### All Common Core: High School - Functions Resources

## Example Questions

### Example Question #1 : Functions Describing A Relationship Between Two Quantities: Ccss.Math.Content.Hsf Bf.A.1

Sally wants to buy a new computer for next year. The computer that she has her eye on costs . Sally works as a dog walker and gets paid an hour. If Sally works eight hours every week, how many weeks of work will it take for her to earn enough money to buy the new computer?

**Possible Answers:**

Sally will need to work weeks.

Sally will need to work weeks.

Sally will need to work weeks.

Sally will need to work weeks.

Sally will need to work weeks.

**Correct answer:**

Sally will need to work weeks.

This question is testing one's ability to recognize functions in everyday situations and build the mathematical model that shows the relationship between two quantities. A question such as this requires examination into the behavior between the quantities, whether it be explicit expression, a recursive process, or a multi-step calculation. It also requires the use of algebraic operations to solve the question at hand and then build a function that models the relationship.

For the purpose of Common Core Standards, writing a function which describes a relationship falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.Math.content.HSF.BF.A). Questions in this cluster depend heavily of building an understanding between real life situations as seen through a mathematical perspective.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify what the question is asking for.

Step 2: Identify what is given/known from the question.

Step 3: Using algebraic methods creating function to describe relationship.

Step 4: Answer the question.

Following the steps listed above for this particular problem is as follows.

Step 1: Identify what the question is asking for.

How many weeks will Sally need to work to earn enough money to buy the new computer?

Step 2: Identify what is given/known from the question.

The computer costs

Sally earns

Sally works

Step 3: Using algebraic methods creating function to describe relationship.

Step 4: Answer the question.

From this model, substitute in the known values and solve for the weeks worked to answer the question.

Using algebraic operations divide by 64 on both sides to calculate the number of weeks Sally will need to work.

### Example Question #2 : Building Functions

Jane wants to buy a new backpack for next year. The backpack that she has her eye on costs . Jane works as a car washer and gets paid an hour. If Jane works hours every week, how many weeks of work will it take for her to earn enough money to buy the new backpack?

**Possible Answers:**

Jane will need to work weeks to buy the new backpack.

Jane will need to work weeks to buy the new backpack.

Jane will need to work weeks to buy the new backpack.

Jane will need to work weeks to buy the new backpack.

Jane will need to work weeks to buy the new backpack.

**Correct answer:**

Jane will need to work weeks to buy the new backpack.

This question is testing one's ability to recognize functions in everyday situations and build the mathematical model that shows the relationship between two quantities. A question such as this requires examination into the behavior between the quantities, whether it be explicit expression, a recursive process, or a multi-step calculation. It also requires the use of algebraic operations to solve the question at hand and then build a function that models the relationship.

For the purpose of Common Core Standards, writing a function which describes a relationship falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.MATH.CONTENT.HSF.BF.A). Questions in this cluster depend heavily of building an understanding between real life situations as seen through a mathematical perspective.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify what the question is asking for.

Step 2: Identify what is given/known from the question.

Step 3: Using algebraic methods creating function to describe relationship.

Step 4: Answer the question.

Following the steps listed above for this particular problem is as follows.

Step 1: Identify what the question is asking for.

How many weeks will Jane need to work to earn enough money to buy the new backpack?

Step 2: Identify what is given/known from the question.

The backpack costs

Jane earns

Jane works

Step 3: Using algebraic methods creating function to describe relationship.

Step 4: Answer the question.

From this model, substitute in the known values and solve for the weeks worked to answer the question.

Using algebraic operations divide by 12 on both sides to calculate the number of weeks Jane will need to work.

### Example Question #2 : Functions Describing A Relationship Between Two Quantities: Ccss.Math.Content.Hsf Bf.A.1

Jenny wants to buy a new bike for next year. The bike that she has her eye on costs . Jenny works mowing lawns and gets paid per lawn. How many lawns will Jenny need to mow to earn enough money to buy a new bike.

**Possible Answers:**

Jenny will need to mow lawns.

Jenny will need to mow lawns.

Jenny will need to mow lawns.

Jenny will need to mow lawns.

Jenny will need to mow lawns.

**Correct answer:**

Jenny will need to mow lawns.

This question is testing one's ability to recognize functions in everyday situations and build the mathematical model that shows the relationship between two quantities. A question such as this requires examination into the behavior between the quantities, whether it be explicit expression, a recursive process, or a multi-step calculation. It also requires the use of algebraic operations to solve the question at hand and then build a function that models the relationship.

