Ninth Grade Test - Excellence in Mathematics Contest - 2002
1. 60 meters of wire weigh 0.8 kg. How many meters of this wire would weigh 2 kg?
A. 24 B. 90 C. 120 D. 140 E. 150
2. The marks on this number line are evenly spaced.
A.
2
P
What number does the mark at point P represent?
2.3 B. 2.6 C. 2.75 D.
5
2.9 E. 3.0
3. Leonora thinks of a secret number. In this sequence: she subtracts 5, multiplies by 5, adds 5, and then divides by 5 to get 2002 as her answer. Don thinks of a secret number. In this sequence: he adds 5, multiplies by 5, subtracts 5, and then divides by 5 to get 2002 as his answer.
What is the sum of their two secret numbers?
A. 2002 B. 3992 C. 3996 D. 4004 E. 20,020
4. The length of a rectangle is twice its width. The perimeter of the rectangle is 48 cm. In square centimeters, what is the area of the rectangle?
A. 64 B. 80 C. 96 D. 128 E. 144
5. In professional baseball, the distance from the pitching mound to home plate is 60 feet, 6 inches. How many seconds does it take a Roger Clemens’ 98 mile per hour fast ball to arrive at home plate? Round your answer to the nearest hundredth of a second. (There are 5280 feet in one mile.)
A. 0.04 B. 0.42 C. 0.52
6. The dimensions of a rectangular box are given.
Ross uses duct tape to secure the box, as shown.
Each of the three wrappings extends completely around the box and there is no overlap at the ends of each wrap.
What length, in meters, of duct tape is required?
D. 0.64 E. 0.91
0.5 m
A. 5.8
D. 8.6
B.
E.
7.4
9.0
C. 7.8
0.6 m
0.8 m
7. The height H, in meters, of a bottle rocket T seconds after it is launched is given by the formula:
H = -9.8T
2 + 120T .
Between the 2 nd second and the 5 th second, how many meters did the rocket rise?
A. 154.2 B. 172.7 C. 271.8 D. 355 E. 2376.8
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Ninth Grade Test - Excellence in Mathematics Contest - 2002
8. 2002 squares, each with area 36 square centimeters, are placed next to each other in one row to form a rectangle. What is the number of centimeters in the perimeter of this rectangle?
A. 24,012 B. 24,018 C. 24,024 D. 24,030 E. 24,036
9. Liberty has x quarters and y dimes. Morgan has y quarters and x dimes. In cents, how much more money does Liberty have than Morgan?
A. 15(x – y) B. 15(y – x) C. 15(x + y) D. 15x + 35y E. None of these
10. ABCD is a 10 cm by 10 cm square.
M and N are midpoints of sides BC and CD.
MP is perpendicular to AN at point P.
Rounded to the nearest tenth of a centimeter,
B
M
C what is the length of MP?
N
A. 5.2 B. 5.6 C. 6.0
P
D. 6.3 E. 6.7
A D
11. Use four distinct digits to form a four-digit number which does not end in the digit “0”. Reverse those four digits to write a second four-digit number.
What is the maximum possible positive difference between those two numbers?
A. 3087 B. 8532 C. 8622 D. 8712 E. 8802
12. The inside of a cylindrical storage drum must be painted with paint that costs $18.60 per gallon. The diameter of the drum is 5 m and its height is 3.4 m. One quart of paint covers 6.5 square meters.
How much does it cost to paint all inside surfaces of the steel drum (side, top, and bottom)? (Assume that you only pay for the amount of paint actually used.)
A. $66.30 B. $67.40 C. $68.63 D. $69.70 E.
13. The points (x, -5) and (2, y) are on the line that contains points (-14, 7) and (10, 1).
What does the sum x + y equal?
$70.05
A. 32 B. 34 C. 35 D. 37 E. 38
14. A square with an area of 40 acres measures 1/4 mile on each side. A forest fire burns 48,000 acres.
How many square miles is that?
A. 75 B. 80 C. 150 D. 160 E. 300
15. The expression: (x y)
3 
(x
3  y ) is equivalent to
A. 3xy(x - y) B. 3xy(y - x) C. 3xy(x-y) - 2y 3 D. -2y 3 E. 0
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Ninth Grade Test - Excellence in Mathematics Contest - 2002
16. Let S equal the number of five-pointed stars on the front cover of this test. This number S is a factor of 2002

N , where N is a whole number. What is the smallest possible value of N?
A. 6 B. 8 C. 10 D. 12 E. 16
17. In a regular hexagon ABCDEF, the area of triangle ADF is what fraction of the area of the hexagon?
A. 1/6 B. 1/3 C. 1/4 D. 3/10 E. 2/5
18. Place the nine integers: -4, -3, -2, -1, 0, 1, 2, 3, 4 into these nine boxes (without repetition) so that the sum of the integers in any two consecutive boxes is a perfect square number.
What number is in the middle square?
A. -3 B. -2 C. 0 D. 1 E. 3
19. The area of a circle is
1

cm 2 . What is the circumference, in centimeters, of the circle?
A. 1 B. 2 C.

