Auntie LeeLee Teach Math - Home



Unit 1: Relationships Between QuantitiesN.Q.1-3: Quantities and Units1. Convert 8 miles to yards. 14080 yards2. Convert 45 miles per hour to feet per minute.3960 feet/minute3. Convert 15,000 feet to miles.2.84 miles4. When Mary goes to school, she drives at an average speed of 55 miles per hour. It takes one hour for Mary to travel to school. Her car travels 20 miles per gallon of gas. Gas costs $3.30 per gallon. How much does Mary spend to travel each mile to school? $0.165 cents per mileHow much money does Mary spend per trip?$9.08 per trip (one-way), $18.15 round trip5. Bob is taking a road trip. He will drive an average speed of 75 miles per hour on the trip. The trip will take a total of 3 hours and 30 minutes. His car travels 24 miles per gallon of gas, and gas costs $3.48 per gallon. How much will Bob spend to travel each mile on his trip? $0.145 cents per mileHow much will his trip cost (one-way)?$38.06 6. The formula for velocity is v = d/t, where d is distance and t is time. If distance is measured in meters and time is measured in seconds, what is the unit rate for velocity?Meters per second7. A box has a volume of 5 m3, a length of 200 cm, and a width of 500 cm. What is the height of the box?50 centimeters (0.5 meters)8. A rectangle has an area of 4 m2 and a length of 50 cm. What is the width of the rectangle?800 centimeters (8 m)9. How many feet are equivalent to ? mile?1320 feet10. A rectangular fish tank contains 3,240 cubic inches of water. The dimensions of the base of the fish tank are 12 inches x 18 inches. How tall is the fish tank?15 inches11. Lauren is building a tree house with her dad. The dimensions of the floor are 9 feet by 6 feet. What is the area of the floor, measured in square?yards?6 yd212. What is the area of a circle with a circumference of 31.4? (Use 3.14 for pi)*Remember, C = 2(pi)r and A = (pi)r2.78.5 u213. What is the circumference of a circle with an area of 28.26? (Use 3.14 for pi)18.84 units14. The rate of water filling a cylinder is represented by the formula r = V/t, where V is the volume measures in meters cubed and t is the time measured in seconds. What is the unit measure for the rate of water filling the cylinder?Meters3 per secondA.SSE.1, 1a, 1b: Structure of Expressions15. [using the formula A = P(1 + r)t] An amount of $800 is deposited into a bank account that pays 5% annual interest. What would be the bank account balance after 8 years?$1181.9616. An amount of $1200 is deposited into a bank account that pays 3.5% annual interest. What would be the bank account balance after 6 years?$1475.1117. [using the formula C = 0.075mt where C is calories burned, m is body weight and t is number of minutes spend jogging) If a person has a body mass of 120 pounds, what would the coefficient for t be?9 18. Two different formulas for calories burned are represented: C1 = 0.072mt and C2 = 0.018mt. One of the activities is running, and one of the activities is walking. Which formula would you expect to go with each activity?C1 goes with running, C2 goes with walking19. The potential energy of an object is found by the formula PE = mgh, where m is mass, g is 9.8 m/s2 (acceleration of gravity), and h is height. If the mass of an object is 10 grams, what would the coefficient of h be?9820. The formula for the growth of a bacteria’s population is A = Po(1.789)0.06t, where Po is the initial population and t is the time in hours. If you begin with 150 bacteria, how many of the bacteria can you expect after 80 hours?2446.9321. The formula for the growth of a bacteria’s population is A = Po(1.789)0.06t, where Po is the initial population and t is the time in hours. If you begin with 150 bacteria, how many of the bacteria can you expect after 80 hours?2446.93A.CED.1-4: Equations and Inequalities22. Two angles of a triangle measure 40o and 100o. What is the measure of the third angle?40o23. Two angles of a triangle measure 23o and 78o. What is the measure of the third angle?79o24. An ant colony starts off with only 10 ants. The colony doubles every day. How long will it take for the ant colony to have at least 1000 ants?7 days25. When Facebook first started, it only had 500 users. The number of people on facebook quadrupled every 2 weeks. How long will it take for Facebook to have at least 1,000,000 users?12 weeks26. Joy starts off with $25 and she makes $7 each week. Brad starts off with $18 and he makes $10 each week. a)What are the equations for Joy and Brad’s income with x being the number of weeks they work?Joy: y = 25 + 7x Brad: y = 18 + 10xb) How much do Joy and Brad both have after 7 weeks of work?Joy: $74 Brad: $8827. Mickey only has $20 to spend at the restaurant. He wants to order at least one entrée and at least one drink. Entrees cost $8 and drinks cost $2. What are all the possible combinations of entrees and drinks Mickey can get?(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2) 1st number entrée, 2nd number drinks28. You only have $40 to spend at Six Flags. Burgers cost $12 each and drinks cost $5. What possible combinations of burgers and drinks can you get at Six Flags?(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (2, 1), (2, 2), (2, 3) 1st number burgers, 2nd number drinks29. The squirrel population in Australia doubles every year. If there are 3,000 squirrels this year, how many squirrels will there be 3 years from now?24,000 squirrels30. A farmer has three times as many carrot plants as potato roots. If there are 24 total plants in his garden, how many are potato roots?p = 831. You have twice as many shirts as you do pants. If you have a total of 18 shirts and pants, how many pants do you have?p = 632. The angles of a triangle measure xo, 3xo, and 6xo. Solve for x. x = 1833. [using the formula Profit = Revenue – Cost (P = R – C)] You invested $4,000 in a business. Each unit of the product you produce costs $1.50 to make, and you are selling each product for $3.50. How many units of the product must be sold in order for you to make a profit?2000 products34. Barry has a water bottle company. He