G.1 – VDOE Released Test Items and other Practice Items
G.1a: Conditional Statements
1. (From 2014 Released SOL) Which is the inverse of the following statement?
If the measure of an angle is 90˚, then it is a right angle.
A.
B.
C.
D.
If the measure of an angle is not 90˚, then it is not a right angle.
If the measure of an angle is not 90˚, then it is a right angle.
If an angle is not a right angle, then its measure is not 90˚.
If an angle is a right angle, then its measure is 90˚.
2. (From 2015 Released SOL) Which is the converse of the following statement? If
𝑎
𝑏
A. If ≠ 𝑐, then 𝑎 ≠ 𝑏𝑐.
B. If 𝑎 = 𝑏𝑐, 𝑡ℎ𝑒𝑛
𝑎
𝑏
= 𝑐.
𝑎
𝑏
= 𝑐, then a=bc.
𝑎
𝑏
C. If 𝑎 ≠ 𝑏𝑐, then ≠ 𝑐.
𝑎
D. If 𝑏 = 𝑐, then 𝑎 ≠ 𝑏𝑐.
3. (From Chesterfield Practice SOL Quizzes)
Which of the following is correctly matched based on the given conditional statement?
GIVEN: If you do not enter the contest, then you cannot win the contest.
A
B
C
D
Inverse: If you cannot win the contest, then you do not enter the contest.
Converse: If you enter the contest, then you can win the contest.
Inverse: If you enter the contest, then you can win the contest.
Converse: If you cannot win the contest, then you enter the contest.
G.1b: Symbolic Notation
1. (From 2014 Released SOL)
Let p represent “two angles are vertical.”
Let q represent “the angles are congruent.”
What is the symbolic representation of the following statement?
“If two angles are congruent, then the angles are vertical angles.”
A. 𝑞 → 𝑝
B. 𝑝 → 𝑞
2. (From 2015 Released SOL)
Let p represent “Brent works this summer.”
Let q represent “Brent takes a vacation.”
Symbolically represent the following argument:
If Brent works this summer, then he will not take a vacation.
Brent takes a vacation.
Therefore, Brent does not work this summer.
C. ~𝑞 → ~𝑝
D. ~𝑝 → ~𝑞
G.1 – VDOE Released Test Items and other Practice Items
3. (From TestNav8 Practice Items)
Let p represent “∠A is acute.”
Let q represent ∠B is acute.”
Create a symbolic representation of the following argument:
∠A is acute if and only if ∠B is acute.
∠A is acute or ∠B is acute.
Therefore, ∠A is acute and ∠B is acute.
4. (From Chesterfield SOL Practice Quizzes) Consider the following statements.
p: two lines are parallel
q: corresponding angles are congruent
Which of the following is the symbolic representation of the argument:
If two lines are not parallel, then corresponding angles are not congruent.
A
B
~𝑞 → ~𝑝
~𝑝 → ~𝑞
C
D
𝑞→𝑝
𝑝→𝑞
G.1c: Determine Validity of a Logical Argument
1. (From 2014 Released SOL) Which is a valid conclusion that can be drawn from these statements?
If a quadrilateral is a rhombus, then it is a parallelogram.
If a quadrilateral is a parallelogram, then its opposite angles are congruent.
A.
B.
C.
D.
Every quadrilateral is a rhombus.
Every parallelogram is a rhombus.
Opposite angles of a rhombus are congruent.
Opposite angles of a quadrilateral are congruent.
2. (From 2015 Released SOL) Given statements:
If a shape is a parallelogram, then opposite angles are congruent.
A rhombus is a parallelogram.
Which is a logical conclusion from the given statements:
A.
B.
C.
D.
A rhombus has opposite angles that are congruent.
The opposite sides of a rhombus are congruent.
The diagonals of a rhombus are congruent.
A rhombus is a quadrilateral.
G.1 – VDOE Released Test Items and other Practice Items
3. (From 2014 Regional Simulation) Select all of the following that represent a valid argument.
I
II
III
IV
V
VI
A. I, II, III
B. I, III, IV
C. II, V, VI
D. III, V, VI
If you live in a mansion, then you have a big heating bill.
Sarah does not have a big heating bill, therefore Sarah does not live
in a mansion.
If it rains, no one will go fishing.
John did not go fishing.
It rained Tuesday.
Jamal knows that if he misses the practice the day before a game,
then he will not be a starting player in the game.
Jamal misses practice on Tuesday.
Jamal concludes that he will not be able to start in the game on
Wednesday.
If Mike visits Alabama, then he will spend a day in Montgomery.
If Mike spends a day in Montgomery, then he will visit the Civil
Rights Memorial.
If Mike visits Alabama, then he will visit the Civil Rights Memorial.
If Ginger goes to the movies, then Marta will go to the movies.
If Yumi goes to the movies, then Ginger will go to the movies.
If Ginger goes to the movies, then so do Yumi and Marta.
The Oak Terrace apartment building does not allow dogs.
Serena lives at Oak Terrace. So, Serena may keep a dog.