Algebra 2 Unit 1 Print

Transcription

1 lgebra 2 Unit 1 Print Question 1 entano spends $170 to order 30 pounds of nuts from an online company. The company charges $3.50 per pound for peanuts and $7.50 per pound for almonds. It also charges a flat fee of $13 for shipping and handling. Which equation can be used to find p, the number of pounds of peanuts entano buys? 3.5p (p 30) 13 = p (p 30) + 13 = p (30 p) 13 = p (30 p) + 13 = /23

2 Question 2 The cost of a taxi ride, in dollars, is $2 for the first quarter mile plus $0.40 for each quarter mile after that. Jameel cannot afford to spend more than $20 on a taxi ride (4m 1) = 20 The equation can be used to find m, the distance, in miles, that Jameel can travel for $20. What is the maximum distance? D 11.5 miles 13.5 miles 14.0 miles 16.0 miles 2/23

3 Question 3 Isaac shoveled 9 of his neighbors' driveways after a snow storm. He charged $25 for a short driveway and $45 for a long driveway. Which equation can be used to find y, the total amount that Isaac charged when x of the driveways are short? D y = 25x + 45 (9 x) y = 45x + 25 (9 x) y = 25x + 45 (9 + x) y = 45x + 25 (9 + x) 3/23

4 Question 4 4/23

5 Penn is using Shipping World's international shipping rates to calculate the shipping cost for her packages. The company charges $30 plus $8 per pound for each package. Which graph models the cost, y, of shipping a package that weighs x pounds? 5/23

6 6/23

7 Question 5 Melissa plans to run her first marathon. Her sponsors have pledged to donate a total of $45 plus $5 per mile that she runs. Graph the equation that models the amount that her sponsors will donate, y, if she runs x miles. 7/23

8 Question 6 n architect measures a beam to be centimeters long, with an accuracy of plus or minus 0.02 centimeter. Which equation can be used to find the limits of the actual length of the beam? D x = 0.02 x = = x = x Question 7 Which number line shows the solution to the inequality 3 2x > 13? D 8/23

9 Question 8 kiva has an international calling card worth $50. Each call to India costs $2.20 per minute. Which function represents the amount of money that kiva has left on her card after speaking for m minutes? D (m) = 2.2m + 50 (m) = 2.2m 50 (m) = 50m (m) = 50m /23

10 Question 9 Dino has $1,000 in a savings account that was started for him when he was born. He has a part time job where he earns $60 each week, and he puts $20 of that into his account each week. n equation could be used to model the amount in his account, y, after x weeks. Which statements are true about a graph of the equation that will show his account balance during a year? heck all that apply. The x axis should be labeled from 0 to 12 months since you want to see the change over a year. The x axis should be labeled from 0 to 52 weeks since you want to see the change over a year. The y axis should be labeled from $0 to $1,000 since the money in the account will not go above $1,000. The y axis should be labeled from $0 to $1,300 since the money in the account will not go above $1,300. The y axis should be labeled from $750 to $1,000 since that is the approximate range of y values for the year. The y axis should be labeled from $1,000 to $2,100 since that is the approximate range of y values for the year. 10/23

11 Question 10 Mike can take the city bus to school, or he can ride his bicycle. One bus ride costs him $1.75. He can bring his lunch to school or buy it there. uying lunch in school costs $2.50. He tries to spend no more than $30 on these options each month. Let x represent the number of lunches that Mike buys in school. Let y represent the number of bus rides that he takes. Which inequality represents all ordered pairs (x, y) that are possible options for Mike? 2.5x y 30 for x 0 and y 0 2.5x y 30 for x 0 and y y 2.5x for x 0 and y 0 D x 1.75y for x 0 and y /23

12 Question 11 The graph shows this system of inequalities, with their shaded solution region. 1 y x y 2x 2 y 2x 3 Which ordered pairs satisfy all three inequalities? heck all that apply. ( 3, 0) ( 2, 5) (0, 0) (2, 2) (3, 4) (6, 3) 12/23