D. 2

E.
2

20. ABC is a right triangle. AD = AE and DE = EB.
The measure of angle CAB is 30 o .
What is the measure of angle CDB?
A. 45 o B. 52.5
o C. 54 o
D. 60 o E. 67.5
o
A
D
E
C
B
21. A person’s “monogram” is his or her three initials, in order: first initial, second initial, and third initial
(for example, RDA). Mr. and Mrs. Pythagoras wish to name their new baby so that her three-letter monogram is in alphabetical order with no letters repeated. For example, AMP or MOP. If the third initial is P for Pythagoras, how many different monograms are possible?
A. 105 B. 120 C. 144 D. 210 E. 225
22. Definition : The Nth Triangular Number, T
N
, equals the sum of the first N whole numbers.
Theorem: The number B is a Triangular Number if and only if 8B + 1 is a perfect square.
Which one of these five numbers is a Triangular Number?
A. 32,231 B. 103,840 C. 131,641 D. 173,466 E. 204,480
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Ninth Grade Test - Excellence in Mathematics Contest - 2002
23. On the coordinate plane, the vertices of a triangle are (3, 7), (3, 19), and (13, 1). In square units, what is the area of this triangle?
A. 60 B. 64 C. 65 D. 68 E. 72
24. x and k are real numbers. What is the sum of all solutions for x of the equation:
 2  k
2 
0 ?
A. -18 B. 18 C. 2k D. k - 9 E. 0
25. In quadrilateral ABCD, AC is perpendicular to BD. Therefore, ABCD must be a
A. Rectangle
E. None of these
B. Rhombus C. Parallelogram D. Square
26. Assume that the distinct lines x + Ay = P and x + By = Q are not parallel.
Express x in terms of A, B, P, and Q.
A.
BP

AQ
B.
P

Q
A

B
C. D.
Q

P
A

B
E. 
BP

AQ
27. During each hand of a card game, Ziggy has a 75% probability of winning 10 points and a 25% probability of losing 25 points. Starting at a score of 0, what is the probability that Ziggy will have a positive score after exactly four hands? Round to the nearest per cent.
A. 32% B. 42% C. 63%
29. The L-shaped region is composed of congruent squares.
D. 74% E. 75%
28. B = pq 2 r 4 , where p, q, and r are distinct prime numbers. The product AB is a perfect cube.
What is a possible value of A?
A. p 2 B. pqr C. p 3 q 3 r 3 D. p 2 qr 2 E. qr 5
P
The length of PQ is 65 cm. What is the area, in square centimeters, of the L-shaped region?
A. 56 B. 65 C. 70 Q
D. 182 E. 28 5 a
30. The repeating decimal: 0.243 = 0.2433333... can be represented as a fraction b
What does the sum a + b equal?
A. 46 B. 118 C. 228 D. 246 E.
in lowest terms.
373
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Ninth Grade Test - Excellence in Mathematics Contest - 2002
31. 1
3 
2
3 
3
3  
2000
3 
2001
3 
2002
3 
N
2 number, N 2 . What does N equal?
The sum of the first 2002 cubes is a square
A. 2,003,001
D. 4,008,004 E. 4,006,002
32. ABCD is a 2 cm by 2 cm square. Points
E, F, G, and H are the midpoints of the sides of the square. In square centimeters, what is the area of region AEPQ?
A.
D.
3/5
1/2
B.
E.
B. 2,005,003
2/5
7/12
C. 2/3
C. 2,006,004
A
H
D
E
Q
P
G
B
F
C
33. How many ordered pairs, (a, b), of whole numbers are solutions of: a
3  b
3 
2002
3
?
A. None B. One C. Two D. Four E. More than four
34. How many different 3-letter arrangement of letters (for example, SIS, PMI, IMP, or III) can be made from the letters in MISSISSIPPI ?
A. 24 B. 27 C. 35 D. 53
35. How many triangles (of any size) can be found in the diagram shown?
A. 9 B. 12 C. 18
E. 60
D. 24 E. 27
36. What is the value of this expression with 2001 terms? (Note that every third term is subtracted.)
1 + 2 - 3 + 4 + 5 - 6 + 7 + 8 - 9 + … + 1996 + 1997 - 1998 + 1999 + 2000 - 2001
A. 665,334 B. 666,333 C. 667,333 D. 667,334 E. 668,334
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Ninth Grade Test - Excellence in Mathematics Contest - 2002
37. The numbers 1 through 16 are entered into a square grid with four rows and four columns. The sum of the numbers in each of the columns is the same.
What is that sum?
A.
D.
30
34
B.
E.
31 C. 32
More than one sum is possible.
38. A fox is pursued by a hound, and the fox starts 63 of her own leaps ahead. The fox makes 4 leaps each time the hound makes 3 leaps. The hound in 5 leaps travels the same distance as the fox in 9 leaps. The hound does catch up to the fox. From the start until the fox catches the hound, what is the sum of the number of leaps that both animals take?
(Adapted from “Elements of Algebra for Secondary Schools”, Webster Wells, DC Heath, 1897.)
A. 250 B. 265 C. 280 D. 315 E. 360
39. How many triangles (of any size) can be found in the diagram shown?
A.
D.
125
256
B.
E.
216
288
C. 225
40. The new census taker has been told that Ms. Pimath always answers truthfully, but not always clearly.
With great fear, the census taker knocks on Ms. Pimath’s door. When she opens the door, he asks,
“How many children do you have?” She responds, “Three.” He continues, “What are their ages?”
Ms. Pimath answers, “The product of their ages is 90 and the sum of their ages is the address of my house.” The census taker looks at the house number, and complains, “That’s not enough information.
Do you have a one-year old child?” When Ms. Pimath responds truthfully, he says with relief, “Thank you, now I know their ages.”
What is Ms. Pimath’s house number? (All of the ages are whole numbers.)
A. 14 B. 16 C. 20 D. 22 E. 24
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