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1 1-1 Variables and Expressions 1. Approximately ounce plastic bottles must be recycled to produce the fiberfill for a sleeping bag. a. Write an expression for the number of bottles needed to make s sleeping bags 85s b. Find the number of bottles needed to make 20, 50, and 325 sleeping bags. 1700; 4250; Adding and Subtracting Real Numbers 2. An iceberg extends 75 feet above the sea. The bottom of the iceberg is at an elevation of -247 feet. What is the height of the iceberg? Add or Subtract: a b c d. 3 2 a. 4 b. 50 c. 5 d Multiplying and Dividing Real Numbers 4. Multiply or Divide: a. (-3) x (6) b. (7)(2) c. (-4)/8 d. 14/ e. 0(4) f. 8/0 g. 0/15 h. (8/5)(6/4) 48 0 undefined 0 = 14 = The speed of a hot air balloon is 3 ¾ mi/h. It travels in a straight line for 1 1/3 hours before landing. How many miles away from the liftoff site will the balloon land? Define your variables! distance = speed x time so distance = 3.75 x = 5 miles. 1-4 Powers and Exponents 6. Simplify each expression: a. 6 3 b c. (-6) 3 d e. (-6) In case of a school closing, the PTA president calls 3 families. Each of these families calls 3 other families, and so on. How many families will have been called in the 4 th round of calls? 3 4 = Square Roots and Real Numbers 8. Find each square root: a. 9 b. 16 c no real answer 9. As part of her art project, Shonda will need to make a square covered in glitter. Her tube of glitter covers 13 square inches. What is the greatest side length Shonda can have for her square? Define your variables! inches
2 10. Classify the following real numbers: a. -32 b. 5 R, Q, I R, Q, I, W, N 1-6 Order of Operations 11. Simplify each expression: a b [3 2 2(3 1.5)] c. 2( 4) d A shop offers giftwrapping services at three price levels. The amount of money collected for wrapping gifts on a given day can be found using the expression 2B + 4S + 7D. On Friday the shop wrapped 10 Basic Packages B, 6 Super Packages S, and 5 Deluxe Packages D. Use the expression to find the amount of money collected for gift wrapping on Friday. 2(10)+4(6)+7(5) = = Simplifying Expressions 13. Find the product using the distributive property: (15)(103) (15)(103) = 15(100)+15(3) = = Simplify the expression: 4x 4 + 3x 2 2x + 7 3x 2 + 2x Introduction to Functions 15. An engraver charges a setup fee of $10 plus $2 for every word engraved. Write a rule for the engravers fee. Then graph the function if you want 5, 10, 15, or 20 words engraved. Define your variables! f(x) = x f(x) = total fee x = # of words engraved f(5) = 20 f(10) = 30 f(15) = 40 f(20) = Solving Equations by Adding or Subtracting 16. y 8 = m + 17 = 33 y=32 m= Solving Equations by Multiplying or Dividing = j/ y = 108 j=-24 y=12
3 2-3 Solving Two-Step and Multi-Step Equations = 4a d = (9 2d) 4a = 8 5d = 9 a = 2 d = 9/5 2-4 Solving Equations with Variables on Both Sides 22. 7n 2 = 5n x + 1 = 7x x x 3 = 12x 4 2n = 8-5x + 11 = -5x +11 x = -1 n = 4 all real number 2-5 Solving for a Variable 25. The formula C = πd gives the circumference of a circle C in terms of its diameter d. The circumference of a bowl is 18 inches. What is the bowl s diameter? Leave the symbol π in your answer. 18 = πd d = Solve for f: f+4 g = 6 f + 4 = 6g f = 6g 4 π 2-6 Rates, Ratios, and Proportions 27. Takeru Kobayashi of Japan ate 53.5 hot dogs in 12 minutes to win a contest. Find the unit rate. Round your answer to the nearest hundredth. Define your variables! 53.5 hot dogs 12 minutes 4.46 hot dogs 1 minute 28. The ratio of the number of bones in the human skull to the number of bones in the ears is 11:3. There are 22 bones in the skull. How many bones are in the ears? Define your variables! 11:3 = 22:6 There are 6 bones in the ears. 29. Serena ran a race at a rate of 10 kilometers per hour. What was her speed in kilometers per minute? Round your answer to the nearest hundredth. Define your variables! 7 Applications of Proportions 10km 1hr 1hr 60minutes = 10km = 0.17km per minute 60minutes
4 30. A flagpole casts a shadow that is 75 feet long at the same time a 6-foot-tall man casts a shadow that is 9 feet long. Write and solve a proportion to find the height of the flagpole. Define your variables! x 75 = 6 9 9x = 450 x = 50 The flagpole is 50 feet tall 2-8 Percents 31. Find 30% of What percent of 45 is 35? % of what number is 85?. 30(80) = 24 x = 35 45x = 3500 x = 77.78% 38 = x 8500 = 38x x = A survey at a local school showed that 38% of students chose chocolate ice cream as their favorite ice cream. Eight hundred students took the survey. How many chose chocolate ice cream? Define your variables! 38 = x x = x = Applications of Percents 35. Find the simple interest paid annually for 2 years on a $900 loan at 16% per year. (I=P*r*t) I = 900(0.16)(2) = 288 $ Mr. Cortez earns a base salary of $26,000 plus a sales commission of 5%. His total sales for one year were $300,000. Find his total pay for the year (300000) = His total pay for the year was $41, Percent Increase and Decrease 37. Find the percent change from 8 to 10. Tell if it is an increase or decrease. 2 8 =.25 It is a 25% increase 38. A student paid $31.20 for art supplies that normally cost $ Find the percent discount = =.40 It was a 40% discount
