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SAT II Math II : SAT Subject Test in Math II

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

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Example Questions

Example Question #151 : Sat Subject Test In Math Ii

varies directly as both and the square of .

If m = 10 and v = 40 , then E= 8,000 .

Evaluate if m = 15 and v = 30 .

Possible Answers:

E = 6,750

E = 9,481

E = 9,000

E = 10,125

E = 13,500

Correct answer:

E = 6,750

Explanation:

varies directly as both and the square of . This means that for some constant of variation ,

$\frac{E}{mv^{2}} = k$ .

Alternatively stated,

$\frac{E_{1}}{m_{1}v_{1}^{2}} = \frac{E_{2}}{m_{2}v_{2}^{2}}$ .

We can substitute the initial conditions for the variables on the left side and the final conditions for those on the right side, then solve for $E_{2}$ :

$\frac{8,000}{10 \cdot 40^{2}} = \frac{E_{2}}{15 \cdot 30^{2}}$

$\frac{8,000}{10 \cdot 40^{2}} \cdot 15 \cdot 30^{2} = \frac{E_{2}}{15 \cdot 30^{2}} \cdot 15 \cdot 30^{2}$

$E_{2} = \frac{8,000 \cdot 15 \cdot 30^{2}}{10 \cdot 40^{2}} = \frac{108,000,000}{16,000}= 6,750$

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Example Question #151 : Sat Subject Test In Math Ii

$4 \sqrt[4] {a}+ 7 \sqrt[4] {b} =18$

$3\sqrt[4] {a} -5 \sqrt[4] {b} = 34$

Evaluate .

Possible Answers:

The system has no solution.

4,096

Correct answer:

4,096

Explanation:

Rewrite the two equations by setting $x = \sqrt [4] {a}$ and $y = \sqrt [4] {b}$ and substituting:

$4 \sqrt[4] {a}+ 7 \sqrt[4] {b} =18$

4x+7y = 18

$3\sqrt[4] {a} -5 \sqrt[4] {b} = 34$

3x-5y = 34

The result is a two-by-two linear system in terms of and :

4x+7y = 18

3x-5y = 34

This can be solved, among other ways, using Gaussian elimination on an augmented matrix:

$\begin{bmatrix} 4& 7\\ 3& -5 \end{matrix} \begin{vmatrix} 18 \\ 34 \\ \end{bmatrix}$

Perform row operations until the left two columns show identity matrix $\begin{bmatrix} 1 & 0\\ 0 &1 \end{bmatrix}$ . One possible sequence:

$R1-R2 \rightarrow R1$

$\begin{bmatrix} 4 - 3 & 7- (-5 )\\ 3& -5 \end{matrix} \begin{vmatrix} 18 - 34 \\ 34 \\ \end{bmatrix}$

$\begin{bmatrix} 1 & 12 \\ 3& -5 \end{matrix} \begin{vmatrix} -16 \\ 34 \\ \end{bmatrix}$

$R2 - 3R1 \rightarrow R2$

$\begin{bmatrix} 1 & 12 \\ 3 - 3(1)& -5 - 3(12) \end{matrix} \begin{vmatrix} -16 \\ 34 - 3(-16) \\ \end{bmatrix}$

$\begin{bmatrix} 1 & 12 \\ 0& -41\end{matrix} \begin{vmatrix} -16 \\ 82\\ \end{bmatrix}$

$R2 \div (-41 )\rightarrow R2$

$\begin{bmatrix} 1 & 12 \\ 0\div (-41 )& -41\div (-41 )\end{matrix} \begin{vmatrix} -16 \\ 82\div (-41 )\\ \end{bmatrix}$

$\begin{bmatrix} 1 & 12 \\ 0& 1 \end{matrix} \begin{vmatrix} -16 \\-2\\ \end{bmatrix}$

$R1 - 12 R2 \rightarrow R1$

$\begin{bmatrix} 1 - 12(0) & 12 - 12(1) \\ 0& 1 \end{matrix} \begin{vmatrix} -16 - 12(-2) \\ 2\\ \end{bmatrix}$

$\begin{bmatrix} 1 & 0 \\ 0& 1 \end{matrix} \begin{vmatrix} 8 \\ 2\\ \end{bmatrix}$

x= 8 and y = 2 . In the former equation, substitute $\sqrt [4] {a}$ back for , and raise both sides to the power of 4:

$\sqrt [4] {a} = 8$

$(\sqrt [4] {a}) ^{4}= 8^{4}$

a = 4,096

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Example Question #151 : Sat Subject Test In Math Ii

Which of the following phrases can be written as the algebraic expression $\left |8-a \right |$ ?

Possible Answers:

The absolute value of the product of negative eight and a number

The absolute value of the difference of eight and a number

Eight subtracted from the absolute value of a number

Eight decreased by the absolute value of a number

The absolute value of the difference of a number and eight

Correct answer:

The absolute value of the difference of eight and a number

Explanation:

$\left |8-a \right |$ is the absolute value of 8 - a , which is the difference of eight and a number. Therefore, $\left |8-a \right |$ is "the absolute value of the difference of eight and a number."

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Example Question #152 : Sat Subject Test In Math Ii

Which of the following phrases can be written as the algebraic expression 7 - (-x) ?

Possible Answers:

The absolute value of the difference of seven and a number

Seven decreased by the absolute value of a number

The opposite of a number decreased by seven

Seven decreased by the opposite of a number

The opposite of the difference of seven and a number

Correct answer:

Seven decreased by the opposite of a number

Explanation:

7 - (-x) is seven decreased by , which is the opposite of a number; therefore, is "seven decreased by the opposite of a number."

