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Home » Calculus vs Precalculus, all you need to know about

Calculus vs Precalculus, all you need to know about

if you ask what is the difference between precalculus and calculus, this is going our topic of today.

In our post, we’ll discover The differences between calculus and precalculus, and also determine which is hard calculus or precalculus.

In addtion respond to some frequent questions students ask about this subject. 

have a fun reading

The differences between calculus and precalculus

Typically pre-calculus is a subject on a topic that students take in the 12th grade in high school while calculus topics are taught thoroughly in college including calculus1, calculus 2, and calculus 3.

Precalculus is a course that students take to prepare for calculus and linear algebra courses in college this course is made for stem Majors meaning branches like engineering mathematics and physics. So it teaches the basics of what students need to know and focus on like algebra and geomtry.

In the pre-calculus course, students study algebra 2 courses combined with some Basics calculus introductions like Limits and continuity Which only represent the subject that belong to calculus.

you could read this related article: algebra 2 vs precalculus.

There are some exceptions where Calculus 1 can be also taught in the last year of some high schools Especially for some math majors,  but in general, students take calculus until they get their first year in college.

So if we compare precalculus and calculus, there is a big difference in complexity because so many people confuse and consider precalculus as precalculus which is not right at all. Calculus is more difficult and complex than precalculus because the students spend their homes 4 years of degree studying all the components of calculus that are:

Multivariable calculus is the most difficult calculus which is advanced so much compared to precalculus. Many students struggle a multivariable calculus as the toughest math college students study in college.

can I take calculus 1 without precalculus?

It is possible to take calculus 1 without precalculus, but it is a bad decision that will reflect your level in Calculus 1 and risk failing it. Most students take pre-calculus so they can build a solid foundation and not struggle and Calculus 1.

Taking calculus 1 without a pre-calculus course Would it be so hard because you will need to study the precalculus subjects and calculus 1 topics at the same time which is not encouraging at all.

Taking a precalculus course has many advantages to preparing for calculus 1:

For instance, in precalculus, you will study Limits and continuity which is one of the principal subjects taught in calculus 1. So you will earn a time when you go to college and not study this subject again from scratch.

In addtion, the precalculus course offers some other courses that will be useful like trigonometry and functions you should be good at before taking calculus 1.

So very difficult to take calculus 1 without a precalculus course, is totally to avoid.

Is calculus 1 harder than precalculus?

yes, calculus 1 is harder than precalculus, calculus 1 is more difficult and challenging for students. Calculus 1 includes the most difficult math topics like limits and continuity, derivatives, integrals, and even in some courses differential equations. These topics require a good understanding and critical thinking ability.

precalculus is easier, In precalculus, students study the elementary topics of high school like algebra 2, trigonometry, and some introductory subjects of calculus. So calculus 1 is way harder than precalculus.

the hardest topics that students study in calculus 1 are 3 :

1 – limits and continuity

if you study precalculus you will have the advantage to study early this topic as we mentioned before in our article. This is one of the principal reasons why precalculus is so important to study for calculus 1.

limits and continuity, are mathematic methods that help to determine where the function is approaching a certain number. we’re going to give a simple real-life number of the use of limits and continuity to have an idea :

For instance, the limits function can help us to determine the maximum speed a car can reach at a certain point on a road.

limits functions are written like this forme below.

what makes limits a little bit hard is the number of rules you should memorize to resolve these equations. It also requires some critical thinking and math technics to solve limits or determine continuity functions.

the key of understand limits is to know how to apply the correct theorems to these subjects.

2 – derivatives 

Derivatives are the second complex subject you will be facing in calculus 1. derivatives are complicated and also require knowing all different types of functions such as polynomials, trigonometric functions, exponential and logarithms, and so on.

Because you’ll be asked to make a derivative for all the types of functions, each one needs to apply different rules that suit.

As a simple definition derivative is a mathematics method to study changes. For instance, when you calculate a speed of a car you use a derivative function like this form below:

this was a simple approximation of what is a derivative, if you want more details you could find them in this link .

3 – integrals 

The last and the most complicated subject you will be facing is integrals. Integral is a mathematics method engineer mathematicians use to determine surfaces and volumes of complex objects that we could not apply the regular rules to calculate.

calculate the air

For instance, there is no official rule to calculate this shape. So the only way to do that is to divide a subject into parts and calculate each part alone, this is the job of integrals.

what makes integral the most complex subject in calculus 1, is that is it based on derivatives of the last topics we talked about. If you suck at derivatives automatically you will be hopeless and weak in integrals.

not only that, integrals require having good and solid foundations in previous courses, especially precalculus or algebra 2.

So if you succeed to follow up with a professor in integrals that means you’ve done good in all the previous high school courses like algebra 1, algebra 2, and geometry. Integrals testes all your math capabilities acquired during the previous years of studies you’ve gone through.