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Math Review: Composition of Functions 381 351 School Tutoring

Math Review: Composition of Functions

By now, you have probably dealt with a cornucopia of functions with two variables; most commonly x and y. To find points that exist within the function you would substitute values into one variable in order to find the other, for example subbing an x value into a linear equation to find it’s corresponding y…

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Differentiation From First Principles 301 244 School Tutoring

Differentiation From First Principles

A key part of any math students academic arsenal is the ability to find the derivative or a function. This is an invaluable skill when dealing with calculus and other higher level mathematics. Not only is being able to understand and preform differentiation, but it is a building block to integrals, another essential higher level…

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Pre-Algebra Tutoring: Relations and Functions 150 150 Deborah

Pre-Algebra Tutoring: Relations and Functions

Overview:  What Are Relations and Functions? A relation in algebra is a set of ordered pairs. The first element of the ordered pair is the domain, and the second element in the ordered pair is the range.  If every first element is paired with only one second element, or every domain has a range, it…

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Physics in Action: The Sounds of The Big Bang 150 150 Deborah

Physics in Action: The Sounds of The Big Bang

Overview:  The Beginnings of The Universe The astrophysical theory of how the universe began has been nicknamed “The Big Bang.”  All matter was compressed into a incredibly dense, superheated mass singularity that exploded.  The resulting energy caused the rapid expansion of the universe, formation into subatomic particles, elements, stars, galaxies, and everything else.  General relativity…

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The Formation of Stars 150 150 Deborah

The Formation of Stars

Overview:  How Stars Are Made Astronomers and physicists have theorized that stellar formation happens when clouds of gas and interstellar dust collapse, molecules of hydrogen attract one another, and nuclear fusion generates energy and heat.  During the process, these young stars are very faint, with energy near the infrared spectrum.  Eventually, when nuclear fusion is…

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Worms, Fruit Flies, and Wounds: A Biology Review 150 150 Deborah

Worms, Fruit Flies, and Wounds: A Biology Review

Worms and Fruit Flies in Biology Most students dissect worms many times over in biology class, as they are ideal for locating organs and experiments involving bodily processes.  In addition, because fruit flies reproduce very quickly, they are useful in demonstrations of traits across generations.  Most recently, scientists have used both common roundworms and fruit…

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Exponents and Scientific Notation 150 150 Deborah

Exponents and Scientific Notation

 Overview:  Exponents and Variables An exponent is a signal for how many times to multiply a number over again.  For example, 26 means the same thing as 2 ∙ 2 ∙ 2 ∙ 2 ∙ 2 ∙ 2 = 64.  If a variable has an exponent, for example, a2, the exponent 2 just means a…

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Conic Sections: Circle, Parabola, Hyperbola, and Ellipse 150 150 Deborah

Conic Sections: Circle, Parabola, Hyperbola, and Ellipse

Overview:  What Is a Conic Section? Conic sections are the curves formed when a right circular cone intersects with a plane.  The angle that the plane  makes when it “cuts through” the cone determines the shape of the section.  The four main types of conic sections are the circle, the parabola, the hyperbola, and the ellipse. The…

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Radian Measure 150 150 Deborah

Radian Measure

Overview:  What Is Radian Measure? The radian measure is another unit of angle measurement.  An angle has the measurement of one radian if the length of the arc it intercepts is equal to the measurement of one radius. The radian measurement has many applications in mathematics and physics, where the more familiar measurement of angles…

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Right Triangles and Trigonometric Functions 150 150 Deborah

Right Triangles and Trigonometric Functions

Overview:  What Are Right Triangles? Right triangles have one angle with a measure of 90o.  As can be shown from the axiom in geometry that the sum of all three angles equals 180o, the sum of the other angles have to equal 90o.   In special right triangles, such as 45o-45o-90o, or 30o-60o-90o, the lengths of…

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