How to Pass Calculus

Three Parts:Knowing the CourseLearning the MaterialPassing the Exams

Calculus is a very advanced mathematics class that can be quite difficult for students. A strong fundamental understanding of algebra and trigonometry is essential to succeeding in a calculus course.[1] There is no quick and easy way to pass calculus, but if you put in the time and the effort, you will be rewarded. Attending class, practicing problems, and reviewing your notes regularly (instead of cramming at the end) will ensure your success!

Part 1
Knowing the Course

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    Read the syllabus. Your professor has spent a lot of time putting together the syllabus and for good reason: it is your guide through the entire course. It details exactly what concepts you will be learning, what part of the book the material corresponds to, and when you have homework, quizzes, and exams.
    • The first day of class, add all of the homework due dates and quizzes/exams to your calendar.
    • Use the syllabus to prepare for each class by reviewing the material ahead of time.
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    Talk to students who previously had your professor. Drawing on their knowledge will help you gauge exactly what you need to do to pass the course. These students will know how the tests were formatted, the level of difficulty, and how much you need to study important topics. They might also know whether there are opportunities for extra credit.
    • Ask to see their exams from past years so you can get an idea of what to expect. Work through those problems for extra practice.
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    Know how much homework, tests, and exams are worth. Knowing exactly what percentage of your grade each assignment makes up, will help keep you on track throughout the semester. If you haven’t been doing so well on the quizzes, but the homework is worth the same amount, really focus on doing well with the homework to keep your grades up.
    • Determine how many hours a week you are going to need to truly get the most out of the course and set aside that time in your schedule.
    • Avoid leaving homework and studying to the last minute.
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    Attend office hours.[2] You will likely have both a TA and a professor who have weekly office hours. Both of them are there to help you learn and understand, but if you are uncomfortable talking directly to the professor, seek out the TA for help. Review the material before you go so you can ask concrete, thoughtful questions instead of just saying, “I’m totally lost.”

Part 2
Learning the Material

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    Review basic algebra and trigonometry. At the level of calculus, you are expected to know and understand the basic algebraic postulates and corollaries. You need to be able to manipulate all the parts of formulas and work with variables. You also need to know, understand, recognize and use all the trigonometric functions and their inverses with relative ease.[3]
    • Quadratic equations, factoring equations, and working with systems of equations are essential skills in calculus.
    • The use, applications, and derivations of the trig identities, trig functions, and inverse trig functions are used extensively in calculus.
    • Memorize all the theorems and formulae.[4] Avoid just memorizing them, but try to understand them and how to derive them. On a more challenging test, you might be asked to apply these theorems and formulae more generally, so make sure you take the time to understand how they work.
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    Read the textbook. Before class, look up what material will be covered and read through that section of the textbook.[5] Try working a few problems to check your basic understanding. Reviewing the material beforehand will help you better understand the more complicated aspects of certain concepts in class.
    • Take notes and be prepared to ask questions in class.
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    Listen and take notes in class. It’s important to actively listen in class to what the instructor is teaching. If the instructor asks questions, think about the answer and raise your hand if you know it. Make class time worthwhile. Write down the examples from class and work through them later.[6]
    • Ask questions. If you don’t understand something during the class, don’t hesitate to ask a question. If you’re wondering about it, it’s likely that many of the other students are too.
    • Review your notes frequently. Do you understand why the instructor did what he or she did at every point? If you don't understand your notes or didn't understand the lecture, try to meet with your instructor and get a concrete understanding of what is going on.
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    Learn how to use a graphing calculator. A graphing calculator is a very powerful tool in calculus, but can be intimidating at first. There are many functions and buttons that take time to learn how to use. Many courses will teach you how to use these as part of the class, but take initiative outside of class to learn them as well.
    • Find online tutorials that work through the particular topic you’re learning.
    • Ask your professor or an older student for guidance on how to use the calculator.
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    Do the homework. The key to all math classes is practice. Do all the problems, and make sure you are doing them correctly by checking your answers. Work through particularly difficult problems with a study group or go to office hours.[7]
    • Doing the homework assignments the day of the lecture will be easier since the material will still be fresh in your mind.
    • Avoid leaving homework until the night before it is due.
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    Do more practice problems than what’s assigned. To do really well, don't just do the assigned homework; do all the problems in the back of the book. Teachers generally assign only the minimum amount of homework required to have a basic understanding, but you should seek greater understanding beyond the basics. The more practice you get, the better.
    • Buy the solutions manual for your textbook and work every problem twice. The first time you'll have to look, the second time you should remember.

Part 3
Passing the Exams

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    Form a study group. Get together with some of your friends and meet at least once a week to do homework and study for tests and quizzes. Working through material with other people is very helpful because they might understand something that you are unsure of. On the flip side, you might be able to explain something to them that they don’t understand.
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    Teach the material to your friends. Teaching difficult concepts in a way that your friends will also understand solidifies your understanding of the material as well.[8] You can even teach really difficult concepts to your parents or siblings. If you can explain everything clearly, you have a very strong understanding of the concepts themselves and have not just memorized the material.
    • If you find it difficult to explain something easily, go back and review that topic further until it makes sense.
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    Truly understand the material. It is easy to simply memorize a formula and use it in the problems you have been told to use them; however, this isn’t true comprehension of the material. If you understand the theory behind the formula and how it works, you will be able to apply it to a more complicated problem in a way that makes sense.[9]
    • Focus on each concept, one at a time, and develop a deep understanding of each one to master calculus.
    • This type of insight cannot be developed overnight, you have to really put in the effort and work on it every day.
    • Reviewing the material on a regular basis helps you avoid having to cram at the end. If you truly understand the material, you will be able to apply the formulas and theories in problems more advanced than if you had just memorized the material.
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    Review problems from quizzes and homework. Look over all your theorems and formulas and review the mistakes you made for the tests. Re-work the problems from the homework and any additional problems from the textbook. Look online for extra practice problems that may be more difficult than the ones you’ve previously done.
    • When you get a quiz back, go through it and try to understand where and how you made mistakes. You’ll be less likely to make that same mistake again.
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    Be physically and mentally ready. Don't cram the night before. Get a good night's sleep and eat a good breakfast.[10] Try to keep test anxiety under control by taking a few deep breaths. Remember that you've practiced the material thoroughly and know it backwards and forwards.


  • If your teacher is unwilling or unable to give you the help you need, get a math tutor or speak with another teacher in your math department. Someone will be able to help you.
  • Tutoring can make a big difference in whether you pass or fail. If you're struggling in calculus, attempt to find an individual tutor such as a university student looking for some extra money. If there are no individuals available, be sure to find a tutoring center that teaches advanced level math, for example, Kumon Math and Reading.
  • If you're taking an AP exam, invest in a review book designed for the exam. It will contain lots of extra practice problems and ways to enhance or solidify your understanding. These are especially useful if you have a mediocre teacher.
  • Depending on what textbook you have, many resources are available online. In addition, many people have published their personal calculus notes online that might provide insight/another perspective on difficult topics.

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Categories: Calculus | Surviving Mathematics