spends $15 in production costs on each water bottle, and spends $1,000 a month on factory rental. He sells each water bottle for $20. How many water bottles does he need to sell each month in order to make a profit?200 water bottles35. What is the solution to the equation P = 2l + 2w solved for l?P-2w236. What is the solution to the equation F = ma solved for a?a = F/m37. What is the solution to the equation V = 2r + s solved for r?r = v-s2*Extra: Which equation is not equivalent to W = 1500 – 150T? Ca.15(100 – 10T) c.1500(1 – 150T) b.125 + 1375 – 10(15T)d.d. 10(150 – 15T)At Metropolis Middle School, the number of cans, N, collected for recycling after a basketball game depends on the number of people, P, who attend the game. The approximate relationship is given by N = 2.5(P – 40) – 100. distribute to get 2.5P - 200a.Is the relationship between the number of cans collected and the number of people attending linear or not? Explain. yes it’s linearb.If 400 people attended the game for the semifinals of the district championship, how many cans would you expect to be collected? 800c.If 300 cans were collected at a game, how many people would you expect to have attended the game? 200d.If 675 cans were collected at another game, how many people would you expect to have attended that game? 350Unit 2: Reasoning with Equations and InequalitiesA.REI.1, 3: Transformations of Equations and Inequalities, Solving Equations/Inequalities38. Is the expression 10x+155 equivalent to 2x + 3?yes (divide everything by 5)39. Solve the equation 3y – 6 = 2(x + 1) for y.y = 2x+8340. Solve the equation 4(2x – 3) = 4y + 8 for y.y = 2x - 541. Solve the equation bx – 3 = 12 for x.x = 15/b42. Solve the equation 9 = 5 – ax for x.x = -4/a43. Solve the inequality 2y + 6 ≥ -3 for y.y ≥ -9/2 44. Solve the inequality 6 – y < -5y > 1145. Solve the inequality 8 – 2y ≤ -2y > 546. Solve this inequality for y: 6a – 3y > 9y < -3 + 2a47. Solve this inequality for y: 5y + 2b ≤ -10y ≤-25b-248. Solve the equation for n. n3+ n5=2n = 15/449. Solve the equation for x. 2x4-x6=5 x = 1550. Solve the equation for a. 4a5+3a2=-3a = -30/2351. Which equation is equivalent to 7a = 3(b – 5) solved for b?b = 73a+552. Which equation is equivalent 2(n + 7) = -3t solved for t?t = 2n+14-353. Solve the following equation: 5(4 – x) = 35. x = -354. Solve the inequality: 2(3 – x) ≥ -4x ≤ 555. Solve the inequality: 9 > -3(4 – x)7 > x or x < 756. Marcia wants to save up for an iPhone. She will save $15 per week from the money she earns working. If an iPhone costs $300, how many weeks will it take her to save enough money?2057. Joe wants to save money for a spring break trip. He will save $16 per week from his job. If his trip will cost a total of $550, how many weeks will it take him to save enough money?35 weeks (need to round up)58. Decide whether 2x + 8 + 4 is equivalent to 2(x + 4) + 4. Explain how you know.yes- distribute59. Joe is getting his first cell phone. His phone will cost $28.99 a month, and he can spend a maximum of $40 a month on his phone. He could add unlimited texting to his phone plan for $15 a month, or he can pay for each text individually. The second option offers an additional rate of $0.10 per text. Joe averages about 10 texts per day. Can Joe afford to add texting to his plan?Not 1st plan ($43.99) and not 2nd play ($58.99)60. Your family is finally getting cable! The monthly flat rate fee for service costs $65.00 a month. Your family budget for cable is $90.00 a month. Your family can get an “additional random bundle” of channels for $25.00 a month, or your family can pick channels one-by-one for $2.00 per channel. After doing a survey, your family knows that they want to add on at least 15 channels. Which option can your family afford? 1st plan (costs $90, 2nd plan costs $95)61. [using the formula d = rt] Two trains, the first traveling 20 miles faster than the second, both start in Chicago and travel in opposite directions. After 5 hours, they are 200 miles apart. We can use the formula below to calculate the rate of the second train:5(r + 20) + 5r = 200What is the rate, r, of the second train?r = 10 mph62. [using the formula d = rt] Two cars, the first traveling 25 miles per hour faster than the second, start at the same point and travel in opposite directions. After 3 hours, they are 225 miles apart. Write a formula to determine the rate, r, of the second car.r = 33.33333 mph63. This equation can be used to find t, the number of hours it takes Moe and Mickey to paint a room. t2+ t3=1 How many hours will it take them to paint the room? (write answer in terms of hours and minutes)6/5 hours, or 1 hour and 12 minutes64. This equation can be used to find h, the number of hours it takes Jane and Jack to clean their rooms. h4+ h12=1 How many hours will it take them? 3 hours65. A ferry boat carries passengers back and forth between Staten Island and New York.It takes 1 hour longer for the ferry to make the trip upstream than downstream.The ferry’s average speed in still water is 20 miles per hour.The river’s current is usually 10 miles per hour.This equation can be used to determine the distance in miles apart the two locations are. d20-10= d20+10+ 1What is d, the distance between Staten Island and New York?d = 15 miles66. Which expression represents all values of x for which the inequality 14+ x4< -2 is true?x < -967. Which expression represents all values of x for which the inequality 3 ≤ x5- 25 is true?x ≥1768. Which expression represents all values of x for which the inequality 32- x2> -1 is true?x < 5A.REI.6- Solve System of Two Linear Equations69. A parking meter contains 27 coins consisting only of dimes and quarters. If the meter contains $4.35, how many of each type of coin is there?16 dimes, 11 quarters70. A bag contains only nickels and dimes. The value of the collection is $2. If there are 26 coins in all, how many of each coin are there? 12 nickels, 14 dimes71. 200 tickets were sold to a college’s annual musical performance. Tickets for students were?$2.50?and for nonstudents?