For the purpose of Common Core Standards, writing a function which describes a relationship falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.MATH.CONTENT.HSF.BF.A). Questions in this cluster depend heavily of building an understanding between real life situations as seen through a mathematical perspective.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify what the question is asking for.

Step 2: Identify what is given/known from the question.

Step 3: Using algebraic methods creating function to describe relationship.

Step 4: Answer the question.

Following the steps listed above for this particular problem is as follows.

Step 1: Identify what the question is asking for.

How many lawns will Jenny need to work to earn enough money to buy the new bike?

Step 2: Identify what is given/known from the question.

The bike costs

Jenny earns

Step 3: Using algebraic methods creating function to describe relationship.

Step 4: Answer the question.

From this model, substitute in the known values and solve for the weeks worked to answer the question.

Using algebraic operations divide by 5 on both sides to calculate the number of lawns Jenny will need to work.

### Example Question #3 : Functions Describing A Relationship Between Two Quantities: Ccss.Math.Content.Hsf Bf.A.1

Jenny wants to save money for her class trip. If Jenny works mowing lawns and gets paid per lawn. How many lawns will Jenny need to mow to save .

**Possible Answers:**

Jenny will need to mow lawns.

Jenny will need to mow lawns.

Jenny will need to mow lawns.

Jenny will need to mow lawns.

Jenny will need to mow lawns.

**Correct answer:**

Jenny will need to mow lawns.

For the purpose of Common Core Standards, writing a function which describes a relationship falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.MATH.CONTENT.HSF.BF.A). Questions in this cluster depend heavily of building an understanding between real life situations as seen through a mathematical perspective.

Step 1: Identify what the question is asking for.

Step 2: Identify what is given/known from the question.

Step 3: Using algebraic methods creating function to describe relationship.

Step 4: Answer the question.

Following the steps listed above for this particular problem is as follows.

Step 1: Identify what the question is asking for.

How many lawns will Jenny need to work to earn ?

Step 2: Identify what is given/known from the question.

Total money saved

Jenny earns

Step 3: Using algebraic methods creating function to describe relationship.

Step 4: Answer the question.

Using algebraic operations divide by 5 on both sides to calculate the number of lawns Jenny will need to work.

### Example Question #4 : Functions Describing A Relationship Between Two Quantities: Ccss.Math.Content.Hsf Bf.A.1

Jane wants to buy a new backpack for next year. The backpack that she has her eye on costs . Jane works as a car washer and gets paid an hour. If Jane works hours every week, how many weeks of work will it take for her to earn enough money to buy the new backpack?

**Possible Answers:**

Jane will need to work four weeks to buy the new backpack.

Jane will need to work three weeks to buy the new backpack.

Jane will need to work five weeks to buy the new backpack.

Jane will need to work seven weeks to buy the new backpack.

Jane will need to work six weeks to buy the new backpack.

**Correct answer:**

Jane will need to work six weeks to buy the new backpack.

Step 1: Identify what the question is asking for.

Step 2: Identify what is given/known from the question.

Step 3: Using algebraic methods creating function to describe relationship.

Step 4: Answer the question.

Following the steps listed above for this particular problem is as follows.

Step 1: Identify what the question is asking for.

How many weeks will Jane need to work to earn enough money to buy the new backpack?

Step 2: Identify what is given/known from the question.

The backpack costs

Jane earns

Jane works

Step 3: Using algebraic methods creating function to describe relationship.

Step 4: Answer the question.

Using algebraic operations divide by on both sides to calculate the number of weeks Jane will need to work.

### Example Question #5 : Functions Describing A Relationship Between Two Quantities: Ccss.Math.Content.Hsf Bf.A.1

Sally wants to buy a new computer for next year. The computer that she has her eye on costs . Sally works as a dog walker and gets paid an hour. If Sally works eight hours every week, how many weeks of work will it take for her to earn enough money to buy the new computer?

**Possible Answers:**

Sally needs to work nine weeks to buy her new computer.

Sally needs to work six weeks to buy her new computer.

Sally needs to work seven weeks to buy her new computer.

Sally needs to work four weeks to buy her new computer.

Sally needs to work five weeks to buy her new computer.

**Correct answer:**

Sally needs to work seven weeks to buy her new computer.

For the purpose of Common Core Standards, writing a function which describes a relationship falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.Math.content.HSF.BF.A). Questions in this cluster depend heavily of building an understanding between real life situations as seen through a mathematical perspective.

Step 1: Identify what the question is asking for.

Step 2: Identify what is given/known from the question.

Step 3: Using algebraic methods creating function to describe relationship.

Step 4: Answer the question.

Following the steps listed above for this particular problem is as follows.

Step 1: Identify what the question is asking for.

