Algebra 2 Final Exam

Transcription

1 Algebra 2 Final Exam Name: Read the directions below. You may lose points if you do not follow these instructions. The exam consists of 30 Multiple Choice questions worth 1 point each and 5 Short Answer questions worth 4 points each for 50 points total. Do your own work. Write your name on each page submitted. Include your name in the file name too. All exams must be completed and submitted to me by Friday, June 9 rd at 11:59PM. All IEP and 504 requirements will be honored. Since I will be grading all of these by hand, multiple choice and short answers must be submitted on the same date. If you chose to wait and submit the short answer questions on a different date than you submit the multiple choice answers, you will lose 2 points/per day. Work must be shown for all Short Answer questions. No work shown = no credit earned. I will not accept corrections for this Final Exam. Review your test before you submit it. You only need to submit the multiple-choice answers sheet and the short answer questions on pages 8, 9, and 10. Any questions, please call me. Page 1 of 10

2 Algebra 2B Amazing Final Exam Name 1. Simplify 64. a) 6 b) 32 c) 8 d) Simplify 5a 3 20a. a) 4a 5a b) 5a 2 4 c) 10a a d) 10a 2 3. Simplify a) 7 14 b) 49 c) d) Simplify ( 16x5 x ) 1 2. a) 1 4x 2 b) 8x 2 c) x2 4 d) 4 x 2 5. Solve. Check for extraneous solutions. (4x 12) = x a) -3; 7 b) 3; 7 c) 3; 7 is an extraneous solution d) 12; 7 is an extraneous solution Page 2 of 10

3 1 6. Let f(x) = 4x + 1 and g(x) = 2x 2 3. Find (f g)(x). a) 2x 2 + 4x + 4 b) 2x 2 + 4x 4 c) 2x 2 4x + 2 d) 2x 2 4x Let (x) = x 2 and g(x) = x 2. Find g(f( 3)). a) 25 b) 7 c) -9 d) For f(x) = x 2, find f 1 (x). Then find f(f 1 (6)). a) f 1 (x) = x + 2 ; 6 b) f 1 (x) = x + 2 ; 6 c) f 1 (x) = x + 2 ; 6 d) f 1 (x) = 1 2 x + 1 ; 4 9. Suppose w and x vary inversely and x = 1.25 when w = 8. Find x when w = 15. a) 10 b) c) 3 d) What is the equation of the vertical asymptote for y = 3 x+7 + 4? a) x = 7 b) x = 7 c) x = 3 d) x = 4 Page 3 of 10

4 11. What is the equation for the translation of the graph of y = 5 x asymptotes at x = 4 and y = 6? a) y = x+6 b) y = 5 x c) y = 5 x d) y = 5 x that has 12. What is the least common denominator for fractions that have denominators of 5x + 10 and 25x 2 100? a) 5(x + 2) b) 5(x 2 20) c) 25(x 2 4) d) 75(x + 2)(x 2 4) 13. Multiply. State restrictions on the variables. 6x + 6 a) 3(x 2) 14 ; x 2 b) 3(x 2) ; x 1 14 c) 2(x 2) 21 ; x 1 d) 2(x 2) ; no restrictions 21 7 x 2 4x Write an explicit formula for the sequence: 3, 5, 7, 9,. Find the twentieth term. a) a n = 3n + 1 ; 61 b) a n = 2n 1 ; 39 c) a n = n + 2 ; 33 d) a n = 2n + 1 ; The third and fifth terms of an arithmetic sequence are 197 and 173. What is the fourth term? a) 180 b) 161 c) 221 d) 185 Page 4 of 10

5 16. Find the 24 th term of the sequence; 4, 0, -4, -8, a) -96 b) -88 c) -100 d) What is the missing term of the sequence -64,, -16, 8? a) 40 b) 32 c) -32 d) What is the 10th term of the geometric sequence 1, 4, 16,? a) 40 b) 180,224 c) 262,144 d) 2,883, Which of the following represents an infinite series? a) 3, 8, 13, 18, 23 b) c) d) 3, 8, 13, 18, 23, 20. Evaluate 4 n=1 (n 1). a) 6 b) 10 c) 12 d) Write an equation for a parabola with a vertex at the origin and a focus at ( -4,0 ). a) y = 1 4 x2 b) y = 1 16 x2 c) x = 1 4 y2 d) x = 1 16 y2 Page 5 of 10

6 22. Write an equation for a parabola with a vertex at (6,3) and a focus at ( 6,6). a) y = 1 (x 24 6)2 + 3 b) y = 1 (x )2 6 c) y = 1 (x 12 3)2 + 3 d) y = 1 (x 12 6) Find the radius and the center of the circle with the equation (x 5) 2 + (y + 6) 2 = 7. a) (-6,6) ; 2.6 b) (5,-6) ; 7 c) (-5,6) ; 7 d) (5,-6) ; Write the equation for the circle pictured here. a) (x 4) 2 + (y + 5) 2 = 36 b) (x + 4) 2 + (y + 5) 2 = 36 c) (x 4) 2 + (y 5) 2 = 36 d) (x + 4) 2 + (y 5) 2 = Which of the following is an ellipse with the y-axis as the major axis? a) x y2 25 = 1 b) x y2 36 = 1 c) x 2 36 y2 25 = 1 d) x y2 36 = 1 Page 6 of 10

7 26. What is the inverse of y = 2x + 6 a) y = 1 2 x+3 b) y = 1 2 x+1 6 c) y = 1 2 x 3 d) y = 1 2 x Find the least common denominator. a) 72x 7 y x 7 y 4 8x 5 y 6 b) 72x 7 y 4 c) x 7 y 6 d) x 5 y You gave your little sister a good push on a swing and it made and arc of 12 ft. On the third swing it made an arc of 8.67 ft. How far did it go on the second swing?. a) 10.2 feet b) feet c) 10.6 feet d) 11.3 feet 29. When you graph y = (x+2)(x 7) 3(x+2)(x+7) a) one b) two c) three d) There are no holes how many holes are there? 30. Why do we rationalize denominators?( Select all that apply) a) Standard math practice does not allow radical in the denominator. b) To make more work for mathematicians. c) We don t want radicals dividing us. d) Mrs. Thorn said so. Page 7 of 10

8 Your Amazing Name: Please carefully transfer all of your multiple-choice answers to this page Page 8 of 10

9 Algebra 2 Amazing Final Exam Short answer questions ( 4 points each) Name A) Explain how you can tell if a rational expression is in simplest form. Include an example with your explanation. B) Rationalize the denominator C) The difference between the reciprocals of two positive odd integers is 2 /15. Find the two integers. Page 9 of 10

10 D) For a Geometric Series explain how you can tell if the series converges or diverges as you keep adding an infinite number of terms to the series. Be sure that your explanation is clear on what it means to converge or diverge. It will help to include an example. E) A department store has marked down its merchandise by 25%. It later decreases by $5 the price of items that have not sold. a) Write a function f (x) to represent the price after the 25% markdown. b) Write a function g(x) to represent the price after the $5 markdown. c) Use a composition function to find the price of a $150 item after both price adjustments. d) Does the order in which the adjustments are applied make a difference? Explain. Page 10 of 10