$3.50. The total amount collected was $537. How many nonstudents purchased tickets for the performance?37 non-students72. Mary’s cell phone costs $20 a month plus $0.15 per minute. Jim’s phone costs $30 a month plus $0.10 per minute. After how many minutes of use will Mary’s phone cost more than Jim’s? 200 minutes73. Tommy’s internet costs $30 a month plus $0.50 per minute. Terry’s internet costs $35 a month plus $0.40 per minute. After how many minutes of use will Tommy’s internet plan cost more than Terry’s? 50 minutes74. Given the system of equations, determine if the given points are solutions of the system:y = 3 + x4x – 3y = 8 a) (10, 3)b) (0, 0)c) (17, 20)d) (34, 40) No No YesNo75. Solve the system of equations: 2x+2y=9 -2x-2y= -9infinite solutions 0 = 076. Solve the system of equations: infinite solutions77. Solve this system of equations: -4x+y=5 4x-y= -9no solution 0 = -478. The band director is comparing t-shirt prices from two companies. Company A charges $10 per shirt plus $2 per letterCompany B charges $15 per shirt plus $1.50 per letterFor what number of t-shirts will the band director’s cost be the same for both companies?1079. Barbara is comparing prices for making bracelets.Store A charges $5 for the string plus $0.50 per beadStore B charges $3 for the string plus $1 per beadFor how many bracelets will Barbara’s cost be the same for both stores?480. A test has twenty questions worth 100 points.? The test consists of True/False questions worth 3 points each and multiple choice questions worth 11 points each.? How many multiple choice questions are on the test?5 multiple choice81. A shop sells twelve-pound bags of potatoes for $12 and eighteen-pound bags of potatoes for $15. If 300 bags of potatoes are purchased for a total of $4140, how many eighteen-pound bags of potatoes were purchased?180 eighteen-pound bags82. The sum of two numbers is 90. The larger number is 14 more than 3 times the smaller number. Find the numbers.19 and 7183. Eldora and Finn went to an office supply store together. Eldora bought 15 boxes of paper clips and 7 packages of index cards for a total cost of $55.40. Finn bought 12 boxes of paper clips and 10 packages of index cards for a total cost of $61.70. Find the cost of one box of paper clips and the cost of one package of index cards.paper clips: $1.85 index cards: $3.9584. a) Which graph shows a system of equations with no solution?Case 2b) Which graph shows a system of equations with one solution? What is the solution?Case 1c) Which graph shows a system of equations with infinite solutions?Case 3A.REI.12- Graphing Solutions of Equations and Inequalities85. Use a number line to display the solution to 2x + 4 ≥ 24.x ≥ 10 (closed circle, shade right)86. Use a number line to display the solution to 9 – 2x < 5.x > 2 (open circle, shade right87. Graph the equation on a coordinate plane: -2x + y = -5y = 2x – 5 (y-intercept -5 and positive slope up 2 right 1)88. Graph the inequality on a coordinate plane: 4x + y < -2y < -4x – 2 (y-intercept 2, negative slope down 4 right 1, dotted line, shade to the left/beneath)89. Graph the inequality on a coordinate plane: y – 5 ≤ 2xy ≤ 2x + 5 (y-intercept 5, positive slope up 5 right 1, solid line, shade to the right/beneath)90. Graph the solution of y ≥x+1 and y< -2x-1 on the coordinate plane.91. Graph the solution of 2x – 2y > -6 and x + y > 2 on the coordinate plane.y < x + 3 and y > -x + 292. Which inequality is represented by the graph below?lefttopy ≤ 2x + 393. Which inequality is represented by the number line? x < -1094. Which pair of inequalities is shown in the graph? BlefttopA. y < -x – 2 and y > -5x – 2B. y > -x – 2 and y < -5x + 2C. y > x – 2 and y > 5x – 2D. y > -2x – 1 and y < 2x – 595. Which pair of inequalities is shown in the graph below?lefttopy > -2 and y < -4x + 296. A 97. Skate Land charges a $50 flat fee for a birthday party rental and $4 for each person. Joann has no more than $100 to budget for her party. Write an inequality that models her situation and display it on the graph below. How many people can attend Joann’s party?50 + 4x < 100 solve to get 12 people who can attendFor graph: y < 50 + 4x and y < 100 (horizontal line)98. Sarah is selling bracelets and earrings to make money for summer vacation. The bracelets cost $2 and the earrings cost $3. She needs to make at least $60. Sarah knows she will sell more than 10 bracelets. Write inequalities to represent the income from jewelry sold and number of bracelets sold.2b + 3e ≥ 60 and b ≥ 10 OR 2x + 3y ≥ 60 and x ≥ 10Equation to graph: y ≥ -2/3x + 20Unit 3: Linear and Exponential FunctionsA.REI.10,11: Represent and Solve Equations and Inequalities Graphically99. Cameron is going to the candy store. He can buy chocolate and jelly beans. He has $30 to spend on candy. If chocolate costs $3 per pound and jelly beans cost $5 per pound, what are the different combinations of candy that he can purchase if he spends exactly $30?x = chocolate, y = jelly beans5 chocolates, 3 jelly beansWhat if Cameron is going to spend no more than $30 on candy? What are the different combinations of candy he can purchase?(0, 1) (0, 2) (0, 3) (0, 4) (0, 5) (0, 6) (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (2, 1) (2, 2) (2, 3) (2, 4) (3, 1) (3, 2) (3, 3) (3, 4) (4, 1) (4, 2) (4, 3) (5, 1) (5, 2) (5, 3) (6, 1) (6, 2) (7, 1) (8, 1) (10, 0)100. Consider the equations y = x + 4 and y = -2x – 2. What is the ordered pair solution to the system of equations? Graph them on the coordinate plane.(-2, 2)101. Graph the inequality x – 3y ≥ 9y ≤ 1/3x – 3102. Graph the inequality –x + y < 4y < x + 4 103. What equations correspond with the graphs shown? y = 2x – 5y = -1/3x + 4104. Which equation corresponds to the points in the coordinate plane?y = 1/2x105. Based on the tables, what common point do the equations y = -2x + 2 and y = x – 4 share? (2, -2)x01234y20-2-4-6 x01234y-4-3-2-10 F.IF.1,2,3: Understand Concept of Function, Function Notation106. Given f(x) = -2x – 4, find f(-4) and f(6).f(-4) = 4 and f(6) = -16107. Given f(x) = 4x + 1, find f(5) and f(0).f(5) = 21 and f(0) = 1108. If g(8) = 4 + 3(8), find g(x).g(x) = 4 + 3x109. If h(-2) = 3(-2), find h(x).H(x) = 3x110. If f(3) = -5 – 2(3), find f(x).f(x) = -5 – 2x111. Graph the function f(x) = -3x + 1 on the coordinate plane.112. A hotdog vendor keeps track of his weekly costs by using the cost function C(x) = 450 + 1.5x, where x is the number of hot dogs sold. a) What is the domain of the cost function? (think real world)all whole #s greater than 0 b) What is the cost of selling 500 hot dogs in a week?