Final Exam F21

Instructions

On your desk: pencil/paper, calculator, Chromebook
On your browser:  this test, and any of the following links
Not allowed:  phones, headphones, other electronics, notes

Desmos - Graphing
Desmos - Scientific
Standard Deviation Calculator
- use POPULATION standard deviation

Formula Sheet

Hints
1) There will be no extraneous solutions; every problem will have a solution.
2) You can use your calculator for the questions involving i. 
3) Use Desmos both to do the work faster and to check your work.

You are not required to show your work on Formative, but if you do, you may get partial credit. Simply type what steps you took to get your answer ("I divided both sides by 6, then subtracted 3) rather than trying to draw in Formative.

After the exam, please take the End of Course Survey.  The survey is anonymous.

When you are finished with both the exam and the survey, close your Chromebook and read, draw, or study quietly.  You may not get out your phone.

Good luck!

1

Tony and Bruce went to the concession stand. Tony bought two hotdogs and a drink and paid $8.00. Bruce bought one hotdog and two drinks and paid $7.00. What is the total cost of four hotdogs and five drinks?

1

Natasha has $50 to buy food for her party. Pizzas cost $6 and sodas cost $1 per bottle. Natasha wants to have at least 4 bottles of soda, and she wants to have more pizzas than soda bottles. Which combinations fit her goals and budget?

Check all that apply (3).

1

For the function f(x) = 2x - 4, the x-intercept is _______  and the y-intercept is _______ .
Use (x, y) format, with exactly one space after the comma.

1

Consider the function f(x) = -\frac{5}{4}(x - 2)^{2} - 5.

What transformations have been applied to the quadratic parent function to create f(x)?

Check all that apply.

1

The quadratic parent function is shifted left 3 units, then reflected over the x-axis. What is the resulting function? You do not have to FOIL.

1

Consider the function f(x) = (x-2)^{2}+1.

The vertex of f(x) is _______ (use (x, y) format).  
The axis of symmetry of f(x) is _______ (your answer should include "=", no spaces, ex. z=5)
As x \rightarrow \infty, f(x) \rightarrow _______ (enter a number, \infty, or -\infty).
As x \rightarrow -\infty, f(x) \rightarrow _______  (enter a number, \infty, or -\infty).

For \infty, use copy/paste from this question.

1

Calculate (2+3i)(1 - 5i) + 2i(3+i).

Enter your answer as a complex number in the form a+bi, with a and b real numbers. No spaces.

1

What is the sum of the solutions to the following equation?
(Find both solutions, then add them together.)

2x^{2} + 11x + 15 = 0.

Enter your answer as a number, no spaces.

1

For the quadratic equation x^{2} - x + 6 = 0, determine the number and type of solutions.

1

For the quadratic equation x^{2} - x - 6 = 0, determine the number and type of solutions.

1

Which of the following are roots of the polynomial 4x^{3}+12x^{2}+x+3?

Check all that apply (3)

1

What is the remainder when the polynomial x^{3} - 5x^{2} + 2x - 6 is divided by (x - 2)?

Enter your answer as an integer, no spaces.

1

For the polynomial p(x), as x \rightarrow \infty, f(x) \rightarrow -\infty and as x\rightarrow -\infty, f(x) \rightarrow -\infty.

Which of the following is true?

1

Match each expression to its equivalent using the properties of exponents.

Draggable item		Corresponding Item
(ab)^{x}		a^{x}b^{x}
b^{x} \cdot b^{y}		b^{x+y}
b^{-x}		\frac{1}{b^{x}}
b^{\frac{x}{y}}		\sqrt[y]{b^{x}}

1

Simplify the expression below. Check by substituting a number for x.

\sqrt[3]{2x} \cdot \sqrt[3]{16x^{4}}

1

Consider the equation

5 - \sqrt{2x+3} = 2

For what value of x is this equation true? Enter your answer as a number, no spaces.

1

Which of the following is the inverse of the function f(x) = \sqrt{x+3} - 5?

Hint: Don't try to do this in your head or by looking at it. Work it out.

1

Let A be a positive, real number. Which of the following is true as x \rightarrow \infty?

1

Find the value of x that satisfies the equation.

2^{x} = 51

Give your answer as a number rounded to two decimal places.

1

Find the value of x that satisfies the equation.

2 \cdot 3^{2x} - 4 = 16

Give your answer as a number rounded to two decimal places.

