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Limits: Reaching for a Goal 150 150 SchoolTutoring Academy

Limits: Reaching for a Goal

A limit can be a difficult concept to grasp in mathematics, as it is a value that is never reached, but is ‘approached’ by an input, or index of some nature. Limits are essential for integrals, continuity and derivatives in calculus. Let f(x) be a given function. Values of f(x) can be made arbitrarily close…

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Complex Numbers Continued: Amplitude 150 150 SchoolTutoring Academy

Complex Numbers Continued: Amplitude

This article assumes you have read our article on Polar Representation of a Complex Number Resuming from there, we had determined t = tan-1(b/a), which is called the amplitude or argument of the complex number a+ib and it is denoted by amp(a+ib). Principal amplitude: The value of t which lies in the interval (-π, π),…

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Concept Learning: Seeing the Lightbulb Come On 150 150 Suzanne

Concept Learning: Seeing the Lightbulb Come On

Concept learning is a type of learning that you can almost see happening. When a student masters a concept, it is like watching a light bulb turn on. On the one hand, it makes it quite simple to assess that student has mastered the concept; however, oftentimes it is getting them there which is the…

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Atomic Properties: Electronegativity 150 150 SchoolTutoring Academy

Atomic Properties: Electronegativity

Electronegativity (EN) is a property that describes an atom’s attraction for electrons in a bond. This property determines the type of bond which forms between two atoms. An atom with a higher electronegativity means it has more attraction for electrons in a bond. Flourine has the highest electronegativity and is assigned a value of around…

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Understanding Percentage Composition 150 150 SchoolTutoring Academy

Understanding Percentage Composition

The Law of Definite Proportions states that elements in a compound are always present in the same proportions by mass. The percent composition is the relative mass of each element in a compound. The mass percent is the mass of an element in a compound expressed as a percentage of the total mass of the…

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What is the “Foot of a Perpendicular”? 150 150 SchoolTutoring Academy

What is the “Foot of a Perpendicular”?

Let ax+by+c=0 be a straight line. If a perpendicular line  is drawn from any point on the plane to this straight line then the  point of intersection of the given straight line and its perpendicular is called the foot of the corresponding perpendicular.  But how to find the coordinates of the foot of the perpendicular…

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Mathematics Review: Factoring 225 225 School Tutoring

Mathematics Review: Factoring

Instead of using the quadratic formula to solve quadratics, we may be able to factor it instead. Factoring is an important part of simplifying and solving equations and will make the problem easier to solve. There are two main types of factoring that we will review: common factoring and factoring quadratics by decomposition. Common Factoring…

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Expanding From Factored Form 150 150 SchoolTutoring Academy

Expanding From Factored Form

The factored form of a quadratic is useful for finding the roots and other properties but sometimes it is useful to expand in order to simplify the equation. Expanding from factored form uses the distributive property of real numbers which states for real numbers x and y, c (x + y) = cx + cy…

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Greatest Common Factor and Lowest Common Multiple 150 150 SchoolTutoring Academy

Greatest Common Factor and Lowest Common Multiple

Being able to determine the greatest common factor (GCF) and least common multiple (LCM) of a set of numbers is a very useful skill. For those who are unsure of what GCF and LCM are: GCF (Greatest Common Factor): The highest number that divides exactly into two or more numbers. LCM (Least Common Multiple): The…

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Algebra: How to Improve Your Factoring 150 150 SchoolTutoring Academy

Algebra: How to Improve Your Factoring

Factorization is the decomposition of an object (number, polynomial, and matrix,etc). It is an important way of finding answer(s) for a polynomial. It also helps with simplification of polynomials. A well developed factoring skill will help you answering algebra questions faster, but a lot of high school students are having problems with it. Here are…

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