Calculus is one subject which students love and hate in equal measure. The subject has interesting concepts that are useful in life but is difficult for students to pass. As a student, you must find a way to pass this subject to improve your scores in math. With calculus, the more you practice and employ effective strategies, the more you master and understand the concepts.
If you're struggling to grasp concepts or aiming to improve your performance in calculus, this blog will be a perfect fit for you. We guarantee practical tips and insights to help you achieve your desire. Let's dive in.
What is Calculus?
In simple terms, calculus is the study of change, accumulation and rate change. The change rate can be considered the derivative, while the accumulation can be considered integral. It deals with derivatives, limits, functions and integrals, making it a hard nut to crack among students. Make no mistake; calculus can be eased out if the students know how to work around it. Below are some tips and techniques which, if effectively followed, can help in getting through calculus and allow you to perform well;
Build a Strong Foundation in Calculus
Math is a subject that builds on the previous concept, which is why you must first build a foundation. This is the main reason some students find it challenging. Ensure you don't miss calculus class. Teachers often elaborate and give simplified examples to help students understand concepts better. Getting explanations from your classmates may not be the same as how the teacher explains, as they can easily forget some key information. Be punctual in class and always sit in an area where you can hear what the teacher is saying without straining. Master basic concepts like limits, derivatives, and integrals before trying other complex topics.
Master standard formulas
Many questions, especially those with trigonometric terms, require manipulation and substitution in the function to which an operation is performed to simplify the function. You must know the specific formula to be used in a particular function. Some of these formulas are;
- d/dx sin x = cos x
- d/dx cos x = -sin x
- d/dx tan x = sec2 x , x ≠ (2n + 1) π / 2 , n ∈ I
- d/dx cot x = - cosec2 x, x ≠ nπ, n ∈ I
- d/dx sec x = sec x tan x, x ≠ (2n + 1) π / 2 , n ∈ I
- d/dx cosec x = - cosec x cot x, x ≠ nπ, n ∈ I
- d/dx sinhx = coshx
- d/dx coshx = sin hx
- d/dx tan hx = sec h2x
- d/dx cot hx = -cosec h2x
- d/dx sec hx = -sech hx tan hx
- d/dx cosec hx = -cosec hx cot hx
Remember the definitions
Many students tend to ignore the definition of terms. In some exams like ALEKS, these definitions are important as they are constantly tested, so ensure you are conversant with concepts of each topic. For example, differentiation is a method used to compute the rate of change of a function f(x) with respect to its input x.
Understand the nature of the function
Most questions will give you a function and set of operations to be performed. You must know if the function is increasing or decreasing, odd or even, its point of maxima and minima etc. You can only understand the insights of a problem and devise a plan to solve it after you understand the function.
Understand fundamental theorem
This concept helps students understand integration and differentiation and how they tend to be the inverse of each other.
Engage in active learning
Participating actively through asking questions and volunteering to try solving calculus equations or being ready to attempt when called upon is important. This enhances your problem-solving skills and reinforces your understanding of concepts. You can also
- Seek help on concepts you don't understand to get an immediate response from your teacher and other students. Ask as many questions as you can on concepts you find challenging.
- Always try to participate in class activities and demonstrations actively. You will most likely remember an event you participated in rather than what was said. This helps to increase the interest and understanding of the concepts and relate the experiences to what is being taught.
- Join a study group to discuss and solve problems. A proper discussion will enable you to learn the methods your colleagues employ to understand difficult concepts. You can also teach your colleagues concepts you have learned through self-practice and theoretical overhauling. Teaching others helps you strengthen your mastery of the topic.
Practice! Practice! Practice!
Practice makes perfect. They say math is like a martial art, and for you to become a master at it, you must practice. Without practice, you won't perform well, nor will you explore the hidden intricacies or handle challenging problems.
- Review math concepts daily before you sleep or at least four times a week if possible. Regular practice lets you keep the concepts fresh in your memory for easy application.
- You can solve problems from textbooks, online resources, or past exams by starting with simple problems and gradually moving on to more complex ones.
- Reflect on mistakes you've made and understand the correct approach. Learn from your errors to avoid repeating them.
Seek help from an Expert
The art of asking questions and seeking help when stuck on math homework is a skill that can greatly enhance your understanding. Math is not easy, and you can only be a master at it by bringing to attention concepts you don't understand your teachers and classmates. This will help efface misconceptions and generate a clear conceptual picture in your mind. Strategies to effectively ask questions and seek help when facing challenges in math homework are;
- If a difficulty arises that you can't work out with your study group, it's prudent to seek help from your lecturer during office hours or go to the math tutor room.
- Write your question in an online calculus platform where the student the problems can be solved by anyone knowledgeable about the concept in question.
- Do not wait until the next day to ask the question because there may not be time, or the instructor may be unable to resolve your problem.
- Consulting instructors and teaching assistants
- Joining study groups or seeking peer tutoring
- Join online forums and communities for calculus discussions
- Hire a personal tutor for individualized guidance
Take your homework and assignments seriously
Teachers' assignments are meant to help you understand the concepts taught in class. The assignments help the teacher know the areas the students know and areas he needs to improve.
