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Common Core: High School - Number and Quantity : High School: Number and Quantity

Study concepts, example questions & explanations for Common Core: High School - Number and Quantity

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All Common Core: High School - Number and Quantity Resources

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Example Questions

Example Question #3 : Vector & Matrix Quantities

Vector $\vec{w}$ , has an initial point of (15, 6) , and a terminal point of (-7,1) . What is the slope of vector $\vec{w}$ ?

Possible Answers:

$\frac{5}{22}$

$-\frac{5}{22}$

$\frac{22}{5}$

Correct answer:

$\frac{5}{22}$

Explanation:

In order to figure out slope, we need to remember how to find slope. Slope can be found be doing rise over run, or simply the change in coordinates over the change in coordinates. In equation form it looks like

$\mbox{Slope}=\frac{y_2-y_1}{x_2-x_1}$ , where y_2, y_1 are the coordinates, and x_2, x_1 are the coordinates.

For this example, we will let y_2=1, y_1=6, x_2=-7, x_1=15 .

$\mbox{Slope}=\frac{1-6}{-7-15}=\frac{-5}{-22}=\frac{5}{22}$

Below is a visual representation of what we just did. The orange arrow is $\vec{w}$ .

Slope5

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Example Question #5 : Vector Magnitude And Direction: Ccss.Math.Content.Hsn Vm.A.1

Vector $\vec{w}$ , has an initial point of (3, 2) , and a terminal point of (-3,5) . What is the slope of vector $\vec{w}$ ?

Possible Answers:

$-\frac{1}{2}$

$\frac{1}{2}$

Correct answer:

$-\frac{1}{2}$

Explanation:

$\mbox{Slope}=\frac{y_2-y_1}{x_2-x_1}$ , where y_2, y_1 are the coordinates, and x_2, x_1 are the coordinates.

For this example, we will let y_2=5, y_1=2, x_2=-3, x_1=3 .

$\mbox{Slope}=\frac{5-2}{-3-3}=\frac{3}{-6}=-\frac{1}{2}$

Below is a visual representation of what we just did. The orange arrow is $\vec{w}$ .

Slope6

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Example Question #1 : Vector & Matrix Quantities

Vector $\vec{w}$ , has an initial point of (-3, -5) , and a terminal point of (-5,6) . What is the slope of vector $\vec{w}$ ?

Possible Answers:

$\frac{2}{11}$

$-\frac{11}{2}$

$\frac{11}{2}$

$-\frac{2}{11}$

Correct answer:

$-\frac{11}{2}$

Explanation:

$\mbox{Slope}=\frac{y_2-y_1}{x_2-x_1}$ , where y_2, y_1 are the coordinates, and x_2, x_1 are the coordinates.

For this example, we will let y_2=6, y_1=-5, x_2=-5, x_1=-3 .

$\mbox{Slope}=\frac{6-(-5)}{-5-(-3)}=\frac{6+5}{-5+3}=\frac{11}{-2}=-\frac{11}{2}$

Below is a visual representation of what we just did. The orange arrow is $\vec{w}$ .

Slope7

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Example Question #3 : Vector & Matrix Quantities

Vector $\vec{w}$ , has an initial point of (-20, 15) , and a terminal point of (0,-8) . What is the slope of vector $\vec{w}$ ?

Possible Answers:

$\frac{23}{20}$

$-\frac{20}{23}$

$-\frac{23}{20}$

$\frac{20}{23}$

Correct answer:

$\frac{23}{20}$

Explanation:

$\mbox{Slope}=\frac{y_2-y_1}{x_2-x_1}$ , where y_2, y_1 are the coordinates, and x_2, x_1 are the coordinates.

For this example, we will let y_2=-8, y_1=15, x_2=0, x_1=-20 .

$\mbox{Slope}=\frac{15-(-8)}{0-(-20)}=\frac{15+8}{0+20}=\frac{23}{20}$

Below is a visual representation of what we just did. The orange arrow is $\vec{w}$ .

Slope8

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Example Question #4 : Vector & Matrix Quantities

Vector $\vec{w}$ , has an initial point of (0, 2) , and a terminal point of (2,7) . What is the slope of vector $\vec{w}$ ?

Possible Answers:

$-\frac{2}{5}$

$\frac{2}{5}$

$\frac{5}{2}$

$-\frac{5}{2}$

Correct answer:

$\frac{5}{2}$

Explanation:

$\mbox{Slope}=\frac{y_2-y_1}{x_2-x_1}$ , where y_2, y_1 are the coordinates, and x_2, x_1 are the coordinates.

For this example, we will let y_2=7, y_1=2, x_2=2, x_1=0 .

$\mbox{Slope}=\frac{7-2}{2-0}=\frac{5}{2}$

Below is a visual representation of what we just did. The orange arrow is $\vec{w}$ .

Slope9

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Example Question #4 : Vector & Matrix Quantities

Vector $\vec{w}$ , has an initial point of (2, -10) , and a terminal point of (8,-1) . What is the slope of vector $\vec{w}$ ?

Possible Answers:

$\frac{3}{2}$

$\frac{2}{3}$

$-\frac{3}{2}$

$-\frac{2}{3}$

Correct answer:

$\frac{3}{2}$

Explanation:

$\mbox{Slope}=\frac{y_2-y_1}{x_2-x_1}$ , where y_2, y_1 are the coordinates, and x_2, x_1 are the coordinates.

