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Math Review of Imaginary and Complex Numbers 150 150 Deborah

Math Review of Imaginary and Complex Numbers

Overview: While positive numbers have both positive and negative square roots, negative numbers do not have square roots within the set of real numbers. The set of imaginary numbers can be used in equations with square roots of negative numbers. Complex numbers have real and imaginary components, and can be used in operations similar to real…

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Math Review of Polygons 150 150 Deborah

Math Review of Polygons

  Overview: Polygons are geometric figures that are made up of line segments.  Many of them, such as triangles, squares, and rectangles, are familiar shapes.  Others, such as heptagons (7 sides) and nonagons (9 sides) are not. How Are Polygons Constructed? Polygons are constructed from the connection of line segments end to end, but not…

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Math Review of Logarithms 150 150 Deborah

Math Review of Logarithms

Overview: Logarithms are useful shorthand to express exponential values.  They have many common applications in mathematics, science, and engineering. What Is the Relationship Between Logarithms and Exponents? The number 10,000 is equal in exponential form to 104, where 10 is the base and 4 is the exponent.  In logarithmic form, log10 10,000 is equal to…

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Chemistry Review of the Mole 150 150 Deborah

Chemistry Review of the Mole

Overview: Atoms and molecules are so tiny that scientists do not usually measure how many of them are needed in a chemical reaction atom by atom or molecule by molecule.  The amount of atoms or molecules are usually measured in a standard unit called a mole.  The number of atoms, molecules, or ions in a…

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Chemistry Review of Gas Laws 150 150 Deborah

Chemistry Review of Gas Laws

Overview: Substances that exist in gaseous form follow the properties of that state of matter.  Although the random motion of individual atoms and molecules is unpredictable, other properties are not.  Some of these properties of this state of matter are known as the gas laws. What Is Boyle’s Law? Boyle’s law relates the pressure of…

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More Problem-Solving Strategies: Identify Subgoals 150 150 Deborah

More Problem-Solving Strategies: Identify Subgoals

Overview: Another important strategy to use when solving math problems is to identify subgoals.  Some problems need to be solved in steps, and then each step can be solved separately.  Many large and complex problems can be solved by using that strategy. What Is the Overall Problem? Suppose an assembly line is set up so…

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More Problem-Solving Strategies: Look for a Pattern 150 150 Deborah

More Problem-Solving Strategies: Look for a Pattern

Overview: One of the problem-solving strategies that is often used in math is to look for a pattern.  Often when exploring problems, the student can notice a relationship between numbers.  This relationship can help to solve the problem by shortening the number of steps it takes to get to a solution. Step 1: Make a…

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Math Review of Equivalent Sentences 150 150 Deborah

Math Review of Equivalent Sentences

  Overview: Solving equations in algebra depends on using equivalent sentences until the solution is found.  Sentences are equivalent if they have the same solution.  For example, sentences such as x +3 = 8 and 2x = 10 are equivalent because in both of them x = 5. How to Use Equivalent Sentences When solving…

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Identity and Equality Properties in Algebra 150 150 Deborah

Identity and Equality Properties in Algebra

Overview: Identity and equality properties in mathematics are some of the keys to solving algebraic equations.  Those properties allow operations to be performed with numbers and variables.  Some of them may have been learned in lower grades, without symbols to represent them. What Are Some Identity Properties? Zero in addition has a special property.  Any…

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Addition and Subtraction of Radicals 150 150 Deborah

Addition and Subtraction of Radicals

Overview: Addition and subtraction of radicals is similar to addition and subtraction of polynomials.  First, like terms must be identified.  Some expressions may have to be simplified before they are in like terms.  Then, they are added or subtracted as needed. What Are Like Terms for Radicals? Monomials such as 5ab and 3ab can be…

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