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NO OMITS ON THE PRACTICE FINALS!! Name____________________________________________________________ Final Review Packet Algebra 2 Final Exam Practice Final 1 Part I Answer 25 out of 30 questions from this part. Each correct answer will receive 2 credits. 1. Which function is NOT one-to-one? (1) {(12,-3), (4, 15), (0, 8), (2, -11)} (3) {(5, 7), (9, 11), (3, 1), (4, 11)} (2) {(2, 0), (-1, 6), (8, 4), (3, -10)} (4) {(1,-5), (2, 2), (8, 6), (1, -4)} (5) OMIT 2. If π(π₯) = 6π₯ β 5 and (π₯) = βπ₯ + 1 , what is the value of π(π(β3)). (1) 24 (2) 19 (3) β17 (4) β22 (5) OMIT 3. What is the solution of the equation log 3 3π₯ = 3 ? 1 (1) 9 (2) 3 (3) 3 (5) OMIT (4) 0 4. The expression 6ab 18b ο 4a 72b3 ο« 9ab 10b is equivalent to (1) 3ab 10b (5) OMIT (2) 3ab 12b (3) ο6ab 2b ο« 9ab 10b (4) ο6ab ο« 9ab 10b 3 5. If π πππ₯ = 5 , what is sin(2π₯) ? 7 (1) 25 9 (2) 25 24 (3) 25 6 (4) 25 (5) OMIT 6. Which graph represents the solution set of |4π₯ β 1| β€ 7 ? (5) OMIT 7. Factored completely the expression 3π₯ 2 + π₯ β 2 is equivalent to (1) (3π₯ β 2)(π₯ + 1) (2) 3(π₯ β 2)(π₯ + 1) (3) (3π₯ + 2)(π₯ β 1) (4) π₯(3π₯ + 1)(π₯ β 2) (5) OMIT 8. Ten students compared their grades on their last math test. Their scores were: 77,55,68,92,85,80,91,94,78,89 To the nearest tenth, what is the sample standard deviation for this set of data? (1) 12.2 (2) 11.6 (3) 10 (4) 12.3 (5) OMIT 9. If a function is defined by the equation f(x) = 3π₯ , which equation represents the inverse of that function? (1) π¦ = log 3 (π₯) (2) π¦ = log (π₯) 3 (3) π¦ = log(3) (4) π¦ = (π₯)3 (5) OMIT 10. The expression (6-i)2 is equivalent to (1) 37 + 12π (2) 35 β 12π (3) 37 β 12π (4) 35+12i (5) OMIT NO OMITS ON THE PRACTICE FINALS!! 11. Factored completely the expression 4π₯ β 64π₯ is equivalent to (1) x2 (4x + 16) (2) 8x(x+2)(x-2) (3) 4x(x+4)(x-4) (4) 8x2(x - 4) (5) OMIT 3 12. If side a=6 and angle A = 62°, find side b correct to two decimal places when angle B = 41°. (1) 4.46 (2) 4.45 (3) 9.64 (4) 9.65 (5) OMIT 13. What are the values of π in the interval 0° β€ π β€ 360° that satisfy the equation 2πππ π β 1 = 0? (1) 30°, 330° (2) 150°, 210° (3) 60°, 300° (4) 120°, 240° (5) OMIT 14. Which graph does not represent a function? (1) (2) (3) (4) (5) OMIT 15. In βXYZ, m<X = 67o , side y = 3 and side z = 10. What is the area of βXYZ to the nearest square inch? (1) 13 (2) 14 (3) 28 (4) 6 (5) OMIT 16. Express (πππ π₯)(π‘πππ₯) as a single trigonometric function. (1) sinx (2) cscx (3) 1 17. The expression πππ4 16 is equivalent to (1) 1/4 (2) 1/2 OMIT (4) cosx (3) 4 (5) OMIT (4) 2 (5) 18. What change will be made to the graph of the equation π¦ = π₯ 2 if the equation is changed to π¦ = (π₯ + 5)2 β 3? (1)shift right 5, up 3 (2)shift right 5, down 3 (3)shift left 5, down 3 (4)shift up 5, left 3 (5)OMIT 19. In simplest form the expression 1 (1) π₯+π¦ 1 1 β π₯ π¦ π¦ π₯ β π₯ π¦ 1 (2) π₯βπ¦ 20. The solution set of βπ₯ β 6 + 4 = 7 (1) {15} (2) {12} equals β1 β1 (3) π₯+π¦ (4) π₯βπ¦ (5) OMIT (3) {9} (4) {-15} (5) OMIT NO OMITS ON THE PRACTICE FINALS!! 