1. Joshua buys two CD's at $14.95 each and three tapes at ...



1. A basketball team has won seven of its first fifteen games. How many wins in their next ten games will raise their winning percentage for the season to 60%?

A. 2 B. 6 C. 7 D. 8 E. 9

2. A B

The length of line segment AB is approximately

A. 6 mm B. 25 mm C. 3 cm D. 8 cm E. 0.5 m

3. The peel of a banana weighs 1/8 of the total weight of the banana. If you buy 3.5 kg of bananas at one kg for $1.10, how much are you paying for the peels? (Round to the nearest cent.)

A. $0.14 B. $0.35 C. $0.41 D. $0.48 E. $0.51

4. If [pic] inches on a map represents 300 miles, what distance does [pic] inches represent?

A. 650 miles B. 660 miles C. 670 miles D. 680 miles E. 690 miles

5. A $20 dollar bill is 15 cm long. If five million dollars worth of $20 bills were laid end-to-end, their length would be

A. 3.75 km B. 37.5 km C. 75 km D. 750 km E. None of these

6. Convert 36.74o to degrees, minutes, and seconds. The number of seconds is

A. 14 B. 24 C. 28 D. 42 E. 44

7. A painter has finished painting 2/3 of a room by 2:00 PM and 3/4 of the same room by 2:30 PM. At this rate, when does he finish painting the room?

A. 3:00 PM B. 4:00 PM C. 4:30 PM D. 5:00 PM E. 5:30 PM

8. If x + y = -23 and x - y = 7 then 2x - y equals

A. -31 B. -1 C. 1 D. 8 E. 15

9. If it takes Jeremy 18 hours to dig a 2 meter by 2 meter by 2 meter hole, how many hours would it take three men (each working at the same rate as Jeremy) to dig a 4 meter by 4 meter by 4 meter hole?

A. 12 B. 18 C. 24 D. 36 E. 48

10. A package of 20 plastic forks costs $0.39 . A package of 24 plastic knives costs $0.45 .

If you wish to purchase the same number of forks and knives,

what is the least amount that you could spend?

A. $3.36 B. $4.20 C. $4.59 D. $5.34 E. $9.18

11. Line segments AB and DE, intersect at point C (which is not one of the endpoints).

m ( ACE = y - 15 ; m ( ECB = 3x ; m ( DCB = x - 2y

x + y equals

A. 81o B. 84o C. 86o D. 90o E. 94o

12. ((x - y) - z ) - ( y - ( z - x )) equals

A. 2x - 2y B. 2x - 2z C. -2y D. -2z E. 0

13. For HOW MANY of these five values for x is x3 < x ?

-5 -1/2 1/2 0.8 5

A. One B. Two C. Three D. Four E. Five

14. AB is the diameter of a circle of radius r with center C. Triangle DAB is an isosceles triangle with DA = DB. The area of the circle equals the area of the triangle DAB. DC equals

A. [pic] B. [pic] C. [pic] D. [pic] E. [pic]

15. 2000 is the sum of 40 consecutive odd integers. The smallest of these is

A. 9 B. 11 C. 27 D. 29 E. 3

16. The three circles are tangent to the rectangle and to each other.

The length of the rectangle is 24 cm.

The area, in square centimeters, of the shaded region is

(Round to the nearest tenth.)

A. 41.2 B. 56.6 C. 84.6

D. 116.6 E. Cannot be determined

17. A rectangle is twice as long as it is wide. If the length of the diagonal of the rectangle is 30 cm, the perimeter of the rectangle is

A. 53.7 cm B. 80.5 cm C. 96.1 cm D. 107.3 cm E. 180 cm

18. Calculate the area of the triangle, in square units, bounded by the three lines:

x = 6 y = x + 9 x + 2y = -6

A. 37.5 B. 120.5 C. 128 D. 147 E. 162

Problems #19 and #20 each use the following information.

The new American Mathematics Competition consists of 25 questions.

The scoring rules are:

Each correct answer: +6

Each wrong answer: 0

Each answer left blank: +2

19. The score of a student who answers 16 questions with 12 correct and 4 wrong answers is

A. 74 B. 80 C. 84 D. 90 E. 96

20. A student has N correct answers and receives a score of 102.

The number of possible values of N is

A. One B. Three C. Four D. Five E. More than five

*****************

21. 20002000 = 2P 5Q P equals

A. 2003 B. 2004 C. 6000 D. 8000 E. 42000

22. In triangle ABC, angle A is 24o larger than angle B and Angle C is twice Angle A.

The measure of angle C minus the measure of angle B equals

A. 39o B. 48o C. 54O D. 60O E. 75o

23. A jogger left home at 3:30 PM, running at an 8 miles per hour pace. Then she turned around and returned home by the same route, at a 7 mile per hour pace. If she arrived home at 4:15 PM, what was the total distance, in miles, that she ran?

