Semester Exam Review

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1 Semester Exam Review Name Date Block MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 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. 1) y = 5x 2 1) A) up (0, 0) B) up (0, 5) C) up (0, 5) D) up (0, 0) 2) y = x 2-7x 2) A) down (0, 0) B) up (0, 0) C) up (0, 0) D) up (0, -7) Find the equation of the axis of symmetry of the parabola. 3) y = x 2 + 3x + 1 3) A) x = 3 2 B) x = 3 C) y = 1 D) x = ) y = 3x2 + 24x ) A) x = -4 B) x = 4 C) x = 5 D) x = -5 Find the vertex of the parabola. 5) y = -3x2 + 30x ) A) (-5, -1) B) (, ) C) (-1, -5) D) (, ) Use a graphing calculator to sketch the graph of the quadratic equation, and then give the coordinates for the x-intercepts (if they exist). 6) y = -4x x ) A) (-2, 0); (5, 0) B) (2, 0); (-5, 0) C) (2, 0); (5, 0) D) (-2, 0); (-5, 0) 1

2 7) y = x 2 + 7x ) A) (2, 0); (-5, 0) B) (2, 0); (5, 0) C) (-2, 0); (5, 0) D) (-2, 0); (-5, 0) 8) y = -x x ) A) (-7, 0); (7, 0) B) (7, 0); (-7, 0) C) (7, 0); (7, 0) D) (-7, 0); (-7, 0) Use a graphing calculator to sketch the graph of the quadratic equation, and then state the domain and range. 9) y = x 2 + 2x + 1 9) A) D: all real numbers; R: (y 0) B) D: all real numbers; R: (y 0) C) D: all real numbers; R: (y 1) D) D: (x 1), R: (y 1) 10) y = x 2 + x ) A) D: all real numbers; R: (y 9.75) B) D: all real numbers; R: (y 9.75) C) D: (x 0), R: (y 0) D) D: all real numbers; R: (y -9.75) 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. 11) y = x 2 + 2x ) A) Increasing: (x < 1), Decreasing: (x > 1) B) Increasing: (x > -1), Decreasing: (x < -1) C) Increasing: (x > 1), Decreasing: (x < 1) D) Increasing: (x < -1), Decreasing: (x > -1) 12) y = x 2 + 2x ) A) Increasing: (x > -1), Decreasing: (x < -1) B) Increasing: (x <1), Decreasing: (x > 1) C) Increasing: (x > 1), Decreasing: (x < 1) D) Increasing: (x < -1), Decreasing: (x > -1) Use a graphing calculator to approximate the vertex of the graph of the parabola defined by the following equation. 13) y = x 2 + x ) A) (0.5, 4.75) B) (-0.5, 4.75) C) (-0.5, 5) D) (0.5, -4.75) 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. 14) 5x 2-9x = 18 x y A) x 2 B) x 5 C) x 3 D) x 4 14) Solve equation by using the quadratic formula. 15) 12x 2 + 5x = 0 15) A) x = ± 5 B) x = , 0 C) x = , 0 D) x = 0 16) 5x 2-2x = 7 16) A) x = 5 7, -1 B) x = 7 5, -1 C) x = 5 7, 1 D) x = 5 7, 0 2

3 Solve the problem. 17) A ball is kicked upward with an initial velocity of 40 feet per second. The ball's height, h (in feet), from the ground is modeled by h = -16t t, where t is measured in seconds. What is the practical domain in this situation? A) 0 t 2.5 B) 0 t 1.25 C) 0 t 10 D) All real numbers 17) Solve. 18) The data set represents a progression of hourly temperature measurements. Use a graphing calculator to determine the quadratic regression equation for this data set. x y A) y = x x B) y = 0.795x x C) y = x x D) y = x x ) The sales for a gaming console for various years are listed in the table below. Sales Year (in billions of dollars) Let s represent the sales (in billions of dollars) at t years since Use your graphing calculator to determine the quadratic regression equation for this data set. A) s = 0.20t t B) s = 0.065t t C) s = 0.065t t D) s = 0.20t t ) 19) 20) If y varies directly as x and y = 54 when x = 9, what is the value of y when x = 3? 20) A) 9 B) 81 C) 36 D) 18 21) If y varies inversely as x and y is 3.5 when x is 4, what is y when x is 5? 21) A) 0.18 B) 2.8 C) 5.6 D) ) If y varies directly as the x 2 and y = 324 when x = 6, what is the value of y when x = 8? 22) A) 432 B) 54 C) 48 D) ) The distance an object falls when dropped from a tower varies directly as the square of the time it falls. If the object falls 144 feet in 3 seconds, how far will it fall in 9 seconds? A) 144 ft B) 1296 ft C) 1134 ft D) 1458 ft 23) 24) If 2.2 pounds of a certain grain cost $1.32, how much will 5.7 pounds of the grain cost? 24) A) $3.42 B) $4.79 C) $4.38 D) $ ) Suppose you are embarking on a journey of 229 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. A) s = T 229 B) T = s 229 C) T = 229s D) T = 229 s 25) 3