$1200 c) If his costs must be below $800 this week, what is the greatest number of hot dogs he can sell?233 hot dogs113. A t-shirt company keeps track of its monthly costs using the cost function C(x) = 1000 + 8x, where x is the number of t-shirts sold. a) What is the domain of the cost function?all whole #s greater than 0 b) What is the cost of selling 500 t-shirts in a month?$5000 c) If the company’s costs must be under $8000 this month, what is the maximum number of shirts they can sell?875 shirts114. Consider the sequence: 3, 8, 13, 18, 23, … a) Is this a finite or infinite sequence?infinite b) What is a1? What is a4?a1 = 3 and a4 = 18 c) What is the domain of the sequence? What is the range of the sequence?domain {1, 2, 3, 4, 5,…} range {3, 8, 13, 18, 23,…]115. Given the function f(n) = -2n + 3, create a table for the sequence for the first 5 terms. What is the domain of the sequence? What is the range of the sequence? domain {1, 2, 3, 4, 5} range {1, -1, -3, -5, -7}116. Write a function that represents this sequence (hint: use arithmetic sequences)n12345an-214710f(n) = 3n - 5117. What function is modeled in this table?x12345F(x)13579f(n) = 2n - 1118. What function is modeled in this table?x12345F(x)29162330f(n) = 7n - 5119. Which explicit formula describes the pattern in this table? Cn13469P2.487.449.9214.8822.32a) n = P x 2.48b) n = P + 2.48c) P = n x 2.48d) P = n / 2.48120. Which explicit formula describes the pattern in this table? Bt257810V10.5426.3536.8942.1652.7a) V = t x 10.54b) V = t x 5.27c) t = V x 5.27d) t x V = 5.27121. If f(-11) = 2(-11) – 6, which function gives f(x)?f(x) = 2x - 6122. If g(4) = 5 – 3(4), which function gives f(x)?g(x) = 5 – 3x123. If h(9) = (9)2 – 1, which function gives h(x)?h(x) = x2 - 1F.IF.4,5,6: Interpret Functions that arise in applications in terms of context124. In 1985, there were 285 cell phone users in the town of Centerville. The amount of cell phone users in Centerville can be represented by the function A(t) = 285(1.75)t, where A(t) is the number of cell phone users and t is the number of years after 1985. (be specific about whole #s v. real #s)a) What are the y-intercepts of the function A(t)?(0, 285)b) What is the domain of the function A(t)?all whole #s greater than 0c) Why are all the t-values non-negative?can’t have negative yearsd) What is the range of A(t)?all whole numbers greater than 285e) Does A(t) have a maximum or minimum value?minimum is 285lefttop125. Each year the country club sponsors a tennis tournament. The tournament starts with 128 players. Each round, half of the players are eliminated. The number of players in the tournament can be represented by the function P(t) = 128(1/2)t, where P(t)represents the number of players and t represents the number of rounds. A portion of the graph of P(t) is shown below. (be specific about real #s or whole #s)a) Even though it is not shown, what is the y-intercept of P(t)?(0, 128)b) Is the function increasing or decreasing?decreasingc) Is the function positive or negative?positived) What is the domain of P(t)? What is the range?all whole numbers between 0 and 128lefttop126. A company uses the function P(x) = 20x + 500 to represent the number of employees, P(x), after x number of years. Use the table of values shown below to answer the questions.x01234P(x)500520540560580a) What is the y-intercept of the function? (0, 500)b) Does the graph of the function have an x-intercept? (noc) Does the function increase or decrease? increase127. Harold bought a boat and is using the function C(x) = 32,000 – 1,680x to represent the depreciation of the boat, where C(x) is the value of the boat and x is the number of years after its purchase. Use the table of values shown below to answer the questions.x01234C(x)32,00030320286402696025280a) What is the y-intercept of the function? (0, 32000)b) Does the graph of the function have an x-intercept? What is it? yes, (19.05, 0)c) Does the function increase or decrease? decrease128. A farmer owns a tractor that can consistently run an average of 15 miles an hour for up to 9 hours. Let y be the distance the tractor can travel for a given x amount of time in hours. The tractor’s progress can be modeled by a function. What is the domain of the function?0 ≤ x ≤ 9 hours129. A production team can consistently make an average of 100 bottles per hour for up to 10 hours. Let y be the total number of bottles the team makes for a given x amount of time in hours. The team’s progress can be modeled by a function. What is the domain of the function?0 ≤ x ≤ 10130. The graph below shows the height of a rock dropped from a cliff. The y-axis represents height of the rock and the x-axis represents the number of seconds after it was dropped. a) What was the initial height of the rock?about 100 feetb) After how many seconds was the rock 50 feet in the air? 1 secondc) After how many seconds was the rock about 12 feet in the air? 3 secondsd) How long did it take the rock to reach the ground?lefttop10 secondsF.IF.7, 9: Analyze Functions using different representations131. Given the function f(x) = -12x+2, identify the following: domain, range, y-intercepts, x-intercepts, maximum/minimum, increasing or decreasing, rate of change, end behavior, positive/negative.domain: all real numbers; range: all real numbers; y-intercept (0, 2); x-intercept (4, 0); no max or min; decreasing; rate of change is -1/2; end behavior is up on the left and down on the right; both positive and negative132. Given the function f(x) = 13x, identify the following: domain, range, y-intercepts, x-intercepts, maximum/minimum, increasing or decreasing, rate of change, end