While helping a student with Precalculus yesterday, I began to remember the challenges I once had with math courses in college.
In high school, I breezed through math subjects like algebra, geometry, and trigonometry. That's when I really lovee math. I wish I could tell you that I breezed through all my college math classes but I can't. Let me tell you where I miscalculated.
After high school I became an engineering science major at my local city university. Even though I eventually completed my degree, it did not come without hardship. In my freshman year, I got past all the basic math classes that I was familiar with. In my Sophmore year, I struggled to catch up to my peers several times. The mistake I made was taking a Precalculus with Calculus class in the Fall of my sophmore year. Having had no previous precalculus experience, I struggled to master both topics at the same time and I failed the class.
The interesting thing about high level math classes is that everything you learn in high school and beyond, you will see again - almost everyday. You need to focus on each of these topics and learn them well. When it was time for me to learn calculus, I didn't know anything about the topics in "pre-calculus." I learned the hard way how important was to know about these topics in advance. That's why the subject of precalculus is so important.
Even now as a tutor, I find that calculus students often have the most trouble with precalculus topics. Common mistakes with precalculus topics lead to self doubt and confusion when they constantly come up with incorrect answers to the problems. Therefore, if students can master the subjects in precalculus, they'll have an easier time with the higher level courses.
Some of the topics that students will need help with are in precalculus are: analyzing and graphing quadratic equations, polynomials, trigonometric functions, trigonometric identities, inverse trigonometric functions, logarithmic functions, rational and exponential functions, complex numbers, inequalities, absolute value, and an introduction to analytic geometry.
My recommendation for anyone is to learn math as early as possible and try not to mix the topics. Give yourself plenty of time to study one topic before going onto the next one. And if you're having trouble with a topic, get help right away. DON'T WAIT. My new student got help with her precalculus topic and she discovered that she was making one simple mathematical error while solving her problems. She's a much happier person now.