Math Spring 08 Midterm Review Problems Page Note: Certain eam questions have been more challenging for students. Questions marked (***) are similar to those challenging eam questions. Let f and g. (***) Evaluate and simplify. Use these functions to answer the net two questions. f g. (B) (E) None of these f.. Evaluate and simplify g (B) (E). Consider the functions S and T. Find T (B) (E) S.
Math Spring 08 Midterm Review Problems Page For a particular car, the following tables show the fuel efficiency of the car as a function of the speed driven, and the average weekly gasoline cost in dollars as a function of the fuel efficiency. Use these tables to answer the net two questions. speed of car in mph f fuel efficiency in miles per gallon fuel efficiency in miles per gallon g average weekly gasoline cost in dollars 55 6 0 5 60 5 65 70 6 0 75 0 8 8. (***) Evaluate ( g f )(70) and give a practical interpretation. ( g f )(70) 0. When a car travels 70 mph, the average weekly gasoline cost is $0. (B) ( g f )(70). When a car travels 70 mph, the fuel efficiency is miles per gallon. ( g f )(70). When a car travels 70 mph, the average weekly gasoline cost is $. ( g f )(70). When a car travels 70 mph, the fuel efficiency is miles per gallon. (E) ( g f )(70) is undefined. 5. (***) Evaluate g () and give a practical interpretation. g (). When a car s fuel efficiency is miles per gallon, the weekly gasoline cost is $. (B) g (). When the weekly gasoline cost is $, a car s fuel efficiency is miles per gallon. g () 5. When a car s fuel efficiency is miles per gallon, the weekly gasoline cost is $5. g () 6. When the weekly gasoline cost is $, a car s fuel efficiency is 6 miles per gallon. (E) g () 70. When a car s fuel efficiency is miles per gallon, the car s speed is 70 mph.
Math Spring 08 Midterm Review Problems Page For an average 50-60 pound person, the following tables show the number of calories a person burns as a function of flights of stairs climbed, and the number of flights of stairs an average person climb as a function of minutes. An average flight of stairs is twelve steps. Use these tables to answer the net two questions. number of flights of stairs climbed f calories burned by an average person time in minutes climbing stairs g number of flights of stairs climbed 5 0 60 6 5 75 8 8 0 0 5 6. Evaluate ( f g)(8) and give a practical interpretation. ( f g)(8) 60. When a person climbs stairs for 8 minutes, the person burns 60 calories. (B) ( f g)(8) 0. When a person climbs stairs for 8 minutes, the person burns 0 calories. ( f g)(8). When a person climbs stairs for minutes, the person climbs 8 flights of stairs. ( f g)(8) 0. When a person climbs 8 flight of stairs, the person burns 0 calories. (E) ( f g)(8) is undefined. 7. (***) Evaluate g (5) and give a practical interpretation. g (5) 75. After 5 flights of stairs are climbed, the person has burned 75 calories. (B) g (5) 75. After 5 minutes of climbing stairs, the person has burned 75 calories. g (5) 0. After the person has climbed 5 flights of stairs, the person has climbed stairs for 0 minutes. g (5) 5. After 5 minutes of climbing stairs, the person has climbed 5 flights of stairs. (E) g (5) 0. After 5 minutes of climbing stairs, the person has climbed 0 flights of stairs.
Math Spring 08 Midterm Review Problems Page M N 8. (***) Determine the domain of if M and 6 N. All real numbers ecept, 0 and (B) All real numbers ecept and All real numbers ecept 0 All real numbers ecept, 0 and (E) All real numbers ecept and R T 9. Determine the domain of T. if R and, (B),,, (E), 0. Determine functions could NOT be choices for f and g so that f g f and g?. Which one of the following f and g (B) f and g f and g f and g
Math Spring 08 Midterm Review Problems Page 5 A stone is tossed into a pond and creates a circular ripple with a radius that increases at a rate of 0 cm/sec. Use this information to answer the net three questions.. Epress the radius of the ripple, r (in cm), as a function of time, t (in seconds). r t 0 t (B) rt 0t r t r t 0 0t (E) rt 0 t. Epress the area of the ripple, A, as a function of the radius, r (in cm). Ar 00r (B) Ar 0 r Ar 00 r Ar 0r (E) Ar r. Evaluate A r 000 (B) r,000 r 60,000 A r, 000 (E), and give a practical interpretation. A r 6,. After seconds, the area of the ripple is 6,000 square cm. A. After seconds, the area of the ripple is,000 square cm. A. After seconds, the area of the ripple is 60,000 square cm.. After seconds, the area of the ripple is,000 square cm. A r 600. After seconds, the area of the ripple is 600 square cm.