4 State the relationship between the graphs of f(x) and g(x). 26) f(x) = -3 x, g(x) = 3 x A) g is shifted to the left 3 units relative to f, otherwise they are the same. B) f and g are reflections of each other about the x-axis. C) g is shifted to the right 3 units relative to f, otherwise they are the same. D) f and g are reflections of each other about the y-axis. 26) Solve. 27) You just started a new job and received a $6500 bonus. You decide to invest this money so that you can purchase a new car in five years. Your local credit union offers a CD paying 5% annual interest compounded semiannually. How much money will you have at the end of five years? A) $10, B) $ C) $ D) $ ) You just started a new job and plan on purchasing a new car in five years. You want to have $7500 as a down payment for the new car. Your local credit union offers a CD paying 6% annual interest compounded semiannually. How much money will you have to invest now to have $7500 at the end of five years? A) $ B) $ C) $ D) $ ) You plan to start a consulting business for software programming. You deposit $340 at the beginning of each month into an account paying 4.5% compounded monthly. How much will be in the account after five years? A) $28, B) $22, C) $28, D) $22, ) You notice the following advertisement in the local newspaper: 27) 28) 29) 30) A 32-foot motorboat for sale price of $34,000; $8000 down and $600 per month for 60 months Determine the total finance charge. A) $2000 B) $6000 C) $10,000 D) $9400 4

5 Solve. Mathematical Models with Applications 31) The Anderson's are ready to purchase their first home. This home sells for $342,000. The Andersons must put down a 15% down payment and they are required to pay 3 points at closing. What is the amount of the mortgage? A) $290,730 B) $342,000 C) $290,700 D) $393,300 32) The Montgomerys borrowed $209,000 at 7.5% for 30 years to purchase a house. Find the monthly payment and the sum of the principal and interest charges. A) $ , $500, B) $ , $552, C) $ , $556, D) $ , $526, ) 32) Solve the problem. 33) After spending $3750 for tables and $3250 for chairs, a convention center manager finds that the total is 8% more than he spent on tables and chairs last year. To the nearest dollar, find the amount that he spent last year. A) $560 B) $3533 C) $6481 D) $ ) After receiving a discount of 5.5% on its bulk order of notebooks, John's Office Supply pays $6993. What was the price of the order before the discount? A) $7400 B) $6608 C) $6958 D) $ ) 34) 5

6 You are planning on purchasing a new car and have your eye on a specific model. You know that new car prices are projected to increase at a rate of 5% per year for the next few years. 35) Find the cost of the car 2 years from now if the current price is $25,000. Write the equation that 35) represents the projected cost C and provide a solution for the problem. A) C = 25,000(1.05) 2 ; $27, B) C = 25,000(2) 1.05 ; $51, C) C = 25,000(2) ; $47, D) C = 25,000(1.05)(2); $52, Without using a graphing calculator, match the graph with its equation. 36) h(x) = 2.7(1.3) x 36) A) B) C) D) 6

7 37) h(x) = -2.8(1.4) x 37) A) B) C) D) Complete the table representing an exponential function. 38) x y A) B) C) D) ) Write the equation of the exponential function that represents the data in the table. 39) x 0 2 y A) y = 2.4(4) x B) y = 2.4 x C) y = 4(2.4) x D) y = 4(x) ) 40) x 0 2 y A) y = 9(0.4) x B) y = 0.4(9) x C) y = 9(x) 0.4 D) y = 0.4(x) 9 40) 7

8 Without graphing, classify the function as increasing or decreasing, and determine f(0). 41) f(x) = 7 1 x 5 41) A) f(0) = 1 ; increasing B) f(0) = 7; decreasing 5 C) f(0) = 1 ; decreasing D) f(0) = 7; increasing 5 Provide an appropriate response. 42) The data in the following table can be approximately modeled by an exponential function. What is the constant ratio of successive y-values? x y A) 1.5 B) 10 C) 1.33 D) ) Solve the problem. 43) Suppose that an investment of $11,000 grows in value at a rate of 0.08% per year. What is the growth factor for this investment? 43) A) 0.08 B) 8 C) 1 8 D) ) The number of VHS movie rentals has declined since the year 2000 due to the popularity of DVDs, as the following table shows. The exponential regression equation was found to be y = 9.79(0.8213) x where x represents the number of years since Use the regression equations to predict the number of VHS movie rentals in ) Year Number of VHS Rentals (in millions) A) 1.37 B) 0.14 C) D) 0 Evaluate the function requested. Write your answer as a fraction in lowest terms. 45) 45) Find tan A. A) tan A = 13 5 B) tan A = 5 13 C) tan A = 12 5 D) tan A =

