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1. |
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 a positive number is always a positive number. |
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B. |
False; the square root of 4 is 2 or -2. |
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C. |
True; squaring a positive number results in a positive number and squaring a negative number results in a positive number. |
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D. |
True; two answers are always more accurate than one answer. |
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Hint |
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2. |
Identify the hypothesis of the following if-then statement.
If Ralph does his math homework, then he will get a good grade on the quiz. |
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A. |
He will get a good grade on the quiz. |
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B. |
Ralph does his math homework. |
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C. |
He will not get a good grade on the quiz. |
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D. |
Ralph may do his math homework. |
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Hint |
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3. |
Determine the converse of the following if-then statement.
If the flowers are yellow, then they are daffodils. |
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A. |
If the flowers are daffodils, then they are yellow. |
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B. |
The flowers are not yellow. |
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C. |
The flowers are not daffodils. |
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D. |
If the flowers are not yellow, then they are not daffodils. |
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Hint |
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4. |
A ______________ is a diagram that can be used to illustrate a conditional. |
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A. |
tree diagram |
B. |
flow chart |
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C. |
bar graph |
D. |
Venn diagram |
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Hint |
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5. |
The Law of Detachment and other laws of logic can be used to provide a system for reaching logical conclusions, called _____________. |
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A. |
inductive reasoning |
B. |
deductive reasoning |
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C. |
detachment reasoning |
D. |
reasonable doubt |
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Hint |
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6. |
Justify step 2 in solving  |
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A. |
Distributive Property (=) |
B. |
Multiplication Property (=) |
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C. |
Subtraction Property (=) |
D. |
Division Property (=) |
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Hint |
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7. |
For the proof shown, provide the reason for part c. |
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A. |
Division Property of Equality |
B. |
Addition Property of Equality |
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C. |
Subtraction Property of Equality |
D. |
Multiplication Property of Equality |
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Hint |
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8. |
If  and  form a linear pair and  find  |
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A. |
86 |
B. |
76 |
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C. |
106 |
D. |
96 |
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Hint |
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9. |
In the figure shown, is complementary to and is complementary to  . Which statement is true if none of the measures of the angles equal 45? |
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A. |
is complementary to . |
B. |
is complementary to itself. |
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C. |
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D. |
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Hint |
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10. |
To show that a conjecture is false, you need to provide one _____. |
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A. |
possibility |
B. |
theorem |
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C. |
guess |
D. |
counterexample |
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Hint |
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11. |
''If you double any number, the result will be an even number.'' is a true conditional. Use the Law of Detachment to reach a logical conclusion. |
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A. |
The result of doubling 234 is an odd number. |
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B. |
If you double an odd number, the result is another odd number. |
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C. |
The result of doubling 317 is an even number. |
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D. |
When you triple a number, the result must be an even number. |
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Hint |
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12. |
Which cannot be used as a reason in a proof? |
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A. |
postulates |
B. |
Algebra properties |
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C. |
Definitions |
D. |
conjectures |
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Hint |
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13. |
For the proof shown, provide statement 3. |
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A. |
AB = EF |
B. |
AB = CD |
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C. |
CD = EF |
D. |
AB = BA |
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Hint |
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14. |
The freshman class of 63 students conducted a survey to compare how many students took Spanish as opposed to French as a foreign language. The results are shown in the Venn diagram. How many students studied neither Spanish nor French? |
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A. |
7 |
B. |
25 |
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C. |
1 |
D. |
14 |
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Hint |
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15. |
Which of the following statements is not a postulate? |
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A. |
Through any two points, there is exactly one line. |
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B. |
If two lines intersect, then their intersection is exactly one point. |
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C. |
A plane contains at least three points not on the same line. |
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D. |
Points that lie of the same plane are said to be coplanar. |
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Hint |
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16. |
Determine the number of line segments that can be drawn connecting pairs of points shown. |
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A. |
4 |
B. |
10 |
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C. |
8 |
D. |
6 |
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Hint |
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