Math Spring 08 Midterm Review Problems Page 6 Your computer s screen saver is an epanding circle. The circle starts in the middle of the screen and epands outwards. With a inch screen, you have a viewing area of a 0 inch radius. The circle reaches the corners in seconds, epanding at a rate of.5 inches per second. Use this information to answer the net three questions.. Epress the radius of the circle, r (in cm), as a function of time, t (in seconds). (B) r t.5 r t. 5t rt.5t r t.5 t (E) rt.5 t 5. Epress the area of the circle, A, as a function of the radius, r (in inches). Ar 5r (B) Ar.5 r Ar 6.5 r A r 6.5r A r r (E) 6. Evaluate A r (B) r 0.5 A r 8. 75 A r 56. 5 (E) r 56.5, and give a practical interpretation. A r 8.75. After seconds, the area of the circle is 8.75 square inches. A. After seconds, the area of the circle is 0.5 square inches.. After seconds, the area of the circle is 8.75 square inches.. After seconds, the area of the circle is 56.5 square inches. A. After seconds, the area of the circle is 56.5 square inches.
Math Spring 08 Midterm Review Problems Page 7 7. Suppose h, where h f g. If f is g?, which one of the following g (B) g g g (E) g D q 0., represents the price. Determine a 8. (***) The demand function for selling bicycles during a week is given by q where q represents the number of bicycles sold and formula for the revenue function. Dq Rq 0.q (B) Rq 0q. q R q 0. Rq 0q.q q R q 0q. (E) q D q 9 0. 75, D represents the 9. The demand function for selling watermelons during a week is given by q where q represents the number of thousands of watermelons sold and q price. Determine a formula for the revenue function. R q 75 9q 0. q (B) Rq 9 0.75q R q 9000 q 750q Rq 9000 750q R q 9q 0.75q (E)
Math Spring 08 Midterm Review Problems Page 8 0. (***) Suppose the revenue and cost functions for a product are given by the functions R q 0.5q 80q C q 60q. Determine a formula for the profit function. and 00 P q 0.5q 60q 00 (B) P q 0.5q 60q 00 P q 0.5q 80 q 00 P q 0.5q 80 q 00 (E) P q 0.5q 60q 00. A local coffee shop owner has determined that the revenue and cost functions for a new coffee product are given by the functions Rq q 0q and C q 5q 00. Determine a formula for the profit function. P q q 5q 00 (B) P q q 5q 00 P q q 5q 00 P q q 5q 00 (E) P q q 5q 00. Determine a formula for the inverse function for 7 g. g 7 (B) g 7 7 g g 7 (E) g 7. (***) Determine a formula for the inverse function for h (B) h h. h h (E) None of these
Math Spring 08 Midterm Review Problems Page 9 y. Use the graph of y f. f given below to determine the graph of the inverse function 6 5-6 -5 - - - - 5 6 - - - - -5 6-6 (B) 6 5 5-6 -5 - - - - - 5 6 - - - -5-6 -6-5 - - - - - 5 6 - - - -5-6 6 6 5 5-6 -5 - - - - - 5 6 - - - -5-6 -6-5 - - - - - 5 6 - - - -5-6
Math Spring 08 Midterm Review Problems Page 0 5. The function R is described by the set of ordered pairs below. R 6 5 9 8 Which one of the following tables describes R? (B) R 6 5 9 8 6 R 5 9 8 R 6 5 9 8 R 6 5 9 8 (E) R 6 5 9 8
Math Spring 08 Midterm Review Problems Page The cost of purchasing unleaded gasoline is given by C. 9, where is the number of gallons of gasoline. The number of gallons of gas used on a car trip is given by f m 0. 08m, where m is the distance traveled in miles. Use this information to answer the net three questions. 6. (***) Evaluate, and give a practical interpretation. (Note: Answers are rounded to decimal places where appropriate.) C 5 0. 57 5 C. When a car travels 5 miles, the number of gallons used is 0.57. (B) C 5 6. 85 5. 85. When $5 is spent, 6.85 gallons of gasoline were purchased. C. When 5 gallons of gasoline is purchased, the cost is $.85. C 5 9. 7 9.7 miles.. When 5 gallons of gasoline is used on a trip, the distance traveled is C. 7. (***) Write an epression for f m C f m 57. 66 m (B) C f m 0. 07 m C f m 0. 08 m C f m 0. 08m (E) C f m 0. 08 8. Evaluate C f 75 C f 75. 7, and give a practical interpretation.. When a car uses 75 gallons of gasoline, the number of miles driven is.7. C f 75.. When a car travels 75 miles, the cost of gasoline is $.. C f 75 68.. When a car travels 75 miles, the cost of gasoline is $68.. C f 75 6.. When a car travels 75 miles, the cost of gasoline is $6.. C f 75 6.. When a car uses 75 gallons of gasoline, the number of miles driven is 6.. (B) 05 5 5 (E) 5
