Mu Applications MAΘ National Convention 2012
For all answers, answer E. “NOTA” means none of these answers is correct.
1. A rectangular pen is to be built against a wall so that only three sides will require fencing. If feet of fencing are to be used, the area of the largest possible pen is
A. B. C. D. E. NOTA
2. Determine the smallest possible slope for a tangent to the curve .
A .0 B. 1 C. 2 D. 3 E. NOTA
3. A circle centered at has an area that changes through time according to the equation. How fast in the radius growing when the circle is tangent to the axis?
A. B. C. D. E. NOTA
4. Evaluate.
A. B. C. D. E. NOTA
5. Circle O has diameter AB and radius length 4 and is the base of a solid whose cross sections perpendicular to AB are squares. What is the volume of the solid?
A. B. C. D. E. NOTA
6. Find the length of the arc along the graph of from to.
A. B. C. D. E. NOTA
7. What is the shortest distance from the origin to the graph of?
A. B. C. D. E. NOTA
8. Oil spilled from a ruptured tanker spreads in a circle whose area increases at a constant rate of 6 square miles per hour. How fast is the radius of the spill increasing, in miles per hour, when the area is 9 square miles?
A. B. C. D. E. NOTA
9. A pipe of negligible diameter is to be carried horizontally around a 90 degree corner from a hallway 8 feet wide into a hallway 27 feet wide. What is the maximum length the pipe can have?
A. B. C. D. E. NOTA
10. A particle is moving along a horizontal line according to the equation . Determine the interval of time when the particle is moving to the left.
A. B. C. D. never E. NOTA
11. An ellipse has the equation. Find the volume formed when this ellipse is rotated about the axis.
A. B. C. D. E. NOTA
12. Evaluate the integral:
A. B. C. D. E. NOTA
13. The cubic equation of the form has a relative maximum at the point and a relative minimum at the point. Where is the inflection point?
A. B. C. D. E. NOTA
14. In the above question, what is the sum of and?
A. B. C. D. E. NOTA
15. A thermometer is placed inside a cool room with a temperature of. Immediately before being placed in the room, the temperature of the thermometer was showing. Using Newton’s Law of Cooling, how long will it take, in minutes, for the thermometer to cool from to if after 5 minutes the thermometer shows?
A. B. C. D. E. NOTA
16. A rectangle has its two lower corners on the axis and its two upper corners on the curve . The area of the largest possible rectangle is
A. B. C. D. E. NOTA
17. The total cost of producing units of carrot cake cupcakes per week is given by . Find the marginal cost when the production level is 100 units per week.
A. $12 B. $24 C. $36 D. $48 E. NOTA
18. Find the average value of on the interval .
A. B. C. D. E. NOTA
19. Use one iteration of Newton’s Method to approximate a zero of . Let be your initial guess.
A. – 1 B. 0.5 C. 1.4 D. 1.5 E. NOTA
20. Find the area of the region bounded by the curve in the first quadrant.
A. B. C. D. E. NOTA
21. Which of the following is equivalent to?
A. B. C. D. E. NOTA
22. What is the probability that a point randomly chosen from within the graph is not within the graph of the curve?
A. B. C. D. E. NOTA
23. The area bounded by the line and the graph of the parabola is cut in half by a line with equation. What is the value of?
A. B. C. D. E. NOTA
24. If, then find.
A. B. C. D. E. NOTA
25. The area of the region enclosed by the polar graph of is
A. B. C. D. E. NOTA
26. Find the length of the curve from to .
A. B. C. 7 D. 8 E. NOTA
27. There is at least one point on the interval such that the tangent line to is parallel to the secant line joining the endpoints. Find the value(s) of .
A. 3 B. 8 C. D. no value on interval E. NOTA
Questions 28 -30 refer to the following information about differentiable functions and .
- 1 / 2 / -3 / -6 / 90 / 0 / 0 / -2 / 0
1 / 2 / 0 / 2 / 9
2 / 4 / 24 / 6 / 36
28. If , then what is ?
A. – 216 B. 36 C. 0 D. 144 E. NOTA
29. If , then what is ?
A. B. 4 C. D. E. NOTA
30. The average rate of change of on the interval is:
A. B. C. D. E. NOTA