2010 Grade 7 Tennessee Middle/Junior High School Mathematics Competition
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1. Which of the following fractions has a terminating decimal equivalent?
A.
B.
C.
D.
E.
Any fraction in simplest terms whose denominator is 1225
Any fraction in simplest terms whose denominator is 1680
Any fraction in simplest terms whose denominator is 320
Any fraction in simplest terms whose denominator is 650
Any fraction in simplest terms whose denominator is 350
2. Consider the following three statements.
Statement 1: When two fractions whose decimal equivalents are terminating are added, the
sum will have a terminating decimal equivalent.
Statement 2: When two fractions whose decimal equivalents are non-terminating are added,
the sum will also have a non-terminating decimal equivalent.
Statement 3: When a fraction whose decimal equivalent is terminating is added to a fraction
whose decimal equivalent is non-terminating, the sum will have a non-terminating decimal
equivalent.
Which of these statements are ALWAYS true?
A.
B.
C.
D.
E.
Only Statement 1 is always true.
Only Statement 2 is always true.
Only Statement 3 is always true.
Only Statements 1 and 3 are always true.
Statement 1 and Statement 2 and Statement 3 are always true.
3. The ratio of red jelly beans to yellow jelly beans in a candy jar is 2:3. The ratio of yellow
jelly beans to green jelly beans in the candy jar is 3:4 and the ratio of green jelly beans to
orange jelly beans is 3:5. What is the ratio of red to orange jelly beans?
A.
B.
C.
D.
E.
The ratio of red to orange jelly beans cannot be determined with the given information.
The ratio of red to orange jelly beans is 2:5.
The ratio of red to orange jelly beans is 4:7.
The ratio of red to orange jelly beans 3:10.
The ratio of red to orange jelly beans is 1:4.
4. The base of a prism is a hexagon. The area of the hexagon is 10.4 square centimeters. The
height of the prism is 1 decimeter. What is the volume of the prism?
A.
B.
C.
D.
E.
10.4 cubic centimeters
104 cubic centimeters
104 cubic decimeters
108.16 cubic decimeters
1081.6 cubic centimeters
2010 Grade 7 Tennessee Middle/Junior High School Mathematics Competition
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5. The graph below shows the total distance traveled by a family over time.
What is the family’s average speed for the first three hours of the trip?
A.
B.
C.
D.
E.
60 miles per hour
120 miles per hour
40 miles per hour
30 miles per hour
75 miles per hour
6. Jason, Mike, and Frank took turns driving from Houston, TX to Miami, FL. First, Jason
3
drove
of the total distance. Next, Mike drive 25% of the total distance. Finally, Frank
11
drove the remaining 567 miles. What is the total driving distance between Houston, TX and
Miami, FL?
€ A.
B.
C.
D.
E.
1,188 miles
1,205 miles
1,104 miles
1,473 miles
1,456 miles
7. Which of the following is not a rational number?
€
€
A. 1. 34
1
B.
3
C. 73%
D. -2.3255
4
E.
625
2010 Grade 7 Tennessee Middle/Junior High School Mathematics Competition
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8. $1000 is invested in an account earning 2.4% annual interest compounded monthly. After 8
months what is the value of the account? Round to the nearest penny.
A.
B.
C.
D.
E.
$1016.00
$1016.11
$1020.18
$1024.00
$1024.32
9. Which of the following numbers could the point labeled A represent on the number line
shown?
A. 11
B. 2.8
67
C.
29
90
D.
28
E. 3
€
€
€
€
10. The product, p, of two prime numbers is between 6 and 55. The first prime is greater than 2
and less than 6. The second prime is greater than 13 and less than 25. What is p?
A.
B.
C.
D.
E.
26
31
33
41
51
11. Let f (x) be the cost of gasoline ($2.69 per gallon) as a function of the number of miles
driven in a car that gets 28 miles per gallon. The equation of this function is f (x) = 2.69 ⋅
What is f (300) and what does it mean?
€
€
€
€
€
€
€
A.
B.
C.
D.