Math Spring 08 Midterm Review Problems Page q f p The function represents the quantity of a certain laptop computer demanded (in thousands of units) when the price is p dollars. Use this information to answer the net two questions. 9. If f,500 70, then which of the following must be true? f (70), 500 (B) f (,500) 70 (E) f 70,500 f,500 70 f,500 70 0. What is the correct interpretation of the statement f (560) 900? 900,000 laptops are demanded when the price is $560. (B) 90,000 laptops are demanded when the price is $560. 560,000 laptops are demanded when the price is $900. 56,000 laptops are demanded when the price is $900.. The cost (in dollars) of introducing a recycling program to p% of the population in a particular town can be modeled by: C 0,000 p f ( p) 0 p 00 00 p Determine the percent of the population the town can put on the recycling program if the budget for the program is $500,000. Round your answer to the nearest 0.% 9.% (B) 9.6% 87.8% 85.% (E) 79.9%
Math Spring 08 Midterm Review Problems Page. The cost (in dollars) of introducing a recycling program to p% of the population in a particular town can be modeled by: C 0,000 p f ( p) 0 p 00 00 p Interpret the meaning of 50,000 6. 5 f. For a cost of $50,000, one can epect 6.5% of the population to be put on the program. (B) For a cost of $6,500, one can epect 50,000 people to be put on the program. For a cost of $6.50, one can epect 50% of the population to be put on the program. For a cost of $50,000, one can epect 6,500 people to be put on the program.. (***) Consider the graph of y g What is the value of g? given below..5 (B). 75 (E) 6 5-6 -5 - - - - 5 6 - - - - -5-6
Math Spring 08 Midterm Review Problems Page The following graph shows the total US population between 0 and 07. Call this population function, where t is measured in months since Jan 0. Use this graph to answer the net two questions. P f t. Estimate f 0 and give a practical interpretation. f 0,000,. 0 months after Jan 0, the total US population was,000,000. f 0,. 0 months after Jan 0, the total US population was,000. f 0,000,. 0 months after Jan 0, the total US population was,000,000. f 0,. 0 months after Jan 0, the total US population was,000. f 0 is undefined. 000 (B) 000 000 000 (E) 5. Estimate f 0,000 0,000 8, and give a practical interpretation. f. A total US population of 0,000 occurred 8 months after Jan 0. (B) 0,000 8 f. A total US population of 0,000 occurred 8 months after Jan 0. f 0,000 8. A total US population of 0,000,000 occurred 8 months after Jan 0. f 0,000. A total US population of 0,000,000 occurred 8 months after Jan 0. f 0,000 is undefined. 8 (E)
Math Spring 08 Midterm Review Problems Page 5 The following graph shows the total France population between 990 and 00. Call this population function, where t is measured in years since 990. Use this graph to answer the net two questions. P f t 6. Estimate f () and give a practical interpretation. f 58,. years after 990, the total France population was 58,800. f. years after 990, the total France population was 58,800,000. f. years after 990, the total France population was 59,00. f. years after 990, the total France population was 59,00,000. 800 (B) 58,800, 000 59, 00 59,00, 000 (E) is undefined. f 7. Estimate f 6,000 8, and give a practical interpretation. f 6,000. A total France population of 6,000 occurred 8 years after 990. f 6,000. A total France population of 6,000 occurred 9 years after 990. (B) 9 f 6,000. A total France population of 6,000,000 occurred 8 years after 990. 8 f 6,000. A total France population of 6,000,000 occurred 9 years after 990. 9 (E) 6,000 f is undefined.
