# Diagnostic Examination 1. Factor Ā x2 - 5x + 6.
(a) (x - 2)(x - 3)
(b) (x + 2)(x + 3)
(c) (x - 2)(x + 3)
(d) x2 - 5 x + 6
(e) (x + 3)(x - 2)
2. The remainder of dividing the polynomial Ā x3 + x2 Ā by Ā x2 +1 Ā is
(a) 1
(b) -x -1
(c) x +1
(d) x
(e) 0
3.
Simplify
 x + 1 (x2 - 2x - 3)

 x - 3 x + 1
(a) 12
(b)
 1 x-3
(c)
 ( x+1 x - 3 ) ( x2 - 2x - 3 x+1 )
(d)
 x+1 (x-3)2
(e)
 1 x+1
4. The distance from the point (1,2) to the point (2,1) is
(a) 21/2
(b) 3
(c) 3(21/2)
(d) 2
(e) 31/2
5. Find the equation of the line through (-1,1) and (5,2).
(a) x - y + 2 = 0
(b) x - 2y - 1 = 0
(c) x + y = 0
(d) x - y - 2 = 0
(e) x - 6y + 7 = 0
6. The line containing the points (1,1) and (1,-1) is perpendicular to the line
(a) y -1 = x -1
(b) y = -x -1
(c) x = 5
(d) y = 2x +1
(e) y = 5
7. Find all solutions to x2-3x + 2 = 0.
(a) x = -1 and x = 2
(b) x = -1 and x = -2
(c) x = 1.1 and x = 2.1
(d) x = 1 and x = 2
(e) x = 1 and x = -2
8. If x = y and x2y2 - 5xy + 6 = 0, then which of the following is possible?
(a) x2 = 6
(b) x2 = 3
(c) x = 2
(d) x = 3
(e) x = 6
9. Find the largest solution of x3 + 4x2 + 3x = 0.
(a) x = 1
(b) x = -3
(c) x = -2
(d) x = -1
(e) x = 0
10. log(6) equals
(a) 3 log(2)
(b) 2
(c) log(2) + log(3)
(d) 3
(e) 2 log(3)
11.
Find the value of x that satisfies the equation
 3 = 6x 2x
(a) 2
(b) 0
(c) 4
(d) 1
(e) 3
12. log(x2 - 2x +1) > log(25) reduces to
(a) x > -4
(b) x < -4 or x > 6
(c) x < 6
(d) x > 6
(e) x < -4
13. If f(x) = x + 5, what is f(3)?
(a) 8
(b) 2
(c) 3
(d) 5
(e) 9
14. If f(x) = 3x + 3 and g(y) = 2y + 5, what is g(f(2))?
(a) 9
(b) 30
(c) 7
(d) 23
(e) All of the other answers are incorrect.
15. If f(x)=3x2 + 3, what is f(f(a))?
(a) Not defined.
(b) All of the other answers are incorrect.
(c) 3a2 + 3
(d) 3(3a2 + 3)2 + 3
(e) 0
16.
The inequality
 xx2 +1 > 0
is equivalent to:
(a) x > 1
(b) x > 0
(c) x = 0
(d) x < 0
(e) x < 1
17. The inequality (x - 1)2 > 1 is equivalent to
(a) 0 < x and x < 2
(b) x < 0
(c) x < -2
(d) x > 2
(e) x < 0 or x > 2
18.
The inequality
 x3-4x2 +3x-5 > 0
is equivalent to:
(a) x is not equal to 0
(b) x = 0
(c) x < 0
(d) x > 0
(e) None of the other answers is correct
19. If 4x - y = 1 and 2x + y = 5, find x and y.
(a) x = 1 and y = 3
(b) x = -1 and y = 5
(c) x = 4 and y = 1
(d) x = 0 and y = 6
(e) x = 0 and y = 3
20. If 5x-6y = 4 and 3x + 4y = 10, then x/y is
(a) 2
(b) 0
(c) Cannot be determined
(d) 1
(e) 3
21. If y + 3x + 2 = 0 and y = x2, then there is a solution with x given by
(a) x = 1
(b) x = 2
(c) Cannot be determined
(d) x = -1
(e) x = 0
22. A right triangle has sides of length 3, 4, and 5. What is the cosine of its smallest angle?
(a) 3/5
(b) 4/3
(c) 3/4
(d) 5/3
(e) 4/5
23. If sin(a) = 1, cos(b) > 0, and sin(b) = 1/2, then sin(a + b) is
(a) 31/2/2
(b) 3/2
(c) 2/3
(d) 2/(31/2)
(e) 1/2
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,-3)
(b) (1,2)
(c) (1,-2)
(d) (1,31/2)
(e) (1,-31/2)