A. 5.5 B. 5.6 C. 5.625 D. 5.75 E. Cannot be determined

24. If 3x + 7 = x2 + k = 7x + 15 , then k equals

A. -3 B. 0 C. 1 D. 4 E. Cannot be determined

25. RS = ST = TZ and segment SP is parallel to segment RZ.

Angle SPZ is a right angle.

If m( RST = 48o , then m( PSZ equals

A. 33o B. 42o C. 45o

D. 48o E. 57o

26. Example: The "sum of digits" of 1656 is 1+6+5+6 = 18 .

HOW MANY whole numbers from 1 to 2000 have their "sum of digits" equal to 25?

A. 10 B. 12 C. 13 D. 15 E. 16

27. Suzanne's birthday is tomorrow (March 19). Suzanne's father, Rick, has his birthday on April 1 (no fooling!). On March 18, 1999, Rick was three times as old as Suzanne. Today (March 18, 2000), Rick is 32 years older than Suzanne. (In this problem, all "ages" are whole numbers.)

What will be the sum of their ages on April 2, 2000?

A. 64 years B. 65 years C. 66 years D. 67 years E. 68 years

28. [pic] is a Real Number if [pic].

The maximum possible value of b - a is

A. 4 B. 8 C. 10 D. 16 E. Not a finite number

29. Rounded to the nearest tenth, the shortest distance between the point (10,7)

and the line: y = -2x + 7 is

A. 8.9 B. 9.2 C. 9.5 D. 9.7 E. 10

30. The four vertices of a square PQRS are P(9, 6), Q(a, b), R(5, 16), and S(c, d) .

The product abcd equals

A. 0 B. 1456 C. 2808 D. 3960 E. 4320

31. In quadrilateral ABCD, BC = CD = DA = x cm and AB = BD = y cm

The set of all possible values of [pic] is

A. [pic] B. [pic] C. [pic]

D. [pic] E. [pic]

32. The first seven terms of a sequence are: 3, 11, -4, -59, -39, 256, 451

This sequence is generated by the rule: an+1 = an - 5an-1

For example: 11 - 5 (3) = -4; -4 - 5 (11) = -59; etc.

In the above sequence, which one of the following terms is a multiple of 12?

A. 96th B. 101st C. 102nd D. 105th E. 108th

33. The radius of circle C is 20 cm.

A 120o sector is removed from circle C.

Segments AC and BC are taped to form

a cone with Vertex C.

What is the volume of the cone?

(Round to the nearest cubic centimeter.)

A. 2775 B. 2996 C. 3723 D. 4163 E. 4475

34. HOW MANY Whole Numbers are counterexamples which show that the following statement is false.

"If N is an odd positive integer the sum of whose digits is 4 and none of whose digits is 0, then N is a prime number."

A. One B. Two C. Three D. Four E. More than four

35. Triangle ABC is an isosceles right triangle with

AB = BC = 2 cm .

Arc BPD is the arc of a circle with center at C.

Arc BQD is the arc of a circle with center at A.

(The diagram is not drawn to scale.)

The area, in square centimeters (rounded to the

nearest hundredth), of the shaded region BPQ is

A. 0.78 B. 1.00 C. 1.14 D. 1.32 E. 1.57

36. In this multiplication problem, replace each letter MEGSL

with a digit chosen from 0 through 9, inclusive. M ( 0 . x 4

Replace identical letters with the same number. -------------

Different letters represent different numbers. LSGEM

The sum M+E+G+S+L equals

A. 20 B. 22 C. 23 D. 26 E. 27

37. [pic] equals [pic] . What does N equal?

A. 40 B. 80 C. 119 D. 239 E. 359

38. In each diagram, ABC is a right triangle,

AB = 20 cm and BC = 10 cm.

As shown, a square is inscribed in each

triangle.

[pic] , the ratio of the areas of the

two squares equals

(round to the nearest hundredth)

A. 0.89 B. 0.94 C. 1.00 D. 1.04 E. 1.09

39. Circle A has radius R. Circle B has radius r. R > r .

Circles A and B are tangent to each other and to the largest circle.

Chord PQ has length 2 and is tangent to circles A and B.

Calculate the area of the shaded region.

A. [pic] B. [pic] C. [pic]

D. [pic] E. [pic]

40.

Always follow the direction of the arrows.

If the above pattern were continued to 15,

the number of distinct paths from 1 to 15 would be

A. 600 B. 610 C. 620 D. 630 E. 640

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24 cm

S

P

Z

T

R

B

C

A

120o

20

A, B

20

C

A

C

D

B

P

Q

A

B

C

A2

A1

A

B

C

A

B

R

r

P

Q

6

4

5

2

1

7

3

8

9

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