behavior, positive/negative.domain: all real numbers; range: all numbers greater than 0; y-intercept (0, 1); no x-intercept; no max or min; decreasing; approaches infinity on left and 0 on the right; positive133. To rent a bike, the cost is $15 for the bike and $4 for each hour you bike. Draw a graph to represent the total cost of renting a bike.y = 15 + 4x134. A bacteria population starts with 20 bacteria and doubles every hour. Draw a function that represents the growth of the bacteria population over hours. y = 20(2)xF.BF.1, 2: Build a function that models a relationship between 2 quantities135. John already has $22 saved. He saves $5 each week so that he can buy a stereo. Write a function to model how much money John will save for x amount of weeks.y = 22 + 5x136. Billy has $1000 in his savings right now. He will withdraw 1/3 of his money each week. Write a function to model this situation.y = 1000(1/3)x137. The terms of a given sequence increase by a constant amount. If the first term is -3 and the fourth term is 3:a) List the first 6 terms in the sequence.-3, -1, 1, 3, 5, 7b) What is the explicit formula for the sequence?2n - 5c) What is the recursive formula for the sequence?an = an – 1 + 2; a1 = -3138. The function f(n) = -2n + 5, create a table for the first 5 terms and identify the domain and range. domain {1, 2, 3, 4, 5} range {-3, 1 -1, -3, -5}139. Which function represents this sequence?n1234…an41236108…a. f(n) = 4n – 1b) f(n) = 3n – 1c) f(n) = 4(3)n – 1d) f(n) = 3(4)n – 1140. Which function represents this sequence?a1234…an962461.5…an = 96(1/4)n - 1141. The first term in the sequence is 2. Which function represents the sequence?a1234…an281420…an = 6n - 4142. The first term in the sequence is -4. Which function represents the sequence?a1234…an-451423…an = 9n - 13143. The points (0, 1), (2, 16), and (3, 64) are on the graph of a function. Which equation represents the function?a. f(x) = 2xb. f(x) = 3xc. f(x) = 4xd. f(x) = 5x144. The points (0, 1), (2, ?), and (3, 1/8) are on the graph of a function. What equation represents the function? (1/2)x145. Use the graph to answer the questions.a) Describe the behavior of the function within the interval -∞lefttop to x = -1.increasingb) Describe the behavior of the function between the interval x = -1 to x = 1.decreasingc) Describe the behavior of the function from x = 1 to ∞increasingF.BF.3: Build New Functions from Existing Functions146. If f(x) = 2x, how will g(x) = f(x) + 4 compare? How will h(x) = f(x) – 2 compare?up 4; down 2147. If f(x) = 3x, how will f(x) + 1 compare? How will f(x) – 5 compare?up 1; down 5148. If f(x) = 2x, how will g(x) = 2f(x) compare? How will h(x) 0.2f(x) compare? How will j(x) = -f(x) compare?vertical stretch; vertical shrink; reflection over x-axis149. Suppose f is an even function and the point (3, 10) is on the graph of f. Name one other point that must be on the graph of f.(-3, 10)150. Suppose f is an odd function and the point (3, 10) is on the graph of f. Name one other point that must be on the graph of f. (-3, -10)151. Suppose f is an even function and the point (-2, 4) is on the graph of f. Name one other point that must be on the graph of f. (2, 4)152. Suppose f is an odd function and the point (-2, 4) is on the graph of f. Name one other point that must be on the graph of f. (2, -4)153. For the function f(x) = 4xa) Write the function that represents a 6 unit translation upward of f(x). 4x + 6b) Write the function that represents a 2 unit translation right of f(x). 4x - 2c) Write a function that represents a reflection over the x-axis of f(x). -4xd) Is the function even, odd, or neiher? neither154. Given the function f(x) = 2x + 1,a) Describe what has happened if g(x) = 6x + 3 (or 3f(x)) vertical stretch by 3b) Compare the function to f(4x). vertical stretch by 4 (steeper)c) What has happened if g(x) = -2x + 1 reflect over x-axis or y-axisd) Which has the fastest growth rate: f(x), 3f(x), or –f(x)? 3f(x) because it’s steeper155. If you are given the function f(x) = -4, is it even, odd, or neither?even156. If it is true for a function that f(-x) = -f(x), is the function even, odd, or neither?odd157. For a given function, f(-9) = 3 and f(9) = -3. Is this function even, odd, or neither?odd158. For a given function, f(7) = -2 and f(-7) = -2. Is this function even, odd, or neither?evenF.LE.1, 2, 3, 5: Construct and Compare Linear and Exponential Models and Solve Problems, Interpret Expressions for Functions in terms of the situation they model159. Your company is offering you two different promotions. You can choose a 3% salary increase per year, or a $50 increase per month. Which option is better if you expect to stay at your company for longer than 15 years?3% salary increase (Graph them)160. The goldfish population in a lake has been increasing each year. The data so far is: 3, 10, 29, 88, …a) Make a scatter plot of the goldfish population. b) What type of model is better—linear or exponential? exponential (multiply by 3)c) How many goldfish should you expect the next year if the trend continues? about 264 161. Given the sequence 4, 9, 14, 19,… does it appear to be linear or exponential? linearWrite a function for the sequence and determine the 25th term of the sequence.f(n) = 5n – 1 and a25 = 124162. Given the sequence1, 4, 16, 64,…does it appear to be linear or exponential? exponentialWrite a function for the sequence and determine the 12th term of the sequence.f(n) = 1(4)n – 1 and a12 = 4194304163. Draw a scatter plot of linear growth and a scatter plot of exponential decay.164. Given the tables below, identify if the rate of change is constant or variable.x12345y2622181410constant, -4 each timex12345y38101730variable165. Charlie has an ant farm. He started with only 12 ants. After one year, he had 68 ants. After 2 years, he had 124 ants. Find a linear function to model the growth of Charlie’s ant farm. y = 56x + 12166. Becky is growing bacteria for a science experiment. She started out with 8 bacteria. After one hour, she had 32 bacteria. After 2 hours, she had 128 bacteria. Write an exponential model for the growth of Becky’s bacteria.y = 8(4)x167. If the parent function is f(x) = mx + b, what is the value of the parameter m for the line passing through the points (4, 10) and (-5, 8)?m = 2/9168. If the parent function is f(x) = mx + b, what is the value of the parameter b for the line passing through the points (-2, 7) and (13, 2)?m = -1/3Unit 4: Describing DataS.ID.1, 2, 3: Summarize, Represent, and Interpret Data on Single Count of Measurable Variable169. Calculate the mean absolute deviation of the following movie costs.