# CH I: Connections to Algebra 1.1) Variables in Algebra 1.2) Exponents and Powers 1.3) Order of Operations 1.4) Equations and Inequalities 1.5) Translating.

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CH I: Connections to Algebra 1.1) Variables in Algebra 1.2) Exponents and Powers 1.3) Order of Operations 1.4) Equations and Inequalities 1.5) Translating Words into Mathematical Symbols 1.6) A Problem Solving Plan Using Models 1.7) Tables and Graphs 1.8) An Introduction to Functions

1.1) Variables in Algebra Let’s take a look at a problem: You are driving to LA at 80 miles per hour. How many miles have you traveled after 2 hours? How about after 5 hours? The problem can be written this way: d = 80x ; x = {2, 5}; d = ? Here, d and x are called variables. The answer, d, will vary depending on the number plugged in for x which in this case are 2 and 5.

1.1) Variable in Algebra (cont.) Let’s solve the problem: d = 80x ; x = {2, 5}; d = ? d = 80(2) = 80 x 2 = 160 d = 80(5) = 80 x 5 = 400 The car will travel 160 miles after traveling for 2 hours at 80 miles/hr. The car will travel 400 miles after traveling for 5 hours at 80 miles/hr.

1.2) Exponents and Powers Look at this: 2³ = 2 x 2 x 2 2³ means you multiply 2 three times. x ³¹= x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x ³¹ means you multiply x thirty one times.

1.2) Exponents and Powers (cont.) BE AWARE! 2x ³ DOES NOT EQUAL ( 2x ) ³. 2x ³ = 2 x x x x x x ( 2x ) ³ = 2x x 2x x 2x

1.3) Order of Operations 1/ First do operations that occur within grouping symbols (parentheses or brackets) 2/ Then evaluate powers 3/ Then do multiplications and divisions from left to right 4/ Finally, do additions and subtractions from left to right.

1.3) Order of Operation (cont.) Left-to-right rule- when there are same types of signs, you operate the left one first. Ex.1) in 4+2+6, you do (4+2) first. Then move on to +6. Ex.2) in 4–2+5, you do the – first. Then move on to +. Ex.3) in 4x2÷3, you do x first. Then move on to ÷.

1.4) Equations and Inequalities Equation: Any statement that has equal sign. Take a look at the following problem: 4 x +1 = 9 When you see a statement, “Find the solution to the equation,” it just means to find the right values for the variable (in this case x).

1.4) equations and Inequalities (cont.) So, we got 4 x +1 = 9 If you subtract 1 from both sides, 4 x +1-1 = 9-1 4 x = 8 Then divide both sides by 4. 4 x /4 = 8/4 x = 2 Yay~!

1.4) equations and inequalities (cont.) There are 4 inequality symbols: > is greater than < is less than  is greater than or equal to  is less than or equal to Is the following statement true? 4 x +1  9 when x ={2,3}

1.4) equations and inequalities (cont.) 4 x +1  9 when x ={2,3} Step1) Replace x with the given value, 2 and 3. 4(2)+1  94(3)+1  9 Step2) Do the calculation 8+1  912+1  9 9  913  9 Step3) answer the question. Is the following statement true? 4 x +1  9 when x ={2,3} {9,13} is greater than or equal to 9. TRUE.

1.5)Translating words into mathematical symbols It’s not that hard, just MEMORIZE these: Sum, more than, plus, increased => + Difference, minus, less than, decreased => - Product, times, multiplied by => x Division is worded a little differently. One fourth of 6 => 6 x ¼ The quotient of 6 and 4 => 6/4 6 divided by 4 => 6/4 Practice problems on pg.30-32. :)

1.6) A Problem Solving Plan Using Models A problem solving plan using models #1) Verbal model-Ask yourself what you need to know to solve the problem. The write a verbal model that will give you what you need to know. #2) Labels-Assign labels to each part of your verbal model. #3) Algebraic Model-Use the labels to write an algebraic model based on your verbal model. #4) Solve-Solve the algebraic model and answer the original question. #5) Check that your answer is reasonable.

1.6) A Problem Solving Plan Using Models Pg.36) You and some friends are at a Chinese restaurant. You order several \$2 plates of wontons, egg rolls, and dumplings. Your bill is \$25.20, which includes tax of \$1.20. Use modeling to find how many plates you ordered. Step1) cost/plate x number of plates = amount of bill – tax. Step2) cost/plate = 2 Number of plates = p Amount of bill = 25.20 Tax = 1.20 Step3) 2p = 25.20 – 1.20 Step4) 2p = 24 p = 12 Step5) We ordered 12 plates

1.7) Tables and Graphs Table time types 1990199520002005 SAT Average English Score. 800700600500 SAT Average Math Score 200300400500

1.7) Tables and Graphs (cont.) Bar GraphLine Graph

1.8) An Introduction to Functions A function is a rule that establishes a relationship between two quantities, called the input and the output. For each input, there is exactly one output—even though two different inputs may give the same output. An input-output table (p.48) describes a function. 1 input => 1 output (Function? O) 1 input => multiple outputs (Function? X)

1.8) An Introduction to Functions (cont.) Take a look at the following equation: h = 250+20t For every value of t (input), there is exactly one value of h (output). Therefore, it is a function. Domain: a group of inputs Range: a group of outputs

Terms Variable Variable expression Value Numerical expression Evaluate Power Exponent Base Grouping symbols Order of operations Left-to-right rule Equation solution Inequality Modeling Verbal model Algebraic model Data Bar graph Line graph Function Input Output Input-output table Domain range

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