21. A circle has a radius of 8 inches. In inches, what is the length of the arc intercepted by a central angle of 2 radians? 1 (1)16 (2) 4 (3) 4 (4) 10 (5) OMIT π₯ 2 β3x+2 22. What is the domain of the function (π₯) = π₯ 2 β9 ? (1) π₯ β 3, β3 (2) π₯ = 2, 1 (3) π₯ β β3 (4) π₯ β 3 (5) OMIT 23. What is the equation of the axis of symmetry of the graph of π¦ = 2π₯ 2 β 8π₯ + 4 (1) π₯ = β4 (2) π₯ = 4 (3) π₯ = β2 (4) π₯ = 2 (5) OMIT 24. Which formula can be used to determine the total number of different 5 letter arrangements that can be formed using the letters in the word PIZZA? 5! 5! 2! (1) 2! (2) 5! (3) 3!2! (4) 5! (5) OMIT 25. The graph at the right represents which of the following equations? (1) π¦ = 1/2πππ π₯ (2) π¦ = π πππ₯ (3) π¦ = πππ π₯ (4) π¦ = 1/2π πππ₯ 26. What is the third term in the expansion of (x + y)4? (1) x2y2 (2) 2x2y2 (3) 6x2y2 (5) OMIT (4) 4x2y2 (5)OMIT 2π₯ 7 π¦ β3 27. Simplify the expression 10π₯ 9 π¦ β6 and only use positive exponents. π₯2 π¦3 (1) 5π¦ 9 (2) 5π₯ 2 π¦9 (3) 5π₯ 2 28. The solution set of 4|10-2x| = 8 is (1) { } (2) {6} (3) {4} π₯2 (4) 5π¦ 3 (5) OMIT (4) {4,6} (5) OMIT 29. Find the sum of the roots S, and the product of the roots P of the quadratic equation π₯ 2 + 5π₯ β 6 = 0 (1) S = -5, P = -6 (2) S = 5, P = 6 (3) S = -5, P = 6 (4) S = 5, P = -6 (5)OMIT 30. Given the equation sin(2π₯ + 18)° = cos (5π₯ β 12)° solve for the value of x (1) 42 (2) 12 (3) 10 (4) 0 (5) OMIT PART II Answer all 5 questions from this part. Show work in your notebook. [Four credits each] 6 31. Find the value of the expression βπ₯=2(4π₯ + 5) 32. Using the formula V = Pert find the value V for an investment of $7200 at an annual rate of 5.8% compounded continuously after 7 years. 33. Express 18 6ββ2 with a rational denominator, in simplest radical form. NO OMITS ON THE PRACTICE FINALS!! 34. Find the center and radius of the circle with the equation: (x β 8)2 + (x + 1)2 = 81 35. Solve the fractional equation for x: 6 5 11 + = π₯β1 2 π₯β1 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 your notebook. [Each question selected is worth 10 points] 36. a) Solve 4x2 + 6x + 10 = 0 expressing the result in simplest a + bi form. b) Solve for all values of x by factoring by grouping. x3 + 6x2 β 25x β 150 = 0 37. a) The table below summarizes the average revenue in thousands of dollars for the annual ticket sales for the local basketball team. Year 1 2 3 4 5 6 7 8 9 Cost 18.0 18.2 18.5 18.9 19.2 19.6 20.0 20.3 20.7 1) Find the linear equation of best fit for the given data. Round decimals to three places. 2) Find the correlation coefficient βrβ correct to 4 decimal places for part a. 3) Use the equation of best fit in part a to estimate the average revenue for the local basketball team in year 15. Round to the nearest dollar. 