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SAT II Math II : Functions and Graphs

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 : Slope

What is the slope of the function:

2y-3=8x+13

Possible Answers:

Correct answer:

Explanation:

For this question we need to get the function into slope intercept form first which is

y=mx+b where the m equals our slope.

In our case we need to do algebraic opperations to get it into the desired form

2y-3=8x+13

2y=8x+16

$y=\frac{8x+16}{2}$

y=4x+8

Therefore our slope is 4

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Example Question #2 : Slope

Find the slope of the following equation:

2x+3y=6

Possible Answers:

$\frac{3}{2}$

$\frac{-2}{3}$

Correct answer:

$\frac{-2}{3}$

Explanation:

To find the slope for a given equation, it needs to first be put into the "y=mx+b" format. Then our slope is the number in front of the x, or the "m". For this equation this looks as follows:

First subtract 2x from both sides:

2x+3y=6

-2x -2x

That gives us the following:

3y=-2x+6

Divide all three terms by three to get "y" by itself:

$\frac{3y}{3}=\frac{-2x}{3}+\frac{6}{3}\rightarrow y=\frac{-2x}{3}+2$

This means our "m" is -2/3

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Example Question #3 : Slope

Find the slope of the following equation:

4y-x=7

Possible Answers:

$\frac{7}{4}$

$\frac{1}{4}$

Correct answer:

$\frac{1}{4}$

Explanation:

To find the slope for a given equation, it needs to first be put into the "y=mx+b" format. Then our slope is the number in front of the x, or the "m". For this equation this looks as follows:

First add x to both sides:

4y-x=7

That gives us the following:

4y=x+7

Divide all three terms by four to get "y" by itself:

$\frac{4y}{4}=\frac{x}{4}+\frac{7}{3}\rightarrow y=\frac{x}{4}+\frac{7}{4}$

This means our "m" is 1/4

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Example Question #1 : Slope

Find the slope of the following equation:

y=6x+3

Possible Answers:

$\frac{1}{6}$

Correct answer:

Explanation:

To find the slope for a given equation, it needs to first be put into the "y=mx+b" format. Then our slope is the number in front of the x, or the "m". For this equation this looks as follows:

y=6x+3

Our equation is already in the "y=mx+b" format, so our "m" is 6.

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Example Question #2 : Slope

Find the slope of the following equation:

y=6-2x

Possible Answers:

Correct answer:

Explanation:

To find the slope for a given equation, it needs to first be put into the "y=mx+b" format. Then our slope is the number in front of the x, or the "m". For this equation this looks as follows:

y=6-2x

To put our equation in the "y=mx+b" format, flip the two terms on the right side of the equation:

y=-2x+6

So our "m" in this case is -2.

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Example Question #1 : Slope

Find the slope given the equation: y=-7x+7y

Possible Answers:

$\frac{7}{6}$

$\frac{8}{7}$

$-\frac{7}{6}$

$\frac{7}{8}$

Correct answer:

$\frac{7}{6}$

Explanation:

Subtract on both sides.

y-7y=-7x+7y-7y

Simplify both sides.

-6y = -7x

Divide by negative 6 on both sides.

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

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

The slope is: $\frac{7}{6}$

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Example Question #6 : Slope

Find the slope of the equation: $\frac{1}{4}y = 2x-2y$

Possible Answers:

$\textup{There is no slope.}$

$\frac{8}{9}$

$\frac{7}{8}$

Correct answer:

$\frac{8}{9}$

Explanation:

To determine the slope, we need the equation in slope intercept form.

y=mx+b

Multiply by four on both sides to eliminate the fraction.

$\frac{1}{4}y \cdot 4=4 (2x-2y)$

y= 8x-8y

Add on both sides.

y+8y= 8x-8y+8y

Combine like-terms.

9y = 8x

Divide by nine on both sides.

$\frac{9y }{9}= \frac{8x}{9}$

$y=\frac{8}{9}x$

The value of , or the slope, is $\frac{8}{9}$ .

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Example Question #11 : Slope

Given the points (3,8) and (-1,3) , what is the slope?

Possible Answers:

$-\frac{4}{5}$

$-\frac{2}{5}$

$-\frac{5}{4}$

$\frac{5}{4}$

$-\frac{5}{2}$

Correct answer:

$\frac{5}{4}$

Explanation:

Write the slope equation.

$m= \frac{y_2-y_1}{x_2-x_1}$

Substitute the points and solve for the slope.

$m=\frac{3-8}{-1-3} = \frac{-5}{-4}$

The answer is: $\frac{5}{4}$

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Example Question #41 : Properties Of Functions And Graphs

What is the vertex of y=-3x^2-5x+3 ? Is it a max or min?

Possible Answers:

$-\frac{5}{6}, \textup{Max}$

$-\frac{5}{3}, \textup{Max}$

$\frac{5}{6}, \textup{Min}$

$-\frac{5}{3}, \textup{Min}$

$-\frac{5}{6}, \textup{Min}$

Correct answer:

$-\frac{5}{6}, \textup{Max}$

Explanation:

The polynomial is in standard form of a parabola.

y=ax^2+bx+c

To determine the vertex, first write the formula.

$x=-\frac{b}{2a}$

Substitute the coefficients.

$x=-\frac{-5}{2(-3)} = -\frac{5}{6}$

Since the is negative is negative, the parabola opens down, and we will have a maximum.

The answer is: $-\frac{5}{6}, \textup{Max}$

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Example Question #1 : Maximum And Minimum

Given the parabola equation y=4x-3x^2 , what is the max or minimum, and where?

Possible Answers:

$\textup{Max}, (-\frac{2}{3},-4)$

$\textup{Min}, (-\frac{2}{3},-4)$

$\textup{Max}, (\frac{2}{3}, \frac{4}{3})$

$\textup{Min}, (\frac{2}{3}, \frac{4}{3})$

$\textup{Max}, (\frac{2}{3},4)$

Correct answer:

$\textup{Max}, (\frac{2}{3}, \frac{4}{3})$

Explanation:

The parabola is in the form: y=ax^2+bx+c

y=-3x^2+4x

The vertex formula will determine the x-value of the max or min. Since the value of is negative, the parabola will open downward, and there will be a maximum.

Write the vertex formula and substitute the correct coefficients.

$x=-\frac{b}{2a} = -\frac{4}{2(-3)} = \frac{2}{3}$

Substitute this value back in the parabolic equation to determine the y-value.

$y=-3( \frac{2}{3})^2+4( \frac{2}{3}) = \frac{4}{3}$

The answer is: $\textup{Max}, (\frac{2}{3}, \frac{4}{3})$

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All SAT II Math II Resources

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SAT II Math II : Functions and Graphs

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

All SAT II Math II Resources

Example Questions

Example Question #1 : Slope

Example Question #2 : Slope

Example Question #3 : Slope

Example Question #1 : Slope

Example Question #2 : Slope

Example Question #1 : Slope

Example Question #6 : Slope

Example Question #11 : Slope

Example Question #41 : Properties Of Functions And Graphs

Example Question #1 : Maximum And Minimum

All SAT II Math II Resources

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