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SAT II Math II : Mathematical Relationships

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

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

Example Questions

Example Question #7 : Properties And Identities

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 .

-x + x

$\left (x+1 \right )^{0}$

0 (x+1)

$0^{x}$

Correct answer:

$\left (x+1 \right )^{0}$

Explanation:

$\left (x+1 \right )^{0}$ is the correct choice.

0 (x+1) = 0 for all values of , since, by the zero property of multiplication, any number multiplied by 0 yields product 0.

-x + x = 0 for all values of - this is a direct statement of the inverse property of addition.

$0^{x} = 0$ , since 0 raised to any positive power yields a result of 0.

$\left (x+1 \right )^{0} = 1$ , since any nonxero number raised to the power of 0 yields a result of 1.

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Example Question #1 : Ratios And Proportions

Solve the proportion: $\frac{2x+3}{2} = \frac{1}{3}$

Possible Answers:

$\frac{7}{6}$

$-\frac{7}{6}$

$-\frac{1}{6}$

Correct answer:

$-\frac{7}{6}$

Explanation:

To solve the proportion, cross multiply the terms.

3(2x+3) = 1(2)

6x+9 = 2

Subtract 9 on both sides.

6x+9 -9= 2-9

6x=-7

Divide by 6 on both sides.

$\frac{6x}{6}=\frac{-7}{6}$

The answer is: $-\frac{7}{6}$

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Example Question #72 : Mathematical Relationships

Solve the ratio: $\frac{5}{9} = \frac{x}{6}$

Possible Answers:

$\frac{54}{5}$

$\frac{10}{3}$

$\frac{3}{10}$

$\frac{11}{9}$

$\frac{5}{54}$

Correct answer:

$\frac{10}{3}$

Explanation:

To solve the proportion, cross multiply.

5(6) = 9x

30=9x

Divide by 9 on both sides.

$\frac{30}{9}=\frac{9x}{9}$

Reduce the fractions.

The answer is: $\frac{10}{3}$

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Example Question #1 : Ratios And Proportions

Determine the value of : $\frac{2x-2}{8} = \frac{8x-2}{3}$

Possible Answers:

$-\frac{11}{29}$

$-\frac{1}{3}$

$-\frac{5}{29}$

$\frac{5}{29}$

$-\frac{5}{4}$

Correct answer:

$\frac{5}{29}$

Explanation:

Cross multiply the fractions.

3(2x-2) = 8(8x-2)

Simplify both sides.

6x-6 = 64x-16

Subtract on both sides.

6x-6 -(6x)= 64x-16-(6x)

-6 = 58x-16

Add 16 on both sides.

-6+16 = 58x-16+16

10= 58x

Divide by 58 on both sides.

$\frac{10}{58}= \frac{58x}{58}$

Reduce both fractions.

The answer is: $x = \frac{5}{29}$

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Example Question #1 : Ratios And Proportions

Solve the proportion: $\frac{x}{3} = \frac{2}{5}$

Possible Answers:

$\frac{15}{2}$

$\frac{6}{5}$

$\frac{5}{2}$

Correct answer:

$\frac{6}{5}$

Explanation:

Cross multiply both sides.

5x = 2(3)

Simplify and solve for x.

5x=6

$\frac{5x}{5}=\frac{6}{5}$

The answer is: $\frac{6}{5}$

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Example Question #1 : Ratios And Proportions

Solve the proportion: $\frac{3x}{5} = \frac{1}{3}$

Possible Answers:

$\frac{5}{6}$

$\frac{5}{9}$

$\frac{2}{3}$

$\frac{3}{2}$

Correct answer:

$\frac{5}{9}$

Explanation:

Cross multiply both sides.

3(3x) = 1(5)

9x=5

Divide by 9 on both sides.

$\frac{9x}{9}=\frac{5}{9}$

The answer is: $\frac{5}{9}$

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Example Question #2 : Ratios And Proportions

Solve the proportion: $\frac{3x}{4} = \frac{8}{3}$

Possible Answers:

$\frac{9}{2}$

$\frac{2}{9}$

$\frac{1}{2}$

$\frac{32}{9}$

Correct answer:

$\frac{32}{9}$

Explanation:

Cross multiply the two fractions.

