Lab Section #:Name:

Final Exam, 2/19/2022

You have until 12:00pm to complete your work for the exam. You then have 12:00pm – 12:45pm to upload your work to Gradescope. All work must be your own. No notes, calculators, or resources of any kind are allowed. Follow all guidelines in the syllabus and previous emails/announcements.

You must work on physical paper. We recommend you print out this template and work directly on it. You can

also work on blank paper as long as it is organized in a similar way as the template (you do not have to rewrite the questions). There are 35 questions, each worth 3 points. All answers must be justified in order to recieve credit.

If you need extra space to show your work, use blank paper and clearly indicate on the template that your work continues on another sheet. Also remember when submitting in Gradescope to tag a question to multiple pages if you use another page to show your work.

1. Find the value of the following expression using the

rules for order of operations.

2. Solve the following equation. Express your answer as

an integer, simplified fraction, or decimal rounded to two

decimal places.

11 + (5)2 ÷ (2 + 3) · 4

1.6w + 5.4 = 1.1w + 6.4

3. Solve the absolute value equation and write your answer

in set notation.

3|y − 1| − 12 = 0

4. Solve the following formula for the indicated variable.

2c =

1

7a

;

4b + 5

solve for b.

5. Consider the following inequality.

−2x − 6 < 3x + 6
(a) (2 pts.) Write the solution using interval notation.
(b) (1 pt.) Graph the solution on a number line.
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
6. Consider the following inequality.
|8 − 2y| ≤ −5
Solve the absolute value inequality and express the solution in interval notation. If there is no solution, write “no solution”.
7. Consider the following inequality.
|2y + 7| − 3 > 0

(a) (2 pts.) Solve the absolute value inequality and express the solution in interval notation.

(b) (1 pt.) Graph the solution set on a number line.

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

2

1

2

3

4

5

6

7

8

9

10

8. Consider the following linear equation.

y = −4x − 2

(a) (2 pts.) Determine the slope and y-intercept (written as an ordered pair) of the equation above. Reduce all fractions to lowest terms.

Slope:

y-intercept:

(b) (1 pt.) Graph the line.

10

8

6

4

2

-10

-8

-6

-4

-2

2

4

6

8

10

-2

-4

-6

-8

-10

9. Find the equation of the line passing through the points

with the given coordinates. Write your answer in slopeintercept form.

(1, 2), (4, 0)

10. Simplify the expression using the properties of exponents. Only include positive exponents in your answer.

3

x2 y −1

x−2 y 2

3

x−1 y −2

x4 y 3

−3

11. Find the product of the binomials using the appropriate special product (difference of two squares, square of a

binomial sum, or square of a binomial difference).

(x + 5)2

12. Divide the polynomial in the numerator by the binomial in the denominator and simplify.

13. Factor the polynomial by grouping, if possible. If the

polynomial cannot be factored, write “not factorable”.

3×4 − x3 − 9x + 4

x+2

20u3 + 35u2 − 4u − 7

14. Completely factor the given polynomial, if possible. If

the polynomial cannot be factored, write “not factorable”.

15. Completely factor the given polynomial, if possible. If

the polynomial cannot be factored, write “not factorable”.

8y 2 − 2×2

2×2 − 16x + 24

4

16. Simplify the following expression. Assume that each

variable is positive.

√

3

16×5

17. Simplify the expression by by combining the radical

terms using the indicated operations. Assume all variables

are positive.

p

p

p

7x 72xy + 8x 2xy + 7x 18xy

18. Rationalize the denominator and simplify, if possible.

19. Consider the following quadratic equation.

3

√

9− 7

x2 − 6x + 1 = −8

(a) (2 pts.) Using the standard form ax2 + bx + c = 0

of the given quadratic equation, factor the left hand

side of the equation into two linear factors.

(b) (1 pt.) Solve the quadratic equation by factoring.

5

20. Solve the quadratic equation using the square root

property. Write the radicals in simplest form.

21. Solve the following quadratic equation by completing

the square. Simplify the solutions and rationalize denominators, if necessary.

(3x − 12)2 = 27

x2 + 6x − 12 = 0

22. Solve the following quadratic equation using the

quadratic formula.

y 2 = −8y + 1

23. Consider the following quadratic function.

y = x2 − 8x + 20

Rewrite the quadratic function in the form

y = a(x − h)2 + k.

6

24. Consider the quadratic function

y = (x − 2)2 + 3

(a) (1 pt.) Identify the vertex. Write your answer as an ordered pair.

(b) (1 pt.) Since a = 1 (see Question 23), we can identify two points on the parabola by finding a point 1 unit to

the right of the vertex and a point 1 unit to the left of the vertex. Find the point on the parabola 1 unit to the

right of the vertex. Write your answer as an ordered pair with an x-value of 3. Find the point on the parabola 1

unit to the left of the vertex. Write your answer as an ordered paid with an x-value of 1.

(c) (1 pt.) Graph the parabola in the space below.

10

8

6

4

2

-10

-8

-6

-4

-2

2

4

6

8

10

-2

-4

-6

-8

-10

25. Consider the function

f (x) =

√

26. Determine the domain of the given relation or function.

√

g(x) = 2 − 9x

5 + 4x.

(a) (1 pt.) Find the value of f (5).

(b) (2 pts.) Find the value of f (a − 2).

7

27. Perform the indicated operation of multiplication or

division on the rational expressions and simplify.

28. Perform the indicated operation of multiplication or

division on the rational expressions and simplify.

3

22

÷

3

y − 3 3(y − 3y 2 )

4

y 2 − 25

÷

(y + 5)2

20

29. Perform the indicated operation of addition on the

two rational expressions and reduce your answer to lowest

terms.

3x + 1

6

+

x2 + 2x + 1 x + 1

30. Simplify the following complex fraction.

5

x2

1

x2

8

−

−

10

x3

4

x4

31. Consider the following equation.

x

2

3x

=

−

x+4

x + 1 x2 + 5x + 4

(a) (1 pt.) State any restriction(s) on the variable, if they exist.

(b) (2 pts.) Solve the equation, if possible. If there is a solution, express your answer as either an integer or a simplified fraction.

33. Find the inverse of the following function.

32. Given two functions f (x) and g(x):

f (x) = 3×2 + 4,

g(x) = 7x − 5,

g(x) =

form their composition (g ◦ f )(x).

9

6

+2

x

34. Acid solution A has a 68% acid concentration, and acid solution B has a 20% acid concentration. How many ounces

each of solution A and solution B must be mixed to produce 100 ounces of an acid solution with a 32% acid concentration?

35. Working together, Candace and Donovan can clean the snow from their driveway in 9 minutes. It would have taken

Donovan, working alone, 36 minutes. How long would it have taken Candace alone?

10

The price is based on these factors:

Academic level

Number of pages

Urgency

Basic features

- Free title page and bibliography
- Unlimited revisions
- Plagiarism-free guarantee
- Money-back guarantee
- 24/7 support

On-demand options

- Writer’s samples
- Part-by-part delivery
- Overnight delivery
- Copies of used sources
- Expert Proofreading

Paper format

- 275 words per page
- 12 pt Arial/Times New Roman
- Double line spacing
- Any citation style (APA, MLA, Chicago/Turabian, Harvard)

Delivering a high-quality product at a reasonable price is not enough anymore.

That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.

You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.

Read moreEach paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.

Read moreThanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.

Read moreYour email is safe, as we store it according to international data protection rules. Your bank details are secure, as we use only reliable payment systems.

Read moreBy sending us your money, you buy the service we provide. Check out our terms and conditions if you prefer business talks to be laid out in official language.

Read more