High School - PreCalculus
When high schoolers are asked about calculus, the first thing that usually comes to mind is the derivative and the integral. These things usually revolve around rates of change and areas under the curve. These concepts, though, cannot be understood well enough without some basics.
For this reason, pre-calculus is one of the subjects taken by high school students. In this subject, the more serious side of calculus is not taught yet. Rather, it’s all about those foundational topics like algebra, trigonometry, and analytic geometry. Calculus is a totally foreign language to those who do not know about these foundational concepts.
Of course, one of the very basic things a student must get the hang of first is algebra. No one can understand calculus without a good level of knowledge of the principles of algebra. Calculus usually involves operations on different algebraic functions. Knowing how the graphs of each function work is also essential because calculus also deals a lot with those graphs.
Trigonometry is another very important theme that keeps popping up in calculus. Operations involving integrals, for instance, make use of trigonometry to make things easier. Thus, students need a good foundational knowledge of trigonometry to succeed in calculus.
Turning shapes into numbers is another thing that students need to get used to. That’s where analytic geometry comes in. Here, students would learn how to find the distance between points, finding the slope of a line, and many others. Students would also have an idea of parabolas, hyperbolas, and how they are made. It’s in analytic geometry that ordinary shapes, like circles and ellipses, can turn into equations and vice versa.
Having a proper understanding of these topics adequately prepares students for the more rigorous field of calculus. Calculus is all about analysis, so students must be very well-versed in analyzing mathematical problems first.