Is Precalculus Harder Than Calculus

[Maricel Fergason]

Precalc, short for pre-calculus, is a course that introduces students to fundamental mathematical concepts such as algebra, trigonometry, and functions. Calc, short for calculus, is a more advanced course that builds upon these concepts and explores topics such as limits, derivatives, and integrals.

Pre calc is considered harder because it requires a strong foundation in algebra and trigonometry, which can be challenging for some students. Additionally, pre calc covers a broader range of topics, whereas calc focuses more on specific applications of calculus.

It is highly recommended to take pre calc before taking calc, as pre calc provides essential knowledge and skills that are necessary for success in calc. However, some students may be able to skip pre calc and take calc directly depending on their math abilities and the requirements of their school or program.

Some tips for succeeding in pre calc and calc include practicing regularly, seeking help from teachers or tutors when needed, and staying organized with notes and assignments. It is also important to have a strong foundation in algebra and trigonometry before taking these courses.

Pre calc and calc have many real-world applications, such as predicting the trajectory of a projectile, determining the optimal route for a vehicle, and analyzing economic trends. Additionally, many fields, such as engineering, physics, and economics, heavily rely on concepts from pre calc and calc for problem-solving and decision-making.

I just received CD precalculus and was searching the board about scheduling when I came across a post listing the chapters required to complete a credit in advanced math. Thinking that was an interesting option, I remembered that our local ps (on block scheduling) offers algebra 3 class and trig class (total of 2 credits for 2 semesters of work).

Months back, CD informed me that precal usually takes 3 semesters to complete; nevertheless. I've always assumed i would assign only one credit for precal. Now I'm wondering why would I only assign 1 credit??

The only thing that makes this an issue for me is that my ds will most likely attend the state university that is only 45 minutes from our home (since it is the only AR university that offers animal science with pre-vet emphasis) and will be "competing" for scholarships/entry with students who will have credits listed differently.

Personally I see Pre-Calc as a two semester course. This is for the ABOVE AVERAGE HIGH SCHOOL student. Average HIGH SCHOOL students may need to take it over 3 or even 4 semesters. The time difference is not due to content--it is due to the MATURITY of the student!

Well, the stats are in and MANY of those students who were 'ready' for Algebra in 8th grade were NOT ready for Pre-Calc in 11th and really NOT ready for Calc in 12th --yet they were being FORCED to take those courses because Texas requires 4 years of High school math to graduate.

In my experience (nearly 20 years working almost exclusively with homeschoolers) I have seen far too many students who were pushed/rushed into Algebra too soon. While many 7th and 8th graders are able to do Algebra 1--it is because they can 'see' the answer (problems are usually too easy)--they are not learning how to LOGICALLY work through steps... Most Algebra 1 programs are written with 'simple' problems so that the students can easily check their logic--when they work problems 'mentally' instead of on paper they are MISSING THE LOGIC.

As far as 'credit' awarded goes... would you award 2 credits for a student who takes 2 years to complete Algebra 1--because they personally had difficulty and NEEDED to move slowly? Most would not (I did not with my oldest dd--she only earned 1 credit over 2 years). Pre-Calc is no different. If the student is NOT mature enough to complete the course in 1 year (already an exception made for high school students) then why should they receive more credit? (at the college level it is often a one-semester credit).

Personally I feel that we are forcing too many students into higher maths too soon... programs are being watered down and many students consider themselves to be math failures--when they may have become MATH LOVERS if they had been given that extra year or two to mentally mature...

The students complete precal in one year (alg 3 and trig)- but they get two credits- which I think is crazy. I guess I'm seeing the impact of 4x4 block scheduling. They take 8 credits/ year. (Our years are FULL with 6.5 credits!) I am amazed at how many "credits" some of these kids graduate with. My ds's friend, a senior this fall, is scheduled for SIX AP classes.:001_huh:

I agree with you, Jann, that Pre-Calc should be a 2-semester/1 credit course. However, my two oldest, both above average math students, each took 3 semesters to complete the CD course. They worked over the summer, and on into the fall of the next year. It is a time-consuming course.

I'd consider dd to be an above average student, but she will take 1 1/2 to 2 years to cover pre-calc. She started algebra very young (grade 6) and took a year and a half to complete that. She did Jacobs geometry comfortably in a year, and struggled to do Foerster's alg II in a year. (In hindsight, we should have slowed down at that point.) The beginning of Foerster's Pre-Calc really slowed her down--and I decided to let her take as much time as she needed. I'm still not sure what we'll do about credits--but I wanted to chime in that above average, but young, students may quite reasonably take more than a year to cover pre-calc.

In a homeschool setting, one tends to do more of the problems, and cover all of the sections in the book. I know that material in a school setting would be skipped due to time. I also think it depends which text is used--some are more cut and dried, some require a lot of thought. The division of topics between algebra II and pre-calc varies too.

I've also been pondering the best approach to young students. I'm sure dd would have done algebra 1 more quickly, and algebra II more easily, had she been older. On the other hand, she has learned a lot about how to work hard through math--something she hasn't had to do for all of courses. Having worked hard, she now feels quite a bit of satisfaction that she is able to work on the last bit of trig without much help from me. We held ds off a bit--he started algebra I in grade 7. He blasted through Jacobs algebra, only slowing down at the very end. He may well need to slow down for algebra II--but I don't think it would have been a good idea to delay algebra I any longer. We'll just slow down when he needs to. Obviously this would be more of an issue in school, where a teacher can't slow down just because a younger child needs more time to mature.

This is a great post! This also lines right up with what my db, who teaches post secondary Physics (and at one place taught some Calculus) who said that most students get to university/college lacking logic and thinking skills. The example he gave was Calculus. He said that students who could factor beautifully in Algebra get to Calculus and can't see when to factor because they don't know why they have to factor.

I agree about most Algebra 1 texts having easy problems. My eldest was ready for Algebra 1 very early. However, after letting her do it slowly for 2 years (she was only 11), I had her redo it with a more rigourous course. She is a mathy girl, but has still found areas that have challenged her. But, and this is most important, she has learned to understand Algebra better; the theory and the whys. She'll be starting Geometry in grade 9, but we'll see how things go. While her goal is to have Calculus done by the end of hs and I write this here, my attitude is more one of let's see how it goes and how much she truly understands.

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