Pre-calculus is a course or a set of courses designed to bridge the gap between easier classes such as algebra and trigonometry with more advanced courses like calculus. We will explore the difficulty of a typical pre-calculus course and help you answer any questions that you may have about the subject.
Is Pre-Calculus Hard?
Pre-calculus is quite hard. The jump in difficulty from algebra II to pre-calculus is significant and far from easy. Students usually find pre-calculus to be a difficult class because it requires strong mastery over your algebraic skills and has a large number of unrelated topics.
Like all other math courses, pre-calculus builds on the concept from earlier courses. As a result, you must have a strong understanding of algebra I, geometry, algebra II as well as basic concepts such as fractions and number operations.
The dual challenge of learning new concepts and mastering your algebraic skills at the same time is what makes pre-calculus really hard. Since the equations become more complicated you will need to constantly improve your algebraic abilities in simplifying problems.
The overwhelming syllabus of a pre-calculus course can be quite deterring. In high school, pre-calculus is taught over multiple semesters since the syllabus is too large by high school standards to condense in a single term.
Pre-calculus typically has the following topics:
- Basic Functions
- Families of Functions
- Quadratic Functions
- Rational and Radical Functions
- Exponential and Logarithmic Functions
- Roots and Rational Exponents
- Systems of Equations and Inequalities
- Trignometric Functions and Identities
- Real and Complex Numbers
- Complex Planes
- Two and Three Dimensional Vectors
- Sequences and Series
- Probability and Probability Distributions
- Introductions to Limits, Continuity, Derivatives and Integrals.
As you can see for yourself learning all these topics, many of which you are unfamiliar with is an uphill task. Luckily many of the topics are not taught in great detail which makes the difficulty of pre-calculus a little more manageable.
This is especially true for topics such as Limits, Continuity, Derivatives, and Integrals which are only introduced at this level. Courses such as Calculus I and Calculus II will further your understanding and application of these concepts.
Another aspect that makes pre-calculus challenging is that most of the topics are largely unrelated at the high school level. Our brains remember things by association. When concepts are unrelated we need to exert more effort to memorize the things being taught in class.
For instance, matrices, probability, polynomials, and exponential functions have little in common at the high school level. In college, these topics are taught as separate courses which makes it easier to relate between things.
Linear Algebra builds on the concepts of matrices whilst probability is taught under the umbrella of statistics in college.
What is the Hardest Part of Pre-Calculus?
The hardest part of pre-calculus is mastering difficult, challenging, and independent topics such as exponential and logarithmic functions, complex numbers, three-dimensional vectors, limits, and trigonometric functions and identities.
Why is Pre-Calculus So Hard?
Pre-calculus is so hard because it requires you to work on your algebraic skills whilst learning largely unrelated material at the same time. The enormous syllabus in pre-calculus will be a big test for your ability to learn quickly and efficiently.
Is Pre-Calculus Harder than Calculus?
Pre-calculus is equally as hard as calculus. Although calculus is more advanced and complex it is not necessarily more difficult. The jump in difficulty from algebra II to pre-calculus is similar to the increase in difficulty between pre-calculus and calculus.
Although, both pre-calculus and calculus are moderately hard courses, students find them difficult due to different reasons.
Calculus generally focuses on a few topics but they are taught with great detail and intensity. Pre-calculus divides its attention between a plethora of unrelated topics but none of them are taught in great depth.
This explains why calculus and pre-calculus are almost equal in terms of difficulty. However, this may not be the case when higher-ranked universities add rigorous proof to their calculus courses. In such cases, calculus courses are definitely harder than their pre-calculus counterparts.
Is Pre-Calculus Easier than College Algebra?
Pre-calculus is not easier than college algebra. College algebra is quite similar to high school-level algebra courses. Generally, pre-calculus is more advanced and difficult since it contains additional topics such as trigonometry which are not taught in college algebra.
Should I take Calculus without Pre-calculus?
Ideally, you should not take calculus without taking pre-calculus because it builds on the ideas of prior courses such as geometry, algebra I, algebra II, and pre-calculus. You may find yourself struggling in your calculus courses if your fundamental math concepts are weak.
Pre-calculus has a plethora of topics that are taught over multiple semesters in high school. Pre-calculus is one of the most important classes you can take because it prepares you for the more advanced courses such as calculus. It serves the purpose of easing the transition from algebra to calculus.
If the college you are planning to go to does not list pre-calculus as a pre-requisite for its calculus courses then it may be a good strategy to learn the pre-calculus concepts before the semester starts. This can help you save both time and money.
Is Pre-Calculus Difficult in college?
Pre-calculus is quite difficult in college. This is because there are a large number of unrelated topics in pre-calculus which you will have to learn in a very short period of time and minimal help from the college. These factors make pre-calculus a difficult course in college.
During high school, pre-calculus is taught over multiple semesters allowing the students to fully understand the topics and not feel overwhelmed by them. You will be able to communicate with the teacher more often and not be overburdened by other challenging courses in high school.
Hence, taking pre-calculus in a high school setting is better and more conducive to learning.
Can I take Pre-Calculus without Algebra 2?
Your school will not typically allow you to take pre-calculus without algebra 2 since pre-calculus is more advanced and builds on the concepts from algebra I, algebra II, and geometry. If you are gifted then they may allow this to happen.
Can you teach yourself Pre-Calculus?
You can definitely teach yourself pre-calculus thanks to the amazing resources you may find in the form of Youtube tutorials and lectures, math forums, textbooks, revision guides, and online courses.
In contemporary society, there are ample resources you can use to become an expert in pre-calculus. Pre-calculus is one of the most basic and popular forms of mathematics. Generally, the greater number of people studying a subject the more resources you will find to learn that subject.
The time it takes to learn pre-calculus entirely depends on your schedule, your understanding of earlier courses, and how quick a learner you are. It should take you 2-4 months of daily studying to learn pre-calculus at a reasonable level of proficiency if you were to study it during your summer vacations. It may take you longer if you are attending school.
Although pre-calculus is quite a hard subject; you can definitely master it by revising consistently, doing the problem sets regularly, and using a wide range of resources to facilitate your learning. Pre-calculus will help you ease into college-level calculus, which is why you should ideally study it at the high school level.