Senior Olympiad

2007

  1. If , then is:

A)–19

B)5

C)23

D)362

E)none of these

  1. If for all real numbers x, then the range of f is:

A)

B)

C)

D)

E)none of these

  1. The vertex of the parabola defined by is:

A)

B)

C)

D)

E)none of these

  1. If is divided by , then the remainder is:

A)1

B)

C)

D)

E)none of these

  1. The unit’s digit of is:

A)0

B)1

C)5

D)7

E)none of these

  1. The area of the triangle bounded by the graphs of and is:

A)

B)

C)

D)

E)none of these

  1. If and , then is:

A)

B)0

C)1

D)2

E)none of these

  1. The coordinates of the vertices of a rectangle are (1, 1), (5, 1), (1, 7), and (5, 7). If a point P is randomly selected within the interior of the rectangle, then the probability that the x-coordinate of P is greater than the y-coordinate of P is:

A)

B)

C)

D)1

E)none of these

  1. If the sum of two numbers is 50 and the product of the same two numbers is 25, then the sum of the reciprocals of these two numbers is:

A)

B)2

C)75

D)1250

E)none of these

  1. The area of the polygon bounded by the graphs of x = 0, and y = 0 is:

A)3

B)4

C)5

D)6

E)none of these

  1. If , and , then F is:

A)46

B)48

C)56

D)58

E)none of these

  1. The sum of the solutions of is:

A)

B)6

C)342

D)343

E)none of these

  1. The negation of “If , then ” is:

A)If , then .

B)If , then .

C) or .

D) and .

E)none of these

  1. The set of all (x, y) such that is:

A)the interior of a circle

B)the exterior of a circle

C)the interior of an ellipse

D)the exterior of an ellipse

E)none of these

  1. The conic section defined by is:

A)a circle

B)a parabola

C)a hyperbola

D)an ellipse

E)none of these

  1. Let. If is a zero of , then the sum of all the real zeros of is:

A)

B)

C)1

D)3

E)none of these

  1. The number of solutions of is:

A)0

B)1

C)2

D)3

E)none of these

  1. If there are 100, 1000, and 10,000 elements in sets A, B, and C, respectively; two elements common to each pair of sets; and one element common to all three sets, then the number of elements in is:

A)1

B)11,093

C)11,107

D)11,109

E)none of these

  1. If 400 books are placed onto thirteen shelves, then at least one shelf must have at least:

A)31 books

B)32 books

C)33 books

D)34 books

E)none of these

  1. The number of subsets of {a, b, c, d, e} that do not contain the letter a is:

A)15

B)16

C)31

D)32

E)none of these

  1. A fair coin is flipped eight times where each flip comes up either ‘heads’ or ‘tails’. The number of possible outcomes that contain exactly three heads is:

A)5

B)8

C)56

D)336

E)none of these

  1. The number of permutations of the letters A, B, C, D, E, F, and G that contain the strings ABC and DE is:

A)24

B)35

C)840

D)5040

E)none of these

  1. Where defined, the expression equals:

A)

B)

C)

D)

E)none of these

  1. The sum, in degrees, of the solutions of in the interval is:

A)

B)

C)

D)

E)none of these

  1. The areaof a parallelogram with an interior angle of measure and two sides of length 8 and 26 is:

A)52

B)104

C)

D)208

E)none of these

  1. If the points , , and lie on the graph of , then equals:

A)

B)6

C)27

D)29

E)none of these

  1. The sum of the solutions of equals:

A)

B)

C)0

D)

E)none of these

  1. If k is a constant such that has no solution (x, y), then k is:

A)

B)0

C)1

D)2

E)none of these

  1. The domain of definition of the real-valued function defined by is:

A)

B)

C)

D)

E)none of these

  1. If tangent lines are drawn from each end of a cm arc on a circle of radius 16 cm, then the smaller angle, in degrees, between the tangent lines is:

A)

B)

C)

D)

E)none of these

  1. The sum of all solutions of in the interval is:

A)

B)

C)

D)

E)none of these

  1. The sum of the solutions of in the interval is:

A)

B)

C)

D)

E)none of these

  1. If , then is:

A)

B)

C)1

D)64i

E)none of these

  1. If , then the sum of the square roots of is:

A)

B)

C)0

D)2

E)none of these

  1. The number of nonempty bit strings of length five or less is:

A)32

B)62

C)64

D)128

E)none of these

  1. The number of functions from {1, 2, 3, 4} into {a, b, c, d} that do not map 1 onto a is:

A)18

B)256

C)456

D)512

E)none of these

  1. The number of functions from {a, b, c, d} into {e, f, g, h} that are not one-to-one is:

A)24

B)64

C)232

D)256

E)none of these

  1. The number of solutions of is:

A)0

B)1

C)2

D)4

E)none of these

  1. The sum of the x and y - coordinates of the point on the graph of that is closest to the graph of is:

A)

B)6

C)

D)10

E)none of these

  1. The number of real numbers x for which is:

A)0

B)1

C)2

D)3

E)none of these

  1. The value of is:

A)

B)

C)

D)

E)none of these

  1. If for all x, then is:

A)

B)

C)

D)

E)none of these

  1. The sum of all the coefficients in the expansion of is:

A)– 2000

B)– 200

C)200

D)2000

E)none of these

  1. If , then is:

A)

B)

C)

D)

E)none of these

  1. If and , then equals:

A)

B)

C)

D)

E)none of these

  1. If and , then is equal to:

A)h

B)

C)f

D)

E)none of these

  1. If the x-intercepts of the graph of are and , then is:

A)

B)

C)3

D)7

E)none of these

  1. The expression equals:

A)0

B)1

C)123456789

D)987654321

E)none of these

  1. If x and y are positive integers such that y is the hundred’s digit of the six-digit integer 492y04 and , then x + y is:

A)6

B)12

C)14

D)15

E)none of these

  1. A simple polygonal region is constructed by sequentially connecting the points , , , , , , and . The area of the region is:

A)24

B)

C)48

D)67

E)none of these