It’s no secret; Grade 12 Calculus is a challenging course. Many students struggle because they are learning new and complicated concepts they’ve never seen before. If you plan on taking calculus, here are some tips to help you prepare for your journey ahead.
1. Plan ahead with a schedule.
You will need a lot of time outside of school to study and do as many practice problems as possible. Because succeeding in calculus requires a lot of practice, you’ll need to make sure you have a lot of time set aside for studying. If possible, try a lighter course load during the semester you plan on taking calculus. Doing so will ensure you have more time to work on practice problems and prioritize your calculus course.
2. Ask your teacher or tutor for details about the course content.
If you already know who your teacher will be, you can send an email or ask them personally for more details about the course. Having more information about the course content will allow you to learn the basics ahead of time. With an early understanding of new topics, you’ll feel comfortable and prepared to learn these topics in more detail. Not only will you have a smooth start to Grade 12 Calculus, but you’ll also get to know your teacher before you begin.
3. Review the concepts you find confusing.
While Grade 12 Calculus introduces many new ideas, you still need to be comfortable with many concepts from earlier math courses. One concept, in particular, is Trigonometry. Having a good understanding of Trigonometry is essential if you want to succeed in Calculus. You will need to be comfortable with using the Unit Circle to solve problems with Trigonometric functions. We also suggest reviewing algebra and
geometry as they are both fundamental concepts of
calculus.
4. Get a head start with practice problems.
If the textbook is available to you, start reading chapters and familiarizing yourself with new and old topics. Textbooks often have a review section of prior material before introducing any new concepts. Take advantage of this to ensure you have a strong base understanding of previous math topics. Once you’re ready, start reading chapters that introduce new problems and practice doing as many questions as you can. If you feel unsure or confused, ask a tutor or a friend for help. Don’t give up!
5. Review logarithmic functions.
Another concept covered in Grade 12 Calculus is logarithmic functions. Here, students will revisit logarithmic functions concepts seen in Advanced Functions but in greater detail. Calculus introduces the natural logarithmic function:
fx=logex, also written as fx=ln x
and the inverse of the exponential function:
fx= ex
Students will need to make connections between these functions as one equation can reverse another. The relationship between the logarithmic function and the inverse of the exponential function is evident when drawing graphs as they reflect each other.
6. Familiarize yourself with Limits and Derivatives.
Limits and Derivatives are two new concepts introduced later in the course. If you have the opportunity to learn about these new topics before you get started, we highly recommend doing so. These concepts have new notations and definitions that require lots of time to learn and understand.
Definition of a Limit:
The limit of a function explains the behaviour of the function near a specific point. The notation fx=L explains that, as x approaches the value a, the value of the function is approaching a limiting value of L.
Definition of a Derivative:
A derivative is used to determine the instantaneous rate of change of a function with respect to the variable. For a function f(x), the derivative function is : f’x or dydx . The derivative function can be solved using:
f’x= fx+h-f(x)h
7. Make good notes and review them often.
As we mentioned above, Grade 12 Calculus introduces many new concepts. The best way to stay on top of everything you learn is to take good and organized notes. Having good notes helps you easily remember new ideas and allows you to review them if you ever run into a problem you find confusing. A good tip for making notes in calculus is to write down example problems and solutions for each concept. Doing so will allow you to familiarize yourself with the details of different functions.
8. Find a friend who also wants to get a head start.
Taking on Grade 12 Calculus ahead of time is challenging to take on alone. If you know someone who plans on taking Calculus, ask them if they want to get ahead on the course content with you. Having someone to work with will motivate you to continue learning and help you remain on top of your studies. Your study-buddy may have different approaches to specific practice problems that you haven’t seen before, and you’re also likely to show your friend a trick or two!
9. Use visual aids and draw pictures.
This tip is very beneficial if you are a visual learner. Drawings and colours are very helpful for breaking down problems and helping you remember or recall new concepts. When reading practice problems, get in the habit of drawing out the question. Doing so will help you understand what the question is looking for and prevent any missed details. Make sure you write out each step of the solution and make connections to the concepts you applied to solve the problem. If you’re still stuck on a challenging question, make sure you ask a tutor or a friend for help.
10. Be confident and trust your abilities.
Grade 12 Calculus can be pretty challenging. If you’re feeling overwhelmed, don’t give up! Remind yourself that these concepts are new and usually take time to grasp fully. Step away from your practice problems to clear your mind and have a fresh start. Make sure you are eating well and exercising to get your blood flowing. Continue to practice when you’re ready, and trust your math abilities. You’ve got what it takes to succeed!
If you follow along with the above tips, you will have all the tools you need to succeed in Grade 12 Calculus. This course requires a lot of time and practice to understand and apply new concepts. Be patient with yourself and always ask for help if you need it. At Success Tutorial School, we offer a number of programs to prepare students for Calculus or assist students currently enrolled in a Calculus course. Contact us to learn more about how we can help you and your child achieve excellent marks and success in Grade 12 Calculus.
Resources used:
Kirkpatrick, C., Crippin, P., Donato, R., & Wright, D. (2007). Calculus and Vectors. Nelson.
