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Pre-calculus is a course that is designed to prepare students for Calculus, either in high school or college. It includes all the mathematical prerequisites for calculus (including algebra, trigonometry and analytical geometry). The surprising thing about pre-calculus topics is that they don’t specifically involve calculus. Instead, they give students a strong foundation that will be used throughout their calculus studies. The emphasis in precalculus is on strengthening a student’s mathematical knowledge base rather than teaching the basics from scratch.
Calculus is a complex branch of mathematics. This branch of mathematics enables you to study how things move, grow, travel, expand, and shrink. Calculus has many practical applications and is included in degree programs for mathematicians, engineers, computer scientists, economists, statisticians, healthcare providers and many other fields.
Before taking calculus, most students are required to complete four years of secondary math (i.e., algebra I, algebra II, geometry, trigonometry.) Pre-calculus is usually a requirement, especially at the college level.
An Advanced Placement Calculus course consists of a full high school academic year of work that is comparable to calculus courses in colleges and universities. Students may choose to take an AP course in calculus in hopes of gaining college credit and/or college placement. The AP Program includes two calculus courses and an exam for each course. The two courses and the two corresponding exams are designated as Calculus AB and Calculus BC.
AP Calculus AB covers basic introductions to limits, derivatives, and integrals. AP Calculus BC covers all AB topics plus additional topics (such as integration by parts, Taylor series, parametric equations, vector calculus, polar coordinate functions, and curve interpolations). An AP Calculus AB or BC course are each usually equivalent to one semester of college calculus.
The main thing to remember about the difference between BC and AB is that Calculus BC is a review and continuance of Calculus AB. BC can be viewed as an offshoot of Calculus AB since all the topics in Calculus AB (single-variable calculus) are also included in Calculus BC. Unlike other math classes (e.g. Algebra I and Algebra II), Calculus AB and Calculus BC do not have to be taken in a specific sequence. This means Calculus BC can be taken without having ever taken Calculus AB. Because it covers more material, however, it will move at a faster pace.