# Project 4 evaluation 34 precalculus: analytic geometry & algebra

Name _________________________________  I.D. Number   _______________________

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## Project 4

Evaluation 34

Precalculus: Analytic Geometry & Algebra (MTHH 043 059)

Be sure to include ALL pages of this project (including the directions and the assignment) when you send the project to your teacher for grading. Don’t forget to put your name and I.D. number at the top of this page!

This project will count for 10% of your overall grade for this course. Be sure to read all the instructions and assemble all the necessary materials before you begin. You will need to print this document and complete it on paper. Feel free to attach extra pages if you need them.

To earn full credit, you must justify your solutions by showing your work.

When you have completed this project you may submit it electronically through the online course management system by scanning the pages into either .pdf (Portable Document Format), or .doc (Microsoft Word document) format. If you scan your project as images, embed them in a Word document in .gif image format. Using .gif images that are smaller than 8 x 10 inches, or 600 x 800 pixels, will help ensure that the project is small enough to upload. Remember that a file that is larger than 5,000 K will NOT go through the online system. Make sure your pages are legible before you upload them.

Be sure to show all your work for full credit.

1. Find the roots of the function, and write the solution in factored form:

f x  x4   3x – 4, if x 2  –2i is one root.

Find a formula for the nth term of the sequence. Show your work.

2.

3. 2, 5, 10, 17, 26, . . .

4.

Find the sums of the given geometric series. Show your work.

5.

  3 k 1

6. 2 4  k 1  

7. Use geometric series to find the rational number represented by the repeating decimal: .036 .

Use the Binomial Theorem to expand each expression. Show your work.

8. 2x14

9. (x  y)5

Use mathematical induction to prove the following statements. Show your work.

10. 3    6   9 . . . 3n   3n(n1)

2

11. 4  4 4 . . . 4 2 3  n 44n 1

3

Let z1 = 3 – 4i  and z2 = – 1 – i . Perform the indicated operations and write the solutions in the form a + bi. Show your work.

12. z – z1  2

z1

13.

z2

14. z2

15. z1 (conjugate)

16. Find a polynomial function with real coefficients that has – 2 and 3i  as its roots. Express your answer is standard form. Show your work.

17. Let z1 = – 2i , z2 = 5 – 2i , z3 = – 3 + 5i . Locate z1, z2, and z3 on the same complex plane.

4

18. Find the value of the sum. Show your work. 2k

k 1

19. Write f x  x 25x 3 in factored form, and find the roots of f (x). Show your work.

20. Find a polynomial function with real coefficients that has 3 and – 2i as its roots. Express your answer is standard form. Show your work.

21. Express the finite sum in summation notation and show your work: – 2 + 4 – 8 + 16 – 32 +

64

Must show your work. If 10 people apply for 3 jobs, in how many ways can people be chosen for the jobs:

22. If the jobs are all the same.

23. If the jobs are all the different.

Find the limit of each expression. Show your work.

2  3n

24. nlim n2  6n

n

25. nlim   52

Declaration

I know that plagiarism is wrong. Plagiarism is to use another’s work and pretend that it is one’s own. I declare that this is my own work.

Signature _________________________________ Student I.D. number ________________

This project can be submitted electronically. Check the Project page under “My Work” in the UNHS online course management system.

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