Afraid of your upcoming Pre-Calc class? Here’s a few tips to relieve the stress!
After finishing their senior calculus class, many math students often report that, out of all their high school math courses, pre-calc was toughest.
The reasons they usually cite include:
It jumps around too much from one random topic to another
Too many weird abstract variables, symbols and equations
Doing matrices by hand is a nightmare!
Here are three tips that will hopefully help you (mentally) prep for the course.
1. Get comfy with being confused because it’s normal! And don’t be afraid to get help!
Those senior calc students are totally right. Pre-calc does jump around a lot, and it is full of mystifying symbols and equations. So don’t feel like you are the only one who is not “getting it” right away. The key is to get a little bit less confused with each exposure to the ideas you get in the classroom and in your homework. And then take what you know and go as far as you can on your own. Finally, note where you are still confused and then get some help from your teacher, a tutor, or a clever friend!
A common sources of confusion early in the course: What is a “function”?
What is a “function”? Sometimes pre-calc teachers expect their new students to already have a firm grip on what a function is, but many students are still fuzzy about it. That’s not a crime! One way to think about it...A function is simply a math rule for what to do with a number. Anyone can make a simple function up. For example, here is a simple rule that can be a math function: “double the number”. As a math function this rule might look like this: y = 2x, where x stands for whatever number you want to double. Simple right?
Well, there is another wrinkle. To actually be an official math function a given math rule has to create only one unique value for each input. For example, the doubling function above would double an input of 5 to create an output of 10; it could not suddenly double 5 and create another number like 12. In other words, a genuine function can’t give you different values for the same input. The doubling function is indeed a function then. Whenever you double a number you only get one unique result.
For comparison, you could ask “Is a coin operated soda-pop machine a function?”. Well, not really...First, let's suppose that every soda is the same price of 1 dollar and there are three flavors: cola, lime and cherry. In this case it would not be a function because for an input of 1 dollar you could get three different results or outputs, either lime, cola or cherry.
Of course, there is more one could say about the definition of functions. For now, just remember that your pre-calc teacher will be using the word function in this specific way. And know that you may have to know this definition in a detailed way at times to get points in your homework and exams!
Again, seek help when you can't go any further on your own.
2. Keep new formulas in a nice organized place in your notes! Collect them the whole year long!
Pre-calc is a formula heavy course. There are formulas for parent functions, trig identities, matrices, vectors, probability problems and conics and on and on. So right away make a doc on your device of choice or block off a special set of pages in your notebook to neatly record the formulas and supply them with any brief margin notes to help you use them correctly. Some students really get into this strategy and color coordinate their formulas according to the unit and so forth. Do what you need to do to make them easily accessible, legible and usable!
Some teachers provide pre-made formula sheets for students while others offer fewer of these kinds of support materials. In any case, you can create your own or supplement what the teacher already provides with more details to help you use them correctly.
3. Make peace with fractions and weird numbers and variables!
Pre-calc, no surprise, requires fraction skills. Fraction skills rust quickly if you don't use them regularly. Some students respond to this fact by pointing out that their graphing calculators can make working with them easy. Fair enough! But do take care that often pre-calc courses feature non-calculator exams and quizzes. Whatever your situation, try to work out those fraction skills during your homework. Then use the calculator when things get rough and to check your hand's work. You will thank yourself, especially if you are planning on doing calculus!
Also, weird numbers and symbols will be the new normal in pre-calc. Greek letters and variables abound as well as abstract problems and maybe some proofs. In other words, you might find yourself asking, like many a math student from ages past, "When am I ever going to use this stuff in real life?" Well, it's reasonable to be frustrated because the answer to that question might be "never" depending what you decide to do after high school. For now, maybe just think of pre-calc as learning a new language, perhaps at the level of Spanish 3 or 4. You have done some introductory math to this point so you can say Hola! and so on. But now you are really going to learn some math language in detail. Once you are done, if you did decently enough you will be able to "read" and "speak" quite a bit more math. Whether that excites you or not I can't say!
Best of luck and seek us out at ATT for all your pre-calc tutoring!