3(3x) = 8(4)

9x=32

Divide by nine on both sides.

$\frac{9x}{9}=\frac{32}{9}$

The answer is: $\frac{32}{9}$

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Example Question #2 : Ratios And Proportions

Solve the proportion: $\frac{2x}{9} = \frac{7}{3}$

Possible Answers:

$\frac{14}{3}$

$\frac{3}{2}$

$\frac{6}{7}$

$\frac{21}{2}$

$\frac{7}{6}$

Correct answer:

$\frac{21}{2}$

Explanation:

Cross multiply the two fractions.

(2x)(3) = (7)(9)

6x = 63

Divide by six on both sides.

$\frac{6x }{6}= \frac{63}{6}$

The answer is: $\frac{21}{2}$

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Example Question #1 : Matrices

Multiply:

$\begin{bmatrix} x&7 \\ y& 3 \end{bmatrix}\begin{bmatrix} 2\\ 7 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix}2 x&7 \\7 y& 3 \end{bmatrix}$

$\begin{bmatrix} 2x+49\\ 2y+21 \end{bmatrix}$

$\begin{bmatrix} 2x+7y\\ 35 \end{bmatrix}$

$\begin{bmatrix}2 x&14 \\7 y& 21 \end{bmatrix}$

$\begin{bmatrix}98x\\ 42y\end{bmatrix}$

Correct answer:

$\begin{bmatrix} 2x+49\\ 2y+21 \end{bmatrix}$

Explanation:

The product of a 2 x 2 matrix and a 2 x 1 matrix is a 2 x 1 matrix.

Multiply each row in the first matrix by the column matrix by multiplying elements in corresponding positions, then adding the products, as follows:

$\begin{bmatrix} x&7 \\ y& 3 \end{bmatrix}\begin{bmatrix} 2\\ 7 \end{bmatrix}$

$=\begin{bmatrix} x \cdot 2+ 7 \cdot 7 \\ y \cdot 2 + 3 \cdot 7 \end{bmatrix}$ \

$=\begin{bmatrix} 2x + 49 \\ 2 y+ 21 \end{bmatrix}$

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Example Question #2 : Matrices

Multiply:

$\begin{bmatrix} x& 5\\ -4& 3 \end{bmatrix}\begin{bmatrix} 6\\ y \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} 30xy \\ -72y \end{bmatrix}$

$\begin{bmatrix} 6x+5y \\ 3y-24 \end{bmatrix}$

$\begin{bmatrix} 6x-4y \\ 3y+30 \end{bmatrix}$

$\begin{bmatrix}6 x&30\\ -4y& 3 y\end{bmatrix}$

$\begin{bmatrix}6 x&5\\ -4y& 3 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 6x+5y \\ 3y-24 \end{bmatrix}$

Explanation:

The product of a 2 x 2 matrix and a 2 x 1 matrix is a 2 x 1 matrix.

Multiply each row in the first matrix by the column matrix by multiplying elements in corresponding positions, then adding the products, as follows:

$\begin{bmatrix} x& 5\\ -4& 3 \end{bmatrix}\begin{bmatrix} 6\\ y \end{bmatrix}$

$= \begin{bmatrix} x \cdot 6 + 5\cdot y \\ -4\cdot 6 + 3 \cdot y \end{bmatrix}$

$= \begin{bmatrix} 6x+5y \\ 3y-24 \end{bmatrix}$

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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 #7 : Properties And Identities

Example Question #1 : Ratios And Proportions

Example Question #72 : Mathematical Relationships

Example Question #1 : Ratios And Proportions

Example Question #1 : Ratios And Proportions

Example Question #1 : Ratios And Proportions

Example Question #2 : Ratios And Proportions

Example Question #2 : Ratios And Proportions

Example Question #1 : Matrices

Example Question #2 : Matrices

All SAT II Math II Resources

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