Precalculus is a math course that helps students learn the skills and concepts needed to understand calculus. Calculus is the study of change in mathematics. Precalculus isn't a separate area of study from algebra, trigonometry, coordinate geometry or calculus; rather, it combines elements of all three areas of study.
History of Precalculus
Sir Isaac Newton is credited with inventing calculus (and therefore precalculus), but there is a lot of debate about that. Some say that Gottfried Wilhelm Leibniz was the true inventor of calculus because he published the first paper on differential calculus in 1684. However, others claim that Sir Isaac Newton gave Gottfried Wilhelm Leibniz the ideas first in a private conversation. The argument of who invented calculus divided the mathematical world, leading even to a broader debate about all of Newton's theories, including his theory of gravitation. In the 400 years following Leibniz's first publication, calculus (and precalculus) has developed from a concept with a small school of adherents in the mathematical world to a course studied in mainstream primary education.
Precalculus covers a variety of mathematical problems, from algebra to trigonometry and beyond. However, precalculus is usually associated with the use of functions, or the graphing of algebraic equations. Precalculus also includes the study of trigonometric equations, linear inequalities, logarithms and exponentials. Usually the student arrives in a precalculus class already having learned trigonometry, linear inequalities and some basic functions. The goal of precalculus is to connect those concepts with the higher-order mathematical problems that are part of calculus.
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Uses of Precalculus and Calculus
Precalculus is widely used in the engineering and scientific fields, as well as in business. Precalculus is useful in the study of economics, particularly in the use of economic models such as the input-output model that analyzes supply and demand trends. Precalculus is also useful in engineering, especially in studying the resiliency and reactions of building materials and structures under various weather conditions, as well as in physics to explain and graph rates of change. Chemistry also uses precalculus to quantify chemical reactions.
Precalculus in High Schools
Students usually take precalculus in high school, typically in the 10th or 11th grade. Precalculus used to be a course reserved strictly for students who were college-bound, but as of 2011 many states require that high school students take precalculus in order to graduate high school. Precalculus is also routinely used on many state standardized tests used to measure student achievement, as well as the SAT and ACT college entrance exams.