  
1. 
The remainder of dividing the polynomial
x^{3}x^{2}+x1
by x1 is


(a)  0 

(b)  2 

(c)  3 

(d)  x 

(e)  1 

  
2. 
Simplify 

(x^{3} + 2x^{2} + 2x + 1)
(x + 1)
 


(a)  x^{2}  x + 1 

(b)  x^{2} + 1 

(c)  x^{2}  2x + 1 

(d)  x^{2} + 2x + 1 

(e)  x^{2} + x + 1 

  
3. 
Evaluate 
( 
1
x

+ 3 ) ( 5 + 
2
x^{2}

). 




(a)  

(b) 

5
x

+ 15 + 
2
x^{3}

+ 
6
x^{2}





(c)  

(d)  All of the other answers are incorrect. 

(e)  

  
4. 
The set of points (x,y) such that
x^{2} + y^{2} = 9
is 

(a)  an hyperbola 

(b)  a parabola 

(c)  a circle of radius 3 centered at (0,0) 

(d)  a circle of radius 3 centered at (1,1) 

(e)  a circle of radius 9 centered at (0,0) 

  
5. 
The set of points (x,y) such that
x^{2} 4x + y^{2} 6y = 15
is a circle centered at 

(a)  (9,4) 

(b)  (0,0) 

(c)  (2,3) 

(d)  (3,2) 

(e)  (4,9) 

  
6. 
The circle with equation
x^{2} + y^{2}  2y = 0
intersects the line y = mx in two distinct points 

(a)  if and only if m < 0 

(b)  if and only if m is not equal to 0 

(c)  if and only if m > 0 

(d)  for no values of m 

(e)  for all values of m 

  
7. 
If 3x + 6 = 12, what is x? 

(a)  All of the other answers are incorrect. 

(b)  x = 4 

(c)  x = 2 

(d)  x = 2 

(e)  x = 0 

  
8. 
If x = y and
x^{2}y^{2}  5xy + 6 = 0, then
which of the following is possible? 

(a)  x = 6 

(b)  x = 2 

(c)  x^{2} = 6 

(d)  x = 3 

(e)  x^{2} = 3 

  
9. 
Find the largest solution of
x^{3} + 4x^{2} + 3x = 0. 

(a)  x = 2 

(b)  x = 1 

(c)  x = 3 

(d)  x = 1 

(e)  x = 0 

  
10. 
log(3/2) equals 

(a)  log(3)  log(2) 

(b)  (1/2)log(3) 

(c)  3 log(1/2) 

(d)  log(2)  log(3) 

(e)  log(2) + log(3) 

  
11. 
log_{2}(x^{2} y^{2}) is equal to which of the following? 

(a)  2log_{2}(x) + 2log_{2}(y) 

(b)  All of the other answers are incorrect. 

(c)  log_{2}(x) + log_{2}(y) 

(d)  [log_{2}(x)]^{2} + [log_{2}(y)]^{2} 

(e)  log_{2}(x^{2}) log_{2}(y^{2}) 

  
12. 
log(x^{2}  2x +1) > log(25) reduces to 

(a)  x < 4 or x > 6 

(b)  x < 6 

(c)  x > 6 

(d)  x > 4 

(e)  x < 4 

  
13. 
If f(x) = 5x  2, what is f(0)? 

(a)  3 

(b)  0 

(c)  2 

(d)  1 

(e)  5 

  
14. 
If h(x) = x^{3}, g(x) = x^{2}+1 and f(x) = x +1, then h(g(f(0))) + f(g(h(0))) is: 

(a)  9 

(b)  16 

(c)  0 

(d)  10 

(e)  4 

  
15. 
If f(x) = 3x + 3 what is f(f(2))?


(a)  30 

(b)  9 

(c)  All of the other answers are incorrect.


(d)  Not defined. 

(e)  81 

  
16. 
The inequality 

is equivalent to: 


(a)  x < 0 

(b)  x > 0 

(c)  x > 1 

(d)  x = 0 

(e)  x < 1 

  
17. 
The expression  5x2  > 1 is equivalent to which of the following? 

(a)  There are no values of x which satisfy this expression. 

(b)  x < 1/5 and x > 3/5 

(c)  x < 1/5 or x > 3/5 

(d)  x < 1/5 

(e)  x < 1/5 or x > 3/5 

  
18. 
[x^{2}  6x + 9]^{1/2} <
 x  1  reduces to 

(a)  x < 1 

(b)  x > 3 

(c)  x < 3 

(d)  x < 2 

(e)  x > 2 

  
19. 
If 3x + 4y = 7 and 5x4y = 1,
then xy is 

(a)  Cannot be determined 

(b)  1 

(c)  2 

(d)  4 

(e)  3 

  
20. 
If 5x6y = 4 and 3x + 4y = 10,
then x/y is


(a)  2 

(b)  Cannot be determined 

(c)  1 

(d)  3 

(e)  0 

  
21. 
If y + 4x  5 = 0 and y = x^{2},
then there is a solution with y given by


(a)  y = 20 

(b)  y = 25 

(c)  Cannot be determined 

(d)  y = 0 

(e)  y = 30 

  
22. 
If a circle has radius 2, then what is the radian measure of
an angle whose vertex is at the center of circle and which cuts an
arc of length 1 along the circle? 

(a)  2pi 

(b)  2 

(c)  pi/2 

(d)  1/2 

(e)  1/(4pi) 

  
23. 
If sin(a) = 1, cos(b) > 0, and sin(b) = 1/2,
then sin(a + b) is 

(a)  3/2 

(b)  1/2 

(c)  3^{1/2}/2 

(d)  2/(3^{1/2}) 

(e)  2/3 

  
24. 
If sin(a + b) = 1 and
tan(a) = 0,
then tan(b) is 

(a)  1/2 

(b)  undefined 

(c)  1 

(d)  0 

(e)  1/4 
