Final Exam
MATH 115 FINAL EXAM Fall 2022 Instructor: A. Wimbish
Exam was compiled from outside sources provided upon request.
NAME: _______________________________
I have completed this assignment myself, working independently and not consulting anyone except the instructor.
INSTRUCTIONS
· The quiz contains 24 problems worth 10 points each for a total of 240 points. This quiz is open book and open notes. This means that you may refer to your textbook, notes, and online classroom materials, but you must work independently and may not consult anyone (and confirm this with your submission). You may take as much time as you wish, provided you turn in your quiz no later than Tuesday December 13.
· Show work/explanation where indicated. Answers without any work may earn little, if any, credit. You may type or write your work in your copy of the Final, or if you prefer, create a document containing your work. Scanned work is acceptable also.
In your document, be sure to include your name and the assertion of independence of work. I WILL NOT ACCEPT MESSY, SCRATCHED OUT WORK THAT I CAN NOT FIND THE FINAL ANSWER.
· If you have any questions, please contact me by e-mail or text XXXXXXXXXX.
1. Solve for x. Show your checked work AND final answer. YOU MUST SHOW ALL WORK TO RECEIVE FULL CREDIT.
2. Find the slope of the line through the points (-2,3) and (4,9). Write your final answer in point slope form. YOU MUST SHOW ALL WORK TO RECEIVE FULL CREDIT.
3. Rationalize the denominator. YOU MUST SHOW ALL WORK TO RECEIVE FULL CREDIT.
4. Solve the inequality. Write your final answer in interval notation. YOU MUST SHOW ALL WORK TO RECEIVE FULL CREDIT.
5. Solve the inequality. Write your final answer in interval notation. YOU MUST SHOW ALL WORK TO RECEIVE FULL CREDIT.
6. Use the 6-step procedure to graph the rational function. YOU MUST SHOW ALL WORK TO RECEIVE FULL CREDIT.
7. Find YOU MUST SHOW ALL WORK TO RECEIVE FULL CREDIT.
f(x) =
g(x) = 3x + 5
8. Find of f(x) = 3x + 6. YOU MUST SHOW ALL WORK TO RECEIVE FULL CREDIT.
9. Solve the equation. YOU MUST SHOW ALL WORK TO RECEIVE FULL CREDIT.
10. You invest $5000 in an account at an annual rate of 1.475% with interest compounding quarterly. Find out how much is in the account (to the nearest cent) after 3 years by using the compound interest formula , where A is the total amount in the account in dollars, P is the principal (amount invested), r is the annual interest rate, n is the number of times compounded per year and t is the time in years. YOU MUST SHOW ALL WORK TO RECEIVE FULL CREDIT.
11. Find the exact value in standard position on the unit circle
tan 330°
12. Find all solutions of the equation in the interval . YOU MUST SHOW ALL WORK TO RECEIVE FULL CREDIT.
13. If cos(θ) = in quadrant I, what is sin(θ)? YOU MUST SHOW ALL WORK TO RECEIVE FULL CREDIT.
14. Verify that (sin(θ) csc(θ)) + (cot(θ) tan(θ)) = 2. YOU MUST SHOW ALL WORK TO RECEIVE FULL CREDIT.
15. Verify that (cotx-cscx)(cotx+cscx) + 1 = 0. YOU MUST SHOW ALL WORK TO RECEIVE FULL CREDIT.
16. Verify that cot(-θ)tan(-θ) + sec(-θ)cos(θ) = 2. YOU MUST SHOW ALL WORK TO RECEIVE FULL CREDIT.
17. Given α=26° γ= 53°, a=9, use the law of sines to find side c. YOU MUST SHOW ALL WORK TO RECEIVE FULL CREDIT.
18. Given a=20, c=29, γ=82°, use the law of sines to find angle α. YOU MUST SHOW ALL WORK TO RECEIVE FULL CREDIT.
19. Given a=37, b=32 and c=25, use the law of cosines to find angle γ. YOU MUST SHOW ALL WORK TO RECEIVE FULL CREDIT.
20. Given a=6, b=10 and γ=120°, use the law of cosines find side c. YOU MUST SHOW ALL WORK TO RECEIVE FULL CREDIT.
21. Find the standard equation of the parabola with vertex (0,0) and focus (0,3). In which direction does the parabola open? YOU MUST SHOW ALL WORK TO RECEIVE FULL CREDIT.
22. Find the standard equation of the circle with center(2,-5) and radius 2. YOU MUST SHOW ALL WORK TO RECEIVE FULL CREDIT.
23. Given Vertices (0,5) and (0,-5) and Foci (0,8) and (0,-8), find the standard equation of the hype
ola. YOU MUST SHOW ALL WORK TO RECEIVE FULL CREDIT.
24. Each of the following equations represents a conic section. Identify the type of conic section: parabola, circle, ellipse of hype
ola.
a.
.
c.
d.
2