1

Find the value of x that satisfies the equation.

2 - e^{x+1 } = 0

Give your answer as a number rounded to two decimal places.

1

Consider f(x) = \frac{3}{4} \cdot (2)^{x}.

f(x) is exponential _______ . (Type "growth" or "decay", no spaces or ")
f(x) has an asymptote of _______ .  (Your answer should include a "=", no spaces, ex. z=5)
As x \rightarrow \infty, f(x) \rightarrow _______ .  (Type a number, \infty, or -\infty).
As x \rightarrow -\infty, f(x) \rightarrow _______  .  (Type a number, \infty, or -\infty).

For \infty, use copy/paste from this question.

1

Consider f(x) = log_{2} (x - 2) + 4.

f(x) has an asymptote of _______. (Your answer should include a "=", no spaces, ex. z=5)
As x\rightarrow\infty, f(x) \rightarrow _______ .  (Type a number, \infty, or -\infty.)

For \infty, copy/paste from this question.

Sandra deposits $6000 to start a savings account.  Her bank gives her 2% annual interest.

1

How much more interest would Sandra earn if her account had five years of interest compounded monthly , instead of five years with annual interest?

Enter your answer as a number rounded to two decimal places.

The table below shows the average movie ticket price every five years since 1968.



The r-values for the regressions are as follows.
LinReg:  0.9861
QuadR:  0.9932
ExpReg: 0.9809
LnReg:  0.9106

1

Use the data from the table below for the following questions.

1

What is the mean of the data? Enter your answer as a number rounded to one decimal place.

1

What is the standard deviation of the data?
Enter your answer as a number rounded to two decimal places.

1

A data set has a mean of 4 and a standard deviation of 1. What is the z-score for a data value of 2.5?

Enter your answer as a number rounded to one decimal place.

1

A data value has a z-score of 1.01. What percent of the population is greater than this data value?

Hint: draw the bell curve and read the question carefully.

A group of 200 people were surveyed about their pet ownership and exercise habits.  The results are shown in the table below.

1

If a person is randomly selected from the group, what is the probability, as a percent, that they own a pet?

Enter your answer as a number, no "%" or spaces.

1

If a person is randomly selected from the group, what is the probability, as a percent, that they don't own pets and don't exercise weekly?

Enter your answer as a number rounded to one decimal place, no "%" or spaces.

1

Final Exam F21

Tony and Bruce went to the concession stand. Tony bought two hotdogs and a drink and paid $8.00. Bruce bought one hotdog and two drinks and paid $7.00. What is the total cost of four hotdogs and five drinks?

Natasha has $50 to buy food for her party. Pizzas cost $6 and sodas cost $1 per bottle. Natasha wants to have at least 4 bottles of soda, and she wants to have more pizzas than soda bottles. Which combinations fit her goals and budget? Check all that apply (3).

Consider the function f(x) = -\frac{5}{4}(x - 2)^{2} - 5.What transformations have been applied to the quadratic parent function to create f(x)? Check all that apply.

The quadratic parent function is shifted left 3 units, then reflected over the x-axis. What is the resulting function? You do not have to FOIL.

Calculate (2+3i)(1 - 5i) + 2i(3+i).Enter your answer as a complex number in the form a+bi, with a and b real numbers. No spaces.

What is the sum of the solutions to the following equation?(Find both solutions, then add them together.)2x^{2} + 11x + 15 = 0.Enter your answer as a number, no spaces.

For the quadratic equation x^{2} - x + 6 = 0, determine the number and type of solutions.

For the quadratic equation x^{2} - x - 6 = 0, determine the number and type of solutions.

Which of the following are roots of the polynomial 4x^{3}+12x^{2}+x+3? Check all that apply (3)

What is the remainder when the polynomial x^{3} - 5x^{2} + 2x - 6 is divided by (x - 2)?Enter your answer as an integer, no spaces.

For the polynomial p(x), as x \rightarrow \infty, f(x) \rightarrow -\infty and as x\rightarrow -\infty, f(x) \rightarrow -\infty.Which of the following is true?

Match each expression to its equivalent using the properties of exponents.

Simplify the expression below. Check by substituting a number for x.\sqrt[3]{2x} \cdot \sqrt[3]{16x^{4}}

Consider the equation5 - \sqrt{2x+3} = 2For what value of x is this equation true? Enter your answer as a number, no spaces.

