ALGEBRA2 PRACTICE FINAL EXAM 3 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. 3 radians in degree measure. 5 (1) 2 (2) 54 1. Express 2. Solve the equation for x: 3 x (1) -2 (3) 108 (4) 216 (5) omit (3) -3 (4) 3 (5) omit 1 9 (2) 2 3. Given the function f ( x) 2 x 2 7 . Find the numerical value of f ( 2) . (1) -23 (2) -15 (3) 1 (4) 9 (5) omit 4. Find the area of a triangle with two adjacent sides of lengths 51 and 35, and the included angle measuring 1260. Express your answer to the nearest tenth. (1) 524.6 (2) 722.0 (3) 1049.2 (4) 1444.1 (5) omit 5. Find the product: (5 i )(9 3i ) . (1) 42 (2) 45 + 3i (3) 42 – 24i (4) 45 – 21i (5) omit 6. Solve the equation 4cosx + 5 = 3 for all x in the interval 0 x 2 . 5 2 5 2 2 4 and and (1) and (2) (3) and (4) (5) omit 3 3 3 3 3 3 3 3 2 bg 7. If f ( x) x 3 find f 216 . (1) -12 (2) -36 (3) 1 36 (4) 1 12 8. The roots of the equation 3x 2 7 x k 0 will be real when k = ? 50 (1) 0 (2) (3) 4 (4) 5 12 9. The value of sin I F is: G H6 J K 2 cosbg 3 2 (2) 1 (1) (3) 2 (4) 5 2 (5) omit (5) omit (5) omit 10. The amplitude of the function y 2 cos(4 x) is: (1) -2 (2) 2 (3) 4 (4) 90 (5) omit 11. When simplified the function f ( x ) sec x cot x sin x is equivalent to: (1) 1 (2) cosx (3) tanx (4) cotx (5) omit 12. Find the value of x, to the nearest ten minutes, given sin x 0.4326 . (1) 2530' (2) 2540' (3) 6430' (4) 6420' (5) omit 13. If x log 7 235 , find the value of x to the nearest hundredth. (1) .36 (2) .47 (3) 2.44 (4) 2.81 (5) omit 14. In which quadrant does the difference of 2 3i , and ,4 7i lie? (1) I (2) II (3) III (4) IV (5) omit b g 15. The expression 5x 2 y in expanded form equals: (1) 25x2 – 4y2 (2) 25x2 + 4y2 (3) 25x2-20xy+4y2 (4)25x2-20xy–4y2 (5)omit 2 8a 2 16a . a 2 4a 4 8a 4a (3) (4) a2 a2 16. Reduce the algebraic fraction to lowest terms: (1) 4 (2) 8a a2 (5) omit 17. The graph of the equation 2 x 2 2 y 2 98 is the conic section: (1) parabola (2) circle (3) ellipse (4) hyperbola (5) omit 1 18. Express 3 log x log y as a single logarithm. 4 x3 3x (1) log x 3 4 y (2) log (3) log 4 y 1 y 4 3 (4) log xy (5) omit 4 19. If y varies inversely with x, and y = 15 when x = 6, find the value of y when x = 9. (1) 10 (2) 3.6 (3) 22.5 (4) 90 (5) omit 20. If f ( x) 3x 2 x and g( x) 8x 5 find g ( f (2)) . (1) 75 (2) 267 (3) 352 (4) 1078 (5) omit 21. Find the solution set for the inequality x 2 4 x 32 0 . (1) 8 x 4 (2) 4 x 8 (3) x 8orx 4 (4) x 4orx 8 (5)omit 22. Find the value of angle X to the nearest degree if arc A = 1650 and arc B = 750. (1) 45 (2) 90 A (3) 120 (4) 240 B X (5) omit 23. What is the solution set for the equation 1 3 (1) (2) 2 2 2x 5 4 6 . 15 (3) 2 (4) 27 2 (5) omit 24. If cos A 0 and tan A 0 , in what quadrant does the terminal side of angle A lie? (1) I (2) II (3) III (4) IV (5) omit 25. Simplify and express in a + bi form: (1) 2 – 2i 4 5i . 2 3i 23 2 i 13 13 (2) (3) 8 i 13 (4) 23 2i 13 (5) omit (3) y( x y) x (4) y( x y) 2 (5) omit x y 26. Simplify the complex fraction: x 1 1 x y (1) y 27. If log x 64 (1) 512 (2) x 3 , find the value of x. 2 (2) .96 x2 . 2x 3 3 (2) x: x 2 (3) 16 (4) 12 (5) omit 28. Find the domain of f ( x ) (1) 3U R x: x V S T 2W R S T U V W 3U R Rx 3 U (4) S S V T 2W T 2V W(5) (3) x omit 29. Solve for all values of x given the equation: 3x 5 30 . (1) 25 U R S T3 V W (2) 25 35 U R S T3 , 3 V W (3) 895 U R R35 25U(5) (4) S , V S V T3 W T3 3 W 3 5 . 5 3 5 1 (4) (5) omit 5 30. Rationalize the denominator and express the answer in simplest terms: (1) 3 5 1 (2) 3 5 (3) 3 5 5 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 5 7 32. For the equation 3x 2 8x 3 0 , find a) the sum of the roots and b) the product of the roots. 33. Write in simplest form: 2 50 3 18 . 34. Solve the equation for x, show all work: tan(10 x 20) 0 cot( x 30) 0 35. Factor the following expression completely: 2 x 3 8x 2 90x . 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. 36. Solve the following equation and express the roots in simplest a + bi form. 2 x 2 4 5x 37. a) One force of 50 pounds and one force of 85 pounds act on a body at the same point so that the resultant force is 66 pounds. Find, to the nearest degree, the angle between the original two forces. b) In acute triangle RST, m <R = 420 , m <T = 1060 , and ST = 55. Find RT to the nearest whole number. 1 38. a) On the same set of axes, sketch and label the graph of y sin x and 2 y 2 cos 2 x in the interval 0 x 2 . b) Based on the graphs drawn in part a find all values of x in the interval graphed where the two functions are equal. 39. The table below represents data gathered by a research company. a) Graph the scatter plot of the given information. b) Find the exponential equation of best fit for the given data. Round decimals to two places. c) Find the correlation coefficient “r” correct to four decimal places. d) Use the equation found in part b, with the rounded values, to estimate the value of y when x = 8. x 1 2 3 4 5 6 y 2 6 10 25 60 120