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ALGEBRA 2 PRACTICE FINAL EXAM June 4 PART I Answer 25 out of 30 questions from this part. Each correct answer will receive 2 credits. Write your answers on the scantron sheet provided. FOR EACH OF THE 5 QUESTIONS YOU OMIT ON PART I, FILL IN CHOICE (5) ON THE SCANTRON SHEET. 1. Given the function f ( x) x 2 3 . Find the numerical value of f ( 4) . (1) -13 (2) -1 (3) 19 (4) −5 (5) omit 2. If x log4 828 , the value of x to the nearest hundredth is: (1) 4.83 (2) 4.84 (3) 4.85 (4) 4.86 (5) omit b g 3. The expression 2 x 1 in expanded form equals: (1) 4 x 2 1 (2) 4 x 2 1 2 (3) 4 x 2 2 x 1 (4) 4 x 2 4 x 1 (5) omit 4. The graph of the equation 2 x 2 5y 2 8 is a: (1)circle (2) hyperbola (3)ellipse (4) parabola (5) omit 5. If y varies inversely with x, and y = 6 when x = 2 , find the value of x when y = 3. 2 (1) 1 (2) 6 (3) 4 (4) (5) omit 3 6. Express (1) 480 8 radians in degree measure. 3 (2) 420 (3) 300 7. Solve the equation for x: 2 x 10 6 (1) −2 (2) 2 (3) 4 (4) 240 (5) omit (4) 5 (5) omit 8. Find the solution set for the inequality x 2 4 x 12 0 . (1) 2 x 6 (2) 6 x 2 (3) x 2 or x 6 (4) x 6 or x 2 (5) omit 9. Find the area of a triangle with two adjacent sides of lengths 6.3 and 10.2, and the included angle measuring 80 . Express your answer to the nearest tenth. (1) 63.3 (2) 31.6 (3) 15.8 (4) 32.1 (5) omit Use the formula Area = (1/2)ab sin C 1 10. Solve the equation 2 sin x 2 0 for all x in the interval 0 x 2 . 5 3 4 7 (1) and (2) and (3) and (4) and (5) omit 3 3 4 4 5 5 6 6 11. Find the product: (2 3i )(5 2i ) . (1) 10 − 6i (2) 10 − 6i2 (3) 16 + 11i 12. If f ( x ) x (1) 9 2 3 (4) 16 − 11i (5) omit b g find f 27 . (2) 3 (3) 1 9 (4) 13. What is the solution set for the equation (1) {13} (2) {7} (3) {7,13} 1 3 x 9 4. (4) {25} (5) omit (5) omit 14. The roots of the equation 3x 2 8x k 0 will be imaginary when k = (1) 3 (2) 4 (3) 5 (4) 6 (5) omit 15. The value of sin (1) −1 FG 3 IJ tanFG IJ is: H 2 K H 4K (2) 0 (3) 1 16. The period of the function y 3 sin (1) 3 (2) 1 3 (4) Undefined (5) omit FG 1 xIJ is: H3 K (3) 120 17. Simplify and express in a + bi form: (1) 1 5 i 12 12 (2) (4) 1080 (5) omit 2i . 5i 1 5 1 5 1 5 i (3) i (4) i 13 13 12 12 13 13 (5) omit 18. Find the value of x, to the nearest degree, given cos x .9731 . (1) 13 (2) 14 (3) 76 (4) 77 (5) omit 19. If Z1 = 8 + 3i and Z2 = 6 − 9i, in which quadrant does Z1 + Z2 lie? (1) I (2) II (3) III (4) IV (5) omit 2 20. Reduce the algebraic fraction to lowest terms: (1) x 5 x2 (2) x 10 x2 (3) x 5 x2 x 2 7 x 10 . x2 4 (4) 7 x 10 4 (5) omit sin 2 cos2 21. When simplified the expression is equivalent to: sec (1) tan (2) sin (3) cos (4) csc (5) omit 2 2 Use the identity sin cos 1 x 22. The expression log 2 is equivalent to: y (1) log x log y (2) 2(log x log y) (3) log x 2 log y (4) log x 2 log y (5) omit 23. If f ( x) 2 x 1and g( x) 4 x 12 find f ( g(3)) . (1) 3 (2) 1 (3) 0 (4) 16 (5) omit 24. Find the value of angle X to the nearest degree if arc A = 146 and arc B = 60 . Use the formula X=(1/2)(arcA-arcB) A (1) 43 (2) 60 (3) 86 B (4) 103 (5) omit X 25. If cos A 0 and sin A 0 , in what quadrant does the terminal side of angle A lie? (1) I (2) II (3) III (4) IV (5) omit 1 1 26. Simplify the complex fraction: 5 x 4 3x x 5 3x 15 3x 15 3x 3 (1) (2) (3) (4) (5) omit 20 20 4 4 27. If log x 64 3 , find the value of x. (1) 3 (2) 4 (3) 2 28. Find the domain of f ( x ) (1) x 3 (2) x 5 x3 . x 5 (3) x 3,5 3 (4) 8 (5) omit (4) x 5 (5) omit 29. Solve for all values of x given the equation: 3x 2 11 . RS T (1) 3, 13 3 UV W (2) {3} (3) RS 13UV T3W RS T (4) 3, 13 3 UV W (5) omit 30. Rationalize the denominator and express the answer in simplest terms: (1) 4 2 (2) 8 2 2 (3) 16 2 (4) 4 8 . 2 (5) omit PART II Answer all 5 questions from this part. Show all work for credit in the white examination booklet provided. [Four credits each.] 31. Solve the following absolute value inequality and graph the solution set on the real number line: x 4 9 . [4] 32. For the equation 2 x 2 7 x 4 0 , find a) the sum of the roots and b) the product of the roots. [4] 33. Write in simplest form: 7 8 3 50 . 34. Solve the equation for x, show all work: sin(2 x 20) cos(6x 10) [4] [4] 35. Factor the following expression completely: 3x 27 . 2 [4] 4 PART III Answer 3 out of the 4 questions in this section. All work necessary to the solution of the question must be written in the white examination booklet or on graph paper, where applicable. [Each question selected is worth 10 points] 36. Solve the following equation and express the roots in simplest a + bi form. x 2 6x 13 0 37. Answer both parts a and b. a) Two men try to pull a pig out of a ditch. One man applies a force of 180 pounds while the other man applies a force of 220pounds. The resultant force is 280 pounds. Find the angle between the two applied forces, rounded to the nearest degree. AND b) In acute triangle ABC, side a = 12, side b = 14, and the m<A = 56 . Find m<C to the nearest degree. 38. a) On the same set of axes, sketch and label the graphs of the 1 equations y 3 sin 2 x and y cos x in the interval 0 x 2 . 2 b) Based on the graphs drawn in part a, determine the number of values of x in the interval graphed where the two functions are equal. 39. The number of home runs hit in the major leagues has increased steadily over the past six years while the number of stolen bases has decreased. The table below contains the data for the past six years for one team. Home 78 82 88 85 93 102 Runs Stolen 91 78 60 55 51 52 Bases a. Graph the scatter plot of the given information. b. Find the linear equation of best fit for the given data. Round decimals to two places. c. Find the correlation coefficient “r” correct to 4 decimal places. d. Use the equation found in part b to estimate the number of Stolen Bases for this team if it hits 120 Home Runs. 5