Junior Olympiad
1. The slope of any line parallel to the graph of is:
A)
B)
C)
D) 3
E) none of these
2. If and , then is:
A)
B)
C)
D)
E) none of these
3. If and , then is:
A)
B)
C) 1
D) 6
E) none of these
4. If , then the value of is:
A)
B)
C) 2
D) 10
E) none of these
5. The largest value of such that divides 10! (with 0 remainder) is:
A) 0
B) 1
C) 2
D) 3
E) none of these
6. Where defined, is:
A)
B)
C)
D)
E) none of these
7. If , then is:
A) 0
B)
C) 1
D) 6
E) none of these
8. If , , and , then is:
A)
B) 0
C) 3
D) 9
E) none of these
9. The value of is:
A)
B)
C)
D)
E) none of these
10. The sum of all values of that satisfy is:
A)
B) 1
C) 3
D) 5
E) none of these
11. Using interval notation, the solution set for is:
A)
B)
C)
D)
E) none of these
12. Using interval notation, the solution set for is:
A)
B)
C)
D)
E) none of these
13. Using interval notation, the solution set for is:
A)
B)
C)
D)
E) none of these
14. The domain of the real-valued function defined by is:
A)
B)
C)
D)
E) none of these
15. If, then is:
A)
B)
C) 0
D) 7
E) none of these
16. If , then, for , is:
A)
B)
C)
D) 0
E) none of these
17. The number of points of intersection for the graphs of and is:
A) 0
B) 1
C) 2
D) 3
E) none of these
18. A circle with center has a diameter of length 4. The coordinates of a point on the circle are:
A)
B)
C)
D) (2,2)
E) none of these
19. The sum of the digits of the integer represented by is:
A) 6
B) 834
C) 842
D) 843
E) none of these
20. If the lengths, in inches, of the edges of a rectangular prism are 4, 5 and 6 respectively, then the surface area, in square inches, of the prism is:
A) 74
B) 120
C) 148
D) 296
E) none of these
21. The number of digits in the integer represented by is:
A) 51
B) 54
C) 102
D) 104
E) none of these
22. If an equilateral triangle is inscribed in a unit circle, then the perimeter of this triangle is:
A)
B) 3
C)
D)
E) none of these
23. If Al and Bob each mentally select one integer at random from , then the probability that the absolute value of the difference between Al’s integer and Bob’s integer is greater than one is:
A)
B)
C)
D)
E) none of these
24. The sum of the values of such that has equal roots is:
A)
B)
C) 2
D) 8
E) none of these
25. If , then is:
A)
B)
C)
D) 1
E) none of these
26. If and are consecutive odd positive integers such that , then is:
A) 56
B) 58
C) 62
D) 64
E) none of these
27. If is divided by , then the remainder is:
A)
B) 2
C)
D)
E) none of these
28. If , , and , then is:
A) 6
B) 8
C) 10
D) 12
E) none of these
29. If , then equals:
A) 2
B)
C) 16
D) 96
E) none of these
30. If , , and are arranged in decreasing numerical order, then the ordering is:
A)
B)
C)
D)
E) none of these
31. If , then is:
A)
B)
C)
D)
E) none of these
32. The number of points of intersection of the graphs of and is:
A) 0
B) 1
C) 2
D) 3
E) none of these
33. The number of distinct solutions of is:
A) 0
B) 1
C) 2
D) 3
E) none of these
34. If , then is:
A) 1
B) 2
C) 3
D) 4
E) none of these
35. If and , then is:
A)
B)
C)
D) 2
E) none of these
36. If for all real numbers , then the range of is:
A)
B)
C)
D)
E) none of these
37. The coordinates for the vertex of the graph of are:
A)
B) (0,4)
C) (1,6)
D)
E) none of these
38. The value of is:
A)
B)
C)
D)
E) none of these
39. If , then is:
A)
B)
C)
D)
E) none of these
40. If is divided by 3 for all positive integers , then the sum of all the remainders is:
A) 0
B) 1
C) 2
D) 3
E) none of these
41. The smallest distance between a point satisfying and a point satisfying is:
A)
B)
C)
D)
E) none of these
42. The area of the largest square that can be inscribed in a unit circle is:
A) 1
B) 2
C) 4
D)
E) none of these
43. An urn contains five white balls and three black balls. If three balls are drawn at random without replacement, then the probability that the three balls drawn are white is:
A)
B)
C)
D) 1
E) none of these
44. The length of the radius of a circle whose area would be doubled by increasing its radius by 1 is:
A)
B)
C)
D) 1+
E) none of these
45. The lengths of the legs of a right triangle are 5 and 10. If the length of the hypotenuse of a similar triangle is 15, then the area of the larger triangle is:
A) 25
B) 45
C) 50
D) 60
E) none of these
46. The set of all values of for which the system does not have a solution is:
A)
B)
C)
D)
E) none of these
47. If for all real numbers, then the maximum value of is:
A) 2
B) 3
C) 6
D) 20
E) none of these
48. The squares on a chess board are numbered consecutively from 1 to 64. If pebbles are placed on the square, then the total number of pebbles on the chess board is:
A) 6109
B) 6110
C) 6111
D) 6112
E) none of these
49. The number of values of for which the graphs of and have exactly two points of intersection is:
A) 0
B) 1
C) 2
D) 3
E) none of these
50. If the vertices of an equilateral triangle are at (0,4), (4,1), and where , then is:
A)
B) 1
C) 2
D)
E) none of these