Which of the following is the inverse of the function f(x) = \sqrt{x+3} - 5?Hint: Don't try to do this in your head or by looking at it. Work it out.

Let A be a positive, real number. Which of the following is true as x \rightarrow \infty?

Find the value of x that satisfies the equation.2^{x} = 51Give your answer as a number rounded to two decimal places.

Find the value of x that satisfies the equation.2 \cdot 3^{2x} - 4 = 16Give your answer as a number rounded to two decimal places.

Find the value of x that satisfies the equation.2 - e^{x+1 } = 0 Give your answer as a number rounded to two decimal places.

How much more interest would Sandra earn if her account had five years of interest compounded monthly , instead of five years with annual interest?Enter your answer as a number rounded to two decimal places.

What is the mean of the data? Enter your answer as a number rounded to one decimal place.

What is the standard deviation of the data? Enter your answer as a number rounded to two decimal places.

A data set has a mean of 4 and a standard deviation of 1. What is the z-score for a data value of 2.5?Enter your answer as a number rounded to one decimal place.

A data value has a z-score of 1.01. What percent of the population is greater than this data value?Hint: draw the bell curve and read the question carefully.

If a person is randomly selected from the group, what is the probability, as a percent, that they own a pet?Enter your answer as a number, no "%" or spaces.

If a person is randomly selected from the group, what is the probability, as a percent, that they don't own pets and don't exercise weekly?Enter your answer as a number rounded to one decimal place, no "%" or spaces.

Tony and Bruce went to the concession stand. Tony bought two hotdogs and a drink and paid $8.00. Bruce bought one hotdog and two drinks and paid $7.00. What is the total cost of four hotdogs and five drinks?

Natasha has $50 to buy food for her party. Pizzas cost $6 and sodas cost $1 per bottle. Natasha wants to have at least 4 bottles of soda, and she wants to have more pizzas than soda bottles. Which combinations fit her goals and budget? Check all that apply (3).

Consider the function f(x) = -\frac{5}{4}(x - 2)^{2} - 5.What transformations have been applied to the quadratic parent function to create f(x)? Check all that apply.

The quadratic parent function is shifted left 3 units, then reflected over the x-axis. What is the resulting function? You do not have to FOIL.

Calculate (2+3i)(1 - 5i) + 2i(3+i).Enter your answer as a complex number in the form a+bi, with a and b real numbers. No spaces.

What is the sum of the solutions to the following equation?(Find both solutions, then add them together.)2x^{2} + 11x + 15 = 0.Enter your answer as a number, no spaces.

For the quadratic equation x^{2} - x + 6 = 0, determine the number and type of solutions.

For the quadratic equation x^{2} - x - 6 = 0, determine the number and type of solutions.

Which of the following are roots of the polynomial 4x^{3}+12x^{2}+x+3? Check all that apply (3)

What is the remainder when the polynomial x^{3} - 5x^{2} + 2x - 6 is divided by (x - 2)?Enter your answer as an integer, no spaces.

For the polynomial p(x), as x \rightarrow \infty, f(x) \rightarrow -\infty and as x\rightarrow -\infty, f(x) \rightarrow -\infty.Which of the following is true?

Match each expression to its equivalent using the properties of exponents.

Simplify the expression below. Check by substituting a number for x.\sqrt[3]{2x} \cdot \sqrt[3]{16x^{4}}

Consider the equation5 - \sqrt{2x+3} = 2For what value of x is this equation true? Enter your answer as a number, no spaces.

Which of the following is the inverse of the function f(x) = \sqrt{x+3} - 5?Hint: Don't try to do this in your head or by looking at it. Work it out.

Let A be a positive, real number. Which of the following is true as x \rightarrow \infty?

Find the value of x that satisfies the equation.2^{x} = 51Give your answer as a number rounded to two decimal places.

Find the value of x that satisfies the equation.2 \cdot 3^{2x} - 4 = 16Give your answer as a number rounded to two decimal places.

Find the value of x that satisfies the equation.2 - e^{x+1 } = 0 Give your answer as a number rounded to two decimal places.

Select the expression that describes the value of the account after t years.

Select the expression that describes the value of the account after t months.

How much more interest would Sandra earn if her account had five years of interest compounded monthly , instead of five years with annual interest?Enter your answer as a number rounded to two decimal places.

According to the r-values, which model best fits the data?

