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GRE Subject Test: Math : Calculus

Study concepts, example questions & explanations for GRE Subject Test: Math

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2 Diagnostic Tests 148 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #9 : Slope & Intercept

The points given lie on a line. Find the slope.

-6,-4,-2,0

-3, -3, -3, -3

Possible Answers:

Slope is undefined.

m = 0

m=2

$m=-\frac{3}{2}$

Correct answer:

m = 0

Explanation:

slope = $\frac{rise}{run}$

rise = changes in y

run = changes in x

-6,-4,-2,0

-3, -3, -3, -3

There is zero change in the coordinates.

The change in the coordinates is that the numbers are increasing by 2 or +2.

slope = $\frac{0}{2}$

m = 0

If the coordinates are the same, then it will be a horizontal line. The slope of a horizontal line is 0.

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Example Question #51 : Calculus

Find the slope of a line that passes through A (3,-1) and B (6,5).

Possible Answers:

m=-2

$m=-\frac{1}{2}$

m=2

$m=\frac{1}{2}$

Correct answer:

m=2

Explanation:

The formula for slope is:

$m = \frac{y_{2} - y_{1}}{x_{2} -x_{1}}$

$m = \frac{5-(-1)}{6-3}$

$m = \frac{5+1}{6-3}$

$m = \frac{6}{3}$

m=2

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Example Question #52 : Calculus

Find the slope of a line that passes through the points S(1,2) and T (6,-8) .

Possible Answers:

$m=-\frac{1}{2}$

$m=\frac{1}{2}$

m=2

m=-2

Correct answer:

m=-2

Explanation:

The formula for slope is:

$m = \frac{y_{2} - y_{1}}{x_{2} -x_{1}}$

$m = \frac{-8-2}{6-1}$

$m = \frac{-10}{5}$

m=-2

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Example Question #53 : Calculus

Find the slope of a line that passes through the points G(-3,-1) and H (-2,-2) .

Possible Answers:

m=0

Slope is undefined.

m=-1

m=1

Correct answer:

m=-1

Explanation:

The formula for slope is:

$m = \frac{y_{2} - y_{1}}{x_{2} -x_{1}}$

$m= \frac{-2-(-1)}{-2- (-3)}$

$m = \frac{-2+1}{-2+3}$

$m=\frac{-1}{1}$

m=1

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Example Question #54 : Calculus

What is the slope of the line: 3x-6y=-14

Possible Answers:

m=1

$m=-\frac {1}{2}$

$m=\frac {1}{2}$

$m=\frac {7}{3}$

Correct answer:

$m=\frac {1}{2}$

Explanation:

Step 1: The current equation is in standard form, where x and y are both on one side of the equal sign..

Step 2: Change the equation to slope-intercept form.. Move the y to the other side

3x=6y-14

Step 3: Move the constant to the other side:

3x+14=6y

Step 4: Divide by the coefficient in front of :

$\frac {3x+14}{6}=\frac {6y}{6}$

Step 5: Split the left side into two fractions and simplify:

$\frac {3x}{6}+\frac {14}{6}=y$

$\rightarrow \frac {1}{2}x+\frac {7}{3}=y$

Step 6. Locate the slope. The slope is the coefficient of the x term.

The slope is $\frac {1}{2}$ , or $m=\frac {1}{2}$

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Example Question #31 : Coordinate Geometry

Find the y-intercept of the equation of a line: x+4y=12

Possible Answers:

b=-3

b=3

$b=\frac {1}{3}$

$b=-\frac {1}{3}$

Correct answer:

b=3

Explanation:

Step 1: Subtract from both sides:

$x-x+4y=-x+12 \implies 4y=-x+12$

Step 2: Divide by the coefficient of the y term..In this case, divide by .

$\frac {4y}{y}=\frac {-x+12}{4}$

Simplify and separate fraction on right side:

$y=-\frac{x}{4}+\frac {12}{4}\implies y=-\frac {1}{4}x+3$

Step 3: Locate the y-intercept (also known as b):

If we compare our equation to the general slope-intercept form: y=mx+b , we see that 3=b ..

The value of is .

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Example Question #51 : Calculus

What is the slope of the line: $2x-4y-8=0$

Possible Answers:

$2/3$

$1/3$

$1/2$

$1/8$

Correct answer:

$1/2$

Explanation:

Step 1: Move the $4y$ to the other side...

$2x-8=4y$

Step 2: Divide by $4$ on both sides...

$\frac {2x-8}{4}=y-> \frac {2x}{4}-\frac {8}{4}=y->\frac {x}{2}-2=y$

The slope is $\frac {1}{2}$ .

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Example Question #52 : Calculus

What is the y-intercept of the equation y=-2x+7 ?

Possible Answers:

Correct answer:

Explanation:

Step 1: Recall what the basic equation is for a line in slope-intercept form..

y=mx+b

m=slope, b=y-intercept...

Step 2: Find m and b in the equation given...

m=, b=..

b=y-intercept=

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Example Question #1 : Finding Equations Of Lines

What is the equation of the line (in slope-intercept form) that goes through the points: (2,4) and (7,8) ?

Possible Answers:

$y=-\frac {4}{5}x-\frac {12}{5}$

$y=-\frac {4}{5}x+\frac {12}{5}$

$y=\frac {4}{5}x+\frac {12}{5}$

$y=\frac {4}{5}x-\frac {12}{5}$

Correct answer:

$y=\frac {4}{5}x+\frac {12}{5}$

Explanation:

Step 1: Find the slope between the two points:

$\frac {y_2-y_1}{x_2-x_1}=\frac {8-4}{7-2}=\frac {4}{5}$

Step 2: Write the slope-intercept form:

$y=\frac {4}{5}x+b$

Step 3. Find b. Plug in (x,y) from one of the points:

$4=\frac {4}{5}(2)+b$

$4=\frac {8}{5}+b$

$4-\frac {8}{5}=b$

$\frac {20-8}{5}=b$

$\frac {12}{5}=b$
Step 4: Write out the full equation:

$y=\frac {4}{5}x+\frac {12}{5}$

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Example Question #1 : Finding Equations Of Lines

What is the equation of a line that passes through points (3,4) and (1,-2) in slope-intercept form?

Possible Answers:

y = 3x-13

y = 3x+13

y = 3x-5

y = 3x+5

Correct answer:

y = 3x-5

Explanation:

To find the equation of the line, first find the slope using the formula:

$m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

The points that the line passes through are (3,4) and (1,-2) .

$m = \frac{-2-4}{1-3}$

$m= \frac{-6}{-2}$

m = 3

Then pick one set of points and place in the form y = mx+b . Either set of points will give you the same equation. Points (3,4) were used.

$4 = 3\times 3 + b$

4 = 9 +b

Subtract from both sides of the equation.

4-9 = 9-9 +b

-5 = b

The equation of the line in slope-intercept form or is

y= 3x-5

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GRE Subject Test: Math : Calculus

Study concepts, example questions & explanations for GRE Subject Test: Math

All GRE Subject Test: Math Resources

Example Questions

Example Question #9 : Slope & Intercept

Example Question #51 : Calculus

Example Question #52 : Calculus

Example Question #53 : Calculus

Example Question #54 : Calculus

Example Question #31 : Coordinate Geometry

Example Question #51 : Calculus

Example Question #52 : Calculus

Example Question #1 : Finding Equations Of Lines

Example Question #1 : Finding Equations Of Lines

All GRE Subject Test: Math Resources

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