TCM Final Review Packet Name Per.

Transcription

1 TCM Final Review Packet Name Per. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Translate the statement into a formula. 1) The total distance traveled, d, at a constant speed of 50 miles per hour is the product of the speed and the number of hours traveled, h. 1) A) d = 50h B) d = 50 - h C) d = D) d = h + 50 Solve the problem. 2) What will the temperature be in degrees Fahrenheit when it is 5 Celsius outside? (Recall the formula 2) A) 41 Fahrenheit B) 66.6 Fahrenheit C) 15.4 Fahrenheit D) 34.8 Fahrenheit Solve the proportion for the given variable. 3) = 3) A) n = 40 B) n = C) n = 2 D) n = 4 Solve. 4) Yearly homeowner property taxes are figured at a rate of $ 1.75 tax for every $100 of home value. Find the property taxes on a condominium valued at $ 167,000. 4) A) $ B) $ C) $ D) $ ) It is recommended that there be at least 11.2 square feet of ground space in a garden for every newly planted shrub. A garden is 25.6 feet by 17.5 feet. Find the maximum number of shrubs the garden can accommodate. 5) A) 40 shrubs B) 128 shrubs C) 3 shrubs D) 13 shrubs Solve the problem. 6) Your associate, who wanted to improve his physical fitness for an event to take place on July 1st, started a diet and exercise regimen on January 1st. He measured his weight on that day and on the 1st of each month thereafter until July 1st. Having met his goals on July 1st, he decided to continue with the regimen and record keeping for the remainder of the year. The data is used to construct a graph, where the number of months since July 1st is the input variable, and the weight lost or gained during each month is the output variable. Note that July 1st is taken to be time zero, since this date is of interest as a reference point. If the graph tells you that 2 pounds were lost in February, in which quadrant is the point for February located? 6) A) Quadrant I B) Quadrant III C) Quadrant II D) Quadrant IV 7) When you were born, your uncle put $1000 into a bank account for you. According to the terms of the account, your investment grows in a manner represented by the following graph.

2 Which variable is the independent variable? Which variable is the dependent variable? If you are 18 years old, how much money is in the account? 7) A) Time; amount; $2100 B) Dollars; years; $2000 C) Time; amount; $2000 D) Dollars; years; $1900 8) The cost of printing a catalog of the products that your company distributes is a flat rate of $59 plus $0.22 per copy. Let C represent the total cost of printing and x represent the number of copies. Write in symbolic form an equation that will relate C and x. Organize the data into a table of values. Begin with 500 copies, increase by increments of 500, and end with 2500 copies. 8) A) C = 59.22x B) C = 59.22x C) C = x D) C = x

3 Solve the equation for x. 9) ( 16x - 20) = ( 15x - 12) 9) A) B) -20 C) 1 D) -1 Solve the problem. 10) The cost in producing a shipment of widgets that you supply to various regional businesses consists of a setup expense of $20 plus $0.22 per widget. Let C be the total cost of producing a shipment, and let x represent the number of widgets in a shipment. Write in symbolic form an equation that will relate C and x. Generate five data points from this equation using equally incremented x values ranging from 100 to 500, and use this data to plot a graph. How many widgets can you include in a shipment if you don't want to spend more than $53.00 making them? 10) A) C = x; 150 widgets can be included in the shipment. included in the shipment. B) C = 0.22x; 20 widgets can be C) C = x; 20 widgets can be included in the shipment.

4 included in the shipment. D) C = x; 100 widgets can be Solve for the specified variable. 11) P = s1 + s2 + s3 for s3 11) A) s3 = s1 + s2 - P B) s3 = P - s1 - s2 C) s3 = P + s1 + s2 D) s3 = s1 + P - s2 Solve the problem. 12) Joe is going to travel to Dallas. He lives 400 miles away and can average 60 miles per hour. Use an equation to represent the distance D from Dallas in terms of h, the number of hours Joe has traveled. 12) A) D= 400h + 60 B) D = h C) D = h D) D = 60h 13) There is a relationship between the expected number of tickets sold for a raffle and the dollar value of the prize for the raffle. The equation T - 6P = 100 describes this relationship, where T is the expected number of tickets sold, and P is the dollar value of the raffle prize. Suppose the expected ticket sales for a certain raffle are Determine the dollar value of the raffle prize. 13) A) $300 B) $1800 C) $250 D) $11,500 Perform the specified translation. 14) The graph on the left is the graph of the function defined by y = f(x).

