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1. |
Looking at several specific situations to arrive at an educated guess is called __________. |
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A. |
guessing |
B. |
a conjecture |
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C. |
deductive reasoning |
D. |
inductive reasoning |
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Hint |
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2. |
Determine if the following conjecture is true or false? Explain. Given: x2 = 4
Conjecture: x = 4 or x = -4 |
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A. |
False; the square root of 4 is 2 or -2. |
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B. |
True; squaring a positive number results in a positive number and squaring a negative number results in a positive number. |
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C. |
True; two answers are always more accurate than one answer. |
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D. |
False; the square root of a positive number is always a positive number. |
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Hint |
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3. |
Determine the contrapositive of the following if-then statement.
If three points are noncollinear, then they form a triangle. |
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A. |
If three points do not form a triangle, then they are not noncollinear. |
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B. |
If three points are not noncollinear, then they do not form a triangle. |
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C. |
If three points form a triangle, then they are noncollinear. |
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D. |
If three points do not form a triangle, then they are noncollinear. |
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Hint |
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4. |
Which statement explains why  |
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A. |
Vertical angles are congruent. |
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B. |
Angles adjacent to the same angle or to congruent angles are congruent. |
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C. |
Angles complementary to the same angle or to congruent angles are congruent. |
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D. |
All right angles are congruent. |
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Hint |
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5. |
Using the following true conditional and hypothesis, which statement would follow from the Law of Detachment?A square has four right angles. WXYZ is a square. |
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A. |
If WXYZ is not a square, then it has four right angles. |
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B. |
If WXYZ has four right angles, then it is a square. |
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C. |
WXYZ has four right angles. |
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D. |
If WXYZ is not a square, then it does not have four right angles. |
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Hint |
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6. |
Two angles are congruent if they are ______. |
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A. |
vertical |
B. |
supplementary |
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C. |
a linear pair |
D. |
adjacent |
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Hint |
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7. |
A counterexample disproves a conditional when ________ . |
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A. |
the hypothesis is true and the conclusion is false |
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B. |
the hypothesis is false and there is no valid conclusion |
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C. |
the hypothesis is true and the conclusion is true |
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D. |
the hypothesis is false and the conclusion is false |
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Hint |
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8. |
Which of the following is a counterexample to the statement that all dogs go to heaven? |
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A. |
All people go to heaven. |
B. |
Ricky's dogs went to heaven. |
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C. |
No people go to heaven. |
D. |
My dog did not go to heaven. |
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Hint |
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9. |
How is 5 is an element of set C written in set notation? |
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A. |
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B. |
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C. |
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D. |
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Hint |
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10. |
Which answer shows all the possible subsets of {2,4,5}? |
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A. |
{2,4,5},{2}, {4}, {5}, {2,4}, {2,5}, {4,5} |
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B. |
{2}, {4}, {5}, {2,4}, {2,5}, {4,5}, |
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C. |
{2,4,5},{2}, {4}, {5}, {2,4}, {2,5}, {4,5}, |
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D. |
{2,4,5},{2}, {4}, {5}, |
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Hint |
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11. |
If A= {0,1,2,3,4}, B={2,4,6,8} and C= {-3, -2, -1, 0}, find  |
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A. |
{-3, -2, -1, 0, 2, 4, 6, 8} |
B. |
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C. |
{0} |
D. |
{-3, -2, -1, 0, 1, 2, 3, 4} |
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Hint |
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12. |
If A= {0,1,2,3,4}, B={2,4,6,8} and C= {-3, -2, -1, 0}, find  |
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A. |
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B. |
{-3, -2, -1, 0, 2, 4, 6, 8} |
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C. |
{0} |
D. |
{-3, -2, -1, 0 ,1, 2, 3, 4} |
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Hint |
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13. |
What is the inverse of the conditional If two angles are vertical angles then they have equal measures? |
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A. |
If two angles do not have equal measures then they are not vertical angles. |
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B. |
If two angles are vertical angles then they do not have equal measures. |
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C. |
If two angles are not vertical angles then they do not have equal measures. |
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D. |
If two angles have equal measure then they are vertical angles. |
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Hint |
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14. |
Using the following conditional, which conclusion would follow from the Law of the Contrapositive? State if it is valid or invalid. If an angle is 20° then it is obtuse. |
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A. |
The angle is not 120°; invalid |
B. |
The angle is obtuse; invalid |
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C. |
The angle is obtuse; valid |
D. |
The angle is not 120°; valid |
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Hint |
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