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Chapter 1
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Chapter 1.1 Variables
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Age Activity Start with your age Step 1: Add 5 to the age Step 2: Multiply the result of Step 1 by 2 Step 3: Subtract twice your age from the result of Step 2 Step 4: Subtract 10 from the result of Step 3 Pick different ages and try again. Talk with the people in your group and explain why you get the answers you get.
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Vocabulary for Chapter 1.1 Variable – A letter that is used to represent one or more numbers. Variable Expressions – A collection of numbers, variables and operations.
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Examples of Variable Expressions 2x 9 + b p – 5
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Let’s write variable expressions from the Age Activity Start with your age Step 1: Add 5 to the age Step 2: Multiply the result of Step 1 by 2 Step 3: Subtract twice your age from the result of Step 2 Step 4: Subtract 10 from the result of Step 3 x (x + 5) 2 x + 5 ((x + 5) 2) – 2x (((x + 5) 2) – 2x) - 10
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Steps to solving Variable Expressions 1.Write the variable expression 2.Substitute values for the variables 3.Simplify the numerical expression y =5 8y 8(5) 40
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Evaluate the expression when y = 5 1)2) y + 33) 5 + 2y 2 5 + 3 8 5 + 2(5) 5 + 10 15
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Evaluate the expression when a = 3 and b = 4 1) a + b 3 + 4 7 2) 2a - b 2(3) - 4 6 - 4 2 3) 3
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Find the average speed of a car that traveled 180 miles from Boise, Idaho to the Minidoka National Wildlife Refuge in 3 hours. Average Speed = miles hour = distance time 60 mph==
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Find the perimeter of the triangle in feet. a = 8 b = 15 c = 17 Perimeter – add all of the sides Perimeter = a + b + c 8 + 15 + 17 40 feet
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The simple interest earned by money P (the principal) at an annual interest rate r for t years is given by Prt. You deposit $650 at a rate of 8% per year. How much simple interest will you earn after one half of a year? Simple interest = Prt P = 650 r = 8% = 0.08 t = ½ = 0.5 =(650)(0.08)(0.5) = $26
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Chapter 1.2 Exponents and Powers
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Use you calculator to fill in the tables. Use the ^ key for the exponents: 2^1 for the first value 2222222 3333333 4444444 5555555 1) 4) 3) 2)
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Vocabulary for Chapter 1.2 Power – An expression like Exponent – The number 6 in the expression Base – The number 4 in the expression
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Use the calculator to evaluate the power 1) 6)5) 4) 3)2) 729 17 1255904936
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Evaluate the expression when a = 1 and b = 2 3)2)1)
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An aquarium has the shape of a cube. Each edge is 2.5 feet long. Find the volume in cubic feet. 2.5ft Volume = length width height Volume =lwh Square – l=w=h=s =s s s =s =(2.5)=15.625 ft
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Chapter 1.3 Order of Operations
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You are ordering a pair of jeans from a catalog. The catalog company charges sales tax on the total purchase amount, plus a shipping fee. The jeans you are ordering cost $20. The sales tax rate is 5% and the shipping fee is $3. Which is the correct way to compute your total bill? Why? A) 20 + 20 0.05 + 3 = 40 0.05 + 3 = 2 + 3 = 5 B) 20 + 20 0.05 + 3 = 20 + 1 + 3 = 21 + 3 = 24 C) 20 + 20 0.05 + 3 = 40 0.05 + 3 = 40 3.05 = 122 D) 20 + 20 0.05 + 3 = 20 + 20 3.05 = 20 + 61 = 81
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Order of Operations Parentheses Exponents Multiply Divide Add Subtract Please Excuse My Dear Aunt Sally
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1. 3 · (5 + 4) 3 · (9) 27 2. 3 · 4² + 1 3 · 16 + 1 48 + 1 49 3. 16 + 4 ÷ 2 – 3 16 + 2 – 3 18 – 3 15 4. 5 · 3² - (6 + ) 5 · 3² - (6 + 4) 5 · 3² - 10 5 · 9 – 10 45 – 10 35 5. 10 ÷ (3 + 2) + 9 10 ÷ 5 + 9 2 + 9 11 6.
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Chapter 1.4 Equations and Inequalities
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Definitions Equation – When an equal sign (=) is placed between two equal expressions Inequality – When an inequality symbol is placed between two expressions
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Examples of Equations 3 – c = 7 5x + 2 = 3 a + 6 = 6 + a
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Check whether the numbers 2, 3 and 4 are solutions of the equation 4x – 2 = 10 x4x – 2 = 10ResultConclusion 2 3 4 4(2) – 2 = 10 4(3) – 2 = 10 4(4) – 2 = 10 6 10 10 = 10 14 10
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Inequality Symbols SymbolMeaning > < is less than is less than or equal to is greater than is greater than or equal to
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Decide whether 4 is a solution to the inequality a) 2x – 1 < 8b) x + 4 > 9c) x – 3 1 2(4) – 1 < 8 7 < 8 4 + 4 > 9 8 > 9 4 – 3 1 1 8 – 1 < 8
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Chapter 1.5 Translations
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AdditionSubtractionMultiplicationDivision times sum total more than decreased by fewer than plusdifference minus quotient product twice ofless multiplied less than increased by half divided fewer
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Translate Verbal Phrases into Algebra 1)3 more than the quantity 5 times a number n. 2)2 less than the sum of 6 and a number m. 3)A number x decreased by the sum of 10 and the square of a number y. 4)The product of seven and a number y is 12. 5)4 cubed divided by a number p. 3 + 5n (6 + m) - 2 x – (10 + y²) 7y = 12 4³ ÷ p
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Translate Expressions into Verbal Phrases 1)9 > 3s 2) 3)3(x – 2) = 10 4)5x - 12 Nine is greater than 3 times a number s. 20 divided by a number n. Three times the difference of x and 2 is 10. 5 multiplied by x minus 12.
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Using a Verbal Model 1)Ben’s hourly wage b at his after school job is $1.50 less than Eileen’s hourly wage e. 2)The distance s to school is 1/5 mile more than the distance c to the Community Center’s swimming pool. 3)The length c of the Colorado River is 3 times the length r of the Connecticut River plus 229 miles b = e – 1.50 s = c + 1/5 c = 3r + 229
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Using a Verbal Model con’t 4) The product of $25 and the number m of club memberships is greater than or equal to $500. 5) The length of the hypotenuse of a right triangle c squared is equal to 4 squared plus 3 squared. 25m ≥ 500 c² = 4² + 3²
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