loose-leaf paper Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.

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1 Class: Date: Algebra 2 Midterm Exam Review 2014 loose-leaf paper Do all work in a neat and organzied manner on Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which is the graph of y = 2(x 2) 2 4? a. c. b. d. Short Answer Describe the pattern in the sequence. Find the next three terms. 2. 1, 2, 6, 16, 44,... 1

2 3. Suppose you drop a tennis ball from a height of 15 feet. After the ball hits the floor, it rebounds to 85% of its previous height. How high will the ball rebound after its third bounce? Round to the nearest tenth. 4. Write a recursive formula for the sequence 8, 10, 12, 14, 16,... Then find the next term. 5. Write an explicit formula for the sequence 7, 2, 3, 8, 13,... Then find a The table shows the predicted growth of a particular bacteria after various numbers of hours. Write an explicit formula for the sequence of the number of bacteria. Hours (n) Number of Bacteria Is the formula a n = 4n(n 1) is explicit or recursive? Find the first five terms of the sequence. Is the sequence arithmetic? If so, identify the common difference , 20, 27, 34, , 21, 42, 77, Find the missing term of the arithmetic sequence 22,, 34,... 2

3 11. Find the arithmetic mean a n of a n 1 = 3.9, a n + 1 = A grocery clerk sets up a display of 12-pack cartons of cola. There are 15 cartons at the base of the triangle and one at the top. How many cartons of cola are needed for the complete display? Is the sequence geometric? If so, identify the common ratio , 12, 24, 48, , 4, 16, 36,... Write the explicit formula for the sequence. Then find the fifth term in the sequence. 15. a 1 = 3, r = 3 Find the missing term of the geometric sequence ,, 1620,... Use the finite sequence. Write the related series. Then evaluate the series , 29, 32, 35, 38, 41, The sequence 15, 21, 27, 33, 39,..., 75 has 11 terms. Evaluate the related series. 3

4 19. Justine earned $17,000 during the first year of her job at city hall. After each year she received a 4% raise. Find her total earnings during the first five years on the job. 20. Evaluate the series to S In June, Cory begins to save money for a video game and a TV he wants to buy in December. He starts with $20. Each month he plans to save 10% more than the previous month. How much money will he have at the end of December? Determine whether the function is linear or quadratic. Identify the quadratic, linear, and constant terms. 22. y = (x + 1)(6x 6) 6x f(x) = (3x + 2)( 6x 3) Identify the vertex and the axis of symmetry of the parabola. Identify points corresponding to P and Q

5 25. A manufacturer determines that the number of drills it can sell is given by the formula D = 3p p 285, where p is the price of the drills in dollars. a. At what price will the manufacturer sell the maximum number of drills? b. What is the maximum number of drills that can be sold? 26. Use the vertex form to write the equation of the parabola. 27. Identify the vertex and the y-intercept of the graph of the function y = 3(x + 2) Write y = 2x x + 14 in vertex form. Write the equation of the parabola in vertex form. 29. vertex ( 4, 3), point (4, 131) Factor the expression x 2 21x 31. 8x x x 2 2x x x x x

6 35. 9x Solve by factoring. 4x x 32 = 0 Solve the equation by finding square roots x 2 = The function y = 16t models the height y in feet of a stone t seconds after it is dropped from the edge of a vertical cliff. How long will it take the stone to hit the ground? Round to the nearest hundredth of a second. 39. Use a graphing calculator to solve the equation 5x 2 + 6x 9 = 0. If necessary, round to the nearest hundredth. 40. Simplify 175 using the imaginary number i. Write the number in the form a + bi Simplify the expression. 43. (2 5i) (3 + 4i) 44. (2 + 5i)( 1 + 5i) Solve the equation x = Find the missing value to complete the square. x 2 + 2x + 6

7 Solve the quadratic equation by completing the square. 47. x x + 14 = 0 Rewrite the equation in vertex form. 48. y = x x + 16 Use the Quadratic Formula to solve the equation x 2 + 9x 2 = x 2 x + 3 = A landscaper is designing a flower garden in the shape of a trapezoid. She wants the shorter base to be 3 yards greater than the height and the longer base to be 7 yards greater than the height. She wants the area to be 155 square yards. The situation is modeled by the equation h 2 + 5h = 155. Use the Quadratic Formula to find the height that will give the desired area. Round to the nearest hundredth of a yard. 52. Write 4x 3 + 8x 2 96x in factored form. Simplify the rational expression. State any restrictions on the variable. 53. n 4 11n n 4 7n Multiply or divide. State any restrictions on the variables. 54. z 2 z + 1 z 2 + 3z + 2 z 2 + 3z 7

8 55. x + 2 x 1 x + 4 x 2 + 4x 5 8

9 Algebra 2 Midterm Exam Review 2014 loose-leaf paper Answer Section Do all work in a neat and organzied manner on MULTIPLE CHOICE 1. A SHORT ANSWER 2. Add the two previous terms and then multiply by 2; 120, 328, feet 4. a n = a n 1 + 2, where a 1 = 8; a n = 5n + 12; a n = 19n 7. explicit; 0, 8, 24, 48, yes, 7 9. no cartons 13. yes, no 15. a n = 3 ( 3) n 1 ; = $92, $ linear function linear term: 0x constant term: quadratic function quadratic term: 18x 2 linear term: 21x constant term: ( 1, 2), x = 1 P'(0, 1), Q'( 3, 2) 25. $30; 2,415 drills 26. y = 3(x + 2) vertex: ( 2, 5); y-intercept: 7 1

10 28. y = 2(x + 3) y = 2(x + 4) x(5x + 7) 31. 4(2x 2 + 3x 4) 32. (x 9)(x + 7) 33. (3x + 5)(x + 7) 34. (4x + 5) (3x + 4)(3x 4) 36. 8, , seconds , i i i i i i, 4 3 i ± y = (x + 5) , ± i yards 52. 4x(x 4)(x + 6) n 2 6 n 2 2 ; n ± 5, n ± 2 z 2 + 2z, z 1, 0, 3 z + 3 (x + 2)(x + 5), x 1, 4 x + 4 2