$9.50, $10.00, $8.00, $7.50, $12.00, $10.00, $9.00, $10.50$1.06170. The following table shows the amount of money Joe and Tom make each day at work. DayJoe’s IncomeTom’s IncomeMonday$65$50Tuesday$30$45Wednesday$55$60Thursday$50$50Friday$40$65a) Who has the greatest median income per day? What is the difference in the median pay for Joe and Tom? medians are the same (both 50)b) What is the difference in the interquartile range for Joe’s income and Tom’s income?Joe IQR = 25 and Tom IQR = 15 so difference is 10171. Use the frequency table below to create a histogram. 19050173355Use your histogram to calculate the lower quartile, upper quartile, and median of the data. lower quartile is 3000-3999; median is 3000-3999; upper quartile is 4000-4999Does the histogram reflect a normal distribution?not normal172. Given the histogram, calculate the following: 190502540a) What is the lower quartile?1-1.5b) What is the upper quartile?2-2.5c) What is the median?1-1.5d) Would you describe this data as normal, bimodal, multimodal, skewed left, or skewed right?skewed left173. Given the histogram, calculate the following: AgeFrequency183205212236257284305a) What is the lower quartile?20-29b) What is the upper quartile?50-59c) What is the median?30-39d) Is this data normal, bimodal, multimodal, skewed left, or skewed right? bimodal174. 19050-4445Ms. Johnson took a poll of the ages of the students she had in her cooking class. She organized the data into this chart:Using the data, make a dot plot, box plot, and histogram.min =18; Q1 = 20; median = 23; Q3 = 28; max = 30Does the data appear to be normalor bell-shaped?kinda normal175. Which histogram below is normal, skewed, or uniform? normaluniformskewed left176. Jessica is a student at Adams High School. These histograms give information about the number of hours of community service completed by each of the students in Jessica’s homeroom and by each of the students in the ninth-grade class at her school. Which conclusion can be drawn from the data?a.The lower quartile of the number of community service hours completed by Jessica’s homeroom is greater than the lower quartile of community service hours completed by each student in the ninth-grade class.b.The upper quartile of the number of the number of community service hours completed by Jessica’s homeroom is lower than the lower quartile of community service hours completed by each student in the ninth-grade class.c.The median of the number of the number of community service hours completed by Jessica’s homeroom is lower than the median of community service hours completed by each student in the ninth-grade class.177. The high and low temperatures for last seven days are below:?Compare the spreads of the data using the Mean Absolute Deviation.a.The average variation from the mean is greater for the highs than the lows.b.The average variation from the mean is the same for the highs and the lows.c.The average variation from the mean is less for the highs than the lows.178. Below are two samples of data.Sample A: 2, 2, 2, 3, 7, 7, 8, 9, 11, 14Sample B: 0, 1, 5, 6, 9, 9, 10, 10, 10, 10Which statement accurately compares the two samples?a.The mean of Sample A is 5 less than the mean of Sample B.b.The IQR of Sample A is greater than the IQR of Sample B.c.The median of Sample A is 2 greater than the median of Sample B.d.The median of Sample A is equal to the median of Sample B.179. The table below shows the number of cars sold by eight salespeople at a car dealership last year. SalespersonCars SoldSalespersonCars SoldBobbie180Paul125Jim172Rita150Lena185Sandeep149Mindy147Tito179Calculate the mean, median, lower quartile, upper quartile, and interquartile range for the data. Then draw a box and whisker plot. mean = 160.875; median = 161; Q1 = 148; Q3 = 179.5; IQR = 31.5; min = 125; max = 185180. Below is a table of ages of volunteers at the Regional Library. The mean age of volunteers is 15. Find the MAD for this data. MAD = 0.8181. Ellen and Sadie played 5 video games and recorded their scores in the table.Which girl had the greater mean absolute deviation for her scores?Ellen (Ellen = 7.2 and Sadie = 5.2)182. The household income for 6 different households is shown. What is the mean absolute deviation for the group (round to the nearest tenth)?Calculate the mean, median, lower quartile, upper quartile, minimum, maximum, and interquartile range. Then draw a box and whisker plot. mean = 54; median = 51.5; Q1 = 45; Q3 = 62; IQR = 17; min = 38; max = 76183. This box and whisker plot show the data from males and females selling candy bars for their school. The top is males and the bottom is females. Which group sold the highest median number of candy bars?females184. What is the best description for the histogram shown below? (normal, uniform, bimodal, multi-outliers, skewed) bimodal185. This table shows the average high temperature, in ?F, recorded in Atlanta, GA, and Austin, TX, over a six-day period. Which conclusion can be drawn from the data? Day 1 2 3 4 5 6 Temperature in °F in Atlanta, GA 85 88 83 79 81 85 Temperature in °F in Austin, TX 80 86 82 80 93 89 a.median same; interquartile range greater for Austin than Atlantab.mean temperature and interquartile range of Atlanta was higherc.mean temperature of Austin was higher and median temperature of Austin was lowerd.mean and median temperatures of Atlanta were higher186. A school was having a canned food drive for a local food bank. A teacher determined the median number of cans collected per class and the interquartile ranges of the number of