Mathematics Department

Students entering Geometry should know how to . . .

 

 

Solve Linear Equations

 

Ex.    4x - 14  =  7x  +  7

       - 4x            - 4x

                -14  =  3x  +  7

                 -7              - 7

                -21  =  3x

                  -7  =  x

 

 

Ex.    4x  3  +  5x  +  2  +  8x  -  6 =  180                  

                                            17x  7  =  180                Simplify first!!

                                                     + 7     +  7

                                                     17x  =  187

                                                          x  = 11

 

Ex.    2(2x - 9)  + 3x  +  2  =  180            

          4x  -  18  + 3x  +  2  =  180             Distribute.

                              7x - 16  =  180             Simplify.

                                   +16      +16

                                       7x  =  196

                                         x  =  28

 

 

 

Practice these equations (and more) at the following web sites!!

• SOLVING EQUATIONS
• Solving Linear Equations Lesson
• StudyWorks! Online : Show Me the Steps: Solving Linear Equations
• Regents Math A: Solve Linear Equations
• Algebra ONLINE: Solving Linear Equations
• Leq: Solving Linear Equations

 

 

Solve systems of equations using substitution

Example A: Solve the systems of equations using substitution:

3y - 2x = 11
         y  = -2x + 9

Solve systems of equations using linear combination

Example B: Solve the systems of equations using linear combination:

x - 2y = 14
x + 3y = 9

Solve quadratic equations using factoring

Example C: Solve the quadratic equation using factoring:

                        x² + 6x – 7 = 0

Solve quadratic equations using quadratic formula

Example D:  Solve the quadratic equation using quadratic formula:

                        x² + 4x – 6 = 0

 

 

You will find help on these topics at the following web sites:

• Examples:  Solving Systems Using Substitution
• Solving Systems Using Linear Combination
• Solving Quadratic Equations Using Factoring
• Solving Quadratic Equations Using the Quadratic Formula
• Practice: Solving Systems Using Substitution and Linear Combo
• Solving Quadratic Equations Using Factoring
• Interact Tutorial: Solving Quadratic Equations by Factoring
• Solving a System by Elimination Method
• http://www.eduscape2000.com/public_html/protect/Algebra1-5/Linear_sys/Subs/subs.html

 

Simplify Expressions

Adding Polynomials

Example:  3x² + 4x – 2 – (4x² + 1)

• http://www.regentsprep.org/Regents/math/math-topic.cfm?TopicCode=polyadd
• Beginning Algebra Tutorial on Adding and Subtracting Polynomials

 

 

Multiplying Polynomials

Example:  (3x² + 4x – 2) (4x² + 1)

•  http://www.regentsprep.org/Regents/math/math-topic.cfm?TopicCode=polymult
• http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/beg_alg_tut28_multpoly.htm

 

Simplify Radicals

Example: 

•  http://www.regentsprep.org/Regents/math/math-topic.cfm?TopicCode=radicals
•  Interact Tutorial: Simplifying Radical Expressions
•  Interact Tutorial: Addition and Subtraction of Radicals 
•  Interact Tutorial: Multiplication and Division of Radicals

 

Plot points and lines on a coordinate plane

Example A:   On a coordinate plane, draw the line whose equation is   y = 2x – 1.

 

Know the definition of and how to use slope

Example B:   What is the slope of the line that goes through the points ( 6, 4 ) and

                    ( -1, 5) ?

Know the equations of horizontal and vertical lines

Example C: What is the equation of the vertical line that passes through ( 5, 2 ) ?

Be able to find the equation of a line given two points on the line

Example D:   What is the equation of the line that passes through ( 6, 3 )  and 

                     ( 4, 5 ) ?

 

You wll find help on these topics at the following web sites:

• Regents Math A: Graphs of Linear Equations: Slope and Intercept
• Intermediate Algebra Tutorial on The Slope of a Line
• Graphing Linear Equations
• raphing Lines 
• Beginning Algebra Tutorial on Graphing Linear Equations
• http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/beg_alg_tut23_slope.htm

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Curator: Rebecca.Bartelt@fcps.edu | Site Map