5.
6.
1.
2.
3.
4.
8.
7.
9.
Eighth Grade Test - Excellence in Mathematics Contest - 2009
A family buys a half-dozen eggs per week for three weeks. For the next two weeks, they buy one dozen eggs per week. Then they buy 2 dozen eggs in one week.
On the average, how many eggs per week did they purchase?
A. 9 B. 10
1
3
C. 10.5 D. 11 E. 22
By exchanging the positions of two digits in the number 965,142 , the new number is 19,980 smaller than the original number. What is the sum of the two digits exchanged?
A. 7 B. 8 C. 9 D. 10
How many of the following five numbers are between
1
2
and
𝟓
𝟖
? 𝝅
𝟓
𝟐𝟎𝟎𝟗
𝟒𝟎𝟏𝟕
𝟐 𝝅
√𝟎. 𝟑 (𝟎. 𝟕) 𝟐
A. 1 B. 2 C. 3 D. 4
E. 13
E. 5
At the Local Harvest restaurant, Rick bought a bowl of vegan chili for $6.25 and a cup of coffee for
$1.35 . Basing each percent on the total cost of the chili and coffee, Rick left a 12% tip and paid 8% sales tax. From a $10 bill, what is the least number of coins (using only pennies, nickels, dimes, and quarters) Rick could have received in change?
A. 7 B. 8 C. 9 D. 11 E. 12
If
𝑁 is a simplified fraction (that is, reduced to lowest terms) and is between 0 and 2, how many
30 values are possible for N?
A. 16 B. 18 C. 20 D. 22 E. 24
With any combination of nickels, dimes, and quarters, how many ways can you make change for 55 cents?
A. 8 B. 10 C. 11 D. 18 E. 20
In the diagram, the area of the circle equals the area of the rectangle.
What is the ratio of the width w of the rectangle to the radius of the circle?
A. 𝜋
B.
2
2 𝜋
C. 1 D.
π
3
E.
π
3
The sum of the reciprocals of 0.4 and 3 is between: w
A. 0 and 1 B. 1 and 1.5 C. 1.5 and 2 D. 2 and 2.5 E. 2.5 and 3
In 1970, Missouri’s 4.7 million population represented 2.30% of the total US population.
In 2000, Missouri’s 5.6 million population represented 1.99% of the total US population.
What was the approximate growth of the US population from 1970 to 2000?
A. 8 million B. 48 million C. 65 million D. 77 million E. 771 million

Eighth Grade Test - Excellence in Mathematics Contest - 2009
10. A solid wood cube, 1 foot on each side, is cut into small cubes, each 2 inches on a side. All of the small cubes are placed one on top of the other. What is the height of this stack?
B. 3 feet C. 6 feet D. 12 feet E. 36 feet A. 1 foot
11. When working on her bicycle, Alicia tried the 7/8 inch wrench which was too large but the 3/4 inch wrench was too small for the bolt.
Which is the only wrench of these five sizes (in inches) which might work for Alicia?
A. 11/16 B. 15/16 C. 6/8 D. 21/32 E. 25/32
12. Rick uses this weighted average formula to grade his Calculus class.
“25% of HW average plus 75% of Test average”
What is Zan’s current grade if her HW average is 72% and her test average is 97%?
A. 84.5% B. 88% C. 88.5% D. 90%
13. How many numbers belong to both of these arithmetic sequences?
𝟐, 𝟕, 𝟏𝟐, 𝟏𝟕, … 𝟏𝟎𝟐 𝑎𝑛𝑑 𝟏𝟏, 𝟏𝟒, 𝟏𝟕, 𝟐𝟎, … 𝟏𝟎𝟏
B. 4 C. 5 D. 6 A. 3
E. 90.75%
E. 7
14. For their stall at Soulard Market, the Schaum’s buy 300 pounds of Jonathan apples at $0.70 per pound and 200 pounds of Fuji apples at $0.75 per pound. They sell these apples at $0.90 per pound. If
“percent profit” equals
𝑷𝒓𝒐𝒇𝒊𝒕
𝑻𝒐𝒕𝒂𝒍 𝑪𝒐𝒔𝒕
*100 , what percent profit did the Schaum’s make if they sold all 500 pounds of apples? Round to the nearest percent.
A. 15% B. 20% C. 25%
15. Point A is the vertex of a square, 4 cm on each side.
What is the length in centimeters of segment AB?
D. 30%
10 cm
E. 40%
A
A. 10 B. 14 C. 6√2
B
12 cm
D. 8√2 E. 2√61 − 4√2
16. The Fibonacci Series starts:
1, 1, 2, 3, 5, 8, …
In the tens’ places of the numbers in this series, which is the last of the ten digits 0 through 9 to make its initial appearance?
A. 0 B. 4 C. 6 D. 7 E. 9
17. How many 7-digit natural numbers are square numbers?
A. 2160 B. 2161 C. 2162 D. 2163 E. 2164