5 Sketch a graph of the function defined by the equation y = f(x) - 1. Describe the type of shift that was performed on the original graph. 14) A) A horizontal shift of the graph of y = f(x), 1 unit to the right. B) A horizontal shift of the graph of y = f(x), 1 unit to the left. C) A vertical shift of the graph of y = f(x), 1 unit downward.

6 D) A vertical shift of the graph of y = f(x), 1 unit upward. Solve the problem. 15) The results of an analysis, on the makeup of garbage, done by the Environmental Protection Agency was published in Some of the results are given in the following table, which for various years gives the number of pounds per person per day of various types of waste materials. For metals, calculate the average rate of change between 1980 and Then interpret what this value means. 15) A) From 1980 to 1988, the number of pounds of metal per person per day decreased by per year. B) From 1980 to 1988, the number of pounds of metal per person per day decreased by per year. C) From 1980 to 1988, the number of pounds of metal per person per day increased by 0.01 per year. D) From 1980 to 1988, the number of pounds of metal per person per day decreased by per year. Determine any data values that are missing from the table, assuming that the data represent a linear function. 16)

7 16) A) missing x: -6; missing y: 23 B) Missing x: -7; missing y: 21 C) Missing x: -7; missing y: 23 D) Missing x: -6; missing y: 22 Solve the problem. 17) What is the slope of a roof that rises 21 feet over a run of 6 feet? 17) A) B) - C) - D) 18) You brake your car from a speed of 55 mph. The table shows data that represent your car's speed versus the amount of time elapsed from the moment that you began to brake. Graph the data. For what interval of time is the speed increasing? For what interval of time is the speed decreasing? For what interval of time is the speed constant? 18) A) None; 0 to 4 seconds; 4 to 6 seconds B)

8 None; 0 to 5 seconds; 5 to 6 seconds C) 0 to 5 seconds; None; 5 to 6 seconds D) 0 to 4 seconds; None; 4 to 6 seconds Find the slope of the line. 19) 4x + 5y = 32 19) A) B) C) - D) - Determine the x- and y- intercepts for the graph defined by the given equation. 20) x = 2 20) A) No x-intercept y-intercept is ( 2, 0) B) x-intercept is (0, 2) No y-intercept C) x-intercept is ( 2, 0) No y-intercept D) No x-intercept y-intercept is (0, 2) Find the equation of the line specified. 21) The slope is 4, and it passes through ( -4, 1). 21) A) y = 4x + 1 B) y = 8x + 17 C) y = 4x + 17 D) y = 4x - 15 Sketch a graph of the given equation. Use your graphing calculator to verify your graph. 22) y = -2x + 5

9 22) A) B) C)

10 D) Determine the slope and the x- and y-intercepts of the line. 23) x = -3 23) A) Undefined slope No y-intercept x-intercept is ( -3, 0) B) Slope is 0 y-intercept is (0, -3) No x-intercept C) Undefined slope No y-intercept x-intercept is (0, -3) D) Slope is 0 y-intercept is ( -3, 0) No x-intercept State the practical meaning of the slope and vertical intercept in the given situation. 24) The cost, in dollars, of a one-day car rental is given by where x is the number of miles driven. 24) A) $33 is the cost per day to rent the car and $0.23 is the cost per mile. B) $0.23 is the cost per day to rent the car and $33 is the cost per mile. C) $33 is the cost per day to rent the car and $23 is the extra cost for unlimited miles. D) $23 is the cost per day to rent the car and $0.33 is the cost per mile. Solve the problem. 25) When going more than 38 miles per hour, the gas mileage of a certain car fits the model where x is the speed of the car in miles per hour and y is the miles per gallon of gasoline. Based on this model, at what speed will the car average 15 miles per gallon? (Round to nearest whole number.) 25)

11 A) 48 B) 73 C) 98 D) 149 Find the equation of the graphed line. 26) 26) A) y = x - 5 B) y = - x - 5 C) y = x + 5 D) y = - x + 5 Solve the problem. 27) The paired data below consist of the temperatures on randomly chosen days and the amount a certain kind of plant grew (in millimeters). Use the regression equation where x is temperature and y is growth in millimeters, to predict the growth of a plant if the temperature is ) A) B) C) D) Graph the piecewise function. 28) f(x) = A) 28)

