Expert: Richard J. Raridon - 11/15/2011

Question
Part 1-1
Select the best answer from the choices provided. (Each question is worth one point)
1. A public opinion poll found that out of a sample of 450 voters, 252 favored a school bond issue. If 20,000 people voted, how many are likely to vote for the bond measure? 15,714  11,200
1,120  10,100

2. The speed of an object falling from rest in a vacuum is directly proportional to the time it has fallen. After an object has fallen for 1.5 seconds, its speed is 14.7 m/s. What is the speed after it has fallen 5 seconds? 20 m/s  51 m/s
49 m/s  50 m/s

3. The centrifugal force acting on an object moving in a circle is directly proportional to the square of the speed of the object. If the force is 2240 newtons when the object is moving 8 m/s, what is the force when the object is moving at 12 m/s? 5,040 n  420 n
840 n  504 n

4. If w is jointly proportional to u and v, and w =2 when u=4 and v=6, what is w when u=3 and v=8? w = 2  w = 4
w = 13  w = 1

5. A number y varies inversely as the square of x. If y = 2 when x = 6, what is y when x = 3? 6  8
10  12

Part 2-1
Select the best answer from the choices provided. (Each question is worth one point)
6. Use synthetic substitution to find P(c) for the given polynomial P(x) and the given number x:


P(x) = 6x3 - x2 + 4x + 3;    c = - 1
3
P(- 1 ) =  16
3 3
 P(- 1 ) =  5
3 2

P(- 1 ) =  4
3 3
 P(- 1 ) =  9
3 8


7. Determine the missing roots:

Equation:  x4 - 3x3 + 4x2 - 6x + 4 = 0

Roots:   

1, 2, iÖ 2
-iÖ 2
 -iÖ 5

-i  iÖ 2


8. Solve for x:

x + 1 =     2
-x + 2  x
x = ±4  x = 1, 4
x = 1, -4  x = -1, 3

Part 3-1
Select the best answer from the choices provided. (Each question is worth one point)
9. List the possible rational roots for the equation:  

x4 + 3x2 - 8x + 10 = 0


{±1, 5, 10}  {±1, ± 2, ± 5, ± 10}
{1, 2, 5, 10}  No answer is correct.

10. The length of a rectangle with constant area varies inversely as the width. When the length is 18 ft, the width is 8 ft. Find the length when the width is 9 ft. 12 ft  14 ft
16 ft  18 ft

Part 4-1
Select the best answer from the choices provided. (Each question is worth one point)
11. Find the distance between the pair of points:

(9, 1) and (2, -1)

d = 9.9  d = 7.28
d = 7  d = 21.17

12. Find the distance between the pair of points:

(0.5,-1) and (-1,1)

d = 3.54  d = 3.55
d = 2.5  d = 0.5

13. Find the midpoint of the segment joining the two points:

(3.45, 0.32) and (1.45, 3.15)

(2.45, 1.735)  (4.90, 3.46)
(1.735, 0.87)  (3.46, 4.90)

14. Find the equation of a circle:

center (-2, 0); passes through (2, 0)

(x + 2)2 + y2 = 16  (x - 2)2 + y2 = 4
(x + 2)2 + (y + 0)2 = 4  (x - 2)2 + y2 = 16

Part 5-1
Select the best answer from the choices provided. (Each question is worth one point)
15. Identify the conic. Choose the conic and its center.

x2 - 4y2 + 6x - 8y = 11

Hyperbola (3, 1)  Hyperbola (-3, -1)
Hyperbola (4, 1)  Hyperbola (-4, 1)

16. Identify the conic. Choose the conic and its center.

16x2 - 9y2 + 64x + 18y + 199 = 0

Hyperbola (-2, 1)  Hyperbola (1, -2)
Hyperbola (-2, -1)  Hyperbola (-1, 2)

17. Rewrite x2 - 4x + y2 + 8y - 16 = 0 in standard form. (x + 2)2 - (y - 4)2 = 4  (x - 2)2 - (y + 4)2 = 4
(x + 2)2 + (y - 4)2 = 36  (x - 2)2 + (y + 4)2 = 36

18. Identify the conic section whose equation is given:
x2 + 10x + y2 + 12y = 60

Circle  Parabola
Ellipse  Hyperbola

Part 5-2
Select the best answer from the choices provided. (Each question is worth two points)
19. Choose the correct foci:

9x2 + 4y2 =9

(0, ±2.5)  (0, ±1.1)
(±2.5, 0)  (±1.1, 0)

20. Choose the correct foci:

y2 = 5x2 + 25

(0, ±5.48)  (0, 7.75)
(±30, 0)  (0, ±30)

Part 6-1
Select the best answer from the choices provided. (Each question is worth one point)
21. Solve:

y4 - 3y3 - 2y2 + 10y - 12 = 0, given root 1 + i

{1 ± i, -2, 3}  {±1, ±2, ±3, 4}
{±2, ±4}  {i ± 2, ±3}

Part 7-1
Select the best answer from the choices provided. (Each question is worth one point)
22. (x2 + 9)1/2 = 5 ±4  16
4  Ö 34


23. 5x = Ö 125
2
3
 3
1
3
 3
2


24. 49x-2 = 7Ö 7
-5
4
 5
4

11
4
 -11
4


Part 8-1
Select the best answer from the choices provided. (Each question is worth one point)
25. If log10 9 = 0.95 and log10 2 = 0.3:

log10 36 =

0.2708  1.2855
1.5563  1.3423

26. Condense to a single log expression:

log5 x - log5 y + 2

log5 5x/y  log5 (x/y) + 2
log5 2x/y  log5 5y/x

Part 9-1
Select the best answer from the choices provided. (Each question is worth one point)
27. Ten years ago Michael paid $250 for a rare 1823 stamp. Its current value is $1000. Find the average annual rate of growth.  40%  11.4%
14.9%  10.2%  

28. Simplify:

eln0.5

0.5  0.20
5  0.05

29. Solve:

1 = 7
ex
ln 1/7  ln 1/7
ln 7  ln 7

30. Solve:
e-2x = 0.2 -0.5 ln 0.2  ln 2.5
2 ln 5  2 ln 2.5

Answer
I answered all the ones that I could understand what you had written.
1. 11,200
2. 49m/s
3. 5040N
4. w=2
5. y=8
6. P(-1) = -8
7. 1,2,+/-i(2^1/2)
9. no answer is correct
10. 16ft
11. 7.28
12. 2.5
13. (2.45,1.735)
14. (x+2)^2 +y^2 = 16
15. (-3,-1)
16. (-2,1)
17. (x-2)^2+(y+4)^2 = 36
18. ellipse
19. 0,+/-1.1
20. 0,+/-5.48
21. (1+/-i,-2,3)
22. +/-4
23. x = 5^1/2
25. 1.5563
26. log5(x/y) +2
27. 14.9%
30. x= -0.5ln(0.2)