Precalculus topics necessary for Calculus

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Discussion Overview

The discussion revolves around the necessary precalculus topics that should be understood before transitioning to calculus. Participants express concerns about the content and pace of their precalculus classes, with a focus on the importance of mastering specific concepts rather than reviewing algebra.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants suggest that a solid understanding of algebra and trigonometry is essential for success in calculus.
  • One participant expresses frustration with the slow pace of their precalculus class, feeling that it focuses too much on algebra review rather than new material.
  • Another participant questions the necessity of a precalculus course, suggesting that it may simply delay the learning of calculus.
  • Some participants propose that limits and trigonometric identities are key concepts to master before studying calculus.
  • A participant mentions self-studying calculus and indicates that they are willing to review any necessary precalculus topics as needed.
  • One participant recommends finding a precalculus textbook aimed at college students to cover more advanced topics, including limits.
  • Another participant shares their experience of self-studying calculus and suggests that encountering new material in calculus is common.
  • Some participants reflect on historical educational paths, noting that precalculus is a relatively recent addition to high school curricula.

Areas of Agreement / Disagreement

Participants express a mix of agreement and disagreement regarding the necessity and content of precalculus. While some emphasize the importance of specific precalculus concepts, others question the overall structure of the course and whether it effectively prepares students for calculus.

Contextual Notes

Participants highlight limitations in their current understanding of precalculus topics and express uncertainty about what specific concepts are essential for calculus. There is also mention of varying educational experiences and curricula over time.

Who May Find This Useful

This discussion may be useful for high school students preparing for calculus, educators seeking to understand student concerns about precalculus, and individuals interested in the relationship between precalculus and calculus concepts.

Ritzycat
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Hello. I'm a high school senior, currently taking a Pre-Calculus class. I am having little trouble understanding the material and I feel the class moves too slowly for my liking.

I want to learn more outside of class on my own, but I don't want to be learning Algebra review. I have heard from other students and people that Pre-Calculus is mostly algebra review - it just contains more trig concepts, and a brief introduction to calculus.

What do I need to understand in pre-calculus before I can move onto calculus?
 
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Ritzycat said:
Hello. I'm a high school senior, currently taking a Pre-Calculus class. I am having little trouble understanding the material and I feel the class moves too slowly for my liking.

I want to learn more outside of class on my own, but I don't want to be learning Algebra review. I have heard from other students and people that Pre-Calculus is mostly algebra review - it just contains more trig concepts, and a brief introduction to calculus.

What do I need to understand in pre-calculus before I can move onto calculus?

Since it's pre-calculus, probably everything.

In order to do well in calculus, you've got to be good at algebra and trigonometry. If your pre-calculus class introduces you to the concept of a limit, that would be worthwhile learning, because calculus uses a lot of limits.
 
Thank you for your response.

I have a very solid hold of algebra and geometry. We are currently studying trigonometric functions and identities which I understand to be important in calculus. However, the vast majority of this class consists of algebra review that I think is unnecessary because I already understand algebra very well.

I want to study the concepts that are very important for calculus, because the class is very light on actual new material. It is moving very slowly. Limits aren't until next semester I think. We spent about 2 weeks learning how to graph trigonometric functions, something I had under my belt at the end of last year. I memorized and know how to apply the trigonometric identities after a few days but we're taking weeks to get through them. I want to know what the distinctively Pre-Calculus concepts I need to master to have a solid hold to begin studying calculus on my own. Not necessarily algebra, because I know it like the back of my hand. I think if I can study the right material on my own I will be able to start studying calculus sooner - at least so I can have a good foundation when I take the course itself in college.
 
Why don't you just go ahead and start studying calculus? If you are as solid at algebra, geometry, and trig as you claim to be, then you should be ready.
 
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Because I am not sure if I am ready or not. I do not know every topic that is covered in the class: Pre-Calculus. I am seeking advice from people who know more about Pre-Calculus than I do because they can probably provide some meaningful advice.

What are all of the brand new, absolutely brand new concepts learned in Pre-Calculus? I do not want to move onto Calculus if I don't know everything in Pre-Calculus. I know Algebra and Geometry, as I have already taken those classes. I want to study new Pre-Calculus material, but that is not what we are doing in class. We are reviewing algebra, which doesn't make sense to me because this is a Pre-Calculus course, not an algebra course.

I don't know how else to say it. I'm not trying to be a smartie pants or hurt anyone's feelings. I just want to know what specific pre-calculus concepts are required for calculus. Not algebra or geometry - I have already taken algebra and geometry.

Examples of brand new concepts I have actually learned so far in Pre-Calculus: Arithmetic/geometric series and trigonometric identities.
 
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In olden times, a student took geometry, trigonometry, and advanced algebra, then on to calculus. Pre-calculus is a relatively recent addition to the HS curriculum. IMO, it just delays the inevitable.

Check out this page:

http://avconline.avc.edu/jdisbrow/whymath.html

Nobody knows if they are ready to take a particular course beforehand. You do your prep work and then forge ahead.
 
Well, I guess I'll give it a shot. If I come across something I don't understand in calc I'll try to review from prior knowledge.
 
Ritzycat said:
Well, I guess I'll give it a shot. If I come across something I don't understand in calc I'll try to review from prior knowledge.

You'll come across plenty of new stuff in calculus that you've never seen before.

In HS, I did some self-study of basic integration and differentiation, I took a calculus class as a senior, and then the summer after I graduated, I took another short course. When I got to freshman calc at college, I had no trouble the first semester, and the second semester went smoothly as well.
 
Well of course, I mean if I come across something in calc that would have required prior knowledge that I do not understand I can go learn that topic.

That is also why I want to self-study, so I can move more smoothly in college! And also a little bit because I have nothing to do this weekend :^)
 
  • #10
Ritzycat,
Find a Pre-Calculus textbook directed at college and university students. The material will go beyond your typical "Intermediate Algebra" for the Algebra topics, and the material will include nearly a whole course-worth of Trigonometry. Good Pre-Calculus books often also include a brief but intense study or introduction to Limits of functions, and Limits of expressions.
 
  • #11
SteamKing said:
In olden times, a student took geometry, trigonometry, and advanced algebra, then on to calculus. Pre-calculus is a relatively recent addition to the HS curriculum. IMO, it just delays the inevitable.
That's pretty much how I did it 40 years ago, but we added analytical geometry between a second year of algebra and calculus. The analytical geometry was the front end of the calculus course.
 
  • #12
Astronuc said:
That's pretty much how I did it 40 years ago, but we added analytical geometry between a second year of algebra and calculus. The analytical geometry was the front end of the calculus course.

By the time I was in school, analytical geometry was included in the algebra courses almost from Day 1. It was taught alongside linear equations and conic sections in a pretty seamless fashion.
 
  • #13
I've begun studying the Limits chapter in the back of my book. There is also a chapter on 3-dimensional geometry, something I was never exposed much to. Not sure if it's important or not, but I'll go through that chapter too nonetheless.
 

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