5 3-1 Graphing and Writing Inequalities 39. Employees at a store must earn at least $8.50. Write and graph an inequality that represents the situation. Define your variables! x = the amount an employee earns x Solving Inequalities by Adding and Subtracting 40. Solve and graph the solutions of x + 12 < 20 x < Solving Inequalities by Multiplying and Dividing 41. Solve and graph the solutions of 7x > 42 x > Solving Two-Step and Multi-Step Inequalities 42. Solve and graph the solutions of b > 61 2b > 16 b > Solving Inequalities with Variables on Both Sides 43. The Daily Info charges a fee of $650 plus $80 per week to run an ad. The People s Paper charges $145 per week. For how many weeks will the total cost at Daily Info be less expensive than the cost at People s Paper? x = number of weeks x < 145x 650 < 65x 10 < x The Daily Info will be cheaper than the People s Paper if you run the ad for more than 10 weeks 3-6 Solving Compound Inequalities 44. The ph level of a popular shampoo is between 6.0 and 6.5, inclusive. Write a compound inequality to show the ph levels of this shampoo and graph the solutions. x = the ph level of the shampoo 6.0 x 6.5
6 4-1 Graphing Relationships 45. Sketch a graph that represents the cost of a car whose price is dropped each week. Is this graph continuous or discrete? Could be considered continuous, as a car s value technically decreases at any point in time. If you only measure its value at the end (or beginning) of a week, then it could be considered discrete. 4-2 Relations and Functions 46. a. Determine if the relation is a function. Why or why not? {(2, 3), (4, 7), (6, 8)} Yes Each input is paired with exactly one output. b. Give the domain and range of the relation. Domain: 2, 4, 7 Range: 3, 7, Writing Functions 47. Manuel has already sold $200 worth of tickets to the school play. The ticket s cost $2.50 each. Write a function rule to describe the total amount of money Manuel will collect after selling additional tickets. Define all variables. Identify the independent and dependent variables. f(x) = x x = number of tickets sold f(x) = total money collected 4-4 Graphing Functions 48 Graph each of the functions: a. g(x) = x + 2 b. f(x) = x 2 3 D:({-2, -1, 0, 1, 2}
7 4-5 Scatter Plots and Trend Lines 49. The following data shows a relationship between the total amount of money collected at the concession stand and the total number of tickets sold at a movie theater. Create a scatter plot of the data then draw and use a trend line to predict the amount of money collected from the concession stand if 150 tickets are sold. Tickets Sold Concession Sales ($) Scatterplot on the calculator. Trend Line: y = 4.14x Arithmetic Sequences y = 4.14(150) = Find the 25 th term of the following sequence: 4, 8, 12, 16, (a n = a 1 + (n 1)d) a 25 = 4 + (25 1)(4) = Identifying Linear Functions 51. Tell if each is a linear function and why or why not a. {(-4, 13), (-2, 1), (0, -3), (2, 1), (4, 13)} b. y = 5x 9 No, the rate of change is not constant Yes, the rate of change is constant (or the highest exponent on a variable is 1) 5-2 Using Intercepts 52. A filmmaker has $6,000 to make a film that costs $75/h to produce. The function f(x) = x gives the amount of money left to make the film after x hours of production. Graph this function using intercepts and explain what each intercept represents. y-int: If the filmmaker has worked 0 hours, they have $6000 left to make the movie x-int: If the filmmaker works 80 hours, they will have $0 left to make the movie
8 5-3 Rate of Change and Slope 53. Find the rate of change for each time period. Does this represent slope? Month Avg. Temp ( o F) : = = 0 3-5: = 7 = :71 63 = = 4 7-8: = 1 = No the rate of change is not constant. 5-4 The Slope Formula 54. Find the slope of the line that goes through the points (2, 5) and (8, 1) = 4 6 = Direct Variation 55. Does the equation represent direct variation? Why or why not? y = 3x Slope-Intercept Form 56. A caterer charges a $200 fee plus $18 per person served. Write an equation that represents the cost as a function of the number of guests served. Define your variables and identify the slope and y-intercept of the equation. x = number of people served y = total cost y = 18x Slope: 18 y-int: Point-Slope Form 57. The cost to stain a deck is a linear function of the deck s area. The costs to stain 100, 250, and 450 square feet are shown below. Write an equation in slope-intercept form that represents the function. Then find the cost to stain a deck whose area is 75 square feet. Area (ft 2 ) Cost ($) slope: = = 5 4 y 150 = (75 100) y = = y 150 = 5 (x 100) 4
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