Should I skip Pre-Cal next year?

[AverteProxy]

Junior in Highschool, and I'm only in Algebra 2 because my school system is stupid. (take algebra 1 in 7th grade, again in the 8th grade because my school doesn't have Geometry for 8th graders, and then come 9th grade, I was told that the Geometry classes were full and I'd have to repeat Algebra 1 AGAIN)

And I really think I can do AP Cal BC. I have taken Physics B, so I think that qualifies me on just about all of the AP Cal BC prerequisites (Algebra, Trig, Geometry). I am currently passing Algebra 2 with a 101 average (to be honest though, I literally do nothing but sleep in that class. I honestly find it to be a joke of a challenge. I sleep in class, do my homework, come in, ace the tests, and continue to sleep.)

I have a 98 average in AP Physics B, 103 with the AP points. (want to be physicist later on in life).

Now - the question is - do you think I should skip pre-cal, and if you think I shouldn't I have no problem studying it over the summer on my OWN TIME so that I am ready for AP Cal. So should I do it?

 

[micromass]

You need some knowledge of trigonometry. Whether you get that from taking trig or taking pre-calc, that doesn't matter. I'd say that is about the only prereq you need for calc.

If you feel comfortable enough that you are able to self-study the theory in the summer, then go for it.

 

[AverteProxy]

You need some knowledge of trigonometry. Whether you get that from taking trig or taking pre-calc, that doesn't matter. I'd say that is about the only prereq you need for calc.

If you feel comfortable enough that you are able to self-study the theory in the summer, then go for it.

Well if I were to quote my Physics teacher 'Physics is 90 percent Triangles' I would think that I am comfortable with the sohcahtoa and inverses of those, etc, from physics. Do you think it's enough to make up for skipping pre-cal?

 

[micromass]

Well if I were to quote my Physics teacher 'Physics is 90 percent Triangles' I would think that I am comfortable with the sohcahtoa and inverses of those, etc, from physics. Do you think it's enough to make up for skipping pre-cal?

Triangles aren't needed in calculus (that doesn't mean you don't need to know them!). So for calculus, you don't need sohcahtoa and such. You need to have a very good grasp on trig identities.

You should know things like

$$\sin^2(x)+\cos^2(x)=1$$

$$\sin(2x)=2\sin(x)\cos(x)$$

$$\cos(x-y)=\cos(x)\cos(y)+\sin(x)\sin(y)$$

and so on.

These identities will be crucial in solving certain integrals.

Also make sure you're comfortable with the inverse trig functions.

 

[AverteProxy]

Triangles aren't needed in calculus (that doesn't mean you don't need to know them!). So for calculus, you don't need sohcahtoa and such. You need to have a very good grasp on trig identities.

You should know things like

$$\sin^2(x)+\cos^2(x)=1$$

$$\sin(2x)=2\sin(x)\cos(x)$$

$$\cos(x-y)=\cos(x)\cos(y)+\sin(x)\sin(y)$$

and so on.

These identities will be crucial in solving certain integrals.

Also make sure you're comfortable with the inverse trig functions.

I know those already from lurking around on the internet, haha. I've picked up a lot of things on the internet, and honestly think I can do it. Thanks for the help

 

[micromass]

I suggest you get the book "basic mathematics" by Lang. Try to self-study that over the summer. The book contains everything you need to know before taclking calculus.

 

[Stengah]

What about AP Calc AB? That would be the most important prerequisite for AP Calc BC.

 

[phoenix:\\]

You need some knowledge of trigonometry. Whether you get that from taking trig or taking pre-calc, that doesn't matter. I'd say that is about the only prereq you need for calc.

If you feel comfortable enough that you are able to self-study the theory in the summer, then go for it.

I actually learned a bit of trigonometry whilst taking calculus. I didn't need to take a course or have any prior trigonometry knowledge before taking calculus.

 

[eumyang]

What about AP Calc AB? That would be the most important prerequisite for AP Calc BC.

That's not necessarily true. In some schools there are tracks within the honors math track, where the really strong students could go straight from Precalculus to AP Calc BC, and the not-as-strong students (but still ahead of the students in the "regular" track) would go from Precalculus to AP Calc AB.

After all, the "A" in Calculus AB stands for Precalculus topics. (The "B" stands for the 1st semester of calculus, while the "C" in Calculus BC stands for the 2nd semester.**)

**Off topic: The MAA Committee on the Undergraduate Program in Mathematics (CUPM) in the 1960's made recommendations for a general curriculum in math. Among the recommendations were courses they called Mathematics 0, Mathematics 1, and Mathematics 2.
Mathematics 0 -> Precalculus
Mathematics 1 -> 1st semester of calculus
Mathematics 2 -> 2nd semester of calculus

When the AP Calculus Development Committee considered how to split the existing course, they largely followed the CUPM model. The basic course would include the precalculus material from Mathematics 0 and assume that the students had mastered the general overview of calculus of Mathematics 1. The more advanced course would cover both Mathematics 1 and Mathematics 2. They may have briefly entertained the notion of calling these courses Calculus 0-1 and Calculus 1-2, but recognizing that the numbers might get confused with AP scores, they instead settled on Calculus AB and Calculus BC.

(http://www.maa.org/columns/launchings/launchings_05_10-3.html)