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Final Exam F21 form B

Last updated almost 4 years ago
37 questions
Note from the author:
Desmos - Graphing
Desmos - Scientific
Standard Deviation Calculator
- use POPULATION standard deviation

Formula Sheet

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.

Good luck!
Desmos - Graphing
Desmos - Scientific
Standard Deviation Calculator
- use POPULATION standard deviation

Formula Sheet

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.

Good luck!
1

Tony and Bruce went to the concession stand. Tony bought one hotdog and one drink and paid $6.00. Bruce bought four hotdogs and two drinks and paid $20. What is the total cost of three hotdogs and one drinks?

1

Kae is on a strict 2000 calorie diet - she cannot eat more than 2000 calories in a day. For safety, she has to eat at least 1000 calories. A serving of grains is 400 calories, and a serving of fruit is 200 calories. She wants to eat more servings of grains than fruits. Which combinations fit Kae's goals?

1
For the function f(x) = 3x + 9, 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{3}{4}(x + 5)^{2} -2 .

What transformations have been applied to the quadratic parent function to create f(x)? Check all that apply.

1

The quadratic parent function is compressed by 1/2, then shifted up 3 units. What is the resulting function?

Use "y=..." format, no spaces.

1
Consider the function f(x) = (x-5)^{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 (7+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.)

3x^{2} + 8x + 4 = 0.

Enter your answer as a fraction, no spaces.

1

For the quadratic equation x^{2} + x + 4 = 0, determine the number and type of solutions.

1

For the quadratic equation x^{2} +x - 5 = 0, determine the number and type of solutions.

1

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

1

What is the remainder when the polynomial x^{3} - 5x^{2} + 2x - 6 is divided by (x - 1)?

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

Simplify the expression below.

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

1

Consider the equation

5 - \sqrt{6x+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?

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} = 41

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

1

Find the value of x that satisfies the equation.

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

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

1

Find the value of x that satisfies the equation.

250 - 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 $4000 to start a savings account. Her bank gives her 6% annual interest.
1

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

1

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

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

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

1

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

Enter your answer as a number rounded to two decimal places. I recommend using three decimal places for the coefficients your calculator gives you.

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 less than this data value?

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 exercise weekly?

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

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.

1

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

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

1

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

Hint: use #33 and #36