13 Question 12 Which shows the solution to this system of equations? 3y + 12 = x 2 2y + 10 = 9x D (2, 2) (2, 4) (4, 2) (4, 4) 13/23

14 Question 13 child care company charges $435 per month for children who attend full time and $275 per month for children who attend part time. This month, they have 35 children registered for a total fee of $12,985. Let x represent the number of children who attend full time and y represent the number of children who attend part time. Which system of equations could be used to model this situation? D x + y = 35 ; 275x + 435y = 12, 985 x + y = 275 ; 35x + 35y = 435 x + y = 435 ; 35x + 35y = 12, 985 x + y = 12, 985 ; 435x + 275y = /23

15 Question 14 eniah sells hats and umbrellas. He charges $7.75 per hat and $9.50 per umbrella. Last week he sold 90 items for a total of $757. Let x represent the number of hats that eniah sold and y represent the number of umbrellas that he sold. Which system of equations could be used to model this situation? D x + y = 7.75 ; 9.5x + 9.5y = 90 x + y = 9.5 ; 7.75x y = 757 x + y = 90 ; 7.75x + 9.5y = 757 x + y = 757 ; 9.5x y = /23

16 Question 15 Graph the piecewise defined function that is given by when and by when. x 0 y = x + 5 x < 0 y = /23

17 Question 16 Graph the function y = 2x + 3. Question 17 onsider the functions f (x) = x + 3 and g (x) = x + 3. The graph of g can be obtained from the graph of f by what transformation?. 17/23

18 Question 18 f (x) = 3x + 2 Let and. (f g) (3) What is? g (x) = 4x D /23

19 Question 19 Wayne's Windows charges a $40 flat fee to cover travel and expenses plus $25 per hour to wash windows at one building. function c(h) can relate the cost of washing a building's windows and the number of hours, h, that it takes to wash them. Wayne's Windows can wash one window pane every 3 minutes. function h(p) can relate the hours that are needed to wash windows and the number of panes, p, in the windows. Which composition of functions describes the cost, c(h(p)), of washing p panes at one building? D c (h (p)) = p c (h (p)) = p c (h (p)) = p c (h (p)) = p 19/23

20 Question 20 Mr. Franklin has a furnace that burns 0.8 gallon of oil per hour in the winter. He pays $1.15 per gallon for oil. Which functions and composition of functions could be used to determine the cost of heating his house for 12 hours? D g (h) = 0.8h c (g) = 1.15g gives the gallons used in h hours; gives the cost of using g gallons; c (g (12)) = 0.92 (12) gives the cost of using the furnace for 12 hours. g (h) = 0.8h c (g) = 1.15g gives the gallons used in h hours; gives the cost of using g gallons; c (g (12)) = 1.95 (12) gives the cost of using the furnace for 12 hours. g (h) = h c (g) = g gives the gallons used in h hours; gives the cost of using g gallons; c (g (12)) = gives the cost of using the furnace for 12 hours. g (h) = h c (g) = g gives the gallons used in h hours ; gives the cost of using g gallons; c (g (12)) = gives the cost of using the furnace for 12 hours. 20/23

21 Question 21 Let f (x) = 3x + 1 and g (x) = x 2 1. (f g)(x) What is the composition? 3 x 3 + x 2 3x 1 3x 2 2 x 2 + 3x D 9 x 2 + 6x Question 22 f (x) = 2x 1 Let and. (g f)(4) What is? g (x) = 4 f (x) D /23

22 Question 23 y = 3x+2 Let. 4 What is the inverse of this function in slope intercept form? y = 4 x 2 3 y = 4 x y = 4x 2 3 D y = 3 x Question 24 f (x) = (3x + 15) Let. What is f 1? f 1 (x) = x 5 3 f 1 (x) = x f 1 (x) = x D f 1 (x) = x /23

23 Question 25 f (x) = 4x 3 g f (g (x)) = x g (f (x)) = x Let. Suppose there is a function such that and. g (x) What is? D g (x) = 4x 3 x 3 g (x) = 4 g (x) = 4x + 3 g (x) = x /23