37. b) St. Francis Prepβs hockey team has 4 games left in the season. The probability that the team will win a game is 0.65. What is the probability to the nearest hundredth, that they will win at least three out of the four games? 38. a) Two forces have magnitudes of 72 pounds and 98 pounds respectively, and act upon a body at an angle of 85° between them. Find, to the nearest whole pound, the resultant force. b) In βABC, side a = 12.5, side b = 16.4, and the measure of angle A = 48°. Find the nearest degree, the measure of <B. 39.Solve the equation below for all values of π on the interval 0o < π < 360o. Round your answer to the nearest whole degree. 6π‘ππ2 π β 7π‘πππ β 20 = 0 NO OMITS ON THE PRACTICE FINALS!! Name____________________________________________________________ Final Review Packet Algebra 2 Final Exam Practice Final 2 Part I Answer 25 out of 30 questions from this part. Each correct answer will receive 2 credits. 1. If π(π₯) = 5π₯ + 1 and g(π₯) = β2π₯ β 3 , what is the value of π(π(4)). (1) β54 (2) β45 (3) 26 (4) β56 (5) OMIT 2. What are the values of π in the interval 0° β€ π β€ 360° that satisfy the equation 2π‘πππ + 2 = 0? (1) 45°, 225° (2) 30°, 210° (3) 135°, 315° (4) 150°, 330°(5) OMIT 3. Express (π πππ₯)(π πππ₯) as a single trigonometric function. (1) tan x (2) cot x (3) 1 (4) csc x (5) OMIT 8 4. If πππ π₯ = 15 , what is cos(2π₯) ? β97 (1) 225 16 (2) 15 16 64 (3) 225 (4) 225 (5) OMIT 5. Which graph represents the solution set of |3π₯ β 6| > 9 ? (5) OMIT 6. Ten students compared their grades on their last math test. Their scores were: 66,75,89,93,95,100,78,65,80,90 To the nearest tenth, what is the sample standard deviation for this set of data? (1) 12.2 (2)12.1 (3) 11.5 (4) 10 (5) OMIT 7. If a function is defined by the equation f(x) = 7π₯ , which equation represents the inverse of that function? (1) π¦ = (π₯)7 (2) π¦ = log(7) (3) π¦ = log 7 (π₯) (4) π¦ = log (π₯) 7(5) OMIT 8. Factored completely the expression 8π₯ 3 β 32π₯ is equivalent to (1) 8x(x+2)(x-2) (2) 8x2(x-4) (3) 8x(x2 β 4) 9. The expression 8β8π₯ 5 β 2π₯β18π₯ 3 is equivalent to (1) 22π₯ 2 β2π₯ (2) 10π₯ 2 β2π₯ (3) 22π₯β2π₯ 3 10. Which graph represents a function? (1) (2) (3) (4) 8x(x+4)(x-4) (4) 15π₯ 2 β2π₯ (5)OMIT (4) (5) OMIT NO OMITS ON THE PRACTICE FINALS!! 11. Which function is NOT one-to-one? (1) {(3,0), (4, -5), (10, 1), (10, 5)} (3) {(1, 8), (-3, 9), (2, -2), (12, 9)} (2) {(4, 1), (-5, 10), (2, -7), (8, 9)} (4) {(6,2), (1, -3), (5, -2), (7, -1)} (5) OMIT 12. In βXYZ, m<X = 48o, side y = 5 and side z = 9. What is the area of βXYZ to the nearest square inch? (1) 17 (2) 16 (3) 15 (4) 33 (5) OMIT 13. The expression πππ2 4 is equivalent to (1) 8 (2) 1/2 (3) 4 (4) 2 (5) OMIT 14. The expression (5 + 3i)2 is equivalent to (1) 34+30i (2) 34 β 30i (3)16 β 30i (4) 16+30i (5) OMIT 15.What