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Example Question #153 : Sat Subject Test In Math Ii

Which of the following phrases can be represented by the algebraic expression $\frac{1}{9 - x}$ ?

Possible Answers:

One divided into the difference of nine and a number

Nine decreased by the multiplicative inverse of a number

The multiplicative inverse of the difference of a number and nine

Nine less than by the multiplicative inverse of a number

The multiplicative inverse of the difference of nine and a number

Correct answer:

The multiplicative inverse of the difference of nine and a number

Explanation:

$\frac{1}{9 - x}$ is the multiplicative inverse of 9 - x , which is the difference of nine and a number. Therefore, $\frac{1}{9 - x}$ is "the multiplicative inverse of the difference of nine and a number".

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Example Question #154 : Sat Subject Test In Math Ii

Which of the following phrases can be represented by the algebraic expression

$\sqrt[3]{x} - 10$

Possible Answers:

Ten decreased by three times the square root of a number

Ten less than the cube root of a number

Ten less than three times the square root of a number

Ten decreased by the cube root of a number

The cube root of the difference of a number and ten

Correct answer:

Ten less than the cube root of a number

Explanation:

$\sqrt[3]{x} - 10$ is ten less than $\sqrt[3]{x}$ , which is the cube root of a number; therefore, $\sqrt[3]{x} - 10$ is "ten less than the cube root of a number".

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Example Question #155 : Sat Subject Test In Math Ii

Which of the following phrases can be represented by the algebraic expression

$20 - \sqrt{x}$

Possible Answers:

The square root of the difference of twenty and a number

Negative twenty multiplied by the square root of a number

The square root of the difference of a number and twenty

Twenty less than the square root of a number

Twenty decreased by the square root of a number

Correct answer:

Twenty decreased by the square root of a number

Explanation:

$20 - \sqrt{x}$ is twenty decreased by $\sqrt{x}$ , which is the square root of a number, so $20 - \sqrt{x}$ is "twenty decreased by the square root of a number".

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Example Question #1 : Translating Words To Linear Equations

Adult tickets to the zoo sell for $\$9$ ; child tickets sell for $\$5$ . On a given day, the zoo sold $5\textup,450$ tickets and raised $\$36\textup,330$ in admissions. How many adult tickets were sold?

Possible Answers:

$2\textup,150$

$2\textup,240$

$2\textup,180$

$2\textup,310$

$2\textup,270$

Correct answer:

$2\textup,270$

Explanation:

Let be the number of adult tickets sold. Then the number of child tickets sold is $5\textup,450 - A$ .

The amount of money raised from adult tickets is ; the amount of money raised from child tickets is $5 \left (5\textup,450 - A \right )$ . The sum of these money amounts is $36,330 , so the amount of money raised can be defined by the following equation:

$9A + 5 (5\textup,450-A) = 36\textup,330$

To find the number of adult tickets sold, solve for :

$9A + 27\textup,250-5A = 36\textup,330$

$4A + 27\textup,250 = 36\textup,330$

$4A + 27\textup,250 - 27\textup,250= 36\textup,330- 27\textup,250$

$4A = 9,080\textup$

$4A \div 4 = 9\textup,080 \div 4$

$A = 2\textup,270$

$2\textup,270$ adult tickets were sold.

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Example Question #4 : Single Variable Algebra

Sarah sells lemonade at the concession stands. She charges fifty cents per cup of lemonade, and twenty five cents for refills. What is the equation that represents the total that she will make from the lemonade stand using the variables cups and refills ?

Possible Answers:

$T= \$0.50 C+\$0.25 R$

T= 50 R+25 C

T=50 C+25 R

$T= \$0.50 R+\$0.25 C$

$T=\$0.75CR$

Correct answer:

$T= \$0.50 C+\$0.25 R$

Explanation:

Sarah charges fifty cents per cup of lemonade:

$\$0.50 C$

Sarah charges twenty five cents for refills:

$\$0.25 R$

Set up the equation by adding the totals.

The answer is: $T= \$0.50 C+\$0.25 R$

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Example Question #1 : How To Simplify Binomials

Solve for :

x^2+2 = 6x-6

Possible Answers:

x=1, 2

x=1,-2

x=-2,-4

x=2,4

Correct answer:

x=2,4

Explanation:

To solve for , you need to isolate it to one side of the equation. You can subtract the from the right to the left. Then you can add the 6 from the right to the left:

x^2+2 = 6x-6

x^2-6x+2 = -6

x^2-6x+8 = 0

Next, you can factor out this quadratic equation to solve for . You need to determine which factors of 8 add up to negative 6:

$(x \ \ \ \ \ \)(x \ \ \ \ \ \) = 0$

(x-2)(x-4)=0

Finally, you set each binomial equal to 0 and solve for :

$x=2 \ \ \ \ \ \ x=4$

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SAT II Math II : SAT Subject Test in Math II

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

All SAT II Math II Resources

Example Questions

Example Question #151 : Sat Subject Test In Math Ii

Example Question #151 : Sat Subject Test In Math Ii

Example Question #151 : Sat Subject Test In Math Ii

Example Question #152 : Sat Subject Test In Math Ii

Example Question #153 : Sat Subject Test In Math Ii

Example Question #154 : Sat Subject Test In Math Ii

Example Question #155 : Sat Subject Test In Math Ii

Example Question #1 : Translating Words To Linear Equations

Example Question #4 : Single Variable Algebra

Example Question #1 : How To Simplify Binomials

All SAT II Math II Resources

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