How are precalculus and analytical geometry different?

In summary: The student should also be aware that there is a lot of material in Calculus which may be new and difficult for him/her.In summary, the student is stressing about where they should be in their college career and feels like they should have been prepared for the course material. They are taking a precalculus course to make up for what they feel they should have learned in high school.
  • #1
Eclair_de_XII
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I'm really stressed out at where I should be in my college career. In high school, I had taken trigonometry and analytical geometry. But when I went to college and took calculus, I was completely dumbfounded on what was being taught. I felt like I should have known the material. Google tells me analytical geometry and precalculus are not all that different. I think I should have been prepared for the course, yet I wasn't. That's why I'm taking a precalculus course right now.

Is analytical geometry a sufficient substitute for precalculus?
 
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  • #2
Which topics did you feel you should have covered in high school, but didn't? Or, which topics did you have trouble with in calculus?
 
  • #3
The precalculus book I have now looks like it's covered much of the material I've learned in high school.

The first day of class, we jumped straight into limits. I don't really know what subjects I felt I needed to cover in high school, though. I did do excellent in the class, though.
 
  • #4
The official AP Calculus course description gives limits as one of the first topics, and does not mention limits in the prerequisites for the course. This fits with my experience with high school and college math more than 40 years ago. Back then we didn't have a separate "precalculus" course, just two years of algebra, a year of plane geometry, and a year of trig and analytic geometry.
 
  • #5
I wasn't exposed to limits until my first calculus course. Typically you're expected to be comfortable with the unit circle (you should know what [itex]\cos 0[/itex] is, etc.), and algebra techniques (logarithm rules, square roots, exponentials, etc.).
 
  • #6
Limits are nearly always the first topic covered in calculus 1. They're covered in pre-calculus courses sometimes, but typically aren't seen until actually reaching calculus in my experience. Limits really are the foundation of what calculus is, so it's a logical starting point for it. A brief (as in one class period) review of the more important aspects of algebra and trig is sometimes covered as well, but this is quite cursory and it's nothing new.

I never took an official pre-calculus course. I took Algebra I, Geometry, Algebra II, College Algebra, Trigonometry, and then Calculus and Analytic Geometry I...etc.
 
  • #7
Another question: How much of the material I will be learning in trigonometry and analytical geometry will I be using in calculus?

I'm taking a precalculus course right now, and I don't want my knowledge to go to waste.
 
  • #8
Pre-Calculus contains Analytic Geometry. Calculus 1,2,3, will use all of Analytic Geometry from Pre-Calculus.
 
  • #9
Thanks.
 
  • #10
A possible problem is that some Pre-Calculuses in a high school might be weak in some topics; in fact such courses may contain weaknesses at higher institutions also. A high schooler seeing himself through the course the first time maybe won't learn enough of the material too well but still pass with C or B. Repeated exposure at the community college or university would be a strong benefit.
 

What is precalculus and analytical geometry?

Precalculus is a branch of mathematics that focuses on preparing students for calculus by covering topics such as functions, graphs, and trigonometry. Analytical geometry is a branch of mathematics that uses algebraic techniques to study geometric shapes and their properties.

What are the main differences between precalculus and analytical geometry?

The main difference between precalculus and analytical geometry is their focus. Precalculus is focused on preparing students for calculus, while analytical geometry is focused on using algebraic techniques to study geometric shapes.

Do precalculus and analytical geometry use the same mathematical concepts?

Yes, both precalculus and analytical geometry use similar mathematical concepts such as equations, functions, and graphs. However, the way these concepts are applied may be different in each subject.

Is precalculus a prerequisite for studying analytical geometry?

Yes, typically precalculus is a prerequisite for studying analytical geometry. This is because precalculus covers fundamental concepts and skills that are necessary for understanding analytical geometry.

How are precalculus and analytical geometry useful in real life?

Precalculus and analytical geometry are used in various fields such as engineering, physics, and economics. They provide a foundation for understanding and solving complex problems in these fields, making them valuable in real-life applications.

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