Diagnostic Examination

Georgia O'Keeffe's Line and Curve

1. The equation, 4x2 - 6x + 10 = 0, has
(a) two real solutions
(b) three real solutions
(c) one real solution
(d) no real solutions
(e) four real solutions
2.
Simplify (x3 + 2x2 + 2x + 1)

(x + 1)
(a) x2 + 1
(b) x2 + 2x + 1
(c) x2 - x + 1
(d) x2 + x + 1
(e) x2 - 2x + 1
3.
Evaluate
( 1

x
+ 3 ) ( 5 + 2

x2
).
(a)
4

x
+ 6

x2
(b)
5

x
+ 6

x2
(c) All of the other answers are incorrect.
(d)
5

x
+ 15 + 2

x3
+ 6

x2
(e)
11

x
+ 15 + 2

x2
4. The area of a right triangle with sides 3, 4, and 5 is
(a) 6
(b) 15
(c) 20
(d) 10
(e) 12
5. Find the equation of the line perpendicular to y = x/3 + 1 through the point (3,2).
(a) y = 3x - 7
(b) y = -x/3 + 3
(c) y = - 3x + 11
(d) y = x/3 + 7
(e) y = x/3 +1
6. The distance from the point (x,y) to the point (2,3) is twice the distance from the point (x,y) to the point (5,7). What is the maximum possible distance from (x,y) to (2,3)?
(a) 10
(b) 15
(c) 4
(d) 25
(e) 5
7. If 2(2x-3) + 5(x + 1) = 6x-7, what is x?
(a) x = 8
(b) x = 4
(c) x = -4
(d) x = -2
(e) x = 2
8. If x = y and x2y2 - 5xy + 6 = 0, then which of the following is possible?
(a) x = 6
(b) x2 = 3
(c) x2 = 6
(d) x = 2
(e) x = 3
9. How many real solutions for x are there to the equation x2 + 3x + 8 = 0?
(a) 2
(b) 3
(c) It cannot be determined.
(d) 0
(e) 1
10. Simplify (x/2x3)(y2/y).
(a) 2x-2y - 1
(b) (1/2)x - 2 y
(c) (x/2)-2 y
(d) (x y2)/(2x3y)
(e) (1/2)x-2 + y
11. What is log3(35)?
(a) 1/3
(b) e
(c) 5
(d) 1/5
(e) 3e
12. Which of the following values of x satisfies log2(3x) + log2(2x) = 3?
(a) x = (4/3)1/2
(b) x = 4
(c) x = 3/5
(d) x = (3/2)1/2
(e) x = 5
13. The function f(x) = x2 has range
(a) The set of all numbers x such that x is greater than or equal to 1
(b) The set of all numbers
(c) The set of all numbers x such that x is greater than or equal to 0
(d) The set of all numbers x such that x is less than or equal to 1
(e) The set of all numbers x such that x is less than or equal to 0
14. The function f(x) = [x2 -1]1/2 has domain
(a) The set of all numbers x such that either x is less than or equal to -1 or 1 is less than or equal to x
(b) The set of all numbers x such that 1 is less than or equal to x
(c) The set of all numbers x such that 1 < x
(d) The interval [-1,1]
(e) The set of all numbers x such that either x < -1 or 1 < x
15. If f(x) = 3x2 + 4 and g(y) = 2y1/2 + 5, what is g(f(2))?
(a) 9
(b) 20
(c) All of the other answers are incorrect.
(d) 10
(e) 13
16. Let a = -3, b = 5, and c = -1. Evaluate |a - b| - (c - a)
(a) 10
(b) 11
(c) 8
(d) -2
(e) 6
17. The inequality (x - 1)2 > 1 is equivalent to
(a) x < -2
(b) x < 0 or x > 2
(c) x > 2
(d) 0 < x and x < 2
(e) x < 0
18.
The inequality
x3
-4x2 +3x-5
> 0
is equivalent to:
(a) x > 0
(b) x is not equal to 0
(c) x = 0
(d) None of the other answers is correct
(e) x < 0
19. If 3x + 4y = 7 and 5x-4y = 1, then xy is
(a) 1
(b) 4
(c) 2
(d) Cannot be determined
(e) 3
20. If 5x-6y = 4 and 3x + 4y = 10, then x/y is
(a) 1
(b) Cannot be determined
(c) 0
(d) 2
(e) 3
21. If y + 4x - 5 = 0 and y = x2, then there is a solution with y given by
(a) y = 25
(b) y = 30
(c) Cannot be determined
(d) y = 20
(e) y = 0
22. A right triangle has sides of length 3, 4, and 5. What is the cosine of its smallest angle?
(a) 4/3
(b) 4/5
(c) 3/4
(d) 3/5
(e) 5/3
23. Which of the following is correct?
(a) cos(.1) < sin(.1)cos(.1) < sin(.1)
(b) sin(.1) < cos(.1) < sin(.1)cos(.1)
(c) sin(.1)cos(.1) < sin(.1) < cos(.1)
(d) sin(.1) < sin(.1)cos(.1) < cos(.1)
(e) cos(.1) < sin(.1) < sin(.1)cos(.1)
24. A line containing the point (0,0) defines an angle of 60 degrees with the x-axis. If the slope of the line is negative then the line must contain the point
(a) (1,-31/2)
(b) (1,-2)
(c) (1,2)
(d) (1,31/2)
(e) (1,-3)