College Algebra Final Exam

Transcription

1 Name: Teacher: College Algebra Final Exam Dodge City Community College This exam must be taken under the following conditions: This exam must not be administered to any student prior to the week of Final Exams (starting May 6 th, 2013). Exceptions must be approved on a case by base basis by the Science/Math Department of Dodge City Community College. During the exam, each student may have one (1) calculator, pencils or pens, and scratch paper (which must be BLANK to begin with) and nothing else. Cell phones or other devices with a wireless connection may NOT be used as calculators. Students may NOT share a calculator. This test must be closed book/closed notes. No notecards or cheatsheets are acceptable. No additional formulas may be provided. Some formulas may be provided on the final. Any formulas not provided, the student is expected to know. At this time, the Science and Math department does not require the test to be completed within any particular time period. Any time limits are left to the discretion of the individual teacher. This exam must be completed in one sitting OR the following steps must be taken: for students that require more than one sitting to complete the exam, the exam must be split up into parts for each sitting. A student MUST complete the part they are given in a particular sitting within that sitting. Once the exams are graded, they must be returned to Dodge City Community College to be used as data for quality improvement/assessment purposes. 1

2 1. Solve the equation: 1 2 x 1 3 = 1 4 x At 8am, Train A leaves the station heading north at 50mph. An hour later, Train B leaves the same station heading south at 60mph. At what time will the two trains be 325 miles apart? 3. Write the equation of a circle that has center (- 2,- 3) and passes through the point (2,5). 2

3 4. Find the x- intercept and y- intercept of the following line, then graph: 2x 3y = 6 College Algebra 5. Solve. Write your answer in interval notation and graph it on a real number line. 2x 1 > 5 6. Solve. x! 2x + 4 = 0 3

4 7. Find the domain and range of the function f x = x Sketch the graph of f x = x Identify the x- and y- intercepts, if they exist. 9. Let f x = x + 3 and g x =!!!!. a. Find fg x and its domain. b. Find f g (x) and its domain. 4

5 10. Find the inverse of the function f x =!!!!!!!. 11. Little Johnny uses his slingshot to fire a stone straight up in the air. The height h of the stone in feet after t seconds is given by h t = 16t! + 48t + 3 a. How long does it take for the stone to reach its maximum height? b. What is the maximum height the stone reaches? c. How long does it take for the stone to reach the ground? (Round to 3 decimal places.) 12. Consider the polynomial P x = x! + 3x! + 12x 16. a. List all possible rational zeros. b. Use synthetic division to find both real zeros. c. Find the rest of the zeros (complex/imaginary zeros). 5

6 13. Let P x = x 4! x + 1! (x + 2). a. Find all the x- intercepts of the graph of P(x) and determine if the graph will cross or touch at each of the x- intercepts. b. Determine the end behavior of the graph of P(x). c. Use this information to sketch the graph of P(x). 6

7 14. Consider the rational function f x =!!!!!!!. a. Find all the zeros of the function. b. Find the equations of any vertical asymptotes. c. Find the equation of the horizontal asymptote. d. Sketch the graph College Algebra 7

8 15. Solve the equation. x x = Solve the inequality x! + 3x Write your answer in interval notation and graph it on the real number line. 17. Let f x = 2!!!. a. Find f(2). b. Find x, if f x = 8. 8

9 18. A certain isotope has a half- life of 100 days. How many ounces of a 10- ounce sample of this isotope will remain after 200 days? Recall the formula A t = A! e!". 19. Graph the function f x = 2!!! 4. Find and plot at least 3 points and identify the asymptote. 9

10 20. Complete parts A and B below: a. Rewrite as a single logarithm. log! 5 2 log! x + 3log! (y) b. Rewrite as a sum or difference of multiples of logs. Use the log rules to break the expression down as far as possible. log! 25xy! w 21. Solve the following equation. Round the answer to 4 decimal places: 2! = 3!!! 22. Solve using any method: 3x + 2y z = 4 2x 3y + z = 11 5x + y z = 0 10

11 23. Solve the following system of equations using any method: y = x 1 y = 1 2 x Sketch the graph of the solution set for the following system of inequalities: y x 1 y < x! 11

12 25. Perform the following row operation on the given matrix: 2R! + R! R! on the matrix Find the determinant of the matrix: