Download finite test - Montana Council of Teachers of Mathematics

MCTM
MONTANA COUNCIL OF TEACHERS OF MATHEMATICS
2009 MATH CONTEST
FINITE TEST
DIRECTIONS: DO NOT WRITE ON THIS TEST. Place the best answer for each question on the separate answer sheet.
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1.
A)
2.
A)
B)
C)
D)
E)
The aquarium at the pet store contains 10 goldfish, 15 beta fish, and 5 angel fish. Fish are equally likely to swim
near your net and be caught. If you purchase the first two fish to swim into your net, what is the probability you
take home at least one angel fish?
20
29
B)
9
29
C)
125
174
D)
25
36
E)
11
36
Which variable would not represent a positive correlation?
Distance travelled on a bicycle versus time taken.
Total cost versus numbers of gallons of gas purchased.
Weight of an apple being eaten versus time it takes to consume the apple.
Energy output of a log fire versus number of logs.
Mold growth versus time.
3. Solve the equation for the value of x: log3 9 + 2 log x = ln e10 − log 2 16
A) 100
B) No Solution
C) 3,162.3
D)
10
E) 210
4. A manufacturer of ski equipment produces snowboards and downhill skis. A snowboard takes 2 hours to
construct and one hour to finish while a pair of skis take three hours to construct and one hour to finish. Due to
labor constraints there are at most 48 hours that can be used for construction and 20 hours for finishing. If the
profit per snowboard is $120 and the profit per pair of skis is $80, what is the maximum profit?
A) $1600
B) $2160
C) $2240
D) $2360
E) $2400
5. How many terms are in the arithmetic sequence 514, 510, 506, … , 2?
A) 127
B) 128
C) 129
D) 130
E) 131
6. Carlton High School has 58 female athletes in volleyball, basketball, and track. The girls are either one sport, two
sport, or three sport athletes. The numbers of one sport and two sport athletes for each sport are represented in the
tables below. How many girls are in all three sports?
One Sport Athletes
Volleyball
16
X
7
5
A) 0
Basketball
Two Sport Athletes
Volleyball
12
X
6
X
10
Track
X
X
B) 1
C) 2
D) 3
Basketball
X
X
Track
X
X
E) 4
7. A bottling company sells energy drinks in cylindrical containers. If they double the height and cut the radius in
half, what happens to the volume of the container?
A) Volume remains the same.
B) Volume is doubled.
D) Volume is decreased by half.
C) Volume is multiplied by 2 2
E) Volume is multiplied by
2.
FINITE TEST 2009 page 2
8. Shannon, Pat and Ryan have different birthdays. Assuming there are 365 days in a year, how many possible
combinations of birthdates could the three people have?
A) 1095
B) 8038030
C) 48228180
D) 48627100
E) 365!
9. Determine the equation for the cubic function
graphed on the right.
1
( x − 2) 2 ( x + 3) B) y = 3( x − 3) 2 ( x + 2)
3
1
C) y = ( x 3 − 2 x 2 − 8 x + 2)
D) y = 3( x − 2) 2 ( x + 3)
3
1
E) y = ( x − 3) 2 ( x + 2)
3
A) y =
10. Tom’s 4-wheel drive pickup gets an average of 14 mpg. He found a newer car that gets 32 mpg. He drives 9,000
miles per year. Assuming gas costs $4.15 per gallon for the whole year, how much will he save each month if he
drives the car instead of the truck?
A) $1500.70
B) $222.32
C) $153.22
D) $125.06
E) $97.27
11. Which of the following systems has an infinite number of solutions?
⎧⎪ y = x 2 + 5
2
⎩⎪ y = 7 − 2 x
⎧ y = 3x − 1
⎩ y = 3x − 5
A) ⎨
⎧3x − 5 y = 7
⎩− 9 x + 15 y = −21
B) ⎨
⎧ y = 7x + 2
⎪
D) ⎨
2
⎪⎩ y = 3 x − 4
C) ⎨
⎧x − y = 4
⎩− 3 x + y = 5
E) ⎨
12. The probability that a 21 year old male driver causes an auto accident decreases by 2% every year starting at age
twenty-one. If the initial probability is 25%, which equation models this probability in years after age 21?
A)
a n = .25(.98) n −1
D)
n −1
a n = .25(1.02) n −1
C) a n = .75(.98)
n
a n = .25(1.02) n +1
E) a n = .25(.98)
B)
Miss Tatum’s First and Third period Algebra II test scores are represented in the following set of box and
whisker plots. Use this information to answer questions 13 – 15.
13. Which class has more students?
A) Period 1
B) Period 3
D) Not enough information
C) They are the same
Period 1
14. Which class has the greatest standard deviation?
A) Period 1
B) Period 3
D) Not enough information
C) They are the same
Period 3
15. Which statistical measure is the same for each class?
A) Mean
B) Mode
C) Range
D) Interquartile Range
E) Median
FINITE TEST 2009 Answer Key
1) B
2) C
3) A
4) E
5) C
6) C
7) D
8) B
9) A
10) D
11) C
12) A
13) D
14) A
15) E