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1.
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Let p
represent
x2 = 15
and let q
represent
x is not a whole number.
Which is a representation of the statement
below?
If x is not a whole number, then x2 = 15.
A) | ~q ® ~p | B) | q ®
~p | C) | q
® p | D) | ~q ®
p |
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2.
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The distance between the points (2, –2) and (7, 3) is:
A) |  | B) | 10 | C) |  | D) | 50 |
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3.
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Assuming these statements are true, Some teachers are young people.
All young people like to
dance.
which of the following is a valid conclusion?
A) | Some young people do not like to dance. | B) | All young people are
teachers. | C) | Some teachers like to dance. | D) | All teachers like to
dance. |
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4.
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The coordinates of the midpoint of  are (6, –4), and the coordinates
of A are (3, –1). What are the coordinates of B? A) | (9, 3) | B) | (0, 2) | C) | (9, –7) | D) | (4.5,
–2.5) |
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5.
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If j  k, and k  c, then:
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6.
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Consider the following
statement.
If 4x =
12, then x = 3.
Which is the converse of the
statement?
A) | If 4x ¹ 12, then x ¹
3 | C) | If x ¹ 3, then 4x ¹
12 | B) | If x = 3, then 4x ¹
12 | D) | If x = 3, then 4x = 12. |
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7.
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Statement: If lines are skew, then they
are not coplanar..
What is the contrapositive of the statement?
A) | If lines are coplanar, then they are not skew. | B) | If lines are not
coplanar, then they are skew. | C) | If lines are skew, then they are
coplanar. | D) | If lines are not skew, then they are coplanar. |
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8.
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Let a represent “x is an even number”.
Let b
represent “x is a multiple of 3”.
When x is 7, which of the
following is true?
A) | ~a ^ b | B) | a ^ b | C) | ~a ^ ~b | D) | a ^
~b |
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9.
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Which of the following groups of statements represents a valid
argument?
A) | Given: All kites have
angles.
All squares have
angles.
Conclusion: All kites are squares. | B) | Given: All four sided figures are
quadrilaterals.
All kites have
four sides.
Conclusion: All kites are quadrilaterals. | C) | Given: All
quadrilaterals have four sides.
All kites have four sides.
Conclusion: All quadrilaterals are kites. | D) | Given: All
squares have congruent angles.
All rectangles have congruent angles.
Conclusion: All rectangles are
squares. |
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10.
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Consider the following arguments. If the first two statements are true, in which
argument is the 3rd statement an incorrect conclusion?
A) | 1 If we win the game, then we will win the championship.
2 If we win the
championship, then we will get a trophy.
3 If we do not get a trophy, then we did not win the
game. | B) | 1 If Pete eats her peas, then she will get cake.
2 If Pete gets cake, then she
will watch SpongeBob.
3 If Pete eats her peas, then she will watch SpongeBob. | C) | 1 If it snows, then
we will stay inside.
2 If we stay inside, then we will play games.
3 If it snows, then we will
play games. | D) | 1 If Vicki studies, then she will pass the test.
2 If Vicki passes the test, then
she will not be grounded.
3 If Vicki is grounded, then she will
study. |
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11.
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Which is the inverse of the statement, If I am in Richmond, then I am in
Virginia?
A) | If I am not in Richmond, then I am not in Virginia. | B) | If I am not in
Virginia, then I am not in Richmond. | C) | If I am in Virginia, then I am in
Richmond. | D) | If I am not in Virginia, then I am in Richmond. |
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12.
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Which of the following statements represents a valid argument?
A) | If a < b and a < c, then b <
c. | C) | If a < b and a < c, then a < b +
c. | B) | If a < b and b < c, then a <
c. | D) | If a >
b and a > c, then c > b. |
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13.
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Which is the converse of the sentence, “If Theresa leaves, then I
will stay.”?
A) | If I stay, then Theresa will leave. | B) | If Theresa does not leave, then I will not
stay. | C) | If Theresa leaves, then I will not stay. | D) | If I do not stay,
then Theresa will not leave. |
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14.
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Which conclusion logically follows the true
statements?
If negotiations fail, the baseball
strike will not end.
If the baseball strike does not
end, the World Series will not be played.
A) | If negotiations fail, the World Series will be played. | B) | If negotiations
fail, the World Series will not be played. | C) | If negotiations do not fail, the baseball
strike will not end. | D) | If the baseball strike ends, the World Series
will be played. |
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15.
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Let p
represent
 and let q
represent
z is a rational number.
Which choice is a representation of the statement
below?
If  ¹ z, then z is a
rational number.
A) | ~p ® q | B) | p ®
q | C) | ~p
® ~q | D) | p ®
~q |
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16.
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Which is the contrapositive of the statement below?
If you
do your homework, then you will be prepared for the test.
A) | If you did not do your homework, then you will not be prepared for the
test. | B) | If you are prepared for the test, then you did your homework. | C) | If you do your
homework, then you will be prepared for the test. | D) | If you are not prepared for the test, then you
did not do your homework. |
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17.
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Which pair of angles is supplementary?
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18.
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Given: B, C, and D are
collinear;
 ACD = 84°
What value of x will ensure that A, C,
and E are also collinear? |  | | |
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19.
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In which group of statements is the conclusion not justified by the
previous pair of statements?
A) | All raphidaes are extinct.
A rodrigues solitaire is a raphidae.
All rodrigues
solitaires are extinct. | C) | All fish live in the water.
Some frogs live in the
water.
Some frogs are fish. | B) | All squares are parallelograms.
All
parallelograms are quadrilaterals.
All squares are quadrilaterals. | D) | All rangers work in the park.
Sally is a
ranger.
Sally works in the park. |
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20.
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Let p = An equation is of the form  . Let q
= Its graph is a line. Argument: If an equation
is of the form  , then its graph is a
line. The graph is not a
line.
Therefore, the equation is not of the form  . Which of the following is the symbolic
representation of the given argument?
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21.
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If the conditional statement
“If
you have a MP3 player, then you have music”
is represented by p ® q, what is the symbolic representation
of
“If you have a MP3 player, then you do not have
music”?
A) | ~q ® p | B) | ~q ® ~p | C) | q ® ~p | D) | p ® ~q |
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22.
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What is the contrapositive of the following statement?
If Joe
goes fishing, then he needs bait.
A) | If Joe goes fishing, then he does not need bait. | B) | If he needs bait,
then Joe goes fishing. | C) | If Joe does not go fishing, then he does not
need bait. | D) | If he does not need bait, then Joe does not go
fishing. |
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23.
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The coordinates of the midpoint of  are:  A) |  | B) |  | C) | (2,
5) | D) | (5, 3) |
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24.
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Consider the following statements.
p: The sum of two angles is
180°.
q: The two angles are supplements.
Which of the following is a symbolic
representation of the statement:
“If sum of two
angles is 180°, then the two angles are not supplements”?
A) | ~q ® p | B) | p ®
~q | C) | q
® ~p | D) | ~q ®
~p |
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25.
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Which set of statements represents an invalid argument?
A) | If I sleep in, then I will miss school.
If I miss school, then I will get
grounded.
If I sleep in, then I will get grounded. | B) | If it is your birthday, then you will get ice
cream.
If you will get ice cream, then you will get cake.
If it is your birthday, then you will
get cake. | C) | If John goes camping, then he will go fishing.
If John goes fishing, then he will
buy bait.
If John does not buy bait, then he will go camping. | D) | If we pass Geometry,
then we will play sports.
If we play sports, then we will get a trophy.
If we do not get a
trophy, then we did not pass Geometry. |
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