cans collected per class for the juniors and for the seniors. ?The juniors collected a median number of cans per class of 35, and the interquartile range was 10. ?The seniors collected a median number of cans per class of 40, and the interquartile range was 8. ?Both the juniors and the seniors had the same third quartile number of cans collected. Which range includes only the numbers that could be the third quartile number of cans collected for both classes?a.25 to 45b.32 to 48c.25 to 48d.40 to 45187. Which set(s) of data have an outlier? a.10, 15, 17, 17, 12c.10, 12, 40, 150, 100b.10, 20, 80, 40, 190d.60, 50, 12, 11, 10188. What is the mean absolute deviation of the set {12, 10, 14, 4, 5}?a.9.0b.3.6c.5.4d.1.8189. The fat contents of seven different sandwiches available at a restaurant are 40, 61, 13, 17, 25, 45, and 30. Find the mean absolute deviation of the fat contents.13.4190. The following box plots show the number of cookies eaten by students in our class. The top box plot represents the cookies eaten by the boys and the bottom box plot represents the cookies eaten by the girls. Based on the box plots, who ate LESS cookies? girls 1 2 3 4 5 6 7 8 9191. A teacher determined the median scores and interquartile ranges of scores for a test she gave to two classes. ?In Class 1, the median score was 72 points, and the interquartile range was 12 points. ?In Class 2, the median score was 78 points, and the interquartile range was 8 points.?Both classes had the same third quartile score. Which range includes only the numbers that could be third quartile scores for BOTH classes?a.72 to 78 points b.78 to 84 pointsc. 72 to 86 pointsd. 78 to 86 pointsS.ID.5, 6, 7, 8, 9: Summarize, Represent, and Interpret Data on Two Categorical and Quantitative Variables; Interpret Linear Models192. Use the table below to answer the questions: a) Which hobby do men and women prefer most?danceb) What percent of those surveyed like TV?32%c) What percent of those surveyed are women who like sports?12%d) What percent of women like to dance?53%Create a conditional frequency table from the table above (convert to decimals!)from left to right, top to bottom: 0.04, 0.2, 0.16, 0.4, 0.32, 0.12, 0.16, 0.6, 0.36, 0.32, 0.32, 1193. lefttopThe table below shows the relationship between age and support for minimum wage. a) Are most people for, against, or no opinion?forb) What percent of those surveyed are against minimum wage?35%c) What percent of the 21-40 age group have no opinion?10%d) What percent of those surveyed are over 60 and in support of minimum wage? 27.5%19050635Create a conditional frequency table from the table above.from left to right, top to bottom: 0.125, 0.1, 0.025, 0.25, 0.1, 0.175, 0.1, 0.375, 0.275, 0.075, 0.025, 0.375, 0.5, 0.35, 0.15, 1194. For each of the scatter plots, decide of a linear or exponential model would be best. linearexponentialexponentiallinear195. Given the table, calculate the linear regression line for the data. Determine if it has a negative or positive correlation. Is the correlation weak or strong?Then, calculate the residuals and make a residual plot to determine the fit of the line. y = 0.68x + 0.11, r = 0.97, strong positive correlationresiduals: -.11, -.29, .33, .35, .07, -.31 residual plot shows it’s an okay fity = -0.74x + 8.3, r = -.99, strong negativeresiduals: -.204, -.312, -.02, -.006, .23, .218, .354, .216, -.318, -.548 residual plot shows bad fit196. Given the scatter plot below, calculate the line of best fit for the data (using a calculator).Then, calculate the correlation coefficient and determine if it is positive or negative and strong or weak.Then, calculate the residuals and make a residual plot to determine the fit of the line.y = 0.5x + 3.1, r = 0.8, strong positive correlationresiduals: -.8, .1, 1.0, -1.8, -.3, 1.1, -.1, -.4, 1.8, -2.3, -0.1 residual plot shows okay fit197. Identify whether the following residual plots are good or bad predictors for regression lines.good fitgood fitbad fit good fitbad fit198. How would you describe the correlation of the two variables based on the scatter plots shown below? (strong, weak, no correlation, negative, positive)A strong positive, B weak positive, C weak neg, D fairly strong neg, E weak neg, F no correlationUnit 5: Transformations in the Coordinate PlaneG.CO.1, 2, 3, 4, 5: Experiment with Transformations in the Plane199. Draw the image of this figure reflected across the x-axis. 200. Draw the image of this figurereflected across y = 3. 201. Draw the image of this figure reflected 202. Draw the image of the figure using the translationacross y = 1. (x, y) (x + 4, y = 2)203. Draw the image according to the rule and identify the transformation. a) (x, y) (x – 2, y + 5)b) (x, y) (-x, -y)translationreflection over x and y axis, or rotate 180c) (x, y) (-x, y)d) (x, y) (x + 1, y + 4)reflection over y-axistranslation right 1 and up 4204. Specify a sequence of transformations that will map the pre-image onto the image.a) reflect over x = -2b) reflect over x = 2c) rotate 180d) translate down 2 and right 4 205. Which transformation(s) map the hexagon onto itself? (think reflections and rotations)reflect over x and y-axis, or rotate 60o206. Which transformation maps the trapezoid onto itself?reflection over y-axis, rotate 360o207. IF the parallelogram below were translated 3 units left and 6 units down, what would be the coordinates of the new image W’X’Y’Z’?W’ (-2, -1) X’ (0, 3) Y’ (5, 3) Z’ (3, -1)208. To plan a scene in an animated movie, Roger rotates the below figure around point P by 90° in a clockwise direction. Which drawing shows the pre-image and the final image? Ba. b.c. 209. Use the diagram to answer the questions. a) If X is reflected across line 3, where will it end up?? Bb) What sequence of transformations will map figure A onto figure B??reflect over 5, then reflect over 3c) What sequence of transformations will map figure D onto figure C??rotate 180, then translate 2 overd) If X is reflected across line 3 and then translated to the right, wlefttophere will it be?C210. Which translation moves ABC to A’B’C’?211. Which