change will be made to the graph of the equation π¦ = π₯ 2 if the equation is changed to π¦ = (π₯ β 1)2 + 2? (1)shift left 1 down 2 (2)shift right 1,up 2 (3)shift up 1 left 2 (4)shift right 1,down 2 (5)OMIT 16. Find the sum of the roots S, and the product of the roots P of the quadratic equation π₯ 2 β 3π₯ β 1 = 0 (1) S = 3, P = 1 (2) S = -3, P = 1 (3) S = 3, P = β1 (4) S = β3, P = -1 (5)OMIT 17. In simplest form the expression (1) 1 (2) 1 π 1 π 1 1β 2 π 1β equals (3) - 1 π 18. What is the solution of the equation log 2 (π₯ + 1) = 4 ? (1) 7 (2) 8 (3) 15 (4) π π+1 (4) 16 (5) OMIT (5) OMIT 19. A circle has a radius of 15 inches. In inches, what is the length of the arc intercepted by a central angle of 3 radians? 1 (1) 5 (2) 45 (3) 5 (4) 18 (5) OMIT 2π₯ 20. What is the domain of the function (π₯) = 3π₯+1 ? (1) π₯ β 1 (2) π₯ = 1/3 (3) π₯ β 0 (4) π₯ β β1/3 (5) OMIT 21. What is the equation of the axis of symmetry of the graph of π¦ = π₯ 2 β 6π₯ + 5 (1) π₯ = β3 (2) π₯ = 3 (3) π₯ = β6 (4) π₯ = 6 (5) OMIT 22. Which formula can be used to determine the total number of different 7 letter arrangements that can be formed using the letters in the word ALGEBRA? 7! 2! 7! (1) 2! (2) 7! (3) 7! (4) 2!5! (5) OMIT NO OMITS ON THE PRACTICE FINALS!! 23. Factored completely the expression4π₯ + 7π₯ + 3 is equivalent to (1)(4π₯ β 3)(π₯ β 1) (2) 4π₯(π₯ β 3)(π₯ β 1) (3)(4π₯ + 3)(π₯ + 1) (4) 4(π₯ + 1)(π₯ β 3) (5) OMIT 2 24. The graph at the right represents which of the following equations? (1) π¦ = 3π πππ₯ (2) π¦ = 3π ππ3π₯ (3) π¦ = π ππ3π₯ (4) π¦ = πππ 3π₯ (5) OMIT 25. What is the fourth term in the expansion of (x β 1)7? (1) 35x4 (2) 35π₯ 3 (3)β35π₯ 4 (4) β35π₯ 3 (5)OMIT 6π₯ 2 π¦ β4 26) Simplify the expression 2π₯ β3 π¦ 2 and only use positive exponents. (1) 3π₯ 5 1 (2) 3π₯π¦ 6 3 (4) 3x5y6 (5) OMIT 27. The solution set of 3|2x-3| = 15 is (1) {1, 4} (2) {-1, -4} (3) {-1,4} (4) {1, -4} (5) OMIT 28. The solution set of β3π₯ β 5 + 1 = 6 (1) {40/3} (2) {10} (4) {10/3} (5) OMIT π¦6 (3) π₯π¦ 6 (3) { } 29. Given the equation sec(3π₯ + 10)° = csc (2π₯ + 15)° solve for the value of x (1) 31 (2) 13 (3) 5 (4) 1 (5) OMIT 30. If side a=7 and angle A = 58°, find side b correct to two decimal places when angle B = 39°. (1) 10.27 (2) 10.26 (3) 5.20 (4) 5.19 (5) OMIT 31. PART II Answer all 5 questions from this part. Show work in your notebook. [Four credits each] Find the value of the expression β5π₯=1(8π₯ β 6) 32. Using the formula V = Pert find the value V for an investment of $8800 at an annual rate of 6.9% compounded continuously after 7 years. 33. Express 7+β5 with a rational denominator, in simplest radical form. 34. 35. 18 Find the center and radius of the circle with the equation: (x + 12)2 + (x + 5)2 = 121 Solve the fractional equation for x: 6 5 13 + 2 = π₯+4 π₯+4 NO OMITS ON THE PRACTICE FINALS!! 