Math Spring 08 Midterm Review Problems Page 6 The following graph shows the average height of men by year for France and for the USA. Call these functions and, where y is measured in years since 80. Use these graphs to answer the net two questions. h F y h A y h A y h F y 8. Estimate 90 h h and give a practical interpretation. F 66 (B) h F 90 67 h F 90 69 h F 90 70 (E) h 90 76. 5 F F 90 9. Estimate 90 A h F. The average height of French men 90 years after 80 was 66 cm.. The average height of French men 90 years after 80 was 68 cm.. The average height of French men 90 years after 80 was 69 cm.. The average height of French men 90 years after 80 was 70 cm.. The average height of French men 90 years after 80 was 76.5 cm. h and give a practical interpretation. A h F 90 (B) h 90 h cannot be determined. h A F. Ninety years after 80, the average height of American men is cm less than the average height of French men. h A h F 90. Ninety years after 80, the average height of American men is cm more than the average height of French men. h A h F 90. Ninety years after 80, the average height of American men is cm less than the average height of French men. h A h F 90. Ninety years after 80, the average height of American men is cm more than the average height of French men. (E)
Math Spring 08 Midterm Review Problems Page 7 0. (***) Determine g for g A, where A is a constant. A g (B) g g A g A A (E) None of these f 00 has a maimum or minimum, and then determine the maimum or minimum value.. Determine whether 8 Ma = 00 (B) Min = 00 Min = 8 Ma = 5 (E) Ma = 8 00 8. Consider the function 9 TRUE? The graph opens up. (B) The graph opens down. The y-coordinate of the verte is 9. The graph has a minimum at the verte. f. Which one of the following statements is
Math Spring 08 Midterm Review Problems Page 8. Determine the formula for the quadratic function in standard form for the parabola graphed below. 5, - - 5 - - - - -5, y y (B) y y y (E)
Math Spring 08 Midterm Review Problems Page 9 The following table shows data for a quadratic profit function. Use this data to answer the net two questions. P (quantity) 0 00 00 500 600 (profit in dollars) -,000,500 9,000 9,500 9,000. Determine an equation for the profit function that fits the data eactly. P ( ) ( 500) 9, 500 0 (B) P ( ) ( 600), 000 P ( ) ( 500) 9, 500 0 P ( ) ( 600), 000 (E) None of these 5. You can see from the table that the profit is zero for some value of 00. The other value of for which profit is zero is: Between 600 and 700 (B) Between 700 and 800 Between 800 and 900 Between 900 and,000 (E) Between,000 and,00 between 0 and 6. Determine a possible formula for the quadratic function, in factored form, that passes through the points, 0,, 0, and,. 6 y (B) y y y (E) y 5
Math Spring 08 Midterm Review Problems Page 0 g. 7. Determine the verte for the quadratic function 8 6, (B) 6,, 5,, 50 (E) 8. A mathematical model for the profit, P, in thousands of dollars, that a company makes in one year from producing units of its product is: P 600 89, 750. What is the maimum profit the company can make? $00,000 (B) $50,000 $75,000 $00,000 (E) $5,000 9. A ball is thrown from a height of 7 feet. Its position above the ground is given by the formula h t 6t 9t 7, where t is measured in seconds. Determine how long it takes for the ball to strike the ground. The time until the ball strikes the ground is: More than. seconds (B) Between.6 and. seconds Between. and.6 seconds Between.6 and. seconds (E) Less than.6 seconds 50. A ball is thrown from a height of 7 feet. Its position above the ground is given by the formula h t 6t 9t 7, where t is measured in seconds. Determine how long it takes for the ball to reach its maimum height. The time until the ball reaches its maimum height is: Less than 0. seconds (B) Between 0. and 0.5 seconds Between 0.5 and 0.8 seconds Between 0.8 and. seconds (E) More than. seconds
