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

What are the components of a vector that has a terminal point of , and an initial point of ?

Possible Answers:

Correct answer:

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. 

Now lets identify what these values are.

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

So the final answer is 

 

Below is a visual representation of what we just did.


Screen shot 2016 03 16 at 1.16.38 pm

Example Question #5 : Vector Components: Ccss.Math.Content.Hsn Vm.A.2

What are the components of a vector that has a terminal point of , and an initial point of ?

Possible Answers:

Correct answer:

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. 

Now lets identify what these values are.

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

So the final answer is 

 

Below is a visual representation of what we just did.

 


Screen shot 2016 03 16 at 1.27.32 pm

Example Question #11 : Vector Components: Ccss.Math.Content.Hsn Vm.A.2

What are the components of a vector that has a terminal point of , and an initial point of ?

Possible Answers:

Correct answer:

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. 

Now lets identify what these values are.

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

So the final answer is 

 

Below is a visual representation of what we just did.

Screen shot 2016 03 16 at 1.33.55 pm

Example Question #12 : Vector Components: Ccss.Math.Content.Hsn Vm.A.2

What are the components of a vector that has a terminal point of , and an initial point of ?

Possible Answers:

Correct answer:

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. 

Now lets identify what these values are.

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

So the final answer is 

 

Below is a visual representation of what we just did.


Comp3

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

Bob is cruising south down a river at  , and the river has  current due west. What is Bob's actual speed?

Possible Answers:

Not possible to find

Correct answer:

Explanation:

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

Bob1Bob2

Since bob is traveling south, and the current is traveling west, 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 Bob 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 #2 : Vector Representation Of Quantities (Velocity, Etc.): Ccss.Math.Content.Hsn Vm.A.3

Amanda is cruising north down a river at  , and the river has  current due east. What is Amanda's actual speed?

Possible Answers:

Correct answer:

Explanation:

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

 

Screen shot 2016 03 17 at 4.15.01 pm 

Since Amanda 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 Amanda 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 behind him at . How fast is the rock going?

Possible Answers:

Correct answer:

Explanation:

Since the rock is going in the opposite direction of Jack, we simply subtract the speed of the rock from how fast Jack is going down the hill. 

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

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

Possible Answers:

Correct answer:

Explanation:

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

Screen shot 2016 03 17 at 4.39.13 pm

Since the airplane is traveling south, and the wind is coming from the west, 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 the airplane 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 #2 : Vector Representation Of Quantities (Velocity, Etc.): Ccss.Math.Content.Hsn Vm.A.3

Jill slides down a hill at , and throws a coin forward at . How fast is the coin going?

Possible Answers:

 

Correct answer:

Explanation:

Since the coin is going in the same direction as Jill, we simply add the speed of the coin and how fast Jill is going down the hill. 

Example Question #4 : Vector Representation Of Quantities (Velocity, Etc.): Ccss.Math.Content.Hsn Vm.A.3

Bob slides down a hill at , and throws his wallet behind him at . How fast is his wallet going?

Possible Answers:

Correct answer:

Explanation:

Since Bob's wallet is going in the opposite direction, we simply subtract the speed of the wallet from how fast Bob is going down the hill. 

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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