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 your notebook. [Each question selected is worth 10 points] 36. a) Solve 2x2 β 2x + 6 = 0 expressing the result in simplest a + bi form. b) Solve for all values of x by factoring by grouping. x3 β x2 β 49x + 49 = 0 37. a) The table below summarizes the average revenue in thousands of dollars for the annual ticket sales for the local basketball team. Year 1 2 3 4 5 6 7 8 9 Cost 10.2 10.5 10.9 11.3 11.7 11.8 12.1 12.3 12.6 1) Find the linear equation of best fit for the given data. Round decimals to three places. 2) Find the correlation coefficient βrβ correct to 4 decimal places for part a. 3) Use the equation of best fit in part 1 to estimate the average revenue for the local basketball team in year 15. Round to the nearest dollar. b) St. Francis Prepβs hockey team has 8 games left in the season. The probability that the team will win a game is 0.85. What is the probability to the nearest hundredth, that they will win at least seven out of the eight games? 38. a) Two forces have magnitudes of 74 pounds and 102 pounds respectively, and act upon a body at an angle of 63° between them. Find, to the nearest whole pound, the resultant force. b) In βABC, side a = 20.1, side b = 22.4, and the measure of angle A = 36°. Find the nearest degree, the measure of <B. 39. Solve the equation below for all values of π on the interval 0o < π < 360o. Round your answer to the nearest whole degree. 6πππ 2 π + 5πππ π β 4 = 0 NO OMITS ON THE PRACTICE FINALS!! NAME:_________________________________________________________________ Final Review Packet Algebra 2 Final Exam Practice Final 3 June 2013 Algebra 2 Final Exam 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. If π(π₯) = 2π₯ + 3 and (π₯) = β3π₯ + 2 , what is the value of π(π(2)). (1) 7 (2) β4 (3) β5 (4) β7 (5) OMIT 2. What are the values of π in the interval 0° β€ π β€ 360° that satisfy the equation 2π πππ + 1 = 0? (1) 210°, 330° (2) 60°, 300° (3) 30°, 300° (4) 30°, 150° (5) OMIT 3. Express (πππ‘π₯)(π πππ₯) as a single trigonometric function. (1) csc x (2) cos x (3) sin x (4) sec x (5) OMIT 24 (5) OMIT 4 4. If π πππ₯ = 5 , what is sin(2π₯) ? 8 12 (1) 5 (2) 25 7 (3) 25 (4) 25 5. Which graph represents the solution set of |2π₯ β 1| β₯ 7 ? (1) (2) (3) (4) 6.Ten students compared their grades on their last math test. Their scores were: 76, 84, 91, 75, 83, 82, 94, 90, 84, 89 To the nearest tenth, what is the sample standard deviation for this set of data? (1) 84.8 (2)6.3 (3) 5.9 (4) 84.0 (5) OMIT 7. If a function is defined by the equation f(x) = 5π₯ , which equation represents the inverse of that function? (1) π¦ = (π₯)5 (2) π¦ = log(π₯) (3) π¦ = log 5 (π₯) (4) π¦ = log (π₯) 5 (5) OMIT 8. Factored completely the expression 6π₯ 3 β 24π₯ is equivalent to (1) (6π₯ 2 β 12)(π₯ + 2) (2) 6π₯(π₯ 2 β 4) (3) 6π₯(π₯ + 2)(π₯ β 2) (4) (π₯ β 6)(π₯ + 2)(π₯ β 2) 9. The expression 3π₯β12π₯ β 5β3π₯ 3 is equivalent to (1) 2π₯β9π₯ 2 (2) π₯β3π₯ (3) βπ₯β3π₯ (4) (3π₯ β 5)β36π₯ 2 (5) OMIT (5)OMIT NO OMITS ON THE PRACTICE FINALS!! 