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  , and the river has  current due east. What is John's actual speed?

Possible Answers:

Correct answer:

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  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 , where  is the hypotenuse, and  are the legs of the triangle, and  have a  angle between them.

For our calculations, let , and 

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

Jack slides down a hill at , and throws a rock ahead of him at . How fast is the rock going?

Possible Answers:

Correct answer:

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. 

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

If an airplane is flying south at , and there are winds going north at , how fast is the plane going?

Possible Answers:

Correct answer:

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.

Example Question #9 : Vector Representation Of Quantities (Velocity, Etc.): Ccss.Math.Content.Hsn Vm.A.3

If an airplane is flying south at , and there are winds going south at , how fast is the plane going?

Possible Answers:

Correct answer:

Explanation:

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

Example Question #31 : Vector & Matrix Quantities

An arrow is shot eastward at , and there are winds going west at , how fast the arrow going?

Possible Answers:

Correct answer:

Explanation:

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

Example Question #32 : Vector & Matrix Quantities

A ship is sailing northeast ward at , and there are winds going southwest ward at . How fast is the ship going?

Possible Answers:

Correct answer:

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.

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

If , and , find 

Possible Answers:

Correct answer:

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 , and the 

So

 

Below is a visual representation of what we just did.

Vecadd

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

If , and , find 

Possible Answers:

Correct answer:

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 , and the 

So

 

Below is a visual representation of what we just did.

Screen shot 2016 03 14 at 3.09.45 pm

Example Question #3 : Add Vectors End To End, Component Wise, And By Parallelogram Rule: Ccss.Math.Content.Hsn Vm.B.4a

If , and , find 

Possible Answers:

Correct answer:

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 , and the 

So

 

Below is a visual representation of what we just did.

Screen shot 2016 03 14 at 3.40.10 pm

Example Question #131 : High School: Number And Quantity

If , and , find 

Possible Answers:

Correct answer:

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 , and the 

So

 

Below is a visual representation of what we just did.

Screen shot 2016 03 14 at 3.45.17 pm

 

All Common Core: High School - Number and Quantity Resources

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