1. Two vehicles start at time t = 0 from the same point A and travel along a straight line so that at each moment t the distance between the second vehicle and A equals the square of the distance between the first vehicle and A. After t = 3 hours, the first vehicle is moving at 3 kilometers per hour and is 9 kilometers away from A. What is the speed, in kilometers per hour, of the second vehicle at t = 3 hours?

 A. 9 B. 18 C. 27 D. 54 E. 81
solution

2. What is the largest possible subset of R that can be a domain for the real-valued function f(x) = (x3-x)1/2 ? A. B. C. D. E. solution

3. What is the first term of the arithmetic sequence whose 8th and 26th terms are 20 and 56 respectively?

 A. 1 B. 2 C. 6 D. 8 E. 9
solution

4. What is the graph of x2- 6y2 = 0 ?

 A. A hyperbola B. The union of two intersecting straight lines C. A point D. An ellipse E. A line through the origin
solution

5. Suppose that over the time period 1970-1990 the population of Central City at time t is proportional to bt for some b > 0. If the population of Central City was 36,000 inhabitants in 1970 and 48,000 inhabitants in 1980, what will the population of Central city be in 1990?

 A. 56,000 B. 58,000 C. 60,000 D. 62,000 E. 64,000
solution

6. The five graphs below have equal scales on the x and y axes. Which one could be the graph of y = 3x4 - 4x3 ?

 A B C D E solution

7. For what value of p does 122p-1 = 5(3.7)p ?

 A. (ln 5 - ln 12)/(ln 3.7 - ln 12) B. (ln 5 + ln 12)/(2 ln 12 - ln 3.7) C. (ln 12)/(2 ln 12 - 5 ln 3.7) D. (ln 12)/(ln 12 - 5 ln 3.7) E. (ln 12 - ln 5)/(2 ln 12 + ln 3.7)
solution

8. Consider the ellipse centered at (2,-1) with axes as shown in the figure below: Its equation is

 A. 4x2+y2+16x-2y+13 = 0 B. x2+4y2-4x+8y+4 = 0 C. x2+4y2+4x-8y+4 = 0 D. 4x2+y2-16x-2y+13 = 0 E. 4x2+y2-16x+2y+13 = 0
solution

9. What are all the asymptotes of the graph of xy + y = (x - 2)2 ?

 A. x = 0 and y = 0 B. x = -1 and y = 0 C. x = -1 and y = 5 - x D. x = -1 and y = x - 5 E. x=-1, y=0, and y=x-5
solution

10. Which of the following is an equation of the ellipse with center (-2,1), major axis running from (-2,6) to (-2,-4), and focus at (-2,5) ?

 A. (x-2)2/25+(y+1)2/16=1 B. (x+2)2/16+(y-1)2/25=1 C. (x-2)2/9+(y+1)2/25=1 D. (x+2)2/9+(y-1)2/25=1 E. (x-2)2/25+(y-1)2/9=1
solution

11. The number of solutions to the following system of equations is,

y2 û xy - |x|y + x|x| = 0

x2 + y2 = 1

 A. 0 B. 1 C. 2 D. 3 E. 4

solution

12. Which of the following subsets of is the largest possible domain for the real-valued function (x2- x)1/2?

 A. B. C. D. E. solution

13. The graph of 9x2 - 54x + 4y2 + 16y + 61 = 0 is

 A. a circle with radius 6 B. a hyperbola centered at (2,3) C. a hyperbola centered at (3,-2) D. an ellipse centered at (2,3) E. an ellipse centered at (3,-2)

solution

14. What is the solution set for the inequality x + 1 <= (6/x)?

 A. B. C. D. E. solution

15. One of the roots of the equation x3 - 7x2 + 25x - 39 = 0 is 3. What are the other 2 roots of this equation?

 A. -1 and 5 B. -1 and 13 C. 2-sqrt(17) and 2+sqrt(17) D. 2 - 3i and 2 + 3i E. 3 - 2i and 3 + 2i
solution

16. If z is the complex number such that (2 - i)z + 4 - 3i = 3iz, then z =

 A. -1 - (11/10)i B. -1 - (1/2)i C. -(1/3) + (5/6)i D. (1/5) - (11/10)i E. (3/4) - (7/4)i
solution

17. Which of the following most closely resembles the graph of y = x2/(x-1)?

 A B C D E solution