E.
f (300) ≈ 28.82 . It means that $28.82 is the cost for gasoline to€drive 300 miles.
f (300) ≈ 10.71. It means that $10.71 is the cost for gasoline to drive 300 miles.
f (300) ≈ 28.82 . It means that $300 is the cost for gasoline to drive 28.82 miles.
f (300) means that the number of miles should be multiplied by 300.
f (300) ≈ 111.52 . It means that $111.52 is the cost for gasoline to drive 300 miles.
x
.
28
2010 Grade 7 Tennessee Middle/Junior High School Mathematics Competition
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12. The top three scorers in a contest share a prize. First place gets 50%, second place 30% and
third place 20%. If first place received $12,000 more than third place, how much did second
place get?
A.
B.
C.
D.
E.
$6,000
$9,000
$12,000
$15,000
$24,000
13. Degrees Kelvin is a scale used by physicists. Zero degrees Kelvin is -461 degrees
Fahrenheit. Zero degrees Fahrenheit is 255 degrees Kelvin. A change of one degree Kelvin
is a change of how many degrees Fahrenheit?
A.
B.
C.
D.
E.
1 degree Kelvin = 1 degree Fahrenheit
1 degree Kelvin ≈ 1.81 degrees Fahrenheit
1 degree Kelvin ≈ 0.55 degree Fahrenheit
1 degree Kelvin = 1.4 degrees Fahrenheit
1 degree Kelvin ≈ 0.55 degrees Fahrenheit
€
€×10−300 and b = 4.5 ×10 500 . Which of the following choices has the greatest
14. Let a = 2.3
value?
€
A. a + b
€ B. a ⋅ b
€
C. a ÷ b
D. b ÷ a
€
E. a 2 + b 2
€
€ 15. George gave John and Sally the same three digit number. John multiplied it by four. Sally
€
multiplied it by five. Then they added their results together. Which of the following could
€
be the sum?
A.
B.
C.
D.
E.
1107
2107
3107
4107
107
16. The game warden wants to know about how many fish are in a lake. One hundred eighty fish
are caught, tagged, and released into the lake. Several days later 300 fish are caught and
examined for tags. Of the 300 caught, 53 had tags. Approximately how many fish are in the
lake?
A.
B.
C.
D.
E.
318
883
906
1019
1960
2010 Grade 7 Tennessee Middle/Junior High School Mathematics Competition
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1
. A fair coin is tossed four times
2
and lands heads up every time. What is the probability that the coin will land heads up on the
next toss?
17. The probability that a tossed coin will land heads up is
€
1
A. The probability that the coin will land heads up on the fifth toss is .
2
 1 5
B. The probability that the coin will land heads up on the fifth toss is   .
2
 4 2
€
C. The probability that the coin will land heads up on the fifth toss is   .
5
€ toss is  1  ⋅ 5 .
D. The probability that the coin will land heads up on the fifth
2
5
€ toss is  1  .
E. The probability that the coin will land heads up on the fifth
 
5
€
18. The heights (in centimeters) of the players on the middle school basketball team are given in
€
the stem and leaf plot below.
18 00
17 22358
16 1114789
15 056888
What is the mean height of the all the players on the team?
A.
B.
C.
D.
E.
169 cm
165.8 cm
161 cm
164 cm
162.5 cm
19. Consider these three statements.
Statement 1: $0.25 = 0.25 cents
Statement 2: $0.25 = 25¢
Statement 3: 0.25¢ is less than a penny
A.
B.
C.
D.
E.
Statement 1 and Statement 2 are true. Statement 3 is false.
Statement 2 and Statement 3 are true. Statement 1 is false.
All three statements are true
Statement 1 and Statement 3 are true. Statement 2 is false.
Only statement 2 is true.
2010 Grade 7 Tennessee Middle/Junior High School Mathematics Competition
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20. A basketball player makes 68% of her free throws on average. What is the probability that
she will make exactly one point on the next one-and-one foul opportunity? (On a one-andone opportunity, the player gets to try a second free throw IF she makes the first one. If she
misses the first shot, she does not get to try the second time.) Round to the nearest percent.
A. 68%
B. 46%
C. 22%
D. 10%
E. 32%
21. The inverse of a function “undoes” the function. For example, if f (x) = x − 6 , then the
INVERSE of f (x) would be g(x) = x + 6 . [Note that f (10) = 4 and g(4) = 10 . In every
case, if f (a) = b , then g(b) = a .] Which of the following functions would be the inverse of
5x − 4
€
f (x) =
?
