March 24, 2015
Answer questions 1-35 on your Scantron. Questions 1-30 will be scored for the Power
Bowl event. In the event of a tie, questions 31-35 will be used as the tiebreaker.
1.
If the width of a rectangle is doubled and the length is increased by 4, then the area is
tripled. What is the original length of the rectangle?
a. 4
2.
e. 16
b. 676,000
c. 82
d. 1,404,000
e. 468,000
b. 19y
c. 54y
d. 79y
e. 124y
Katie, Sunny, and 3 other boys make a team for a quiz show. In how many different ways can 5
people be seated in a row if Katie and Sunny sit next to each other?
a. 24
5.
d. 10
If y = 4x and z = 6y, then what does 12x + 4y + 12z equal?
a. 9y
4.
c. 8
If a computer login is assigned as follows: 3 letters followed by two one-digit numbers, how many
different logins can be made? Assume that letters and digits cannot be repeated.
a. 1,757,600
3.
b. 6
b. 30
c. 48
d. 52
e. 60
A certain jar contains 80 jelly beans: 26 white, 20 green, 15 yellow, 11 red, and 8 purple. If a jelly
bean is to be chosen at random, what is the probability that the jelly bean will be neither red nor
purple?
a. .325
b. .575
c. .023
d. .7625
e. .2375
8th Grade Power Bowl
Page 1
6.
A car got 26 miles per gallon using gasoline that cost $2.75 per gallon. Approximately what was
the cost, in dollars, of the gasoline used in driving the car 270 miles?
a. $10
7.
d. $40
e. $50
!
b. -3
c. 0
d. 3
!
! (!!!)
?
e. 9
Suppose that x and y are positive integers and y2 – x2 = 143. Find one possible value of x + y.
a. 11
9.
c. $30
What is the product of all valid solutions of the fractional equation !" !!! =
a. -9
8.
b. $20
b. 13
c. 15
d. 17
e. 19
Lines j and k are parallel below. Find the measure of angle ACB given that the measure of
angle ABC is 41° and the measure of angle DCA is 56°.
a. 41°
b. 97°
c. 83°
d. 79°
e. There is not enough information to tell.
!
10. When ! is written in decimal form, the decimal
a.
b.
c.
d.
e.
Terminates after 10 decimal places
Terminates after 17 decimals places
Is infinite, but repeats a sequence of digits
Is infinite, and does not repeat a sequence of digits
Terminates after 18 decimal places
8th Grade Power Bowl
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11. If 30 students in one class had an average of 97% and 22 students from another class
had an average of 85%, what is the average in percent of all 52 students. Round your answer to
the nearest whole percent.
a. 92%
b. 91%
c. 90%
d. 93%
e. 59%
12. The volume of a certain cone is 524 dm3. What is the volume of a cylinder that has a congruent
base and height to the cone?
a. 1572 dm3
13.
b. 1048 dm3
c. 524 dm3
d. 175 dm3
e. 699 dm3
The average of 18 consecutive odd numbers is 50. What is the largest of these 18 numbers?
a. 59
b. 67
c. 69
d. 79
e. 85
14. There are two pints in a quart and four quarts in a gallon. During one lunch period a cafeteria
serves 700 half-pints of milk. How many gallons of milk are served in one lunch period?
a. 43.3 gallons
b. 43.75 gallons
c. 44 gallons
d. 87.25 gallons
e. 87.5 gallons
15. On a 20 km run-and-walk, Sean averages 12 km/hr running and 7 km/hr walking. If he spends
twice the amount of time running as he does walking, how long did it take Sean to complete the 20
km race? Round to the nearest minute.
a. 77 minutes
16.
b. 104 minutes
c. 116 minutes
d. 129 minutes
e. 155 minutes
A 200 ml mixture is 80% water and 20% bleach. How much water must be added to dilute the
mixture to 5% bleach?
a. 160 ml
b. 300 ml
c. 320 ml
d. 600 ml
e. 640 ml
8th Grade Power Bowl
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17. Which transformation could have produced A’B’C’ below?
a. A reflection over the x-axis
b. A 90° clockwise rotation about point D
c. A 90° clockwise rotation about point E
d. A 90° clockwise rotation about point F
e. A reflection over x-axis and then a reflection over the line x=5
8th Grade Power Bowl
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18. Below are 3 pictures in a sequence of pictures. Picture 1 uses 11 toothpicks. Tom wishes to
continue to build the pictures in the sequence using toothpicks. What is the first picture that
will use at least 1000 toothpicks?
a. Picture 197
b. Picture 198
c. Picture 199
d. Picture 200
e. Picture 200
19. Along the Mississippi River, the distance from Hannibal, Missouri, to the Gulf of Mexico is
about 1500 miles. To estimate the speed of his raft, Tom Sawyer measures that it drifts 65 feet in
20 seconds. If this rate stays constant and Tom drifts 12 hours each day, which is the best
estimate of the number of days it would take Tom to drift from Hannibal to the Gulf of Mexico?