12 B) C) D) Solve the system algebraically. 29) y = 8x - 7 8x - y = -5 29) A) ( -2, -4) B) ( -2, 4) C) inconsistent; no solution D) ( 2, 4)

13 Solve the system graphically. 30) 4y + 20 = 0 x - 2y = 12 30) A) ( -5, 2) B) ( 2, -5) C) ( -5, -2) D) ( 2, 5) Solve the inequality algebraically. 31) -3 < 2x ) A) -4 < x 0 B) -4 x 0 C) -4 x < 0 D) -4 < x < 0 Solve. 32) A store sells tents, sleeping bags, and camp stools. A customer buys a tent, 3 sleeping bags, and 2 camp stools for $ 215. The price of the tent is 6 times the cost of a camp stool. The cost of a sleeping bag is $ 35 more than the cost of a camp stool. Find the cost of each item. 32) A) $ 60 for a tent; $ 45 for a sleeping bag; $ 10 for a camp stool B) $ 60 for a tent; $ 50 for a sleeping bag; $ 15 for a camp stool C) $ 60 for a tent; $ 45 for a sleeping bag; $ 11 for a camp stool D) $ 66 for a tent; $ 45 for a sleeping bag; $ 11 for a camp stool Translate the following into an inequality statement. 33) x is at most -3 or is greater than 8. 33) A) x -3 or x > 8 B) x -3 or x < 8 C) x < -3 or x 8 D) x > -3 or x 8 Solve. 34) You own a hot dog cart in your city. Your monthly profit is determined from the expression 1.50x - 75, where x represents the number of hot dogs sold each month. The number 1.50 in the expression is the profit for each hot dog. The cost of leasing the hot dog cart is the number 75 in the expression. Your profit has been fluctuating between $ 1700 and $ 2200 per month. Determine approximately between what two values your hot dog sales have to be to realize this range of profit. 34) A) 1083 x 1416 B) 1183 x 1516 C) 1183 x 1517 D) 1083 x 1417 The feasible region for a set of constraints is given. The feasible points are indicated in each corner of the graphed region. Complete the table to determine the minimum or maximum value, as indicated, of the objective function. 35) Determine the maximum value of the objective function P= 7x + 3y.

14 35) A) 36 B) 44 C) 100 D) 16 Solve the system of linear inequalities. 36) x - y 0 y -4x ) A) B)

15 C) D) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Determine the corner points of the solution set of the system of linear inequalities. 37) x 0 x 4000 y 0 y 2000 x + y 7500

16 37) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the linear programming problem. 38) Minimize the objective function: C = 25x + 35y subject to the following constraints: 150x + 100y x + 50y 550 x 0 y 0 A) 345 B) 275 C) 0 D) 455 Solve. 38) 39) A dietitian needs to purchase food for patients. She can purchase an ounce of chicken for and an ounce of potatoes for Let number of ounces of chicken and number of ounces of potatoes purchased per patient. Write the objective function that describes the total cost C per patient per meal. 39) A) C = 0. 25x y B) C = 0.0 3x y C) C = 3y + 25y D) C = 25x + 3y Solve the linear programming problem. 40) An appliance manufacturer must ship at least 200 stoves to two warehouses, one in Grenston, the other in Mariville. Each warehouse can hold as many as 150 stoves at one time. Grenston currently holds 30 stoves, while Mariville has 40 in the warehouse. It costs $17 to ship one stove to Grenston and $13 to ship one to Mariville. How many stoves should be shipped to each warehouse to minimize the cost of shipping? What is that minimum cost?

17 40) A) The minimum cost will be $ 2920 when 120 stoves are shipped to Grenston and 80 stoves are shipped to Mariville. B) The minimum cost will be $ 3040 when 90 stoves are shipped to Grenston and 110 stoves are shipped to Mariville. C) The minimum cost will be $ 2960 when 90 stoves are shipped to Grenston and 110 stoves are shipped to Mariville. D) The minimum cost will be $ 3080 when 120 stoves are shipped to Grenston and 80 stoves are shipped to Mariville. For the given equation, find the values of a, b, and c, determine the direction in which the parabola opens, and determine the y-intercept. Enter these findings into the table. 41) y = 6 + 2x ) A) B) C) D) Find the equation of the axis of symmetry of the parabola. 42) y = + 7x ) A) x = 7 B) x = C) y = 5 D) x = - Find the vertex of the parabola and determine if it is a minimum or maximum. 43) f(x) = -2x2 + 4x ) A) ( 1, 3); maximum B) ( 1, 3); minimum C) ( 1, -3); maximum D) ( 1, -3); minimum Use a graphing calculator to sketch the graph of the quadratic equation, and then determine the coordinates of the x- intercepts (if they exist).

