Ninth Grade Test - Excellence in Mathematics Contest - 2005
Ninth Grade Test - Excellence in Mathematics Contest - 2005
1.A hundredth of a billion plus a thousand thousands equal how many millions?
A. 1B. 1.1C. 2D. 10.1E. 11
2.2005 is the Nth number in this arithmetic sequence: 80, 87, 94, 101, …
What is N?
A. 275 B. 276 C. 286 D. 287 E. 2005 is not in this sequence
3.According to the novel, “The Da Vinci Code”, the number of members of the Priory of Scion is one more than the sum of the first six positive powers of three. If true, how many members does the Priory of Scion have?
A. 64B. 364 C. 442D. 1093E. 3280
4.The human genome consists of approximately 6 billion base pairs and if stretched out would be 6 feet long. Approximately how many genome base pairs would be in a piece that is inch long?
A. 1.3 million B. 1.3 billion C. 130,000 D. 5.2 millionE. 62.5 million
5.Between the year 2000 and 2005, US Postal rates for first-class letters have increased
from: “34 cents for the first ounce and 21 cents for each additional ounce (or part of an ounce)”
to: “37 cents for the first ounce and 23 cents for each additional ounce (or part of an ounce)”.
What is the increase in postage for mailing a first-class letter that weighs 5.2 ounces?
A. 10 centsB. 11 centsC. 12 centsD. 13 centsE. 15 cents
6.Tatiana’s piggy bank is filled with pennies, nickels, dimes, and quarters. If she has at least five of each coin and has a total of $5.03, what is the least total number of coins that she could have in her piggy bank?
A. 23B. 34C. 36D. 38E. 39
7.APD is a line, and
What is the measure of
A. 14oB. 90oC. 104o
D. 118oE. Cannot be determined
8.Jenn’s 16-ounce soda is 60% Mr. Pibb and 40% Sprite. Gregg’s 24-ounce soda is 25% Barq’s and 75% Sprite. They combine their two sodas, mix, and then pour four 10-ounce glasses. What percent Sprite is in each 10-ounce glass?
A. 50%B. 57.5%C. 60%D. 61%E. 62.5%
9.The point (7, 5) is reflected about the y = x line to point P. Then point P is reflected about the x-axis to point Q. What is the sum of the coordinates of point Q?
A. –2B. 2C. –12D. 12E. None of these
10.The lines represented by the equations bx – 6y = c and 12x + dy = -70 are parallel. What does the product bd equal?
A. –72B. –2C. 2D. 72E. 1/2
11.The Mount St. Helens volcano in Oregon which erupted in 1980 is showing activity again in 2005. Currently 117 cubic feet per second of lava is oozing out. If all the lava released in one week were evenly spread over one square mile, approximately how deep would it be? (1 mile = 5280 feet)
A. 0.04 feetB. 2.5 feetC. 34 feetD. 223 feetE. 13,402 feet
12.On a clock, at 10:20 what is the measure of the smaller angle between the minute hand and the hour hand?
A. 168oB. 170oC. 174oD. 175oE. 180o
13.A treadmill records the following speeds for a 40-minute workout. According to the record on the treadmill, what distance in miles was covered? Assume that each speed was a whole number.
A. 3B. 3.5C. 4D. 4.5E. 5
14.For how many ordered pairs (x, y) of positive integers x and y does ?
A. 0B. 1C. 2D. An infinite number
E. A finite number, but greater than 2
15.Four tangent congruent circles of radius 6 cm are inscribed
in a rectangle. If P is a vertex and Q and R are points
of tangency, what is the area of triangle PQR?
A. 27 cm2B. 45 cm2 C. 54 cm2D. 108 cm2E. 180 cm2
16.If and , what is the value of k?
A. 2B. 13C. 3D. E.
17.If a, b, c, and d are distinct numbers and ax + b = cx + d, what does x equal?
A. B. C. D. E.
18.A square and a rectangle have equal areas. The length of the rectangle is 4 times its width. What is the ratio of the perimeter of the rectangle to the perimeter of the square?
A. 1B. C. D. E. 2
19.If , what does the sum equal?
A. 7B. 12C. 18D. 21E. 24
20.Janu wishes to share five identical strands of licorice equally among eight people. What is the minimum number of cuts that must be made? Assume that each cut cuts only one piece of licorice and that she may use a ruler.
A. 5B. 6C. 7D. 8E. 11
21.A random number between 0 and 1 is selected. What is the probability that the number is closer to 0 than to 0.7?
A. 30%B. 35% C. 40%D. 50%E. 60%
22.For any natural numbers m and n with m>n, the three numbers: 2mn, m2 - n2 , and m2 + n2 form a “Pythagorean Triplet”. That is, these natural numbers could be the lengths of the three sides of a right triangle. If m=17 and n=11, what is the number of square units in the area of the right triangle formed using the above formulas?