How many weeks will Sally need to work to earn enough money to buy the new computer?

Step 2: Identify what is given/known from the question.

The computer costs

Sally earns

Sally works

Step 3: Using algebraic methods creating function to describe relationship.

Step 4: Answer the question.

Using algebraic operations divide by on both sides to calculate the number of weeks Sally will need to work.

### Example Question #6 : Functions Describing A Relationship Between Two Quantities: Ccss.Math.Content.Hsf Bf.A.1

Bob wants to save enough money to buy his mom a new necklace that costs . If Bob earns an hour, how many hours will Bob need to work?

**Possible Answers:**

Bob will need to work hours.

Bob will need to work hours.

Bob will need to work hours.

Bob will need to work hours.

Bob will need to work hours.

**Correct answer:**

Bob will need to work hours.

Step 1: Identify what the question is asking for.

Step 2: Identify what is given/known from the question.

Step 3: Using algebraic methods creating function to describe relationship.

Step 4: Answer the question.

Following the steps listed above for this particular problem is as follows.

Step 1: Identify what the question is asking for.

How many hours will Bob need to work to earn ?

Step 2: Identify what is given/known from the question.

Price of necklace is .

Bob earns

Step 3: Using algebraic methods creating function to describe relationship.

Step 4: Answer the question.

Using algebraic operations divide by 2 on both sides to calculate the number of hours Bob will need to work.

### Example Question #7 : Functions Describing A Relationship Between Two Quantities: Ccss.Math.Content.Hsf Bf.A.1

Bob wants to save . If Bob earns an hour, how many hours will Bob need to work to reach his savings goal?

**Possible Answers:**

Bob will need to work hours to reach his savings goal.

Bob will need to work hours to reach his savings goal.

Bob will need to work hours to reach his savings goal.

Bob will need to work hours to reach his savings goal.

Bob will need to work hours to reach his savings goal.

**Correct answer:**

Bob will need to work hours to reach his savings goal.

Step 1: Identify what the question is asking for.

Step 2: Identify what is given/known from the question.

Step 3: Using algebraic methods creating function to describe relationship.

Step 4: Answer the question.

Following the steps listed above for this particular problem is as follows.

Step 1: Identify what the question is asking for.

How many hours will Bob need to work to earn ?

Step 2: Identify what is given/known from the question.

Total savings goal is .

Bob earns

Step 3: Using algebraic methods creating function to describe relationship.

Step 4: Answer the question.

Using algebraic operations divide by on both sides to calculate the number of hours Bob will need to work.

### Example Question #8 : Functions Describing A Relationship Between Two Quantities: Ccss.Math.Content.Hsf Bf.A.1

Bob wants to save enough money to buy his mom a new necklace that costs . If Bob earns an hour, how many hours will Bob need to work?

**Possible Answers:**

Bob will need to work eight hours.

Bob will need to work ten hours.

Bob will need to work five hours.

Bob will need to work six hours.

Bob will need to work nine hours.

**Correct answer:**

Bob will need to work nine hours.

Step 1: Identify what the question is asking for.

Step 2: Identify what is given/known from the question.

Step 3: Using algebraic methods creating function to describe relationship.

Step 4: Answer the question.

Following the steps listed above for this particular problem is as follows.

Step 1: Identify what the question is asking for.

How many hours will Bob need to work to earn ?

Step 2: Identify what is given/known from the question.

Price of necklace is .

Bob earns

Step 3: Using algebraic methods creating function to describe relationship.

Step 4: Answer the question.

Using algebraic operations divide by on both sides to calculate the number of hours Bob will need to work.

### Example Question #9 : Functions Describing A Relationship Between Two Quantities: Ccss.Math.Content.Hsf Bf.A.1

Bob wants to save enough money to buy his mom a new necklace that costs . If Bob earns an hour, how many hours will Bob need to work?

**Possible Answers:**

Bob will need to work four hours.

Bob will need to work eight hours.

Bob will need to work two hours.

Bob will need to work five hours.

Bob will need to work three hours.

**Correct answer:**

Bob will need to work four hours.

Step 1: Identify what the question is asking for.

Step 2: Identify what is given/known from the question.

Step 3: Using algebraic methods creating function to describe relationship.

Step 4: Answer the question.

Following the steps listed above for this particular problem is as follows.

Step 1: Identify what the question is asking for.

How many hours will Bob need to work to earn ?

Step 2: Identify what is given/known from the question.

Price of necklace is .

Bob earns

Step 3: Using algebraic methods creating function to describe relationship.

Step 4: Answer the question.

Using algebraic operations divide by on both sides to calculate the number of hours Bob will need to work.

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