Estimate the value of a movie ticket in 2023 (x=12). (Use coefficients rounded to three decimal places each.)Choose the closest value.

What is the mean of the data? Enter your answer as a number rounded to one decimal place.

What is the standard deviation of the data? Enter your answer as a number rounded to two decimal places.

A data set has a mean of 4 and a standard deviation of 1. What is the z-score for a data value of 2.5?Enter your answer as a number rounded to one decimal place.

A data value has a z-score of 1.01. What percent of the population is greater than this data value?Hint: draw the bell curve and read the question carefully.

If a person is randomly selected from the group, what is the probability, as a percent, that they own a pet?Enter your answer as a number, no "%" or spaces.

If a person is randomly selected from the group, what is the probability, as a percent, that they don't own pets and don't exercise weekly?Enter your answer as a number rounded to one decimal place, no "%" or spaces.

If a person is randomly selected from the group, what is the probability, as a percent, that they own a pet or they exercise weekly?Enter your answer as a percent rounded to two decimal places, no "%" or spaces.

If a person is randomly selected from the group, what is the probability, as a percent, that they own a pet, given that they exercise weekly?Enter your answer as a number rounded to two decimal places, no "%" or spaces.

Are pet-ownership and exercise habits independent or dependent events?Hint: use #33 and #36

Select the expression that describes the value of the account after t years.

Select the expression that describes the value of the account after t months.

According to the r-values, which model best fits the data?

Estimate the value of a movie ticket in 2023 (x=12). (Use coefficients rounded to three decimal places each.)Choose the closest value.

If a person is randomly selected from the group, what is the probability, as a percent, that they own a pet or they exercise weekly?Enter your answer as a percent rounded to two decimal places, no "%" or spaces.

If a person is randomly selected from the group, what is the probability, as a percent, that they own a pet, given that they exercise weekly?Enter your answer as a number rounded to two decimal places, no "%" or spaces.

Are pet-ownership and exercise habits independent or dependent events?Hint: use #33 and #36

Natasha has $50 to buy food for her party. Pizzas cost $6 and sodas cost $1 per bottle. Natasha wants to have at least 4 bottles of soda, and she wants to have more pizzas than soda bottles. Which combinations fit her goals and budget?

Check all that apply (3).

Consider the function f(x) = -\frac{5}{4}(x - 2)^{2} - 5.

What transformations have been applied to the quadratic parent function to create f(x)?

Check all that apply.

Calculate (2+3i)(1 - 5i) + 2i(3+i).

Enter your answer as a complex number in the form a+bi, with a and b real numbers. No spaces.

What is the sum of the solutions to the following equation?
(Find both solutions, then add them together.)

2x^{2} + 11x + 15 = 0.

Enter your answer as a number, no spaces.

Which of the following are roots of the polynomial 4x^{3}+12x^{2}+x+3?

Check all that apply (3)

What is the remainder when the polynomial x^{3} - 5x^{2} + 2x - 6 is divided by (x - 2)?

Enter your answer as an integer, no spaces.

For the polynomial p(x), as x \rightarrow \infty, f(x) \rightarrow -\infty and as x\rightarrow -\infty, f(x) \rightarrow -\infty.

Which of the following is true?

Simplify the expression below. Check by substituting a number for x.

\sqrt[3]{2x} \cdot \sqrt[3]{16x^{4}}

Consider the equation

5 - \sqrt{2x+3} = 2

For what value of x is this equation true? Enter your answer as a number, no spaces.

Which of the following is the inverse of the function f(x) = \sqrt{x+3} - 5?

Hint: Don't try to do this in your head or by looking at it. Work it out.

Find the value of x that satisfies the equation.

2^{x} = 51

Give your answer as a number rounded to two decimal places.

Find the value of x that satisfies the equation.

2 \cdot 3^{2x} - 4 = 16

Give your answer as a number rounded to two decimal places.

Find the value of x that satisfies the equation.

2 - e^{x+1 } = 0

Give your answer as a number rounded to two decimal places.

How much more interest would Sandra earn if her account had five years of interest compounded monthly , instead of five years with annual interest?

Enter your answer as a number rounded to two decimal places.

What is the standard deviation of the data?
Enter your answer as a number rounded to two decimal places.

A data set has a mean of 4 and a standard deviation of 1. What is the z-score for a data value of 2.5?

Enter your answer as a number rounded to one decimal place.