A. 93.5B. 31,416C. 34,440D. 65,680E. 76,670
23.Charlene’s birthday, March 19, is one week before her dad’s birthday and one month before her mom’s birthday. On her dad’s birthday in 2005, Charlene noticed that her age (in years) was exactly 1/3 of her dad’s age (in years). On her mom’s birthday in 2006, Charlene’s age (in years) will be exactly 1/3 of her mom’s age (in years).
Charlene’s mom was born in 1955. In what year was Charlene’s dad born?
A. 1953B. 1954C. 1956D. 1957E. 1958
24.The labels of two fair 6-sided dice are shown on their networks, below.
When these two dice are rolled, what is the probability that the number rolled on die A will be greater than the number rolled on die B?
A. 1/2B. 1/3C. 1/4D. 5/12E. 7/18
25.At high tide, a ship drops its anchor straight down using L feet of chain. When the tide drops 10 feet, the ship drifts sideways 100 feet until the chain is again straight. In feet, what is the length L of the chain?
A. 101 B. 160C. 340D. 445E. 505
26.In a group of 12 students, the heights of the seven boys are: 160 cm, 172 cm, 158 cm, 172 cm, 180 cm, 152 cm, and 161 cm. The heights of the five girls are: 158 cm, 170 cm, 150 cm, 165 cm, and 142 cm. When a sixth girl joins the group, the median heights of the boys and the girls are equal. What is the height of the new girl?
A. 160 cmB. 161 cmC. 162 cmD. 163 cmE. 164 cm
27.The tickets for a play cost $12 and $18. When all of the seats are sold, $3228 is collected. If exactly one-half of the $12 tickets were converted to $18 tickets, they would have collected $3666. What is the total number of seats in this theater?
A. 222B. 224C. 226D. 228E. 230
28. In preparation for the 2005 National Scrabble Tournament in Reno, Chuck asks, “During a game, there are 93 letter tiles that I have not yet seen and my opponent randomly selects seven of them for his rack of tiles. Among the 93 tiles, I know that there are four tiles with ‘S’ and two ‘blank’ tiles. To the nearest percent, what is the probability that my opponent picks at least one ‘S’ or ‘blank’ tile?”
A. 22%B. 25%C. 32%D. 38%E. 46%
29.On this Magic Star, the sum of any four numbers in a row equals the same number. What is the value of the sum A+B?
A. 13B. 15C. 16D. 20E. 23
30.You are given three right isosceles triangles, one square,
and one parallelogram with the measurements shown.
What is the perimeter of the square you can construct
using all five of these shapes?
A. 4B. 8C.
D. E.
31.From the 4th term on, the terms of this sequence are generated by the rule:
“Each term is the sum of the previous three terms.”
What is the value of the term immediately following 179?
5, 9, _____, _____, _____, _____, 179, _____
A. 208B. 244C. 276D. 306E. 329
32.Determine the largest 5-digit integer such that the product of its five digits is 7!.
What is the sum of those five digits?
A. 28B. 29C. 30D. 31E. 32
33.From a collection of four right-handed work gloves and five left-handed work gloves, you randomly select three gloves without replacement. What is the probability that you will select at least one right-handed glove and at least one left-handed glove?
A. B. C. D. E.
34.How many zeroes are at the end of the product:
A. 216B. 36C. 40D. 48E. 60
35. In , cm, cm, and the measure of angle B is less than 90o. If the length of side is a whole number of centimeters, what is the positive difference between the shortest and longest possible lengths of side?
A. 27cmB. 28 cmC. 29cmD. 42 cmE. 43 cm
36.Each vertex of these six triangles is at a lattice point of this square
grid. What is the sum of the numeric labels of all the right triangles?
A. 27B. 31C. 43
D. 47E. 59
37.In a small 7-seat school bus, students P, Q, and R sit on the left side behind the driver, D. Students S, T, U, and V sit on the right side. The long bus ride starts at 9:00 am. Every 10 minutes, all the students move forward one seat, except the student in seat 1 moves to seat 7 and the student in seat 4 moves to seat 3. The first such move occurs at 9:10 am.
At 12:05 pm, which two students are in seats 1 and 4?
A. P and TB. S and VC. R and U
D. R and VE. Q and U
38.How many different right triangles with integral side lengths have one side of length 40?
A. Fewer than 6B. 6C. 7D. 8E. More than 8
39.Among the final eight teams in the collegiate basketball tournament, Harry hopes that IL will be champion. In the quarterfinals, those eight teams are paired into four games. The local newspapers pick these four teams to win those games.
- The Post Dispatch predicts that MU, UW, FL, and UCONN will win;
- The Tribune predicts that FL, UCONN, TN, and CIN will win;
- The Daily Planet predicts that AZ, TN, FL, and CIN will win.
Who does IL play in their quarterfinal game?
A. FLB. AZC. UCONND. UWE. TN
40.From the center of a 15 by 15 array of 1 by 1 squares, a 3 by 3 array of 1 by 1 squares is removed. From the remaining squares, how many 2 by 2 squares are there that are unions of four 1 by 1 squares?
A. 171B. 180C. 187D. 200E. 209