Expert: Richard J. Raridon - 5/24/2011

Question
1. If a, b, and c are positive, and a divided by b is equal to b divided by c, then b is called the mean proportion, or geometric mean, between a and c. Find the mean proportion between the pair of numbers: 3 and 27. b = 9  b = 81
b = 27  b = 18

2. If a, b, and c are positive, and a divided by b is equal to b divided by c, then b is called the mean proportion, or geometric mean, between a and c. Find the mean proportion between the pair of numbers: 5 and 15. 5Ö 3
 b = 3
b = 75  3Ö 5


3. The volume V of a given mass of gas varies directly as the absolute temperature T and inversely as the pressure P. If V = 462 cm3 when T = 42 degrees and P = 40 kg/cm2, what is the volume when T = 30 degrees and P = 30 kg/cm2? 400 cm3  410 cm3
420 cm3  440 cm3

Part 2-1
Select the best answer from the choices provided. (Each question is worth one point)
4. Divide using synthetic division:

2u4 - 5u3 - 12u2 + 2u - 8
  u - 4    
2u3 + 3u2 + 2  2u4 + 3u2 + 2u
2u2 + 3u + 2  2u3 + 3u2 - 2

5. Solve given the root indicated:

Equation:  x4 - 5x2 - 10x - 6 = 0

Root:  -1 + i {3, 1, -1, ±i}  {-1 ± i, 3, -1}
{3, -1, -1 + i}  {-1, -i, i, 1}


Part 3-1
Select the best answer from the choices provided. (Each question is worth one point)
6. 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.


Part 4-1
Select the best answer from the choices provided. (Each question is worth one point)
7. 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)


8. Find the coordinates of Q given that M is the midpoint of line segment PQ:

P(6, -2) and M(0, 5) (4, 8)  (6, -12)
(-6, 12)  (12, -6)


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

(Ö 2 , 1)
and(-Ö 2 , 0)
(0, 0.5)  (0.5, 0)
(Ö 1 , -2)
 (Ö 2 , -1)


Part 5-1
Select the best answer from the choices provided. (Each question is worth one point)
10. 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)


11. Identify the conic section whose equation is given:

4x2 - 16y2 = 16 Circle  Parabola
Hyperbola  Ellipse


Part 5-2
Select the best answer from the choices provided. (Each question is worth two points)
12. 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)
13. Choose the real solution of the system:

8x2 + y2 = 25 and 8x2 - y2 = 39 (-7, 0)  (2.65, 1)
No real solution  (7,0)


14. Find the length of a side of each of two squares given that the sum of their perimeters is 44 ft and the sum of their areas is 73 ft2. 8 ft, 2 ft  10 ft, 4 ft
8 ft, 3 ft  12 ft, 3 ft

15. A number y varies jointly as x and one over the square root of z.  If y=300 and x=5 and z=9, what is y when x=18 and z=36? 600  540
980  235

Part 7-1
Select the best answer from the choices provided. (Each question is worth one point)
16. David paid $9.50 for some 15 cent, 25 cent, and 45 cent stamps. He bought 38 stamps and the number of 25 cent stamps was 8 more than twice the number of 45 cent stamps. How many of each type did David buy? 10 15-cent; 22 25-cent; 8 45-cent  12 15-cent; 20 25-cent; 6 45-cent
10 15-cent; 20 25-cent; 8 45-cent  12 15-cent; 10 25-cent; 8 45-cent

17. Simplify:

4  -3/2
9
12
13
 2
3

27
8
 27

18. Simplify:

The cube root of four to the six y power 16y  32y
64y  4y


19. Simplify:

252.4
55.8
2  2 60
29

1
5
 5

Part 8-1
Select the best answer from the choices provided. (Each question is worth one point)
20. Simplify the logarithm:

log6 6 6  36
1  12


21. Express the logarithm in terms of log2M and log2N:

log2 (M/N)7 7(log2M + log2N)  14(log2M - log2N)
14(log2M + log2N)  7(log2M - log2N)


22. Solve the equation:

logb (x2 + 7) = 2/3logb 64 9  3
Ö 23
 ±3


23. Find the value of the expression to three significant digits:

log3 x = 4.3 112  113
400  311


Part 9-1
Select the best answer from the choices provided. (Each question is worth one point)
24. One thousand dollars is invested at 12% interest compounded monthly. Determine how much the investment is worth after 1 year. $1,126.83  $1,010.00  
$1,269.13  $1,136.83

25. The value of a new $3500 sailboat decreases 10% per year. Find its value after 10 years.  $1,220.37  $2,150.00  
$3,150.00   $1,825.24  

26. Write in exponential form:
ln 100 = 4.61  e100 = 4.61  4.61e = 100
e4.61 = 100  100e = 4.61

27. Write the equation in logarithmic form:
e7 = 1097 ln 1097 = 7  7 ln = 1097
ln 7 = 1097   1097 ln = 7  

28. ln e10 100   10
1/100  1/10

29. Simplify:
ln 0  1   Undefined
0  2

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

GRADE 12

Answer
Ordinarily I don't like to answer that many questions for one person since I get several requests every day, but some of these were pretty simple.  However, I didn't understand what you were asking on questions 17, 19, 20, 21, and 22.
You need to indicate exponents as x^2 or square roots as y^1/2
1. 9
2. 5(3^1/2)
3. 440 cm^3
4. 2u^3+3u^2+2
5. x^3+3x^2+4x+2
6. no answer is correct
7. 2.45, 1.735
8. -6, 12
9. 0, 0.5
10. -2, 1
11. hyperbola
12. 0,+/-5.48
13. no real solution
14. 8ft and 3ft
15. 540
16. 12 15cents, 20 25cents, 6 45cents
18. 16^y
23. 113
24. $1,126.83
25. $1220.37
26. e^4.61 = 100
27. ln(1097)= 7
28. 10
29. undefined
30. -0.5ln(0.2)