A data value has a z-score of 1.01. What percent of the population is greater than this data value?

Hint: draw the bell curve and read the question carefully.

If a person is randomly selected from the group, what is the probability, as a percent, that they own a pet?

Enter your answer as a number, no "%" or spaces.

If a person is randomly selected from the group, what is the probability, as a percent, that they don't own pets and don't exercise weekly?

Enter your answer as a number rounded to one decimal place, no "%" or spaces.

Natasha has $50 to buy food for her party. Pizzas cost $6 and sodas cost $1 per bottle. Natasha wants to have at least 4 bottles of soda, and she wants to have more pizzas than soda bottles. Which combinations fit her goals and budget?

Check all that apply (3).

Consider the function f(x) = -\frac{5}{4}(x - 2)^{2} - 5.

What transformations have been applied to the quadratic parent function to create f(x)?

Check all that apply.

Calculate (2+3i)(1 - 5i) + 2i(3+i).

Enter your answer as a complex number in the form a+bi, with a and b real numbers. No spaces.

What is the sum of the solutions to the following equation?
(Find both solutions, then add them together.)

2x^{2} + 11x + 15 = 0.

Enter your answer as a number, no spaces.

Which of the following are roots of the polynomial 4x^{3}+12x^{2}+x+3?

Check all that apply (3)

What is the remainder when the polynomial x^{3} - 5x^{2} + 2x - 6 is divided by (x - 2)?

Enter your answer as an integer, no spaces.

For the polynomial p(x), as x \rightarrow \infty, f(x) \rightarrow -\infty and as x\rightarrow -\infty, f(x) \rightarrow -\infty.

Which of the following is true?

Simplify the expression below. Check by substituting a number for x.

\sqrt[3]{2x} \cdot \sqrt[3]{16x^{4}}

Consider the equation

5 - \sqrt{2x+3} = 2

For what value of x is this equation true? Enter your answer as a number, no spaces.

Which of the following is the inverse of the function f(x) = \sqrt{x+3} - 5?

Hint: Don't try to do this in your head or by looking at it. Work it out.

Find the value of x that satisfies the equation.

2^{x} = 51

Give your answer as a number rounded to two decimal places.

Find the value of x that satisfies the equation.

2 \cdot 3^{2x} - 4 = 16

Give your answer as a number rounded to two decimal places.

Find the value of x that satisfies the equation.

2 - e^{x+1 } = 0

Give your answer as a number rounded to two decimal places.

How much more interest would Sandra earn if her account had five years of interest compounded monthly , instead of five years with annual interest?

Enter your answer as a number rounded to two decimal places.

Estimate the value of a movie ticket in 2023 (x=12).

(Use coefficients rounded to three decimal places each.)

Choose the closest value.

What is the standard deviation of the data?
Enter your answer as a number rounded to two decimal places.

A data set has a mean of 4 and a standard deviation of 1. What is the z-score for a data value of 2.5?

Enter your answer as a number rounded to one decimal place.

A data value has a z-score of 1.01. What percent of the population is greater than this data value?

Hint: draw the bell curve and read the question carefully.

If a person is randomly selected from the group, what is the probability, as a percent, that they own a pet?

Enter your answer as a number, no "%" or spaces.

If a person is randomly selected from the group, what is the probability, as a percent, that they don't own pets and don't exercise weekly?

Enter your answer as a number rounded to one decimal place, no "%" or spaces.

If a person is randomly selected from the group, what is the probability, as a percent, that they own a pet or they exercise weekly?

Enter your answer as a percent rounded to two decimal places, no "%" or spaces.

If a person is randomly selected from the group, what is the probability, as a percent, that they own a pet, given that they exercise weekly?

Enter your answer as a number rounded to two decimal places, no "%" or spaces.

Are pet-ownership and exercise habits independent or dependent events?

Hint: use #33 and #36

Estimate the value of a movie ticket in 2023 (x=12).

(Use coefficients rounded to three decimal places each.)

Choose the closest value.

If a person is randomly selected from the group, what is the probability, as a percent, that they own a pet or they exercise weekly?

Enter your answer as a percent rounded to two decimal places, no "%" or spaces.

If a person is randomly selected from the group, what is the probability, as a percent, that they own a pet, given that they exercise weekly?

Enter your answer as a number rounded to two decimal places, no "%" or spaces.

Are pet-ownership and exercise habits independent or dependent events?

Hint: use #33 and #36