### 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

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:**

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

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:**

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:**

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:**

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:**

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:**

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:**

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.

### 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:**

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.

### 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:**

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.

### Example Question #131 : High School: Number And Quantity

If , and , find .

**Possible Answers:**

**Correct answer:**

So

Below is a visual representation of what we just did.

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