For this example, we will let y_2=-1, y_1=-10, x_2=8, x_1=2 .

$\mbox{Slope}=\frac{-1-(-10)}{8-2}=\frac{-1+10}{8-2}=\frac{9}{6}=\frac{3}{2}$

Below is a visual representation of what we just did. The orange arrow is $\vec{w}$ .

Slope10

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Example Question #11 : Vector & Matrix Quantities

Vector $\vec{w}$ , has an initial point of (-6, 11) , and a terminal point of (10,-12) . What is the slope of vector $\vec{w}$ ?

Possible Answers:

$\frac{23}{16}$

$\frac{1}{21}$

$-\frac{1}{21}$

$-\frac{23}{16}$

Correct answer:

$-\frac{23}{16}$

Explanation:

$\mbox{Slope}=\frac{y_2-y_1}{x_2-x_1}$ , where y_2, y_1 are the coordinates, and x_2, x_1 are the coordinates.

For this example, we will let y_2=-12, y_1=11, x_2=10, x_1=11 .

$\mbox{Slope}=\frac{-12-11}{10-(-6)}=\frac{-23}{16}=-\frac{23}{16}$

Below is a visual representation of what we just did. The orange arrow is $\vec{w}$ .

Slope11

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Example Question #12 : Vector & Matrix Quantities

Vector $\vec{w}$ , has an initial point of (-11, -5) , and a terminal point of (11,1) . What is the slope of vector $\vec{w}$ ?

Possible Answers:

$-\frac{3}{11}$

$\frac{3}{11}$

$-\frac{11}{3}$

$\frac{11}{3}$

Correct answer:

$\frac{3}{11}$

Explanation:

$\mbox{Slope}=\frac{y_2-y_1}{x_2-x_1}$ , where y_2, y_1 are the coordinates, and x_2, x_1 are the coordinates.

For this example, we will let y_2=1, y_1=-5, x_2=11, x_1=-11 .

$\mbox{Slope}=\frac{1-(-5)}{11-(-11)}=\frac{1+5}{11+11}=\frac{6}{22}=\frac{3}{11}$

Below is a visual representation of what we just did. The orange arrow is $\vec{w}$ .

Slope12

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Example Question #1 : Vector Components: Ccss.Math.Content.Hsn Vm.A.2

What are the components of a vector that has a terminal point of (5,10) , and an initial point of (2,3) ?

Possible Answers:

<7,3>

<3.5, -3>

<3,7>

<-3,-7>

<0,0>

Correct answer:

<3,7>

Explanation:

In order to determine what the components of this vector has, we need to remember how to find components of a vector. It's simply the difference between the terminal point and initial point. The first step is to write an equation for what our "new" x and y are.

$x=\mbox{(x in terminal point)}-\mbox{(x in initial point) }$

$y=\mbox{(y in terminal point)}-\mbox{(y in initial point) }$

Now lets identify what these values are.

$\\ \mbox{(x in terminal point)}=5 \\ \mbox{(x in initial point)}=2 \\ \mbox{(y in terminal point)}=10\\ \mbox{(y in initial point)}= 3$

x=5-2=3

y=10-3=7

To write this in component form, we need to put our , and into .

So the final answer is <3,7>

Below is a visual representation of what we just did.

Term

The blue line is our original vector, and the red line is the same vector, but begins at the origin rather than at the initial point.

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Example Question #2 : Vector Components: Ccss.Math.Content.Hsn Vm.A.2

What are the components of a vector that has a terminal point of (5,-10) , and an initial point of (-2,3) ?

Possible Answers:

<-13,7>

<-13,-7>

<7,-13>

<-7,13>

<13,7>

Correct answer:

<7,-13>

Explanation:

n order to determine what the components of this vector has, we need to remember how to find components of a vector. It's simply the difference between the terminal point and initial point. The first step is to write an equation for what our "new" x and y are.

$x=\mbox{(x in terminal point)}-\mbox{(x in initial point) }$

$y=\mbox{(y in terminal point)}-\mbox{(y in initial point) }$

Now lets identify what these values are.

$\\ \mbox{(x in terminal point)}=5 \\ \mbox{(x in initial point)}=-2 \\ \mbox{(y in terminal point)}=-10\\ \mbox{(y in initial point)}= 3$

x=5-(-2)=7

y=-10-3=-13

To write this in component form, we need to put our , and into .

So the final answer is <7,-13>

Below is a visual representation of what we just did.

Comp2

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Common Core: High School - Number and Quantity : High School: Number and Quantity

Study concepts, example questions & explanations for Common Core: High School - Number and Quantity

All Common Core: High School - Number and Quantity Resources

Example Questions

Example Question #3 : Vector & Matrix Quantities

Example Question #5 : Vector Magnitude And Direction: Ccss.Math.Content.Hsn Vm.A.1

Example Question #1 : Vector & Matrix Quantities

Example Question #3 : Vector & Matrix Quantities

Example Question #4 : Vector & Matrix Quantities

Example Question #4 : Vector & Matrix Quantities

Example Question #11 : Vector & Matrix Quantities

Example Question #12 : Vector & Matrix Quantities

Example Question #1 : Vector Components: Ccss.Math.Content.Hsn Vm.A.2

Example Question #2 : Vector Components: Ccss.Math.Content.Hsn Vm.A.2

All Common Core: High School - Number and Quantity Resources

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