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Common Core: High School - Number and Quantity : Vector & Matrix Quantities

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

6 Diagnostic Tests 49 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #6 : Vector Representation Of Quantities (Velocity, Etc.): Ccss.Math.Content.Hsn Vm.A.3

John is cruising north down a river at $5\: \uptext{mph}$ , and the river has $10\: \uptext{mph}$ current due east. What is John's actual speed?

Possible Answers:

$11.2\:\text{mph}$

$15.2\:\text{mph}$

$12.2\:\text{mph}$

$14.2\:\text{mph}$

$13.2\:\text{mph}$

Correct answer:

$11.2\:\text{mph}$

Explanation:

In order to figure this out, we need to create a picture.

Screen shot 2016 03 18 at 10.44.23 am

Since John is traveling north, and the current is traveling east, they are perpendicular to each other. This means that they are $90^{\circ}$ to each other. The next step is to use the Pythagorean Theorem in order to solve for what speed John is actually going.

Recall that the Pythagorean Theorem is $h=\sqrt{A^2+B^2}$ , where is the hypotenuse, and , are the legs of the triangle, and A,B have a $90^{\circ}$ angle between them.

For our calculations, let A=5 , and B=15 .

$h=\sqrt{5^2+10^2}=\sqrt{25+100}=\sqrt{125}\approx11.2\:\uptext{mph}$

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Example Question #3 : Vector Representation Of Quantities (Velocity, Etc.): Ccss.Math.Content.Hsn Vm.A.3

Jack slides down a hill at $37\:\text{mph}$ , and throws a rock ahead of him at $20\:\text{mph}$ . How fast is the rock going?

Possible Answers:

$47\:\text{mph}$

$37\:\text{mph}$

$20\:\text{mph}$

$57\:\text{mph}$

$17\:\text{mph}$

Correct answer:

$57\:\text{mph}$

Explanation:

Since the rock is going in the same direction as Jack, we simply add the speed of the rock to how fast Jack is going down the hill.

$\text{Rock Speed}=37+20=57$

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Example Question #8 : Vector Representation Of Quantities (Velocity, Etc.): Ccss.Math.Content.Hsn Vm.A.3

If an airplane is flying south at $500\:\frac{\text{km}}{\text{hr}}$ , and there are winds going north at $150\:\frac{\text{km}}{\text{hr}}$ , how fast is the plane going?

Possible Answers:

$400\:\frac{\text{km}}{\text{hr}}$

$650\:\frac{\text{km}}{\text{hr}}$

$500\:\frac{\text{km}}{\text{hr}}$

$150\:\frac{\text{km}}{\text{hr}}$

$350\:\frac{\text{km}}{\text{hr}}$

Correct answer:

$350\:\frac{\text{km}}{\text{hr}}$

Explanation:

Since the airplane and the wind are going in opposite directions, we simply subtract the speed of the wind from the speed of the plane.

$\text{Airplane Speed}=500-150=350$

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Example Question #1 : Vector Representation Of Quantities (Velocity, Etc.): Ccss.Math.Content.Hsn Vm.A.3

If an airplane is flying south at $1000\:\frac{\text{km}}{\text{hr}}$ , and there are winds going south at $500\:\frac{\text{km}}{\text{hr}}$ , how fast is the plane going?

Possible Answers:

$1000\:\frac{\text{km}}{\text{hr}}$

$500\:\frac{\text{km}}{\text{hr}}$

$1250\:\frac{\text{km}}{\text{hr}}$

$250\:\frac{\text{km}}{\text{hr}}$

$1500\:\frac{\text{km}}{\text{hr}}$

Correct answer:

$1500\:\frac{\text{km}}{\text{hr}}$

Explanation:

Since the airplane and the winds are going the same direction, we simply add the airplane and wind speeds together.

$\text{AIrplane Speed}=1000+500=1500$

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Example Question #11 : Vector Representation Of Quantities (Velocity, Etc.): Ccss.Math.Content.Hsn Vm.A.3

An arrow is shot eastward at $125\:\text{mph}$ , and there are winds going west at $4\:\text{mph}$ , how fast the arrow going?

Possible Answers:

$125\:\text{mph}$

$121\:\text{mph}$

$100\:\text{mph}$

$129\:\text{mph}$

$4\:\text{mph}$

Correct answer:

$121\:\text{mph}$

Explanation:

Since the arrow and the wind are going in opposite directions, we simply subtract the wind speed from the speed of the arrow.

$\text{Arrow Speed}=125-4=121$

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Example Question #12 : Vector Representation Of Quantities (Velocity, Etc.): Ccss.Math.Content.Hsn Vm.A.3

A ship is sailing northeast ward at $150\: \text{knots}$ , and there are winds going southwest ward at $60\:\text{knots}$ . How fast is the ship going?

