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STANDARD 5
MEASUREMENT AND DISCRETE MATHEMATICS
(Grades 9 - 12)
Vocabulary
algorithm
common ratio
discrete
geometric series
probability
simple interest
arithmetic mean
arithmetic progression
compound interest
cycle
enumeration
equivalent
graph
infinite
progression
recursive
success
arithmetic sequence
diagram
matrix (matrices) schematic
arithmetic series
digraph
failure
finite
net
sequence
common difference
directed graph
geometric progression
network
series
Problems
1. Suppose you live in Tucson and have friends who live in Dallas, Los Angeles, and Phoenix. You can fly directly to
Phoenix and Los Angeles but not Dallas. Your friend in Dallas can fly directly to Phoenix or Los Angeles but not
Tucson. From Phoenix and Los Angeles, your friends can fly directly to any of the other locations. Which graph
represents the data given?
2. On the first three tests you earned grades of 93, 72, and 82. On the same tests your friend Rick earned 82, 60, and 92,
while Sandy got 72, 81, and 96. Which of the matrices represents the data?
3. What is the 105th term for the following geometric sequence? 1, 3, 9, 27, 81, ...
a) 3105
b) 3(105)
c) 3104
d) 3 + 105
4. You put $10 into your piggy bank each week for two years. How much money will you have in your piggy bank at
the end of two years?
a) $20.00
b) $520.00
c) $1,000.00
d) $1,040.00
5. A bank account has an initial balance of $100 and earns interest at a rate of 1% per month, how much interest will the
account earn in 4 months? The interest is compounded monthly.
a) $4.06
b) $104.06
c) $400.00
d) $140.00
6. A rocket travels 1 mile the first minute. If the rocket doubles its speed every minute, what is the distance traveled by
the rocket in the 10th minute?
a) 100 miles
b) 512 miles
c) 1023 miles
d) 1024 miles
7. The local telephone company has a sub-network of five cities, Jackson, Bedrock, South Park, Smallville, and
Gotham. A long distance call is any call which must be routed through another city to reach its destination. Which of the
following phone calls, placed between two cities, is not a long distance phone call given the following connection
scheme?
a) Bedrock - South Park
b) Jackson - Smallville
c) Gotham - Jackson
d) South Park - Gotham
e) Smallville - Bedrock
8. Suppose a car hits a telephone pole and breaks the line connecting Bedrock and Jackson so that no telephone calls can
go directly through (no local calls). What is the minimum number of cities a long distance call must now be routed
through in order to reach Jackson from Bedrock?
a) 0
b) 1
c) 2
d) 3
e) 4
Questions 9,10 and 11 will refer to the following map.
9. Given the above schematic, how many routes are there to get from city A to city F? Each route may go through any
city at most once.
a) 2
b) 3
c) 7
d) 4
e) 6
10. A Cycle is a route that begins and ends at the same vertex, without using any edge or vertex twice (except the end).
How many cycles of different lengths are there in the above graph?
a) 2
b) 3
c) 4
d) 5
e) 6
11. What is the length of the shortest possible cycle?
a) 3.6 miles
b) 15.6 miles
c) 23.8 miles
d) 24.8 miles
e) 27.2 miles
12. You have been hired to install an automated sprinkler system for a fixed price of $700. Each sprinkler head will cost
you $25 and each foot of pipe/hose will cost you $2. After laying out the yard you end up with the following
information:
You must water all of the plants and one sprinkler head is needed for each of the plants only, not the water tap. Which
of the following layouts would you use to maximize your profits?
a)
b)
c)
d)
13. Given the following matrix,
Which of the following finite graphs represent the data?
14. Given:
Which of the following matrices describes this finite graph?
15. Given:
Which of the following matrices describes this network?