Eighth Grade Test - Excellence in Mathematics Contest - 2009
18. To make these equations true, what is the sum of the numbers in the two boxes?
Round your answer to the nearest whole number.
0.36
=
𝟓𝟒
=
𝟓𝟎
A. 18 B. 37 C. 144 D. 168 E. 289
19. A cylinder is a snug fit for four spheres (you might call them tennis balls  ), each of radius r.
What is the ratio of the height of the cylinder to the circumference of one of the spheres?
A.
2 𝜋𝑟
B.
4 𝜋
C.
4 𝜋𝑟
D.
8 𝜋
E.
8 𝜋𝑟
20. By replacing the four variables a, b, c, and d in the expression below with the four numbers
𝟏
𝟑
,
𝟏
𝟐
, 2 , and 3 , what is the greatest possible value of the expression? 𝒂 𝒄
+ 𝒅 𝒃
A. 2 B. 3 C. 12 D. 13 E.
13
16
21. In his comeback in the 2009 Tour of California, Lance Armstrong took 14 th place in the 15-mile time trial by completing it in 31 minutes, 56 seconds. Rounded to the nearest tenth, what was his average speed in miles per hour?
A. 28.1 mph B. 28.2 mph C. 28.5 mph D. 28.6 mph E. 28.9 mph
22. As shown, the centers of 3 small congruent, tangent, circles lie along the diameter of the large circle. What is the ratio of the circumference of the large circle to the sum of the circumferences of the three small circles?
A. 3/2 B. 2/3 C. π/3 D. 3/π E. 1
23. As shown, the centers of 3 small congruent, tangent, circles lie along the diameter of the large circle. What is the ratio of the area of the large circle to the sum of the areas of the three small circles?
A. 1 B. 3 C. π D. π 2 /3 E. 9
24. What is sum of the two distinct prime factors of 2009?
A. 48 B. 90 C. 98 D. 294 E. 2009
25. Determine the sum, S, of the first 15 terms of the geometric series: 1, 2, 4, 8, 16, 32, ….
.
What is the sum of the digits of S?
A. 22 B. 25 C. 26 D. 28 E. 30

Eighth Grade Test - Excellence in Mathematics Contest - 2009
26. Of 100 students, 84 are taking Algebra, 30 are taking Chinese, while 24 are taking both Algebra and
Chinese. How many of the 100 students are taking neither Algebra nor Chinese?
B. 10 C. 12 D. 20 E. 34 A. 6
27. Two fair standard 6-sided dice are rolled. What is the probability that the sum of the two numbers rolled is 9 or larger?
A. 1/6 B. 4/11 C. 1/3 D. 5/18 E. 11/36
28. 20 fence posts are used to build a fence around a square plot. With one pole at each corner, the distance between adjacent poles on the fence is 6 m. What is the area, in square meters, of the square?
A. 150 B. 576 C. 625 D. 900 E. 961
29.
Lyle’s sock drawer has 8 black, 6 blue, and 4 brown socks. Getting up before dawn, without looking,
Lyle reaches in and selects N socks. What is the least value of N to guarantee that, in terms of color, he selects at least two pairs of socks? (The first pair may be, but need not be, the same color as the second pair.)
A. 5 B. 6 C. 7 D. 8 E. More than 8
30. Among 20 items, the N th item is worth $N. For example, the 3 rd item is worth $3 and the 12 th item is worth $12. These 20 items are shared among 3 friends so that the value of the items that each friend receives is equal.
What is the maximum number of items that one person could receive?
A. 8 B. 9 C. 10 D. 11
31. For how many 7-digit numbers does the 4-digit sequence “ 2009 ” appear?
E. 12
A. 1,000 B. 1900 C. 3600 D. 3,700 E. 4,000
32. When the date March 6, 2009 is written: 03/06/09 , the month, day, and year form an increasing arithmetic sequence. Including March 6, 2009, how many dates in 2009, when written in this format, form an increasing arithmetic sequence?
A. 2 B. 3 C. 4 D. 5 E. More than 5
33. The first names of the 14 members of the Math Department are:
John, John, Rick, Rick, Chris, Chris, Anne, Anne, Sharon, Daba, Rita, Brian, Teresa, and Pat
If two members of the department are randomly chosen for a task, what is the probability that they have the same name?
A. 1/7 B. 3/7 C. 2/49 D. 1/91 E. 4/91

Eighth Grade Test - Excellence in Mathematics Contest - 2009
34. Complete this Magic Square with the numbers 1, 2, 3, 4, 5 , and 6 so that the sums of the three numbers in each of the two rows and in each of the two columns are the same. Which number is in the square marked A?
A. 2
D. 5
B. 3
E. 6
C. 4
3
3
35. With 36 passengers registered for the Missouri ARML bus trip to Iowa, Mr. Potter charged each passenger the total cost of the bus divided by the number of passengers. At the last minute, 9 more passengers registered. After a recalculation of the cost per passenger, Mr. Potter gave $17 back to each of the original 36 students.
What is the sum of the digits of the total cost in dollars of using the bus?
A. 7 B. 9 C. 14 D. 15 E. 17
36. The product of the ages of the three children of the Coburn family is 3240. The children’s ages in years are equally spaced. Which of these is the age of one of these three children?
A. 9 B. 10 C. 16 D. 18 E. 20
37. 49 distinct 2-digit whole numbers are chosen. Which one of these statements must be true?
A. Their product is even B. Their product is odd
D. Their sum is odd
C. Their sum is even
E. Their product is divisible by 3
38. On a 2-day camping trip, Elaine, George, and Jerry take along a bag of N almonds for snacks. After all fall asleep, George wakes and decides to eat his share, 1/3, of the almonds. Later, Elaine awakes and eats K almonds (K is a whole number). Later Jerry awakes and eats 1/3 of the remaining almonds.
Of course, Jerry did not get his ‘full share’ of the N almonds – in fact, he ate exactly 1/2 of his fair share. How many almonds did Jerry eat?
A. K B. K/2 C. 2K/3 D. 2K
39. On this 2 by 3 grid, how many distinct paths of length 3 start at vertex A?
On any one path, you may never retrace any part of your route.
D. 10 E. 11 A. 6 B. 8 C. 9
E. K/3
A
40. Martha, her brother, her son, and her daughter are the four pitchers on a softball team. Of these four, the worst pitcher’s twin, who is also one of these four, and the best pitcher are of opposite gender.
The worst pitcher and the best pitcher are the same age.
Who is the best pitcher?
A. Martha
C. Martha’s son
B. Martha’s brother
D. Martha’s daughter
E. The best pitcher cannot be determined from given information
A