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Form A Math 2015 Common Part of Final Exam December 17, 2002
INSTRUCTIONS: Please enter your NAME, ID NUMBERS, FORM designation, and CRN on your op-scan sheet. The CRN should be written in the upper right-hand box labeled "Course". Do not include the course number. In the box labeled "Form," write the appropriate test form letter shown above. Darken the appropriate circles below your ID number and Form designation. Use a #2 pencil.
Mark your answers to the test questions in rows 1-18 of the op-scan sheet. You have 1 hour to complete this part of the final exam. Your score on this part of the final exam will be the number of correct answers. Turn in the op scan sheet with your answers and the question sheets, including this cover page, at the end of this part of the final exam. Any additional parts of the exam will begin after all students have completed this common part.
Exam Policies: You may not use a book, notes, formula sheet, or a calculator or computer. Giving or receiving unauthorized aid is an Honor Code Voilation.
Signature_________________________________________________
Name (printed)_____________________________________________
Student ID#_______________________________________________
- An amusement park wants to keep track of approximately how many people are in the park at any given time. Their ticket machine is not working, so periodically, a person stands at the main gate and summarizes the net rate at which people are entering and leaving at that time. Since the park opens at 10 AM, the information during the first two hours is the most crucial to obtain, and is summarized below.
Time 10 : 00 AM 10 : 20 10 : 40 11 : 00 11 : 20 11 : 40 12 : 00 PM Net Rate People Enter or Leave HPeople ê minuteL
Assuming that the rate at which people enter the park continually decreases throughout the day, which of the following must be true at 12:00 PM?
Between 1,400 and 2,500 people are in the amusement park.
Between 1,131 and 1,241 people are in the amusement park
Between 25000 and 27,620 people are in the amusement park
Between 22,620 and 24,820 people are in the amusement park
- The graph below represents a graph of the derivative, f H x L of a function F H x L. Suppose we are given that F H 0 L = 2 and F H 4 L = 12. Use the fundamental theorem of calculus to find the value of A on the graph below.
1 2 3 4 x
y H2, AL
fHxL
1) A = 10
2) A = 5
3) A = 2.
4) A = 2
- The length of time your new television is expected to last has a density function given by the function p H t L, where t is measured in years. Which expression gives you the probability that your television will last between 8 and 10 years?
10 p H t L „ t
p H 10 L - p H 8 L
(^) Ÿ 0^ t^ H p H 10 L - p H 8 LL „ t
p ' H 10 L - p ' H 8 L
- You take a pottery class and create a 16-inch tall canister with circular cross sections. You measure the diameter at various heights up the canister as:
Height from Bottom of Canister HinchesL 0 4 8 12 16 Diameter of Canister HinchesL 12 10 8 9 10
Approximate the volume of the canister using the Trapezoidal Rule.
Volume ≈ ÅÅÅÅ^12 (4) [pH 6 L 2 + 2pH 5 L 2 + 2pH 4 L 2 +2* pH4.5L^2 + pH 5 L 2 ] in 3
Volume ≈ ÅÅÅÅ^12 (4)[p(6) + 2p(5) + 2p(4) + 2p*(4.5) + p(5)] in 3
Volume ≈ ÅÅÅÅ^13 (4) [H 6 L 2 + H 5 L^2 + H 4 L 2 + H4.5L^2 + H 5 L 2 ] in 3
Volume ≈ ÅÅÅÅ^13 (4) [pH 6 L 2 + 4pH 5 L 2 + 2pH 4 L 2 +4* pH4.5L^2 + pH 5 L 2 ] in 3
- Which of the following approximates (^) Ÿ 15 x^2 „ x by Simpson's Rule with n = 4 subintervals?
1) ÅÅÅ^13 H 1 + 4 H 2 L 2 + 2 H 3 L 2 + 4 H 4 L 2 + H 5 L 2 L
2) ÅÅÅ^13 H 1 + 2 H 2 L 2 + 4 H 3 L 2 + 2 H 4 L 2 + H 5 L 2 L
3) ÅÅÅ^43 H 1 + 4 H 2 L 2 + 2 H 3 L 2 + 4 H 4 L 2 + H 5 L 2 L
4) ÅÅÅ^43 H 1 + 2 H 2 L 2 + 4 H 3 L 2 + 2 H 4 L 2 + H 5 L 2 L
- Which of the following is the average value of g H tL = e t^ over the interval 0 § t § 5?