Math Spring 08 Midterm Review Problems Page 5. A horticulturist has determined that the number of inches a young redwood tree grows in one year is a function of the annual rainfall, r (in inches), given by g r 0.0r r What is the maimum number of inches a young redwood can grow in a year? The maimum number of inches is: Less than inches (B) Between.9 and. inches Between. and.6 inches Between. and 5. inches (E) Between.7 and 5. inches When an apple orchard owner plants 65 trees on an acre of ground, he gets an average yield of 500 apples per tree per year. For each additional tree planted per acre, the annual yield per tree drops by 0 apples. Use this information to answer the net two questions. 5. Let represent the number of additional trees above 65. Determine a formula for the number of trees (T) and the number of apples per tree. (B) (E) T 65 and A 500 T 65 and A 500 T 65 and A 500 0 T 65 and A 500 T 65 and A 500 0 5. Calculate the number of trees that should be planted per acre to produce the maimum crop of apples and use that value to determine the maimum yield? The maimum yield is: 7,000 apples (B) 0,000 apples 97,500 apples 98,000 apples (E) 00,000 apples
Math Spring 08 Midterm Review Problems Page The manager of an 80-unit apartment comple is trying to decide what rent to charge each month. At a rent of $800, all 80 units are full. On the average, one additional unit will become remain vacant for each $5 increase in rent. Use this information to answer the net three questions. 5. Let represent the price charged for rent. Find an epression for the number of apartments that are rented as a function of. A 80 A 5 A 5 A 5 A 80 (B) 80 80 (E) 55. Determine how many apartments should remain vacant each month to maimize revenue. Less than 0 (B) Between 0 and 5 Between 5 and 0 Between 0 and 5 (E) More than 5 56. Determine the maimum monthly revenue from the apartment comple. Less than $50,000 (B) Between $50,000 and $75,000 Between $75,000 and $00,000 Between $00,000 and $5,000 (E) More than $5,000
Math Spring 08 Midterm Review Problems Page A charter flight charges a fee of $00 per person plus $ per person for each unsold seat on the plane. The plane holds 00 passengers. Use this information to answer the net two questions. 57. Determine the price for each seat that is received when revenue is at its maimum. Less than 75 (B) Between 75 and 5 Between 5 and 75 Between 75 and 5 (E) Greater than 5 58. Determine the maimum revenue from the charter flight. Less than $6,000 (B) Between $6,000 and $67,000 Between $67,000 and $69,000 Between $69,000 and $7,000 (E) More than $7,000
Math Spring 08 Midterm Review Problems Page Bob s high school is performing a musical. If each ticket is priced at $9.50 then 600 tickets will be sold. For each $0.0 increase in price, 6 fewer tickets will be sold. Use this information to answer the net two questions. 59. Determine the price that should be charged for each ticket to maimize the revenue. Less than $9.60 (B) Between $9.60 and $9.80 Between $9.80 and $0.00 Between $0.00 and $0.0 (E) More than $0.0 60. Determine the maimum possible revenue from the musical ticket sales. More than $600 (B) Between $6000 and $600 Between $5900 and $6000 Between $5800 and $5900 (E) Less than $5800 6. (***) The height of a leaf above the ground after it falls from a tree is given by the formula s t.8t 7., where time is given in seconds and height is given in feet above the ground. When would the leaf land on the top a person s head if the person was seated on the ground under the tree and their head was.7 feet above the ground? The amount of time is: Between.5 and.6 seconds (B) Between. and.5 seconds Between. and. seconds Between. and. seconds (E) Between. and. seconds
Math Spring 08 Midterm Review Problems Page 5 A company has determined that the demand function for a dining room table is given by p 00 where p is the price per table and is the number of tables sold. The fied cost of producing a line of dining room tables is $00,000 and each table costs $00 to make. Use this information to answer the net three questions. 6. Determine a simplified formula for the revenue function. R 00 (B) R 00 R 00 R 00 (E) R 00 6. Determine the quantity that should be manufactured to maimize revenue. The quantity is: Less than 950 tables (B) Between 950 and 050 tables Between 050 and 50 tables Between 50 and 50 tables (E) More than 50 tables 6. (***) Determine the quantity that should be manufactured to maimize profit. The quantity is: Less than 950 tables (B) Between 950 and 050 tables Between 050 and 50 tables Between 50 and 50 tables (E) More than 50 tables 65. As part of a physics eperiment, Ming drops a baseball from the top of a 50-foot tall building. The distance h, in feet, that the ball travels is given by h 6t, where t is measured in seconds. For how many seconds will the baseball fall? Round your answer to the nearest tenth of a second.. sec (B).7 sec 6. sec. sec (E).9 sec
