Concepts Students Will Use and Understand

/ ACC CCGPS Coordinate Alg./Analytic Geo.
Unit 2 Systems
Volume 1 Issue 2
References
Holt Mathematics Course 3 Text Connection:
Chapter 11: Lesson 6
Chapter 12: Lesson 7 Extension
Holt Mathematics Course 3 Text Online:
http://go.hrw.com/resources/go_mt/hm3/so/c3ch11bso.pdf
http://my.hrw.com/math06_07/nsmedia/homework_help/msm3/msm3_ch11_06_homeworkhelp.html /

Dear Parents:

Below you will find a list of concepts that your child will use and understand while completing Unit 2 Systems. Also included are references, vocabulary and examples that will help you assist your child at home.

Concepts Students will Use and Understand

·  Given a problem in context, write an appropriate system of linear equations or inequalities.
·  Solve systems of equations graphically and algebraically, using technology as appropriate.
·  Graph the solution set of a system of linear inequalities in two variables.
·  Interpret solutions in problem contexts.

Vocabulary

Coefficients: a numerical factor in a term of an algebraic expression.
Intersecting Lines: lines that have one point in common or all points in common.
Linear Combination Method: a technique for solving a system of equations that involves combining two equations in order to eliminate one of the variables and solving for the remaining variable. Adding, subtracting, or multiplying a system of equations to help solve the system.
Substitution Method: a technique for solving a system of equations that involves replacing one variable with an equivalent expression and solving for the remaining variable.
System of Linear Equations: two or more equations that together define a relationship between variables usually in a problem situation. A system of equations can have no solution, one solution, or many solutions.
System of Inequalities: two or more inequalities that together define a relationship between variables usually in a problem situation. A system of inequalities can have no solution or multiple solutions
Try http://intermath.coe.uga.edu/ for additional help.
www.ceismc.gatech.edu/csi
ACC CCGPS Coordinate Alg./Analytic Geo.
Unit 2 Systems
Symbols
Less than
Less than or equal to
> Greater than
Greater than or equal to /

Example 1

Solve the system of equations using any method you choose.
2x + y= 7
x – 3y= 0

Example 2

Solve the system of inequalities by graphing:

y ≤ 2x+4

Example 3

A soccer team is scheduled to play 14 games during a season. Their coach estimates that it needs at least 20 points to make the playoffs. A win is worth 2 points and a tie is worth 1 point. Write a system of inequalities and determine how many ways there are for the team to make the playoffs.
Links:
http://www.purplemath.com/modules/systlin1.htm
http://www.regentsprep.org/Regents/math/ALGEBRA/AE3/indexAE3.htm
http://www.regentsprep.org/Regents/math/ALGEBRA/AE85/indexAE85.htm
http://www.regentsprep.org/Regents/math/ALGEBRA/AE9/indexAE9.htm / Key
Example 1
(3,1)
Example 2

Example 3
The two inequalities are: and . The solution region contains 25 combinations for the team to make the playoffs.
/ ACC CCGPS Coordinate Alg./Analytic Geo. Unit 2
Equal or Not
Volume 1 Issue 3
References
Mathematics Course 3 Text Connection:
Chapter 1: Lessons: 2-3, 7-8
Chapter 2: Lessons: 7- 8
Chapter 11: Lessons: 1-5
Holt Mathematics Course 3 Text Online:
http://go.hrw.com/resources/go_mt/hm3/so/c3ch11aso.pdf
http://go.hrw.com/resources/go_mt/hm3/so/c3ch11bso.pdf
http://go.hrw.com/hrw.nd/gohrw_rls1/pKeywordResults?keyword=mt7+hwhelp11
http://go.hrw.com/math/extra/course3/3_10_Music/3_10_Music_07.htm /

Dear Parents

Below you will find a list of concepts that your child will use and understand while completing Unit 2 Equal or Not. Also included are references, vocabulary and examples that will help you assist your child at home.

Concepts Students will Use and Understand

·  Use algebraic expressions, equations, or inequalities in 1 variable to represent a given situation.
·  Simplify & evaluate algebraic expressions, including those with exponents.
·  Solve and interpret algebraic equations and inequalities in 1 variable, including those with absolute values.
·  Graph the solution of an equation or an inequality on a number line.

Vocabulary

Absolute Value: The distance a number is from zero on the number line. Examples: |-4| = 4 and |3| = 3
Addition Property of Equality: For real numbers a, b, and c, if a = b, then a + c = b + c. In other words, adding the same number to each side of an equation produces an equivalent equation.
Additive Inverse: Two numbers that when added together equal 0. Example, 3.2 and -3.2
Algebraic Expression: A mathematical phrase involving at least one variable. Expressions can contain numbers and operation symbols.
Equation: A mathematical sentence that contains an equals sign.
Evaluate an Algebraic Expression: To perform operations to obtain a single number or value.
Inequality: A mathematical sentence that contains the symbols >,<,≥,or ≤.
Inverse Operation: Pairs of operations that undo each other. Examples: Addition and subtraction are inverse operations and multiplication and division are inverse operations.
Like Terms: Monomials that have the same variable raised to the same power. In other words, only coefficients of terms can be different.
Linear Equation in One Variable: an equation that can be written in the form ax + b = c where a, b, and c are real numbers and a 0
Multiplication Property of Equality: For real numbers a, b, and c (c ≠0),if a +b,then ac =bc.In other words,multiplying both sides of an equation by the same number produces an equivalent expression.
Multiplicative Inverses: Two numbers that when multiplied together equal 1. Example: 4 and ¼.
Solution: the value or values of a variable that make an equation a true statement
Solve: Identify the value that when substituted for the variable makes the equation a true statement.
Variable: A letter or symbol used to represent a number.
Math 8 Unit 3 Equal or Not
Symbols
absolute value bars
Less than
Less than or equal to
> Greater than
Greater than or equal to /

Example 1

In front of a new ride at the amusement park is a pole that is 160 cm tall. On the pole is a sign that says, “To ride this attraction, your height must be within 30 cm of the height of this pole, inclusive.” Let h be the height of a rider and express the message on the sign algebraically using an absolute value inequality and using a compound inequality.

Example 2

Solve the following for x and graph the solution of the inequality on a number line:
a. 7 + x 1 – 2x b. 8 – 3(x – 5) = 12 c. A = h(x + b)
Links:
http://purplemath.com/modules/ineqlin.htm
http://purplemath.com/modules/solvelin.htm
http://www.purplemath.com/modules/solveabs.htm
http://regentsprep.org/Regents/math/solvin/LSolvIn.htm
www.ceismc.gatech.edu/csi / Key
Example 1
|h – 160| 30 ; Solutions: h 190 and h130; this can be written as 130h190
Example 2
a.  7 + x 1 – 2x
6 -3x
-2 x or x-2 -2
b.  8 – 3(x – 5) = 12
8 – 3x + 15 = 12
- 3x + 23 = 12
-3x = -11
x =
c.  A = h(x + b)
2A = hx + hb
2A – hb = hx