ÅÅÅ^15 e t+^1
ÅÅÅ^15 e 5
He 5 - 1 L
ÅÅÅ^15 He 5 - 1 L
- Suppose that P H tL is the cumulative distribution function for the length of time people have to wait in the doctor's office.. Which of the following is the meaning of the statement P H 1 L = 0.6?
- 40% of people get to see the doctor within an hour.
- Suppose that P H tL is the cumulative distribution function for the length of time people have to wait in the doctor's office.. Which of the following is the meaning of the statement P H 1 L = 0.6?
40% of people get to see the doctor within an hour.
1% of people must wait 0.6 hours to see the doctor.
60% of people get to see the doctor within 1 hour.
100% of people get to see the doctor within 6 hours.
- A bicyclist is pedaling along a straight road with velocity, v, as in the graph below. Suppose the cyclist starts 15 miles from a lake, and that positive velocities take her away from the lake and negative velocities towards the lake. When is the cyclist farthest from the lake, and how far away is she then?
0
5
10
15
20
25
30
35
0 1 2 3 4 5 6
t, hours
v, mph
At 4.5 hours the cyclist is 34 miles away.
At 6 hours the cyclist is 87 miles away.
At 4.5 hours the cyclist is 49 miles away.
At 6 hours the cyclist is 34 miles away.
- (^) Ÿ t^2 sinH t^3 L „ t =
t^2 cosH t^3 L + C
- ÅÅÅÅ^13 t^3 cosH t^3 L + C
3 cosI t^
4 ÅÅÅÅÅÅ 4 M + C
- The traffic pattern, measured in cars entering and leaving per hour, in a parking lot over a 6 hour period is described in the graph below. Three of the statements are correct. Which statement about the traffic pattern is not correct?
- (^) Ÿ 03 2 xe x^^2 „ x =
e^9 - 1
9 e^9
9 H e^9 - 1 L
3 e^27
- Four thousand Virginia Tech freshmen participated in a survey asking how many hours per week they spend on doing homework. The density function, p H t L = 0.005 t , with time t in hours and 0 § t § 20 , that describes the fraction of freshmen per each hour is graphed below. Which one of the following statements is correct?
5 10 15 20 t^ HhoursL
fraction of freshmen per hour
One thousand freshmen spend approximately14 hours per week on doing homework.
The mean hours per week that freshmen spend on doing homework is less than the median hours per week that freshmen spend on doing homework.
If T is the median hours per week and P is the cumulative distribution function, then P H T L = 1.
If T is the mean hours per week, then (^) Ÿ 0^ T^ p H t L „ t = (^) Ÿ T^20 p H t L „ t.
- (^) Ÿ 3 è!!!!!!!!!!!!!! 6 x - 5 „ x
- ÅÅÅÅ^43 H 6 x - 5 L ÅÅÅÅÅ^32
ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ 4 è!!!!!!!! 61 x - ÅÅÅÅÅÅÅ!!!!! 5 + C
ÅÅÅÅ^13 H 6 x - 5 L ÅÅÅÅÅ^32
- ÅÅÅÅÅÅÅÅè!!!!!!!! 6 1 ÅÅÅÅÅÅÅÅ x - !!!!! 5 ÅÅÅ + C
- Which of the following gives the total area of the shaded regions enclosed by the graph of y = f H x L and the x -axis?
-2 -1 1 2 3 x
1
2
y
fHxL
-2 -1 1 2 3 x
1
2
y
- (^) Ÿ-^32 f H x L „ x
0 f H x L „ x + (^) Ÿ 2
3 f H x L „ x
1 f H x L „ x + (^) Ÿ 2
3 f H x L „ x - (^) Ÿ- 2
0 f H x L „ x - (^) Ÿ 1
2 f H x L „ x
- Ÿ-^22 f H x L „ x + (^) Ÿ 23 f H x L „ x
