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Pre-Calculus

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Tips for Factoring Polynomials
Tips for Factoring Polynomials 970 1024 Teaching Staff

Polynomial Factoring:   As in many fields, the manner in which we approach a problem In mathematics can greatly affect how we go about solving it. By finding the factors…

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The Physics of Spinning Objects
The Physics of Spinning Objects 150 150 Deborah

Overview Any spinning object rotates around a central point called an axis. Tops, dreidels, gyroscopes, and spinning eggs rotate, rise, and seem to defy gravity, as long as they are moving.…

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Math Review of Leibniz, Newton, and the Development of Calculus
Math Review of Leibniz, Newton, and the Development of Calculus 150 150 Deborah

Overview One of the biggest controversies in science in the early 18th century was around the development of a new mathematical tool called calculus. In Europe, the mathematician, philosopher, and scientist…

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Math Review of Roulettes and Cycloids
Math Review of Roulettes and Cycloids 150 150 Deborah

Overview Roulettes are special types of curves that are made when one curve is rotated around another by a fixed point. They are in Euclidean space, and can be described…

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Math Introduction to Infinitesimals
Math Introduction to Infinitesimals 150 150 Deborah

Overview Using infinitesimal quantities to approximate measurement of any item is an ancient way to determine the size and shape of irregular objects. Although it was very controversial in the…

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Math Introduction to Integrals
Math Introduction to Integrals 150 150 Deborah

Overview Finding integrals, or integration, is the opposite of finding the derivative in calculus. The concept is closely connected with functions, and was independently discussed by both Newton and Leibniz…

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Math Introduction to Derivatives
Math Introduction to Derivatives 150 150 Deborah

Overview A derivative of a function describes its rate of change at a particular point on the function. The rate of change doesn’t have to be constant, so it can…

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Math Review of Real, Complex, and Hyperreal Numbers
Math Review of Real, Complex, and Hyperreal Numbers 150 150 Deborah

Overview Real numbers are the rational and irrational numbers that people deal with in everyday life. Hyperreal numbers include numbers that are infinitely large, infinitely small, or infinitesimal, along with…

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Math Review of More Properties of Circular Functions
Math Review of More Properties of Circular Functions 150 150 Deborah

Overview The unit circle has as its center the origin point of the Cartesian coordinates x and y, and has a radius 1. The trigonometric functions are also called circular…

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Math Review of Applications of Circular Functions
Math Review of Applications of Circular Functions 150 150 Deborah

Overview Circular trigonometric functions can be applied to situations in physical, biological, and social sciences involving data that follows a pattern that is not linear. Many of those patterns are…

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