3
€
€
€
€
€
€3
A. g(x) =
5x − 4
€
€
€
€
B. g(x) =
3
5x + 4
C. g(x) =
3x − 4
5
D. g(x) =
4 − 3x
5
E. g(x) =
3x + 4
5
€
22. A circular region with a diameter of 5 inches is cut from a sheet of paper. Then a sector is
cut out of the circle. The central angle of the sector is 75˚. What is the area covered by the
€
sector that was cut out? (Round to the nearest square inch.)
A. The area of the sector is 4 square inches.
B. The area of the sector is 16 square inches.
C. The area of the sector is 5887 square inches.
D. The area of the sector is 1472 square inches.
E. The area of the sector is 3 square inches.
2010 Grade 7 Tennessee Middle/Junior High School Mathematics Competition
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23. A tetrahedron is a three-dimensional figure whose four faces are all triangles. What would
be the surface area of a tetrahedron composed of four congruent equilateral triangles that are
10 centimeters on each side? (Round to the nearest square centimeter.)
A.
B.
C.
D.
E.
The surface area of the tetrahedron is 346 square centimeters.
The surface area of the tetrahedron is 200 square centimeters.
The surface area of the tetrahedron is 400 square centimeters.
The surface area of the tetrahedron is 150 square centimeters.
The surface area of the tetrahedron is 173 square centimeters.
24. Which statement must be TRUE about an isosceles trapezoid?
A.
B.
C.
D.
E.
The diagonals of the trapezoid bisect each other.
Every pair of adjacent angles is congruent.
Every pair of opposite sides is congruent.
The diagonals of the trapezoid are congruent.
Every pair of adjacent angles is supplementary.
25. In the figure below, the measurements of the various segments are given.
Which of the statements is FALSE?
A.
B.
C.
D.
E.
The area of triangle ABD = the area of triangle DBC.
Triangle ABD is an isosceles triangle.
Triangle BDC is an acute triangle.
The area of triangle BCD is 7.5 square centimeters.
Triangle ABD is an obtuse triangle.
26. Which statement is FALSE?
A.
B.
C.
D.
E.
Every pyramid with a triangle base has 4 vertices.
Every prism with a hexagon base has 18 edges.
Every prism with a square base has 8 vertices.
Every pyramid with a pentagon base has 6 faces.
Every pyramid with a square base has 4 faces.
2010 Grade 7 Tennessee Middle/Junior High School Mathematics Competition
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27. Which of the following choices is not equal to the others?
A. 0.375% of 800
B. 3.75 x 8
C. 0.0375 x 80
2
D. 800 ÷ 266
3
E. 37.5% of 8
28. The graph below shows the amount of fuel left in the tank of an airplane as time elapses.
€
What is the slope of the graph?
A. The slope is 100 gallons per hour.
B. The slope is 1, and it has no meaning with respect to the airplane.
C. The slope is -1, it has no meaning with respect to the airplane.
D. The slope is -100 gallons per hour.
E. The slope is -100, and it has no meaning with respect to the airplane.
2010 Grade 7 Tennessee Middle/Junior High School Mathematics Competition
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29. The first four figures of a sequence are shown below. How many dots would be in the 50th
figure in the sequence?
A.
B.
C.
D.
E.
50 2 − 48
50 2 − 50
52 2 − 52
52 2 − 50
52 2 − 51
€
€
€
€ 30. What is the relationship between the two triangles shown below?
€
A. Triangle B′C′D′ is a 60˚ clockwise rotation of triangle BCD about point A.
B. Triangle B′C′D′ is reflection of triangle BCD over segment j.
C. €Triangle B′C′D′ is the composition of a reflection of triangle BCD over segment j
followed by a 60˚ counterclockwise rotation about point A.
€
D. Triangle B′C′D′ is the composition of a 60˚ counterclockwise rotation about point A
€followed by a reflection of triangle BCD over segment j.
E. Triangle B′C′D′ is a translation of triangle BCD by vector EF.
€
€