SAT II Math II : Properties and Identities

Study concepts, example questions & explanations for SAT II Math II

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Example Questions

Example Question #1 : Properties And Identities

What property of arithmetic is demonstrated below?

Possible Answers:

Transitive

Associative

Commutative

Distributive

Identity

Correct answer:

Commutative

Explanation:

The statement shows that two numbers can be added in either order to achieve the same result. This is the commutative property of addition.

Example Question #2 : Properties And Identities

What property of arithmetic is demonstrated below?

Possible Answers:

Transitive

Reflexive

Identity

Distributive

Inverse

Correct answer:

Identity

Explanation:

The fact that 0 can be added to any number to yield the latter number as the sum is the identity property of addition.

Example Question #3 : Properties And Identities

What property of arithmetic is demonstrated below?

Possible Answers:

Transitive

Associative

Identity

Symmetric

Inverse

Correct answer:

Inverse

Explanation:

For every real number, there is a number that can be added to it to yield the sum 0. This is the inverse property of addition.

Example Question #4 : Properties And Identities

What property of arithmetic is demonstrated below?

Possible Answers:

Reflexive

Symmetric

Commutative

Transitive

Symmetric

Correct answer:

Reflexive

Explanation:

That any number is equal to itself is the reflexive property of equality.

Example Question #5 : Properties And Identities

What property of arithmetic is demonstrated below?

If  then .

Possible Answers:

Symmetric

Transitive

Commutative

Reflexive

Associative

Correct answer:

Symmetric

Explanation:

If an equality is true, then it can be correctly stated with the expressions in either order with equal validity. This is the symmetric property of equality.

Example Question #6 : Properties And Identities

What property of arithmetic is demonstrated below?

Possible Answers:

Commutative

Associative

Identity

Transitive

Distributive

Correct answer:

Commutative

Explanation:

The statement shows that two numbers can be added in either order to yield the same sum. This is the commutative property of addition.

Example Question #7 : Properties And Identities

Which of the following sets is not closed under multiplication?

Possible Answers:

All of the sets in the other four responses are closed under multiplication.

Correct answer:

Explanation:

A set is closed under multiplication if and only the product of any two (not necessarily distinct) elements of that set is itself an element of that set. 

 

 is closed under multiplication since the product of two even numbers is even:

 

 is closed under multiplication since the product of two perfect squares is a perfect square:

 

 is closed under multiplication since the product of two square roots of positive integers is the square root of a positve integer:

 

But , as can be seen here, is not closed under multiplication:

Example Question #71 : Mathematical Relationships

Which expression is not equal to 0 for all positive values of ?

Possible Answers:

All four expressions given in the other choices are equal to 0 for all positive values of .

Correct answer:

Explanation:

 is the correct choice.

 for all values of , since, by the zero property of multiplication, any number multiplied by 0 yields product 0.

 for all values of  - this is a direct statement of the inverse property of addition.

, since 0 raised to any positive power yields a result of 0. 

, since any nonxero number raised to the power of 0 yields a result of 1.

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