If you ever felt overwhelmed by calculus, you’re not alone.
calculus is one of the most difficult math topics, harder than any topic you studied in high school. But you have to understand that calculus is not only hard for you, it is hard for all students.
we’re going to list 13 principal reasons that make calculus very difficult to study and how to overcome that.
1. You didn’t focus enough on precalculus
if you face difficulties comprehending the complexities of limits, derivatives, and integrals you’re likely to have weak foundations in precalculus.
the best choice students have to make and we recommend is to take precalculus in high school. studying precalculus in high school is much better than in college.
2. you have weak foundations
One of the main difficulties that students often face when studying calculus is the lack of a strong foundation in previous calculus courses, such as Calculus 1.
Calculus is a subject built upon fundamental concepts from algebra, trigonometry, and precalculus.
A weak understanding of these concepts can make the learning process more challenging.
A report exposed at Educationweek, showed that the best predictor of earning a B or better in college calculus was a student earning no less than As in high school Algebra 1 and 2 and geometry.
If students haven’t fully grasped key concepts like functions, limits, differentiation, and integration in Calculus 1, they may struggle to comprehend the more advanced topics that follow. for these reasons we find students struggling in advanced caluclus courses like caluclus 2.
Furthermore, we find a lot of students struggling in some basics topics of math like:
- Simplifying expressions
- manipulating equations
these skills are essential to facilitate problem-solving in calculus. If you haven’t developed these skills adequately in previous high school math courses like algebra1 and Algebra 2, we invite you to go back and revisit them.
You may be ignoring some tricks that you should learn in high or even middle school. we encounter this problem with many students who study in college following a stem branch that focuses a lot on calculus.
3. calculus is unexpectedly hard
Many students enter their calculus courses without fully anticipating the level of difficulty and the substantial time and effort required to grasp the subject. As a result, a lot of students fail this course as you will see in the graph below.
this study is made by ‘OneClass’ which exposes the highest topic rates of failure in college.
As you can see college algebra is the first topic with a 50% fail rate followed by calculus 1 with 30%. and finally, Physics 101 which is also one of the hardest physics courses in the third position.
if you have excelled in earlier math courses and think that calculus will come easily to you you’re wrong.
However, you will soon realize that calculus presents unique challenges that demand a significant investment of time and effort to overcome.
Furthermore, calculus introduces new ideas and techniques that may initially seem unfamiliar and complex like:
- differential equations
this topic was very tiring, we’ve been spending hours solving differential equations and making derivatives. making one mistake means you have to repeat the operation from scratch.
so there are no shortcuts when it comes to studying calculus, is going to be difficult and draining. especially when you reach your second-year calculus 3 and differential equations they are so difficult
4 . studying in college is hard
calculus is hard but studying in college makes it more difficult and let me explain why.
this is obvious because college students face many problems the essential ones are:
- Fast-Paced Learning Environment: College courses typically cover a vast amount of material in a relatively short period. This fast-paced learning environment can make it challenging for students to fully grasp and internalize complex calculus concepts, leading to a sense of being overwhelmed or falling behind.
- Time Management: College life often involves balancing multiple responsibilities, such as attending classes, completing assignments, studying, and participating in extracurricular activities or part-time jobs. This can make it difficult for students to allocate sufficient time and effort to understand and practice calculus, which requires consistent and focused study.
- Transition to Independent Learning: College places greater emphasis on independent learning and self-discipline. Students are expected to take responsibility for their own education, seek help when needed, and manage their study habits effectively. you can’t ask a professor as much as you want like you were in high school.
So if you face some hardships you’re not alone, you have to be patient and double your efforts.
5. you don’t know how to study calculus
in college you will have to study calculus on your own which is challenging and has many obstacles, one of the most interesting ones is the absence of feedback.
it means you won’t have immediate access to an instructor or peers who can provide feedback on your understanding and problem-solving approach. instead of spending hours or maybe days stuck at one single math problem, you can easily figure it out in the presence of a professor.
in my earlier days when I was a student, I remember making this mistake, I was learning by solving exercises without giving a lot of focus to notions of a lecture.
but when I go to the exam I discover that most rules I’ve learned by doing were wrong. so if you love to solve the problem on your own this is my message.
Calculus problems are different so you can learn from them without understanding well a lesson. don’t make the mistake of working hard and forgetting to work smart.
6. don’t take advantage of office hours
there is a survey mentioned in Student Voice survey, exposed to 2000 college students showing that students rarely attend office hours.
