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Algebra

Math Review of Multiplying and Dividing Rational Expressions

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Overview The process of multiplying and dividing rational expressions is similar to multiplying and dividing rational numbers.  In order to multiply, first multiply the numerators, then the denominators, and then simplify the expression.  Division is the inverse of multiplication, so multiply by the reciprocal (or inverse) of the divisor, and then simplify the expression. Multiplying…

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Math Review of Simplifying Rational Expressions

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Overview A rational expression has one polynomial in the numerator and one polynomial in the denominator, which means that the numerator is divided by the denominator.  However, the denominator cannot be solved to zero, because division by zero is undefined.   Definition A statement such as (x2 +3)/(y +6) is a rational expression, because it…

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Math Review of Graphing Compound Inequalities

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Overview Inequalities can be graphed along the number line by solving the inequality and then graphing it.  Conjunctions are true when both statements of an inequality are true.  Disjunctions are true when either one or both statements of an inequality are true.  Both conjunctions and disjunctions can form the basis for truth tables. Review of…

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Math Review of Digit and Coin Problems

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Overview Some very common word problems are problems involving digits and problems involving coins.  Like motion problems, these word problems can also be solved using equations in two variables. Setting up a Digit Problem Any two-digit number can be written as 10x +y where x is the number in the tens column and y is…

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Math Review of Uniform Motion Problems

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Overview Problem-solving strategies can also be used to solve uniform motion problems that use the relationship between distance, rate, and time.  Students can first understand the problem, develop and carry out a plan, find the answer, and then check the answer. Understand the Problem Suppose one car leaves Calgary, Alberta, Canada traveling north at 56…

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Math Review of Problem Solving with Systems of Equations

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Overview Systems of two equations with two variables can also be used to solve problems.  In order to solve the problem, it can be translated to a system of equations.  Once the problem is understood, students can make a plan, find the answer, and check to make sure it is correct. Understand the Problem In…

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Math Review of Solving Systems by Addition

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Overview Besides solving systems of equations by graphing and substitution, systems of equations can also be solved by addition.  Math students can choose the best method for the problem at hand.  Sometimes this process is called “solving systems of equations by elimination”. Using Addition Although some systems of equations can be solved by substitution, other…

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Math Review of Solving Systems by Substitution

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Overview One of the ways to solve systems of equations is by graphing the equations.  However, graphing the equations is not always the most accurate method to solve them.  If one variable in a system is represented in terms of the other variable in the system, the systems can be solved by substitution. Using Substitution…

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Math and Physics Review of Curling and Bobsled

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Overview Curling and bobsled are winter sports that rely on friction against an icy track or surface. In curling, a special stone is moved by a combination of momentum and friction against a sheet of ice. Team players use a variety of strategies to determine which of their stones will score the highest. In bobsledding…

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Math Review of Representing Solid Figures

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Overview Three-dimensional solid figures can be represented by the two-dimensional pattern of polygons that create them. The pattern, called a net, is a visual representation that illustrates the formula for the surface area of the three-dimensional figure. If the net were folded, it would produce that figure. Representation of Cylinders The net for a cylinder…

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