Math Spring 08 Midterm Review Problems Page 6 Consider the graph of the polynomial questions. S shown below. Use this graph to answer the net three 66. What is the smallest degree that S could have? (B) 5 6 (E) 7 67. What is the sign of the leading coefficient of Positive (B) Negative S? 68. What is the sign of the constant term of S? Negative (B) Positive Zero
Math Spring 08 Midterm Review Problems Page 7 69. Consider the polynomial function f 5 polynomial f?. What is the degree of the (B) 5 6 (E) None of these 70. Consider the polynomial function 5 behavior of the graph. P. Determine the end P P approaches approaches as as approaches approaches (B) P approaches as approaches as P approaches approaches P P approaches as approaches approaches approaches as P P approaches approaches approaches as as approaches
Math Spring 08 Midterm Review Problems Page 8 According to their website, American Airlines limits the size of checked baggage in such a way that the length + width + height of the bag can be no more than 6 inches. Suppose a piece of luggage has length and width equal to inches. Then the maimum height the bag could be is inches. Use this information to answer the net three questions. 6 7. (***) Write a function to epress the volume of such a piece of luggage as described above. V 6 (B) V 6 V 6 V 6 V 6 (E) 7. What is an appropriate domain for this function, given the contet? 0, (B) 0, 6,, 6 (E) 0, 7. (***) Use the graph of this function to determine the maimum volume of such a piece of luggage. The maimum volume is: Less than 7000 cubic inches (B) Between 7000 and 8000 cubic inches Between 8000 and 9000 cubic inches Between 9000 and 0,000 cubic inches (E) More than 0,000 cubic inches
Math Spring 08 Midterm Review Problems Page 9 7. Which one of the following could be the graph of a polynomial of degree with a negative leading coefficient? (B)
Math Spring 08 Midterm Review Problems Page 0-6 -5 - - - - 5 6-6 -5 - - - - 5 6 75. Determine an equation for the polynomial graphed below. Leave your answer in factored form., y (B) y y y (E) y 76. Determine the equation for the polynomial function in factored form that has the following characteristics. Zeros at, 0,, and Passes through the point 8, y (B) y 8 y 5 y (E) y
Math Spring 08 Midterm Review Problems Page 77. Use the graph to determine all the real zeros of P ( ) 5 0. The smallest real zero is: (B) 5 (E) 78. Determine all the real zeros of g ( ) 6. The largest real zero is: (B) 6 (E) 6 79. Determine all the real zeros of h. The largest real zero is: (B) (E) None of these 80. Consider the polynomial function f 8 statements is FALSE?. Which one of the following is a zero of f (B) f has only one real zero The end behavior of the graph is f approaches as approaches as approaches approaches and f The y-intercept of the graph is 0, 8 (E) is a factor of f
Math Spring 08 Midterm Review Problems Page 8. (***) The function f 0.67.5.8 8. approimates the number of Facebook friends a person has after the first 5 days of creating their Facebook account. Assume the value of represents the start of that day. During the middle of which day would a person first have 00 Facebook friends? During day 7 (B) During day 8 During day 9 During day 0 (E) During day
Math Spring 08 Midterm Review Problems Page Spring 08 Midterm Study Guide Answers Question Answer Question Answer Question Answer B 8 D 55 D E 9 A 56 C E 0 C 57 C C A 58 A 5 B A 59 B 6 A E 60 E 7 C A 6 B 8 A 5 C 6 C 9 A 6 B 6 D 0 C 7 C 6 B D 8 B 65 B E 9 E 66 C E 0 D 67 A A E 68 A 5 E B 69 D 6 E E 70 D 7 D C 7 E 8 C 5 D 7 E 9 E 6 A 7 C 0 B 7 E 7 C D 8 B 75 A C 9 C 76 E B 50 D 77 B C 5 C 78 E 5 A 5 E 79 D 6 B 5 D 80 E 7 D 5 B 8 D