Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Eileen studied the sum of the angles in pentagons and made a conjecture.
Which conjecture, if any, did she most likely make?  a. | The sum of the angles in a pentagon is always 180°. | b. | The sum of the
angles in a pentagon is always 360°. | c. | The sum of the angles in a pentagon is always
540°. | d. | It is not possible to make a conjecture. |
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2.
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Jason created the following table to show a
pattern.
| Multiples of 27 | 54 | 81 | 108 | 135 | 162 | | Sum of the Digits | 9 | 9 | 9 | 9 | 9 | | | | | | |
Which conjecture could Jason make, based solely on this evidence?
Choose the best answer. a. | The sum of the digits of a multiple of 27 is equal to 9. | b. | The sum of the
digits of a multiple of 27 is an odd integer. | c. | The sum of the digits of a multiple of 27 is
divisible by 9. | d. | Jason could make any of the above conjectures, based on this
evidence. |
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3.
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Janice created the following table. | Number | 23 | 28 | 73 | | Sum of the Digits | 5 | 10 | 10 | | | | |
Based on this evidence, which conjecture might Janice make? Is the
conjecture valid? a. | A number whose digits sum to a multiple of 10 will be 2 less than a multiple of 5;
no, this conjecture is not valid. | b. | The sum of the digits of a number that is 2
less than a multiple of 5 is a multiple of 5; no, this conjecture is not valid. | c. | The sum of the
digits of a number that is 2 less than a multiple of 5 is a multiple of 5; yes, this conjecture is
valid. | d. | A number whose digits sum to a multiple of 10 will be 2 less than a multiple of 5;
yes, this conjecture is valid. |
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4.
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Randolph made the following conjecture. The sum of a multiple of 4 and a multiple of
8 must be a multiple of 2.
Which choice, if either, is a counterexample to this
conjecture?
1. 4 + 8 =
12
2. 8 + 8 = 16
a. | Choice 2 only | b. | Choice 1 and Choice 2 | c. | Choice 1
only | d. | Neither Choice 1 nor Choice 2 |
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5.
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All cats are mammals. All mammals are warm-blooded. Tashi is a cat.
What can
be deduced about Tashi?
1. Tashi is warm-blooded.
2. Tashi is a
mammal.
a. | Choice 1 and Choice 2 | b. | Neither Choice nor Choice 2 | c. | Choice 1
only | d. | Choice 2 only |
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6.
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Hali is a fitness instructor. People who take
Hali’s exercise class regularly soon become very fit. Regular exercise makes people feel happy.
Joshua takes Hali’s exercise class regularly. What can be deduced about
Joshua?
1. Joshua is very fit. 2. Joshua feels happy. a. | Choice 2 only | b. | Choice 1 only | c. | Neither Choice 1 nor
Choice 2 | d. | Choice 1 and Choice 2 |
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7.
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Which of the following choices, if any, uses
deductive reasoning to show
that the sum of two even numbers and one odd number is an odd
number?
a. | (2x + 1) + (2y + 1) + (2z + 1) = 2(x + y +
z) + 3 | b. | 6 + 6 + 7 = 19 and 4 + 6 + 3 = 13 | c. | 2x +
2y + (2z + 1) = 2(x + y + z) + 1 | d. | None of the above
choices |
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8.
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What type of error, if any, occurs in the
following proof?
3 = 3 – 1
2(3) = 2(3 – 1)
2(3) +
1 = 2(3 –1) + 1
6 +
1 = 4 + 1
7 = 5
a. | a false assumption or generalization | b. | an error in reasoning | c. | an error in
calculation | d. | There is no error in the proof. |
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9.
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What type of error, if any, occurs in the
following proof?
5 = 5
2.5(5) = 2.5(2 + 3)
2.5(5) +
1 = 2.5(2 + 3) + 1
12.5 +
1 = 10 + 4
13.5 = 14
a. | a false assumption or generalization | b. | an error in reasoning | c. | an error in
calculation | d. | There is no error in the proof. |
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10.
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Determine the unknown term in this pattern.
17, 14, ____, 8, 5, 2,
–1
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11.
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Which number should appear in the centre of Figure 4? | | | | Figure 1 | Figure 2 | Figure 3 | Figure 4 | | | | |
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12.
