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SAT II Math II : Mathematical Relationships

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

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All SAT II Math II Resources

2 Diagnostic Tests 130 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #25 : Absolute Value

Solve:

$\left | 135\right |$

Possible Answers:

135

135e

ln(135)

Correct answer:

135

Explanation:

The lines on the outside of this problem indicate it is an absolute value problem. When solving with absolute value, remember that it is a measure of displacement from 0, meaning the answer will always be positive.

$\left | 135\right |=135$

For this problem, that gives us a final answer of 135.

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Example Question #26 : Absolute Value

Solve:

$\left | -12\right |$

Possible Answers:

$\frac{-1}{12}$

log(-12)

Correct answer:

Explanation:

$\left | -12\right |=12$

For this problem, that gives us a final answer of 12.

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Example Question #27 : Absolute Value

Solve:

$\left | 25\right |$

Possible Answers:

$\frac{1}{25}$

Correct answer:

Explanation:

$\left | 25\right |=25$

For this problem, that gives us a final answer of 25.

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Example Question #1 : Properties And Identities

What property of arithmetic is demonstrated below?

y + 8 = 8 + y

Possible Answers:

Transitive

Identity

Distributive

Commutative

Associative

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.

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Example Question #2 : Properties And Identities

What property of arithmetic is demonstrated below?

0 + Z = Z

Possible Answers:

Transitive

Identity

Inverse

Reflexive

Distributive

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.

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Example Question #3 : Properties And Identities

What property of arithmetic is demonstrated below?

M + (-M) = 0

Possible Answers:

Associative

Inverse

Identity

Symmetric

Transitive

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.

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Example Question #4 : Properties And Identities

What property of arithmetic is demonstrated below?

$m \angle ABC = m \angle ABC$

Possible Answers:

Symmetric

Reflexive

Transitive

Commutative

Symmetric

Correct answer:

Reflexive

Explanation:

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

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Example Question #5 : Properties And Identities

What property of arithmetic is demonstrated below?

If $m \angle 1 = m \angle 2$ then $m \angle 2 = m \angle 1$ .

Possible Answers:

Transitive

Associative

Commutative

Reflexive

Symmetric

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.

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Example Question #6 : Properties And Identities

What property of arithmetic is demonstrated below?

$m \angle ABC + 45^{\circ } = 45^{\circ } + m \angle ABC$

Possible Answers:

Commutative

Identity

Associative

Distributive

Transitive

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.

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Example Question #7 : Properties And Identities

Which of the following sets is not closed under multiplication?

Possible Answers:

$\left \{ 2, 4, 6, 8, 10...\right \}$

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

$\left \{ i, 2i, 3i, 4i, 5i...\right \}$

$\left \{ 1, 4, 9, 16, 25,...\right \}$

$\left \{ \sqrt{1}, \sqrt{2}, \sqrt{3}, \sqrt{4}, \sqrt{5} ... \right \}$

Correct answer:

$\left \{ i, 2i, 3i, 4i, 5i...\right \}$

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.

$\left \{ 2, 4, 6, 8, 10...\right \}$ is closed under multiplication since the product of two even numbers is even:

$2N \cdot 2M = 4MN = 2 (2MN)$

$\left \{ 1, 4, 9, 16, 25,...\right \}$ is closed under multiplication since the product of two perfect squares is a perfect square:

$N^{2} \cdot M^{2} = (NM)^{2}$

$\left \{ \sqrt{1}, \sqrt{2}, \sqrt{3}, \sqrt{4}, \sqrt{5} ... \right \}$ is closed under multiplication since the product of two square roots of positive integers is the square root of a positve integer:

$\sqrt{N} \cdot \sqrt{M} = \sqrt{NM}$

But $\left \{ i, 2i, 3i, 4i, 5i...\right \}$ , as can be seen here, is not closed under multiplication:

$2i \cdot 3i = 2\cdot 3 \cdot i \cdot i = 6 \cdot i^{2} = 6 (-1)= -6 \notin \left \{ i, 2i, 3i, 4i, 5i...\right \}$

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All SAT II Math II Resources

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SAT II Math II : Mathematical Relationships

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

All SAT II Math II Resources

Example Questions

Example Question #25 : Absolute Value

Example Question #26 : Absolute Value

Example Question #27 : Absolute Value

Example Question #1 : Properties And Identities

Example Question #2 : Properties And Identities

Example Question #3 : Properties And Identities

Example Question #4 : Properties And Identities

Example Question #5 : Properties And Identities

Example Question #6 : Properties And Identities

Example Question #7 : Properties And Identities

All SAT II Math II Resources

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