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Math Review of Operations with Polynomials with More than One Variable 150 150 Deborah

Math Review of Operations with Polynomials with More than One Variable

Overview Polynomials with more than one variable are often used in applications when one variable has a relationship with another. Special attention to combining like terms is essential to solving them correctly. Combining Like Terms The expressions that contain like terms have exactly the same variables with the same exponents. For example, 3x2y4 can be…

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Math Review of Direct and Inverse Variation 150 150 Deborah

Math Review of Direct and Inverse Variation

Overview Direct and inverse variation refer to relationships between variables, so that when one variable changes the other variable changes by a specified amount. Both direct and inverse variation can be applied in many different ways. Figure 1: Definitions of direct and inverse variation. Direct Variation Direct variation means that as one variable increases, another…

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Math Review of Random Numbers 640 426 School Tutoring

Math Review of Random Numbers

Overview:  What Are Random Numbers? In a set of random numbers, the numbers do not follow any pattern.  Each number has an equal probability of occurring, and each number event is independent of any others .  Most of the time, numbers that are close to random are generated by computer programs or calculator programs designed…

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Math Review of Multiplying and Simplifying Rational Expressions 150 150 Deborah

Math Review of Multiplying and Simplifying Rational Expressions

Overview Rational expressions may include constants or variables in the numerator and denominator.  If the variable is in the denominator, values of the variable that cause the denominator to equal 0 must be excluded, because division by 0 is undefined. Rational Expressions Rational expressions can include variables or constants in the numerator or denominator.  If…

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Review of Nonstandard English: Idiom Errors 400 267 School Tutoring

Review of Nonstandard English: Idiom Errors

Overview:  What Do the SAT and ACT Test in English Grammar? The SAT and ACT test for formal, academic, standard English, which is not necessarily the same way that students speak or write.  Many errors are especially insidious because the correct form and the incorrect form are very close.  However, some idiom errors involve words…

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Math Review of Least Common Multiples and Denominators in Rational Expressions 150 150 Deborah

Math Review of Least Common Multiples and Denominators in Rational Expressions

Overview Rational expressions are like fractions, and must have common denominators in order to be added or subtracted.  In order to find the smallest denominator in common, the least common multiple should be found between the denominators.  The least common multiple can also be calculated when the denominators are algebraic expressions. Least Common Multiple The…

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Math Review of Multiplying and Simplifying Radical Expressions 150 150 Deborah

Math Review of Multiplying and Simplifying Radical Expressions

Overview Radical expressions contain one or more radicands, or expressions underneath root signs. They can be multiplied following rules for non-negative real numbers. Radical Expressions Radical expressions that do not have variables, such as √9 or √25 or even 6√5 are already familiar.  The radicand can also be a monomial, such as √(9x2) or over a…

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Math Review of Factoring Sums or Differences of Cubes 150 150 Deborah

Math Review of Factoring Sums or Differences of Cubes

Overview Sums or differences of cubes can be factored similarly to other quadratic equations. They follow a pattern that is a little more complex than factoring quadratic equations. Sum of Cubes A sum of cubes is an expression such as x3 + a3, where both members of the expression are perfect cubes. Suppose the expression…

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Math Review of Division and Reciprocals of Rational Expressions 150 150 Deborah

Math Review of Division and Reciprocals of Rational Expressions

Overview Division of rational expressions is similar to division of real numbers. In order to divide by a rational expression, the rational expression is changed to its reciprocal, then multiplied. Reciprocals The product of two reciprocals is 1, whether the expression is a number, a monomial with variables, or a polynomial. For example, the reciprocal…

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Math Review of the Square Root Property 150 150 Deborah

Math Review of the Square Root Property

Overview The square root property is an important shortcut to use when solving quadratic equations, or any equation that asks for square roots and powers of 2. It uses the definition of a square root to solve for a variable. Definition The definition of the square root of a positive real number in symbol form…

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