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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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All SAT II Math II Resources

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

Example Questions

Example Question #1 : Range And Domain

What is the domain of the function? $y=\sqrt{-10x+3}$

Possible Answers:

$-\frac{3}{10}\leq x\leq \frac{3}{10}$

$x\leq \frac{3}{10}$

$\textup{All real numbers.}$

$x\leq- \frac{3}{10}$

$x\geq \frac{3}{10}$

Correct answer:

$x\leq \frac{3}{10}$

Explanation:

Notice this function resembles the parent function $y=\sqrt {x}$ . The value of must be zero or greater.

Set up an inequality to determine the domain of .

$-10x+3\geq 0$

Subtract three from both sides.

$-10x+3-3\geq 0-3$

$-10x\geq -3$

Divide by negative ten on both sides. The sign will switch.

$\frac{-10x}{-10}\geq \frac{-3}{-10}$

The domain is: $x\leq \frac{3}{10}$

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Example Question #3 : Properties Of Functions And Graphs

What is the range of the function $f(x)=\frac{2}{x}-3$ ?

Possible Answers:

All real numbers.

All real numbers except .

Correct answer:

All real numbers except .

Explanation:

Start by considering the term $\frac{2}{x}$ . $\frac{2}{x}$ will hold for all values of , except when x=0 . Thus, $\frac{2}{x}-3$ must be defined by all values except since the equation is just shifted down by .

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Example Question #11 : Properties Of Functions And Graphs

What is the range of the equation $y=\frac{1}{5}$ ?

Possible Answers:

$[\frac{1}{5},\infty]$

$\textup{There is no range.}$

$[\frac{1}{5}]$

$(-\infty, \infty)$

$[-\frac{1}{5}, \frac{1}{5}]$

Correct answer:

$[\frac{1}{5}]$

Explanation:

The equation given represents a horizontal line. This means that every y-value on the domain is equal to $\frac{1}{5}$ .

The answer is: $[\frac{1}{5}]$

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Example Question #1 : X Intercept And Y Intercept

What is the x-intercept and y-intercept of:

y=2x-8

Possible Answers:

x-intercept= 4

y-intercept= -8

x-intercept=2

y-intercept=-4

x-intercept = 1

y-intercept = -2

x-intercept=-8

y-intercept=4

Correct answer:

x-intercept= 4

y-intercept= -8

Explanation:

The x-intercept is the value of x that will result in the y value equalling zero and the y-intercept is the y value that results when the x equals zero.

Therefore we replace x with zero to find the y-intecerpt.

y=2(0)-8

y=-8

Now we replace the y with a zero and find our x-intercept

0=2x-8

8=2x

4=x

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Example Question #2 : X Intercept And Y Intercept

What is the y-intercept and x-intercept of the function:

y-4=x+8

Possible Answers:

x-intercept=12

y-intercept=12

x-intercept=-12

y-intercept=12

x-intercept=-10

y-intercept=10

x-intercept=-1

y-intercept=2

Correct answer:

x-intercept=-12

y-intercept=12

Explanation:

To find the x and y intercept of the function we need to do algebraic opperations first and then plug in zero for x to find the y-intercept and plug in zero for y to find the x-intercept.

y-4=x+8

y=x+12

y-intercept

y=0+12=12

x-intercept

0=x+12

-12=x

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Example Question #3 : X Intercept And Y Intercept

Define $g(x)=5- \log _{4}\left ( x+5 \right )$ .

Give the -coordinate of the -intercept of the graph of (nearest hundredth).

Possible Answers:

3.84

4.83

4.14

6.16

4.60

Correct answer:

3.84

Explanation:

Evaluate g(0) :

$g(x)=5- \log _{4}\left ( x+5 \right )$

$g(0)=5- \log _{4}\left ( 0+5 \right )$

$=5- \log _{4} 5$

$=5- \frac{\ln 5}{\ln 4}$

$\approx 5- \frac{1.6094}{1.3863}$

$\approx 5- 1.16$

$\approx 3.84$

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Example Question #4 : X Intercept And Y Intercept

Define $f(x) = 2 \cdot 3^{x-4}- 7$

Give the -coordinate of the -intercept of the graph of (nearest hundredth).

Possible Answers:

4.42

6.98

4.18

The graph of has no -intercept.

5.14

Correct answer:

5.14

Explanation:

Set f(x) = 0 and solve for :

$f(x) = 2 \cdot 3^{x-4}- 7$

$2 \cdot 3^{x-4}- 7= 0$

$2 \cdot 3^{x-4}=7$

$3^{x-4}=\frac{7}{2} = 3.5$

$\ln \left (3^{x-4} \right )= \ln 3.5$

$(x-4 ) \ln 3 = \ln 3.5$

$x-4 = \frac{\ln 3.5}{ \ln 3} \approx \frac{1.2528}{1.0986} \approx 1.14$

$x\approx 5.14$

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Example Question #5 : X Intercept And Y Intercept

Define $g(x) = 3 + \sqrt[4]{3x-5}$ .

Give the -coordinate of the -intercept of the graph of (nearest hundredth).

Possible Answers:

1.50

1.68

4.50

4.32

The graph of has no -intercept.

Correct answer:

The graph of has no -intercept.

Explanation:

Evaluate g(0) :

$g(x) = 3 + \sqrt[4]{3x-5}$

$g(0) = 3 + \sqrt[4]{3\cdot 0-5}$

$g(0) = 3 + \sqrt[4]{ -5}$

A negative number does not have a real even-numbered root, so g(0) is not a real number. Therefore, the graph of has no -intercept.

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Example Question #5 : X Intercept And Y Intercept

Define $f(x) = 4 + \sqrt[5]{2x-9}$ .

Give the -coordinate of the -intercept of the graph of (nearest hundredth).

Possible Answers:

The graph of has no -intercept.

5.20

5.55

2.45

2.80

Correct answer:

2.45

Explanation:

Evaluate f(0) :

$f(x) = 4 + \sqrt[5]{2x-9}$

$f(0) = 4 + \sqrt[5]{2 \cdot 0 -9}$

$= 4 + \sqrt[5]{ -9}$

$\approx 4 + (-1.55)$

$\approx 2.45$

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Example Question #3 : X Intercept And Y Intercept

Define $h(x) = 12 + \sqrt[3]{3x-7}$ .

Give the -coordinate of the -intercept of the graph of (nearest hundredth).

Possible Answers:

13.17

The graph of has no -intercept.

13.91

10.83

10.09

Correct answer:

10.09

Explanation:

Evaluate h(0) :

$h(x) = 12 + \sqrt[3]{3x-7}$

$h(0) = 12 + \sqrt[3]{3\cdot 0 -7}$

$= 12 + \sqrt[3]{ -7}$

$\approx 12 +(-1.91)$

$\approx 10.09$

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All SAT II Math II Resources

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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 #1 : Range And Domain

Example Question #3 : Properties Of Functions And Graphs

Example Question #11 : Properties Of Functions And Graphs

Example Question #1 : X Intercept And Y Intercept

Example Question #2 : X Intercept And Y Intercept

Example Question #3 : X Intercept And Y Intercept

Example Question #4 : X Intercept And Y Intercept

Example Question #5 : X Intercept And Y Intercept

Example Question #5 : X Intercept And Y Intercept

Example Question #3 : X Intercept And Y Intercept

All SAT II Math II Resources

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