# Diagnostic Examination

1.
Simplify
1

 1+ 1 x+1
(a)
 x+1
(b)
 x+1 2
(c)
 1 x+1
(d)
 1 x+2
(e)
 x+1 x+2
2.
Simplify
 (3 a2 b-3)-4 (12ab3)-5
(a) 48a-3b27
(b) 96a-13b27
(c) 48a-13b-27
(d) 96a-3b27
(e) All of the other answers are incorrect.
3.
Evaluate
 ( 1 x + 3 ) ( 5 + 2 x2 ).
(a)
 5 x + 6 x2
(b)
 11 x + 15 + 2 x2
(c) All of the other answers are incorrect.
(d)
 5 x + 15 + 2 x3 + 6 x2
(e)
 4 x + 6 x2
4. Find the midpoint of the line segment between (-2,1) and (4,5).
(a) (-1,1)
(b) (1,3)
(c) (3,-1)
(d) (3,3)
(e) (3,1)
5. Which of the following points is closer to the point (1,1) than the point (2,2) is to (1,1)?
(a) (0,1)
(b) (0,0)
(c) (2,0)
(d) (0,2)
(e) (1, 5/2)
6. A circle contains the four vertices of a square with diagonal of length 6. The area of the region outside the square and inside the circle is
(a) 36pi - 36
(b) 36
(c) 9pi - 9
(d) 36 pi
(e) 9pi - 18
7. Let f(x) = 3x + 2. For which x is f(x) = -2?
(a) -2/3
(b) 0
(c) 4/3
(d) -4/3
(e) -3/2
8. If x = y and x2y2 - 5xy + 6 = 0, then which of the following is possible?
(a) x2 = 6
(b) x2 = 3
(c) x = 3
(d) x = 6
(e) x = 2
9. How many real solutions for x are there to the equation x2 + 3x + 8 = 0?
(a) 2
(b) It cannot be determined.
(c) 0
(d) 1
(e) 3
10. log(3/2) equals
(a) log(2) + log(3)
(b) (1/2)log(3)
(c) log(3) - log(2)
(d) log(2) - log(3)
(e) 3 log(1/2)
11. What is log3(35)?
(a) 3e
(b) e
(c) 5
(d) 1/3
(e) 1/5
12. log(x2 - 2x +1) > log(25) reduces to
(a) x < -4 or x > 6
(b) x < -4
(c) x > 6
(d) x > -4
(e) x < 6
13. The function f(x) = x2 has range
(a) The set of all numbers x such that x is less than or equal to 0
(b) The set of all numbers x such that x is greater than or equal to 1
(c) The set of all numbers x such that x is less than or equal to 1
(d) The set of all numbers
(e) The set of all numbers x such that x is greater than or equal to 0
14. If f(x) = 3x + 3 and g(y) = 2y + 5, what is g(f(2))?
(a) 9
(b) 30
(c) 23
(d) All of the other answers are incorrect.
(e) 7
15. If f(x) = 3x2 + 4 and g(y) = 2y1/2 + 5, what is g(f(2))?
(a) 10
(b) 13
(c) 20
(d) 9
(e) All of the other answers are incorrect.
16. The expression 40 < 5x < 80 is equivalent to which of the following?
(a) All of the other answers are incorrect.
(b) 8 < x < 16
(c) 35 < x < 75
(d) 8 > x < 16
(e) 8 < x > 16
17. The inequality x3 < 2x2 -x reduces to
(a) x < 1
(b) x > 1
(c) x < 0
(d) x > 0
(e) x < 0 or x is not equal to 1
18.
Under which of the following conditions does   x   satisfy
 x + 2 | x - 1 | > 0
(a) x + 2 > 0
(b) x - 1 > 0 and x + 2 > 0
(c) x is not equal to 1 and x + 2 > 0
(d) All of the other answers are incorrect.
(e) There are no values of x which satisfy this expression.
19. If 5x - 6y = 4 and 3x + 4y = 10, find x and y.
(a) x = -2 and y = -1
(b) x = 4 and y = 1
(c) x = -2 and y = 2
(d) x = 2 and y = 1
(e) x = 2 and y = -2
20. If 5x-6y = 4 and 3x + 4y = 10, then x/y is
(a) Cannot be determined
(b) 0
(c) 1
(d) 2
(e) 3
21. If y + 3x + 2 = 0 and y = x2, then there is a solution with x given by
(a) x = 2
(b) x = 1
(c) Cannot be determined
(d) x = 0
(e) x = -1
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) 1/(4pi)
(b) 2pi
(c) 1/2
(d) pi/2
(e) 2
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) < sin(.1)cos(.1) < cos(.1)
(d) cos(.1) < sin(.1) < sin(.1)cos(.1)
(e) sin(.1) < cos(.1) < sin(.1)cos(.1)
24. A triangle has sides of length 5, 5 and 8. What is the sine of its smallest angle?
(a) 3/8
(b) 5/8
(c) 4/5
(d) 3/5
(e) 8/5