Calculus is an advanced branch of mathematics that can be quite difficult for students. To be successful in a calculus course, a good understanding of the fundamentals of algebra and trigonometry is essential. There is no quick and easy way to pass a calculation, but if you put in the time and effort, you will be rewarded. Attending classes, practicing problem solving, and reviewing your notes on a regular basis (rather than trying to learn everything at the last minute) will be the pillars of success!
Part 1 of 3: Know the characteristics of the course
Step 1. Read the syllabus
Your teacher has spent a lot of time designing the syllabus, and for good reason, as they will guide you through the entire course. It details exactly what concepts you are going to learn, what part of the book the material corresponds to, and when you will have homework, practical work, and exams.
- On the first day of school, copy all the due dates for assignments and practical assignments or exams on your calendar.
- Use the program to prepare for each class, reviewing the material in advance.
Step 2. Talk to other students who have had your teacher
Take advantage of their knowledge to assess exactly what you need to pass the course. These students will know what is the format of the exams, the level of difficulty and to what extent it is necessary to study the most important topics. They can also tell you if the teacher provides opportunities for extra points.
Ask them to show you their exams from previous years to get an idea of what to expect. Try to solve those problems so you can practice more
Step 3. Analyze how much homework, practical work and exams represent in your final grade
By knowing exactly what percentage of your grades each practical assignment represents, you will be able to follow up throughout the semester. If your work hasn't done very well, but your homework is worth the same, focus on doing your homework well to keep your grades up.
- Determine how many hours a week you will really need to get the most out of the course and set aside that amount of time in your schedule of activities.
- Avoid leaving homework and studying until the last minute.
Step 4. Attend office hours
It is possible that in addition to the full professor, there is an assistant professor and both offer consultation hours. Both teachers will be there to help you learn and understand, but if you don't feel comfortable speaking directly with your teacher, ask the assistant teacher for help. Review the material before you go so you can ask smart, concrete questions instead of just saying "I'm completely lost."
Part 2 of 3: Learn the Material
Step 1. Review the basics of algebra and trigonometry.
It is assumed that if you study calculus you should already know and understand the basic algebraic postulates and corollaries. You have to be able to master all parts of the formulas and work with variables. You should also know, understand, identify, and use all trigonometric functions and their inverses with relative ease.
- Quadratic equations, factoring equations, and systems of equations are all essential topics you must know in calculus.
- In calculus, trigonometric identities and functions, inverse functions, their application and their derivations are widely used.
- Memorize all the theorems and formulas. Avoid just memorizing them and try rather understand them and learn to derive them. On difficult exams, you may be asked to apply those theorems and formulas in more general cases, so be sure to take your time to understand how they work.
Step 2. Read the textbook
Before each class, find the material to be used and carefully read that section in the textbook. Try to solve some problems to check your knowledge. Reviewing the material beforehand will help you better understand the more complicated aspects of certain topics in class.
Take notes and be prepared to ask questions in class
Step 3. Listen and take notes in class
It is important to actively listen to what the teacher is trying to teach in class. If the teacher asks questions, think about the answer and raise your hand if you know it. Take advantage of class time. Write down the examples they see in class and try to solve them later.
- Make questions. If you don't understand something during class, feel free to ask questions. If you're confused, chances are a lot of the students are too.
- Check your notes frequently. Do you understand why the teacher did what he did at each step? If you do not understand your notes or have doubts about what you read, try to meet with your teacher to explain specifically what he did.
Step 4. Learn to use a graphing calculator
Graphing calculators are a very powerful calculus tool, although they can be intimidating at first. There are many functions and buttons that may take a while to learn. Many courses teach you to use them as part of class, but it would also be good if you have initiative to learn how to use them outside of class.
- Look online for tutorials that develop the particular topic you are learning.
- Ask your teacher or a former student to help you learn to use the calculator.
Step 5. Do your homework
In all math classes, the key is practice. Solve all the problems and make sure you are doing them right by checking the answers. Try to solve particularly difficult problems with a study group or with the help of your teacher during office hours.
- Do your homework the same day as class, so it will be easier for you since the material will be fresh in your mind.
- Avoid leaving homework for the night before your due date.
Step 6. Solve more practical problems than assigned
To do really well, don't settle for the assigned task; solve all the problems in the back of the book. Teachers generally assign only the minimum amount of homework that is required to achieve a basic understanding, but you might want to set out to learn beyond the basics. The more you practice, the better.
Buy the solutions manual from your textbook and try to solve each problem twice. The first time you will have to look. For the second you will have to remember it
Part 3 of 3: Pass the Exams
Step 1. Form a study group
Find a couple of friends and get together at least once a week to do homework and study for tests and practical assignments. Reviewing the material with other people is very useful because other people might understand things that are not very clear to you. On the other hand, you could explain things to them that they don't understand.
Step 2. Explain the material to your friends
Teaching difficult concepts to your friends in a way that they understand will also reinforce your knowledge of the material. You can even teach really difficult concepts to your parents or siblings. If you can explain the concepts clearly, it means that you have understood them very well and that you have not simply memorized the material.
If you find it very difficult to fluently explain a topic, re-read the material and go over that topic in greater depth until it makes sense
Step 3. Really understand the material
Memorizing a formula and using it in the problems they tell you is easy. However, this does not mean that you have really managed to understand the material. By understanding the theory behind the formula and how it works, you can apply it in a way that makes sense to more complicated problems.
- Concentrate on each concept, one by one, and try to develop a true understanding of each topic to master calculus.
- This type of analysis cannot be achieved overnight. You need to put in effort and work at it every day.
- Reviewing the material regularly will help you avoid cluttering your head with knowledge at the last minute. If you really understand the material, you will be able to apply the formulas and theories in more advanced problems much better than if you simply memorize it.
Step 4. Review the problems of practical work and exams
Go over all the theorems and formulas, and review the mistakes you made on the tests. Solve your homework problems and additional textbook problems again. Search online for problems to keep practicing and try to make them more difficult than the ones you have solved before.
When corrected papers are returned to you, review them and try to understand where and why you made a mistake. That way you will be less likely to make the same mistake again
Step 5. Prepare yourself physically and mentally
Don't try to crowd your head with knowledge the night before. Get a good night's sleep and eat a good breakfast that day. Try to keep your test anxiety under control by taking deep breaths. Remember that you have practiced a lot and you already know the material perfectly.
- If your teacher won't or can't help you with what you need, get a math tutor or talk to another teacher in the math department. There will always be someone willing to help you.
- Mentoring can make the difference between passing and failing. If you are struggling with calculus, try to find an individual tutor, for example a college student who wants to earn extra money. If you can't find an individual tutor, be sure to find a tutoring center where they teach math at an advanced level, for example Kumon Math and Reading.
- If you are taking an advanced position test, invest in a book that is specially designed for that test. In it you will find additional practice problems and methods to improve or strengthen your knowledge. These books are especially helpful if you have a mediocre teacher.
- Depending on the textbook you use, you can find many resources online. Also, many people post their calculation notes online. These notes may give you deeper insight or another perspective on difficult topics.