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Which number should go in the grey square in this Sudoku puzzle? 
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13.
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Which number should go in the grey square in this Sudoku puzzle? 
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14.
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Colin and Erynn are playing darts. Colin has a score of 75. To win, he must reduce his score to zero and have his last
counting dart be a double.
Which of the following scores on the dart board, in order, would give
him the win? |  | | |
a. | 15, 20, double 20 | b. | 0, 15, triple 20 | c. | double 20, 20,
15 | d. | 10, 20, double 15 |
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15.
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Which angle property proves ÐPYD =
90°?  a. | corresponding angles | b. | alternate interior angles | c. | alternate exterior
angles | d. | supplementary angles |
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16.
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Which angle property proves ÐDAB =
120°?
a. | vertically opposite angles | b. | alternate exterior angles | c. | alternate interior
angles | d. | corresponding angles |
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17.
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Which are the correct measures for ÐKLM,
ÐKLN, and ÐNML?  a. | ÐKLM = 117°, ÐKLN = 36°, and ÐNML =
124° | b. | ÐKLM = 71°, ÐKLN = 24°, and ÐNML =
63° | c. | ÐKLM = 73°, ÐKLN = 67°, and ÐNML =
117° | d. | ÐKLM = 63°, ÐKLN = 28°, and ÐNML =
117° |
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18.
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Which are the correct measures for ÐWXZ,
ÐUZY, and ÐVYX?  a. | ÐWXZ = 166°, ÐUZY = 109°, and ÐVYX =
89° | b. | ÐWXZ = 162°, ÐUZY = 106°, and ÐVYX =
92° | c. | ÐWXZ = 162°, ÐUZY = 106°, and ÐVYX =
88° | d. | ÐWXZ = 152°, ÐUZY = 116°, and ÐVYX =
88° |
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19.
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Determine the value of b. 
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20.
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Determine the value of a.
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Short Answer
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21.
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All camels are mammals. All mammals have lungs to breathe air.
Humphrey is a
camel. What can be deduced about Humphrey?
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22.
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What type of error occurs in the following deduction? Briefly justify your
answer. A hair with Elmo’s DNA is discovered at the
scene of a crime. Therefore, Elmo was at the scene of the crime.
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23.
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Determine the measure of ÐBDE.
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24.
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Determine the measure of ÐRTQ.
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25.
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Determine the value of x. 
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Problem
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26.
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Make a conjecture about the temperature on July
6, 2011, in Olds, Alberta, based on the information in the chart below. Summarize the evidence that
supports your conjecture.
| Year | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | | Maximum Temperature (°C) | 20.8 | 17.0 | 22.8 | 23.4 | 24.8 | 25.8 | 20.0 | 18.2 | | | | | | | | | |
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27.
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Tyler made the following conjecture: A polygon with four right angles must be a
rectangle.
Matthew disagreed with Tyler’s conjecture, however, because the
following figure has four right angles, and it is not a rectangle.  How could
Tyler’s conjecture be improved? Explain the changes you would make.
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28.
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Annabeth wrote the following equations. The
results led her to make the conjecture that the sum of three consecutive perfect squares is divisible
by 3.
Let n be the first integer. n2 + (n +
1)2 + (n + 2)2 = n2 +
(n2 + 2n + 2) + (n2 + 4n +
4)
n2 + (n + 1)2 + (n +
2)2 = 3n2 + 6n +
6
n2 + (n + 1)2 + (n +
2)2 = 3(n2 + 2n +
2)
But in checking her work, Annabeth found the following counterexample, so she knew
she had made an error. 1 + 4 + 9 = 14 Determine what Annabeth’s error is. What
should her result have been?
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29.
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Eldon, Pierre, Manny, and Burt swam a race. Early in the race, Eldon led Pierre
by
3 m, while Manny was behind Burt by 2 m. Burt was ahead of Pierre by 1 m. By the halfway
point, Eldon and Burt had exchanged places, although they were still the same distance apart. Manny
had pulled even with Eldon. Over the last part of the race, Manny dropped 1 m behind Eldon, and
Pierre passed Burt. Who finished third?
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30.
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Given LM || JK and ÐLMJ =
ÐKMJ, prove JK = KM. 
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