- Try doing the assignment by yourself first, or seek guidance from other educational platforms that will outline the concepts clearly.
- If you struggle with concepts, spend about two hours on each assignment or more. After finishing your homework, you can practice with other textbook problems on the same topic.
- Do not fall behind with the assignments. The more you delay your assignments, the more you will perform poorly, which will devastate your academic and professional profiles.
Read the syllabus in detail
Mastering the calculus syllabus will improve your performance in this subject and give you a head start. Reading ahead of the teacher enables you to familiarise yourself with the concepts, making it easier to understand as the teacher elaborates.
- Do a quick read-over of the appropriate text sections, not for mastery but to know what to expect. It is easier to learn what you expect than a foreign concept.
- Study new and old topics before the next class. Many things happen between the previous and next class that can make you forget the concepts you had previously learned. As we had said earlier, math always builds on concepts, and if you forget the old concept, it won't be easy to know the new one.
Everyone who is a master at anything will tell you that everything begins with self-belief. Once you believe in yourself, you can achieve anything. Math is not easy for many people, but it can be fun and intellectually rewarding with a little determination and self-belief.
Poor performance in calculus can go away through magic, where you wave a magic wand, and everything transforms. If one intends to improve in math, he has to stay consistent.
Calculus assignments and exams often have time constraints. Practice working under time pressure by setting time limits for solving problems during practice sessions. This will help you improve your speed and accuracy during exams. Some strategies for time management are;
- Create a study schedule and allocate each subtopic time to enable you to cover all the topics. Review everything to keep them fresh in your mind.
- Practising time-constrained problem-solving exercises using practice tests from past exams and others in the textbook. Time yourself to know the time you need to allocate for each question. This will enable you not to lose too much time on a question and finish the task on time during exams.
Use technology in your study
In today's digital age, there is a wealth of online resources and tools available that can significantly enhance your performance in calculus. Remember to critically evaluate the credibility and accuracy of online resources and tools. Seek recommendations from trusted sources, like educational institutions, to ensure the quality of your resources.
- Use math-related apps and tools that assist in calculations, problem-solving, and graphing to streamline your math homework and help you tackle complex problems efficiently.
- Explore online math simulations like PhET Interactive Simulations and the National Library of Virtual Manipulatives to visualize mathematical concepts dynamically and interactively.
- Accessing online lectures, video tutorials, and practice problems. After completing your homework, you can go through online lectures, video tutorials, and practice problems to emphasize and review the concepts. These resources can provide alternative explanations, examples, and practice problems to enhance your understanding. This will help memorize the concepts, processes, and terminologies.
- Use online resources and interactive tools to improve your understanding of calculus concepts when you are tired of reading notes and textbooks. Watch video lectures and tutorials and engage in virtual simulations and experiments.
Apply calculus to daily life experiences
Calculus can be used as a simple way of thinking, explaining unknown occurrences and solving complex problems around us. Calculus analyzes constant change and helps us act with more foresight and find optimal solutions to problems due to continuous change. For example, differential calculus deals with the rate of change like blood pressure, heart rate, stock market, bacteria population, and a footballer's speed. We use this information to analyze curved graphs to map these events and find instantaneous rates.
Use calculus tricks
Use calculus tricks to help you ace your exams. For example, One time, on some lower-level math test, I forgot the volume of a cone. However, if you know some easy integration techniques, you don't need to waste time memorizing that information. Set up an integral whose bounds are from 0 to b, where b is the height of the cone. Now suppose you have some linear function y=mx. This is the function you need to integrate. To solve for m, let y equal the radius of the cone and x the height. Now you have your function y=(radius/height)x. Revolve this around the x-axis, and you are done!
Here's a question that could be on the SAT: let f(x)=x^2 + 17x - 405. Find the vertex. Of course, you could plug in (-b/2a) for x, but you might not remember that. Instead, you can find f' (x) and solve for zero, which will always be the vertex of a quadratic.
How to solve calculus problems
Many calculus problems may seem intimidating at first glance. You can break down complex problems into simpler components to make them more manageable and approachable using the following strategies are;
- Although math is a practical subject, you must learn theoretical concepts and formulas before applying them. Ensure you study each question's problem and requirement before trying to solve them.
- Break down the complex problem into simple, manageable steps. Identify what is given, what needs to be found, and which concepts or techniques can be applied to solve it.
- Visualizing the concepts to gain a deeper understanding of the problem. Utilize graphs, diagrams, and illustrations to visualize and interpret the problems.
- Apply the appropriate methodology using standard or arranging-like terms in the case of algebra. Apply the appropriate formulas and techniques to achieve a correct answer.
- Double-check your answer for accuracy. You can use a different approach to solve the equation and determine if it produces the same answer.
- Practice a variety of problems in your textbooks or past papers. Analyze and learn from solved examples and create a problem-solving toolkit for common calculus scenarios.
Many calculus problems may seem intimidating at first glance. Still, you can break down complex problems into simpler components to make them more manageable. Incorporating these strategies into your calculus journey gives you the tools and knowledge to excel in this challenging subject. Remember, improving your performance in calculus is a gradual process, and persistence combined with the right strategies will pave the way to success.