7. You should have to prepare for it differently
I don’t know if you have taken Ap courses or not, but if you don’t I can say that you missed a lot.
Taking AP courses is crucial for preparing for calculus. They provide a solid foundation in advanced math, especially pre-calculus topics.
According to ‘Educationweek‘, 800,000 students nationwide take calculus in high school, which is 15% of all high schoolers, and nearly 150,000 take the course before 11th grade.
AP courses cover a wide range of calculus topics, like limits, derivatives, and integrals, allowing you to explore deeply.
By performing well on the AP Calculus exam, you may be able to receive college credit, allowing you to bypass introductory calculus courses in college like Calculus 1. This not only saves you time but also enables you to enroll in more advanced and specialized math courses earlier in your college career.
if you didn’t take the course, is not the end you still have a chance to succeed without it, you just have to push much effort to align with students who have taken the Ap course.
for the student who is still in high school, I will tell them that there is an alternative to the Ap calculus course which is an honors calculus each one has its own pros and cons.
8. you have limited time to study calculus
College calculus courses are condensed. Typically students take all calculus courses in the first 2 years of college, calculus 1 and 2 in the first year, in addition to calculus 3 in the second year.
this timeline is condensed and not enough for students to prepare easily, especially when they have other obligations like part-time jobs or other activities.
for this reason, I highly recommend that high school students take precalculus in high school before college this is very helpful and future headache relief.
9. the transition from algebra to calculus is not fluent
you are used to algebra since you’ve been in middle school, which means studying only algebra for 7 or 8 years before you discover What is calculus.
so studying something new is not easy, especially calculus. many students get terrified when they see signs like these:
so it is a matter of time and energy you devote. don’t waste your time trying to find shortcuts to study less or understand calculus without suffering, because you will need.
10. bad professor makes caluclus very hard as it seems
I remember in my last high school year, we had one of the most terrible professors in math that I’ve seen. She wasn’t explaining at all, and when we ask him about some things we don’t understand she in most cases repeats this expression.
I don’t have to go back and explain to you what you missed in precedent years
I remember the first score of the first exam in our class was (7/20) kind of a C-. One of my colleagues was very brilliant in math, and he was shocked. at that moment he was thinking of completely dropping out of school.
for me, I had (0.5/20) which is nothing or maybe say I got 0. I remember this year was one of the most terrible years I lived in my high school life.
you don’t have to be living the same experience, but if you feel that you don’t catch up with your prof maybe is time to change or diversify using other resources like the internet. maybe go and check these following resources and see where you will find yourself.
- Khan Academy (https://www.khanacademy.org/):
- MIT OpenCourseWare (https://ocw.mit.edu/):
- Coursera (https://www.coursera.org/):
- Paul’s Online Math Notes (http://tutorial.math.lamar.edu/):
- Calculus.org (http://www.calculus.org/):
11. math is not for you
I will not be discouraging but not all people are going to work as engineers or physicists, self-esteem is important in that case. if you work very hard and do all that matters but still without reasons maybe is a time of major shift.
this message is specially dedicated to people who are in their first year studying some difficult majors like math or physics. or maybe the people their parents forced them to do stem because of money. I’m going to tell you that a math, engineering, or physics degree is not going to make you rich.
if your primary focus is money and you don’t like your major, you are wasting your time and risking getting into debt without even getting a degree.
At that moment you have many choices, you could shift to a computer science major is not an easy major, but is easier than math or physics majors. or you could learn to code and get a high-salary job without even having a degree.
12. people skip trigonometry
I’ve heard a lot of people saying that they don’t like or hate trigonometry. They don’t give it importance in precalculus courses which cost them a lot impacting badly their grades in calculus exams.
listen this is what I’m going to say.
trigonometry is everywhere in calculus you will find it in:
you have to be aware of trigonometry functions especially the applications of cosine, sine, and tang you can’t skip them at all.
if you want to discover more about this subject I wrote a details article that differentiates between calculus and trigonometry, you could check it to know what I’m talking about.
13. Calculus is hard because it means explaining other harder topics
Calculus is used in the most advanced sciences, for instance, in Physics calculus is applied to a wide range of advanced applications, such as classical mechanics, electromagnetism, quantum mechanics, and relativity.
even though there is a specific course called calculus-based physics students take to focus on these topics.
sometimes we find a lot of students asking between math and physics but they don’t know that physics is totally based on math, especially caluclus.
I’ve written a good post about this topic that includes also a video comparing math and physics you will find it by clicking the previous expression.