Expert: Richard J. Raridon - 10/19/2011

Question
I need help studying for a test I want to make sure I have the right answers, thanks!

1. If w varies directly as 2x - 1, and w = 9 when x = 2, find x when w = 15.

x = 2  x = 36
x = 5  x = 3


2. If p varies inversely as the square root of q, and p = 12 when q = 36, find p when q = 16.

p = 4.5  p = 0.056
p = 18  p = 1.8


3. If y varies inversely as x and y = 4 when x = 9, what is x when y = 72?

2  4
0.4  0.5


4. The current in an electric circuit of constant voltage varies inversely as the resistance. When the current is 30 amps, the resistance is 20 ohms. Find the current when the resistance is 25 ohms.

24 amps  22 amps
20 amps  16 amps


5. The length of a rectangle with constant area varies inversely as the width. When the length is 18, the width is 8. Find the length when the width is 9.

12  14
16  18


6. Solve using the given root:

2x3 + 9x2 + 7x - 6 = 0; -2

{-2,0.5, 3}  {-2,0.5,-3}
{-2,-0.5,-3}  {-2,1,0}


7. Solve using the given root:

2z3 + z2 - 8z + 3 = 0; 1.5

-1 ± Ö 2
 -1 ± 2 Ö 2

-3 or 1  3 or -1


8. Find a polynomial equation with integral coefficients that has the roots:

1, -1.5, 2

2x3 - 3x2 - 5x + 6 = 0  2x3 + 3x2 - 7x + 6 = 0
2x3 - x2 - 5x + 6 = 0  2x3 + 3x2 - 5x - 6 = 0


9. Solve for n:

Ö 2n + 4 = 6
n = 12  n = -2
n = -16  n = 16


10. List the possible rational roots for the equation:

4x4 + 4x3 + 17x2 + 16x + 4 = 0

{±1, ± 4, ± 0.5}  No answer is correct.
{1, 2, 4, 0.5, 0.25}  {±1, ± 2, ± 4, ± 0.5, ± 0.25}


11. Assume that y varies directly as x. If y = 4 when x = 0.5, find y when x = 2.

y = 4  y = 16
y = 6  y = 8


12. Find all roots of the equation

x3 - x2 - 14x + 24 = 0

-4, 2, 3  4, 2, 3
0, 4  -4, 3


13. Find all roots of the equation

6y5 - 13y4 - 6y3 + 17y2 - 4 = 0

-1, -0.5, 2/3, 1, 2  1, 0.5, 2/3, -1, -2
-1, 0.5, 1, 2  0, -1, -0.5, 2/3, 1, 2


14. Find the distance between the pair of points:

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

d = 9.9  d = 7.28
d = 7  d = 21.17


15. Find the midpoint of the line segment joining the two points:

(-a, b) and (2a, 4b)

(1.5a, 2.5b)  (0.5a, 1.5b)
(0.5a, 2.5b)  (2a, 0.4b)


16. 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)


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

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

(-0.25, 0)  (0, -0.25)
(0.25, 0)  (0, 0.25)


18. Find an equation of the perpendicular bisector of line segment AB:

A(2, 1), B(-2, 3)

y = 2x - 2  y = 2x + 2
y = 4x - 2  y = 4x + 2


19. If the focus of a parabola is F(-3, -1) and vertex is V(1, -1), what is the directrix?

D: x = 5  D: x = -1
D: x = -3  D: x = -5


20. Identify the conic section whose equation is given: (5y - x)(5y + x) = 100

Circle  Hyperbola
Ellipse  Parabola


21. Choose the real solutions of the system:

y2 = 2x  and  x2 + y2 = 8

(-2, -2); (-2, 2)  (4, 4); (-4, 4)
(2, -2); (-2, -2)  (2, 2); (2, -2)


22. The area of a rectangle is 48 m2. The length of a diagonal is 10 m. Find the perimeter of the rectangle.

28m  14m
42m  80m


23. The lines with equations x = 2, x = 5, y = 7, and y = 3 form a rectangle. What is the area of this rectangle?

12  14
15  28

24. Solve the system:

a + 3b + 4c = 6

a - 2b + c = 10

2a + 3b - c = 0

(4, -2, 2)  (4, 2, -2)
(-4, 2, -2)  (-4, -2, 4)


25. The sum of the length, width, and height of a rectangular box is 75 cm. The length is twice the sum of the width and height. The width exceeds the height by 5 cm. Find the dimensions.

50 cm by 10 cm by 15 cm  40 cm by 10 cm by 25 cm
45 cm by 15 cm by 15 cm  45 cm by 10 cm by 15 cm


26. 5x = Ö 125
2
3
 3
1
3
 3
2


27. Solve:

log6x = 3

18  2
54  216


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

log2 1/MN

- (log2M + log2N)  log21 (log2M + log2N)
2(log2M + log2N)  2(log2M - log2N)


29. Condense to a single log expression:

log5 x - log5 y + 2

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


30. 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

Answer
1. x=3
2. p=18
3. x=0.5
4. 24
5. 16
6. -2,0.5,-3
7. -1+/-2^1/2
8. 2x^3-3x^2-5x+6
9. the way you wrote it made it appear to be (2n)^1/2 +4 instead of what you meant, (2n+4)^1/2, answer is 16
10. no answer is correct
11. 16
12. -4,2,3
13. -1,1,2,-0.5,2/3
14. 7.28
15. 0.5a,2.5b
16. -6,12
17. -0.25,0
18. y=2x+2
19. 5,-1
20. hyperbola
21. (2,2);(2,-2)
22. 28m
23. 12
24. 4,-2,2
25. 50,10,15
26. x = 5^1/2
27. you meant log base 6 (x) = 3 so x = 216
30. $1126.83