9 46) Mathematical Models with Applications 46) Find sin A. A) sin A = 3 5 B) sin A = 5 4 C) sin A = 4 3 D) sin A = 4 5 Find the surface area of the figure. Use 3.14 for. Round your answer to hundredths. 47) 47) 7 ft 39 ft 49 ft A) 3143 sq. ft B) 5054 sq. ft C) 2527 sq. ft D) 13,377 sq. ft Find the volume of the specified cone. Use 3.14 for, and round your answer to the nearest whole number. 48) Diameter = 3 cm, Height = 9 cm 48) A) 85 cu. cm B) 127 cu. cm C) 57 cu. cm D) 21 cu. cm Solve the equation for x. 49) 1 5 (10x - 25) = 1 (20x - 8) 49) 4 A) 1 10 B) -10 C) 1 D) -1 Find the surface area of the figure. Use 3.14 for. Round your answer to hundredths. 50) 50) 2 in. A) sq. in. B) sq. in. C) sq. in. D) sq. in. 9

10 Solve. 51) The data set represents a bimonthly progression of gasoline prices over the course of several months in an unspecified city. Use a graphing calculator to determine the quadratic regression equation for this data set. x y A) y = x x B) y = x x C) y = x x D) y = x x ) Use a graphing calculator to approximate the vertex of the graph of the parabola defined by the following equation. 52) y = -2x 2 + 6x ) A) (1.5, 1) B) (-1.5, ) C) (1.5, -3.5) D) (1.5, 5.5) Solve the equation for x. 53) 1 4 (8x - 12) = 1 (6x - 4) 53) 2 A) 1 6 B) -1 C) 1 D) -6 54) 9x - (7x - 1) = 2 54) A) 1 B) C) D) Solve the problem. 55) 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. 55) Elapsed Time (seconds) Speed (mph) 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? A) B) 0 to 4 seconds; None; 4 to 6 seconds None; 0 to 4 seconds; 4 to 6 seconds 10

11 C) Mathematical Models with Applications D) None; 0 to 5 seconds; 5 to 6 seconds 0 to 5 seconds; None; 5 to 6 seconds Sketch a graph of the given equation. Use your graphing calculator to verify your graph. 56) y = 3x ) A) B) 11

12 C) D) State the relationship between the graphs of f(x) and g(x). 57) f(x) = 1 x 2, g(x) = 1 x 4 57) A) g is symmetric about the y-axis, and f is symmetric about the origin. B) g is closer to the x-axis, and f is closer to the y-axis. C) g is symmetric about the y-axis, and f is symmetric about the x-axis. D) g is closer to the y-axis, and f is closer to the x-axis. Solve the problem. 58) Find the break-even point for the given cost and revenue equations. Round to the nearest whole unit. C = 50n + 300,000 R = 95n A) 2069 B) 45 C) 145 D) ) The maximum weight for an elevator is 1500 pounds. You need to move boxes each weighing 30 pounds, and you weigh 160 pounds. Write an inequality that can be used to determine the maximum number of boxes that you can place in the elevator at one time. Assume only you and the boxes are in the elevator. A) n 1500 B) n C) n D) n ) 59) Determine the slope and the x- and y-intercepts of the line. 60) x = -2 60) A) Slope is 0 B) Undefined slope y-intercept is (-2, 0) No y-intercept No x-intercept x-intercept is (0, -2) C) Undefined slope No y-intercept x-intercept is (-2, 0) D) Slope is 0 y-intercept is (0, -2) No x-intercept 12

13 Answer Key Testname: MMA SEMESTER EXAM REVIEW 1) D 2) B 3) D 4) A 5) B 6) A 7) D 8) C 9) B 10) B 11) B 12) A 13) B 14) C 15) C 16) B 17) A 18) C 19) C 20) D 21) B 22) D 23) B 24) A 25) D 26) B 27) C 28) D 29) B 30) C 31) C 32) D 33) C 34) A 35) A 36) B 37) D 38) A 39) C 40) A 41) B 42) A 43) D 44) A 45) D 46) D 47) B 48) D 49) D 50) D 13

14 Answer Key Testname: MMA SEMESTER EXAM REVIEW 51) D 52) D 53) B 54) A 55) B 56) C 57) B 58) D 59) A 60) C 14

15 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30) 31) 32) 33) 34) 35) 36) 37) 38) 39) 40) 41) 42) 43) 44) 45) 46) 47) 48) 49) 50) 51) 52) 53) 54) 15

16 55) 56) 57) 58) 59) 60) Mathematical Models with Applications 16