18 44) y = + 13x ) A) ( 5, 0), ( 8, 0) B) ( 5, 0), (-8, 0) C) (-5, 0), (-8, 0) D) (-5, 0), ( 8, 0) Use a graphing calculator to sketch the graph of the quadratic equation, and then determine the domain and range. 45) y = x ) A) D: all real numbers; R: (y 8.2) B) D: x 0.2; R: y 8 C) D: x 0.2; R: all real numbers D) D: all real numbers; R: y 8.2 Use a graphing calculator to sketch the graph of the quadratic equation, and then determine the x-intervals over which the graph is increasing and decreasing. 46) y = x ) A) Increasing: x < ; Decreasing: x > B) Increasing: x < -7; Decreasing: x > -7 C) Increasing: x < 0.625; Decreasing: x > D) Increasing: x < ; Decreasing: x > Use a graphing calculator to approximate the vertex of the graph of the parabola defined by the following equation. 47) y = -5-6x ) A) ( 3, 6.8) B) ( -0.6, 3.2) C) ( 0.6, 6.8) D) ( -0.6, 6.8) Completely factor the polynomial. 48) - 6y ) A) (y - 6)(y + 6) B) C) D) (y - 3)(y + 3) Determine one solution of the quadratic equation numerically. That is, complete the table of (x, y) ordered pairs, and estimate the value of x that results in the required y-value. 49) - 8x + 14 = 11 49) A) x 0.5 B) x 0.3 C) x 0.2 D) x 0.4 Solve equation by using the quadratic formula. 50) x = -6 50) A) x =, B) x = -, - C) x =, D) x = -, - Solve the following equation by factoring. 51) = + 7a 51) A) a = 5, B) a = 5, 2 C) a = 5 D) a = -5, Solve. 52) A ball is thrown upward from the top of a 96-foot building. The height, h (in feet), of the ball is modeled by on its way down? where t is measured in seconds. After how many seconds will the ball pass the top of the building 52) A) 5 sec B) 4 sec C) 7 sec D) 96 sec

19 53) The sales for a gaming console for various years are listed in the table below. Let s represent the sales (in billions of dollars) at t years since A reasonable model is the model to predict sales in ) Use A) $5.85 billion B) $7.16 billion C) $6.41 billion D) $7.71 billion Sketch the graph of the following pair of functions. Describe the differences and similarities in the graphs. 54) y = 2-1, y = ) A) The graph y = is shifted horizontally 6 units to the left of y = 2-1. B) The graph y = is shifted vertically 6 units below y = 2-1.

20 C) The graph y = is shifted horizontally 6 units to the right of y = 2-1. D) The graph y = is shifted vertically 6 units above y = 2-1. Solve. 55) y varies inversely as x and y = 8 when x = 13. Determine the value of x when y = ) A) 3.08 B) 15.6 C) 0.33 D) 5 56) Suppose you are embarking on a journey of 326 kilometers. Assume that you travel the entire distance at a constant speed. Express your time to complete this journey as a function of your speed. 56) A) T = 326s B) T = C) T = D) s = State the relationship between the graphs of f(x) and g(x).

21 57) f(x) =, g(x) = 57) A) g is symmetric about the y-axis, and f is symmetric about the origin. B) g is symmetric about the y-axis, and f is symmetric about the x-axis. C) g is closer to the x-axis, and f is closer to the y-axis. D) g is closer to the y-axis, and f is closer to the x-axis.

22 1) A 2) A 3) D 4) A 5) A 6) B 7) C 8) D 9) D 10) A 11) B 12) C 13) A 14) C 15) A 16) D 17) D 18) A 19) D 20) C 21) C 22) A 23) A 24) A 25) B 26) A 27) A 28) C 29) C 30) B 31) A 32) A 33) A 34) C 35) B 36) D 37) The corner points are (4000, 0), (4000, 2000), (5500, 2000) and (7500, 0). 38) B 39) A 40) C

23 41) A 42) D 43) A 44) A 45) A 46) C 47) D 48) C 49) D 50) D 51) B 52) A 53) D 54) D 55) D 56) C 57) C