(1 mile = 5280 feet)
a. 28 days
b. 56 days
c. 96 days
d. 112 days
e. 192 days
20. In the figure below, 𝐴𝐷 and 𝐵𝐶 are perpendicular to 𝐴𝐵. Find the perimeter of the figure.
The drawing is not to scale.
a. 30.5 m
b. 31 m
c. 31.5 m
d. 32 m
e. 32.5 m
8th Grade Power Bowl
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21. Shaun starts to list the powers of 3: 3; 9; 27; …. He stops once all ten digits { 0, 1, 2, 3, 4, 5, 6,
7, 8, 9 } have appeared somewhere in his list. Of those ten digits, which is the last to appear in
his list?
a. 0
b. 1
c. 4
d. 5
e. 6
22. In square ABCD, P is the midpoint of 𝐴𝐵 and Q is the midpoint of 𝐵𝐶. If the length of 𝑃𝑄 is 8
cm, what is the area of ABCD? a. 64 cm2
b. 128 cm2
c. 256 cm2
d. 64 2 cm2
e. 128 2 cm2
23. Of these five numbers: -8; -4; 9; 11; 15; how many make the following compound inequality
true?
−𝟕 < 𝟏𝟓 − 𝟐𝒙 ≤ 𝟐𝟑
a. 0
b. 1
c. 2
d. 3
e. 4
d. 64
e. 12
24. If x + y = 20 and x – y = −6, what does x2 – y2 equal?
a. -120
b. -36
c. 36
!
25. Erin wants to budget her spending and decides she can spend ! of her paycheck in the first week.
!
If she instead spends ! of paycheck during the first week, by what percent of her total paycheck
did she exceed her budget amount for the first week?
a. 5%
26.
b. -5%
c. 12%
d. 20%
e. 25%
In the following expression, the variables a, b, c, and d are replaced by the numbers 1, 2, 3, and
4, but not necessarily in that order. Each letter is for a different number. What is the minimum
possible value of: a * bc – d?
a. -2
b. -1
c. 0
d. 1
e. 2
8th Grade Power Bowl
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27. What is the length of the diagonal of a rectangle with a width of 8 cm and a perimeter of 46 cm?
a. 17 cm
b. 23 cm
d. 145 cm
c. 120 cm
e. 8 2 cm
28. If N + 4 is an odd number, then how many of these four numbers must be odd?
3N;
a. 0
b. 1
4N+1;
N 2;
c. 2
𝐍!𝟏
𝟐
d. 3
e. 4
29. If the perimeter of rectangle ABCD is 160 inches and CD = 48 inches, what is the area of
triangle AED?
a. 640 in2
30.
b. 704 in2
c. 768 in2
d. 840 in2
e. 767 in2
Use this box-and-whisker graph to answer the following questions.
What is the Interquartile Range of the data set?
a. 9
b. 16
c. 19
d. 46
e. 75
8th Grade Power Bowl
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31. Find the value of
𝟏
𝟏
a. − 𝟐
𝟒
b. 𝟏𝟎
𝟖
c. 𝟑
𝟓
d. 𝟓
e. 𝟐
32. Point C is the center of this regular decagon, What is the measure of angle CAB?
a. 36°
b. 45°
c. 54°
d. 72°
e. 90°
33. In what quadrant do the lines y = -2x – 3 and -2x + 4y = 12 intersect?
a. I
b. II
c. III
d. IV
e. They do not intersect
34. Triangle PQR is an equilateral triangle inscribed in right triangle ABC. If the measure of angle
PAQ is 20° , what is the measure of angle BQR?
a. 60°
b. 70°
c. 75°
d. 80°
e. 90°
35. In November 2013, Rick’s daughter Jan will be one billion seconds old. In what year was she
born?
a. 1976
b. 1979
c. 1982
d. 1985
e. 1987
8th Grade Power Bowl
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