Possible Answers:

$150\: \text{knots}$

$210\: \text{knots}$

$90\:\text{knots}$

$60\:\text{knots}$

$200\: \text{knots}$

Correct answer:

$90\:\text{knots}$

Explanation:

Since the direction of the ship and the wind are going in opposite directions, we simply subtract the speed of the wind from the speed of the ship.

$\text{Ship Speed}=150-60=90$

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Example Question #131 : High School: Number And Quantity

If v=<0, 4> , and w=<-3, -2> , find v+w .

Possible Answers:

v+w=<6,3>

v+w=<0,-2>

v+w=<3,6>

v+w=<2,-3>

v+w=<-3,2>

Correct answer:

v+w=<-3,2>

Explanation:

This problem is asking us to add vectors , and . To add vectors together, we need to sum up like components together. This means that we sum up the x's , and the y's .

x=0+(-3)=-3

y=4+(-2)=4-2=2

v+w=<-3,2>

Below is a visual representation of what we just did.

Vecadd

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Example Question #2 : Add Vectors End To End, Component Wise, And By Parallelogram Rule: Ccss.Math.Content.Hsn Vm.B.4a

If v=<1, -4> , and w=<-1, 9> , find v+w .

Possible Answers:

v+w=<5,0>

v+w=<5,2>

v+w=<2,5>

v+w=<0,5>

v+w=<-2,5>

Correct answer:

v+w=<0,5>

Explanation:

This problem is asking us to add vectors , and . To add vectors together, we need to sum up like components together. This means that we sum up the x's , and the y's .

x=1+(-1)=1-1=0

y=-4+9=5

v+w=<0,5>

Below is a visual representation of what we just did.

Screen shot 2016 03 14 at 3.09.45 pm

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Example Question #31 : Vector & Matrix Quantities

If v=<-1, 8> , and w=<1, -6> , find v+w .

Possible Answers:

v+w=<-2,14>

v+w=<2,-2>

v+w=<0,2>

v+w=<-2,2>

v+w=<2,0>

Correct answer:

v+w=<0,2>

Explanation:

This problem is asking us to add vectors , and . To add vectors together, we need to sum up like components together. This means that we sum up the x's , and the y's .

x=-1+1=0

y=8-6=2

v+w=<0,2>

Below is a visual representation of what we just did.

Screen shot 2016 03 14 at 3.40.10 pm

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Example Question #1 : Add Vectors End To End, Component Wise, And By Parallelogram Rule: Ccss.Math.Content.Hsn Vm.B.4a

If v=<-1, 4> , and w=<-2, 2> , find v+w .

Possible Answers:

v+w=<-6,3>

v+w=<6,-3>

v+w=<3,6>

v+w=<-3,6>

v+w=<3,-6>

Correct answer:

v+w=<-3,6>

Explanation:

This problem is asking us to add vectors , and . To add vectors together, we need to sum up like components together. This means that we sum up the x's , and the y's .

x=-1+(-2)=-3

y=4+2=6

v+w=<-3,6>

Below is a visual representation of what we just did.

Screen shot 2016 03 14 at 3.45.17 pm

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All Common Core: High School - Number and Quantity Resources

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Common Core: High School - Number and Quantity : Vector & Matrix Quantities

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 #6 : Vector Representation Of Quantities (Velocity, Etc.): Ccss.Math.Content.Hsn Vm.A.3

Example Question #3 : Vector Representation Of Quantities (Velocity, Etc.): Ccss.Math.Content.Hsn Vm.A.3

Example Question #8 : Vector Representation Of Quantities (Velocity, Etc.): Ccss.Math.Content.Hsn Vm.A.3

Example Question #1 : Vector Representation Of Quantities (Velocity, Etc.): Ccss.Math.Content.Hsn Vm.A.3

Example Question #11 : Vector Representation Of Quantities (Velocity, Etc.): Ccss.Math.Content.Hsn Vm.A.3

Example Question #12 : Vector Representation Of Quantities (Velocity, Etc.): Ccss.Math.Content.Hsn Vm.A.3

Example Question #131 : High School: Number And Quantity

Example Question #2 : Add Vectors End To End, Component Wise, And By Parallelogram Rule: Ccss.Math.Content.Hsn Vm.B.4a

Example Question #31 : Vector & Matrix Quantities

Example Question #1 : Add Vectors End To End, Component Wise, And By Parallelogram Rule: Ccss.Math.Content.Hsn Vm.B.4a

All Common Core: High School - Number and Quantity Resources

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