figure represents a rotation of figure 1? translate down 4 and right 8Figure 3212. Draw the image of this figure if it is reflected across the y-axis, and then reflected over the x-axis. Unit 6?: Connecting Algebra and Geometry Through CoordinatesG.GPE.4, 5, 6, 7- Use coordinates to prove simple geometric theorems algebraically213. Line m is represented by the equation y = 2x + 3. What is the equation of the line that is perpendicular to line m and passes through the point (-6, 1)??y = -1/2x - 2214. Given line l is y = 4x + 3, what is the equation of the line that is perpendicular to line l and runs through the point (2, -7)??y = -1/4x – 6.5 or y = -1/4x – 13/2215. Write an equation of the line that is perpendicular to the line y = 2x + 8 and passes through the point (6, -2)?.y = -1/2x + 1216. What is the equation of the line that is parallel to the line 5x + 20y = 10 and passes through the point (8, 3)??y = -1/4x + 5217. Write an equation of the line that is parallel to the line 2x + 4y = 6 and goes through the point(6, 4).y = -1/2x + 7218. Write an equation for the perpendicular bisector for the line segment shown in the graph.y = -11/2x – 63/4219. Write an equation of a line perpendicular to y = 13x+6 that passes through the point (2, -3).y = -3x + 3220. Determine if the point (-1, √7) lies on a circle centered at the origin and containing the point (3, 0).No, but if i twas (-1, √8) it would?!221. Determine if the point (4, 5) lies on a circle centered at (2, 2) and containing the point (2, -2).no222. Determine if the point (0, √3) lies on a circle centered at (-1, 3) and containing the point (-1, 1).no223. Rectangle ABCD has coordinates A(1, 1), B(1, 3), C(4, 3). Find the coordinates of D.D (4, 1)224. Prove that EFGH is a rhombus if the vertices given are E(-2, 3), F(0, 4), G(2, 3), H(0, 2).all 4 sides equal, d = √5225. The coordinates for the vertices of a right triangle are (1, 4), (6, 4), (6, 1). Calculate the area of the right triangle. Calculate the perimeter of the right triangle.P = 8 + √34 or 13.8?; A = 7.5226. Classify the quadrilateral LMNO with vertices L(-3, 4), M(3, 3), N(5, 7), and O(-1, 8).Then, prove that the diagonals bisect each other. What formula do you use??parallelogram, sides are √37 and 3√2, use distance formula to prove diagonals bisect227. Determine the most precise name for the quadrilateral shown. How can you PROVE it?? rhombus, all sides are √5 using distance formula228. A rhombus has vertices at (0, 0), (1, 4), (5, 5), and (4, 1). Prove that the diagonals of the rhombus are perpendicular. Prove that all 4 sides are congruent. Then find the perimeter. use slope to prove perpendicular?: (5, 5) and (0, 0) slope is 1, (1, 4) and (4, 1) slope is -1, so they are negative reciprocals?; sides measure √17?; P = 4√17 or 16.5229. Classify the quadrilateral with vertices P(-2, 1), A(1, 4), R(4, 1), and T(1, -2). Prove it using coordinate geometry (distance, slope). Then, find the perimeter and area. square, sides are 3√2 and perpendicular?; P = 12√2 or 17 and A = 18230. Find the point, M, that divides segment AB into a ratio of 32 if A is at (0, 15) and B is at (20, 0).(12, 6)231. Find the point, M, that divides segment AB into a ratio of 5:2 if A is at (-1, 2) and B is at (8, 15).(38/7, 79/7)232. Given the points P(-4, -2) and Q(4, -10), what are the coordinates of the point on directed line segment PQ that partitions PQ in the ratio 4:1?(12/5, -42/5)233. Given the points A(-4, -2) and B(4, -10), what are the coordinates of the point on directed line segment AB that partitions AB in the ratio 53? (1, -7)234. Given the points A(-33, 0) and B(0, 44), find the coordinates of the point P on directed line segment AB that partitions AB in the ratio 47?(-21, 16)235. Given the points P(2, 3) and Q(5, 9), find the coordinate M that partitions directed line segment PQ in a ratio of 1:2. (3, 5)236. Find the coordinate, T, that divides AB into a ratio of 3:1 if A is at (-1, -6) and B is at (-5, 2).(-4, 0)237. Find the coordinate, T, that partitions segment AB in a ratio of 32 if A is (2, -2) and B is (-3, 8). (-1, 4)238. Find the coordinate, T, that divides AB into a ratio of 2:1 if A is at (-1, 2) and B is at (5, 12). (3, 26/3)239. Triangle ABC has vertices at (2, 4), (-5, -3), and (2, -3). Find the perimeter and area of the triangle.P = 14 + 7√2 or 23.9 and A = 24.5240. Find the perimeter and area of rectangle with vertices A(-5, 0), B(3, 2), C(-4, -4), D(4, -2). P = 6√17 or 24.7 and A = 34241. Given a rectangle with vertices E(-3, 5), F(1, 4), G(-1, -4), H(-5, -3), calculate the perimeter and area of the rectangle. Then use distance formula to prove the diagonals bisect each other. P = 6√17 or 24.7 and A = 34; use distance formula to prove diagonals bisect by finding the two distances and proving they’re the same242. Classify the quadrilateral with vertices at (-5, 3), (3, 5), (5, -3), and (-3, -5). Then find the perimeter and area of the quadrilateral.Square, P = 8√17 or 33 and A = 68243. Classify the quadrilateral with vertices at (-5, 2), (-1, 4), (4, -1), and (-4, -5). Then find the perimeter of the figure.trapezoid (slopes are parallel, m = ?); P = 6√5 + 10√2 or 27.6244. Quadrilateral ABCD has vertices at A(-3, 4), B(3, 2), C(5, -4), and D(-1, -2). What type of quadrilateral is ABCD? How do you know? What is the perimeter of ABCD?rhombus because all sides 2√10; P = 8√10 or 25.3245. A triangle has vertices at (9, 15), (20, 13), and (20, 5). Calculate the perimeter and area of the triangle. sides are 8, 5√5, and √221; P = 34.0 and A = 20√5 or 44.7246. Triangle ABC has vertices shown. What is the area and perimeter of the triangle?sides are √68 for 2 legs and 2√34 for hypotenuse; A = 34; P = 2√34 + 4√17 or 28.2247. Use the graph to calculate the area and perimeter of the triangle shown. sides are 3, 4, 5; P = 12 and A = 6248. Triangle PQR has vertices at P(-3, 1), Q(1, 3), and R(3, -2). Find the perimeter and area of the triangle. sides are 3√5, 2√5, and √29?; P = √29 + 5√5 or 16.6 and A = √145 or 12.0 ................
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