathwonk]

here is one my favorite algebra books. its free too.

http://books.google.com/books?id=X8...&resnum=5&ved=0CCQQ6AEwBA#v=onepage&q&f=falsethis book, by a famous genius, takes you from "what is a quantity?" to solving 3rd and 4th degree equations, and more.

 

[Sankaku]

Calculus is typically not easy except for the gifted, even when they have taken the normal sequence of prerequisites.

In this case, being gifted usually has little to do with success. There are really only two things that make Calculus difficult for students. The first is shaky foundations. The second is that Calc I & II usually compress far too much into a short span, to please the various departments that use them as prerequisites for other courses.

As for the first, it is still good to look ahead and see what you can figure out. However, when you realize that you don't have the tools to continue, it gives good motivation to go back and cover your prerequisites well. Don't be fixated on Calculus, though. There are many areas of mathematics that are worth exploring even at the high-school level. Look for books and websites on discrete math, basic set theory and simple proofs.

 

[dudebroIII]

hey, just want to encourage you. math is taught at a terrible level in this country, and your position is not unusual. it's good that you're showing interest now - maybe you can take some classes over the summer to accelerate your speed. starting calculus with no geometry/trig and spotty algebra would be difficult. a good goal would be to complete 1) calculus, 2) basic linear algebra, 3) learn how to do proofs/basic number theory before college. that would make you very well prepared, especially the latter one

 

[HeLiXe]

Hi Willis,

Calculus can be easy for some and difficult for others, but one thing is certain--it is necessary to have a good foundation in algebra and trig...and even geometry. If you're curious about calculus, there is nothing wrong with having a look through, but mastering algebra 1 and 2, trig, and geometry will give you all of the tools you need to be really strong in calc. Good luck with everything!

 

[Willis666]

Thanks for the answers guys. Since Christmas is coming, i'll buy myself some geometry/algebra books.

 

[BloodyFrozen]

I am in 9th grade and learned Calculus (single variable) as a self study in my 8th grade summer, but it did take time to get to there. Assuming you are ambitious enough, it is very possible to learn it as a 9th grader. I would also like to say learn Alg I well, then geometry. Finally combine Alg II and Precalculus because they are very similar. Precalculus and a review of Alg II, trigonometry, and a small introduction for single variable Calculus. Good Luck!

May I ask why you would like to learn Calculus (what kind of Calculus - single var, multi var?) as a ninth grader though?