16. Which algorithm can be used to solve the equation ax + b = c for x?
a)
b)
1. Add a & b.
2. Subtract the result from c.
1. Add b to both sides of the equation.
2. Divide both sides by a.
c)
d)
1. Subtract b from both sides of the equation.
2. Divide both sides by a.
17. Given the formula for the area of a trapezoid, A =
result?
a)
(1/2)(h)(
1.Subtract b from both sides of the equation
2. Multiply both sides by a.
a + b), which algorithm will not always yield the correct
b)
1. Add a & b
2. Multiply the sum by 1/2
3. Multiply this product by h
c)
1. Add a & b
2. Multiply the sum by 1/2
3. Divide this product by h
d)
1. Multiply h by 1/2
2. Add a & b
3. Multiply the above results
1. Add a & b
2. Multiply the sum by h
3. Multiply the product by 1/2
18. Take a number (n), and multiply it by itself. Then multiply that result by (n). The result can be expressed by:
a) 3n
b) n 3
c) n(n + n)
d) n + 3
19. Given A + C the algorithm (A)(D) + (B)(C) can be used for what purpose?
B D
(B)(D)
a) Solving a proportion
b) Finding a common denominator
c) Adding fractions with unlike denominators
d) Multiplying fractions
20. Given three numbers, a, b, & c, which of the algorithms will always yield the arithmetic mean?
1. Add 3 numbers and then divide by three.
2. Divide each of three numbers by 3 and then add the results
3. Add 3 numbers then multiply by 1/3
4. Divide each number by 1/3 then add the results
a) 1 & 2 only
b) 2 & 3 only
c) 1, 2, & 3
d) each result will be different
21. Which of the algorithms is not equivalent to the others?
a) Multiply by 2, then add 10
c) Multiply by 2, add 14, then subtract 4
b) Add 5, then multiply by 2
d) Multiply by 2, then add 5
22. Suppose you toss a coin and then toss the same coin again, recording the results after each toss. Listed below are the
possible outcomes. Which is the list of all the possible outcomes?
a) HH, HT, TH, TT
b) TT, TH, HH, TH
c) HT, TH, TT, HT
d) HH, HT, TT
23. The map above shows five towns connected by roadways. Suppose you are in town A and need to drive to town D.
Of the possible routes listed below, which route will not work?
a) A-C-D
b) A-B-E-D
c) A-B-C-D
d) A-B-D
24. Suppose you roll two number cubes, numbered one through six. What is the probability that you roll a sum of nine?
a) 5/36
b) 1/6
c) 1/18
d) 1/9
25. Using the target above, what is the probability of hitting the circle with a dart, providing the dart hits the target?
a) .283
b) .36
c) .783
d) .717
26. In a single elimination basketball tournament, how many games would be played if sixteen teams entered the
tournament?
a) 16
b) 15
c) 9
d) 8
27. You have three pairs of shorts and four T-shirts. How many different outfits can you wear by choosing one pair of
shorts and one T-shirt?
a) 7
b) 8
c) 12
d) 18
28. A company that manufactures car stereos uses a five-digit serial number consisting of two letters followed by three
numbers (ex: AB221, CC030). How many different serial numbers can the manufacturer create?
a) 676,000
b) 520,000
c) 650,000
d) 468,000
29. Suppose you have four books to place on a bookshelf. How many different ways can you order these books?
a) 12
b) 16
c) 24
d) 36
Use the following for questions 30 and 31.
Computer Network: Suppose your school decides to link six computer to each other without any kind of separate
junction box or server. One way to get the "best" network is to use the least amount of cable. Because of the location of
each computer, it is not possible to run cable directly between every pair of computers. The matrix below shows which
computers can be linked directly as well as how much cable is needed. The computers are represented by letters and the
distances are in meters. The graph represents the data in the matrix.
30. Which finite graph best represents the least amount of wire needed for the network?
31. Suppose each computer can have a maximum two of the networking cables connected to it. Which finite graph best
represents the least amount of cable needed for the network?
32. TUSD statistics show that roughly 80% of mathematics textbooks are returned each year in usable form. The
following matrix shows the number of textbooks distributed at two high schools. Write a corresponding matrix that
shows the number of returned, reusable textbooks that these schools can expect to receive.
33. Turn around time of an airliner for Fly Away Airlines from arrival to departure involves multiple tasks. Some of the
tasks can be done simultaneously. The tasks involved include unloading the arriving passengers (UP), cleaning the
cabin of the airplane (CC), unloading the arriving luggage (UL), boarding the departing passengers (BP), and loading
departing luggage (LL). The relationships among the tasks and the approximate amount of time needed to accomplish
each of them are represented in the following digraph.
What is the minimum turn around time of an airliner for Fly Away Airlines? Explain your .