10. Which function is NOT one-to-one? (1) {(2,3), (-4, 5), (7, -6), (9, 11)} (2) {(6, 0), (-3, 9), (3, 5), (8, -6)} (3) {(-10, 2), (6, 1), (9, -5), (8, 12)} (4) {(0,7), (2, -1), (8, 3), (11, -1)} (5) OMIT 11. In βXYZ, m<X = 52o , side y = 4 and side z = 11. What is the area of βXYZ to the nearest square inch? (1) 44 (2) 17 (3) 35 (4) 18 (5) OMIT 12. Which graph does not represent a function? (1) (2) (3) (4) (5) OMIT 13. The expression πππ3 81 is equivalent to (1) 1/4 (2) 5 (3) 27 (4) 4 14. The expression (2 + 4i)2 is equivalent to (1) β12 + 0π (2) β12 + 16π (3) 20 + 0π (4) 20 + 16i (5) OMIT (5) OMIT 15.What change will be made to the graph of the equation π¦ = π₯ 2 if the equation is changed to π¦ = (π₯ + 3)2 β 1? (1) shift left 3, down 1 (3) shift up 3, left 1 (2) shift right 3, up 1 (4) shift right 3, down 1 (5)OMIT 16. Find the sum of the roots S, and the product of the roots P of the quadratic equation π₯ 2 β 4π₯ β 7=0 (1) S = 7, P = 4 (2) S = 4, P = 7 (3) S = 4, P = β7 (4) S = β4, P = 7 (5)OMIT 17. In simplest form the expression 2π₯β8 (1) π₯ 2 β4 2π₯ 2 β8π₯ (2) 2π₯ 3 β4π₯ 2 π₯ 8 β 2 π₯ 1β 4 π₯ equals 2 (3) π₯ 18. What is the solution of the equation log 5 4π₯ = 2 ? 5 25 (1) 4 (2) 8 (3) 4 (4) β2 4 (4) 25 (5) OMIT (5) OMIT 19. A circle has a radius of 12 inches. In inches, what is the length of the arc intercepted by a central angle of 4 radians? 1 (1) 3 (2) 24 (3) 3 (4) 48 (5) OMIT NO OMITS ON THE PRACTICE FINALS!! π₯β3 20. What is the domain of the function π(π₯) = 2π₯+8 ? (1) π₯ β 3 (2) π₯ = 3 (3) π₯ β β4 (4) π₯ β 4 (5) OMIT 21. What is the equation of the axis of symmetry of the graph of π¦ = 3π₯ 2 + 6π₯ + 2 2 2 (1) π₯ = 3 (2) π₯ = β 3 (3) π₯ = β1 (4) π₯ = 1 (5) OMIT 22. Which formula can be used to determine the total number of different 12 letter arrangements that can be formed using the letters in the word CIRCUMFERENCE? 13! 13! 13! (1) 7! (2) 3!+2!+2! (3) 13! (4) 3!2!2! (5) OMIT 23. Factored completely the expression 2π₯ 2 + 5π₯ β 3 is equivalent to (1)(2π₯ + 3)(π₯ β 1) (2)(2π₯ β 1)(π₯ + 3) (3)π₯(π₯ β 1)(π₯ + 3) (4)(2π₯ + 1)(π₯ β 3) (5) OMIT 24. The graph at the right represents which of the following equations? (1) π¦ = 2π πππ₯ (3) π¦ = 2π ππ2π₯ (5) OMIT (2) π¦ = π ππ2π₯ (4) π¦ = 2πππ 2π₯ 25. What is the third term in the expansion of (x β 6)5? (1) 360x3 (2) β360π₯ 3 (3)β30π₯ 4 (4) 30π₯ 4 (5)OMIT 12π₯ 2 π¦ β5 26) Simplify the expression 15π₯ 4 π¦ β6 and only use positive exponents. 4π₯ 6 (1) 5π¦ 11 4π¦ (2) 5π₯ 2 (3) 4π¦ 11 5π₯ 2 27. The solution set of 2|4x +8| = 56 is (1) {β9, 5} (2) {-5, 9} (3) {5} 28. The solution set of β2π₯ + 3 β 5 = 2 (1) {2} (2) {23} (3) {3} (4) 4π₯ 2 5π¦ (5) OMIT (4) {9} (5) OMIT (4) {-26} (5) OMIT 29. Given the equation tan(2π₯ β 8)° = cot (4π₯ β 16)° solve for the value of x (1) 30 (2) 4 (3) 34 (4) 19 (5) OMIT 30. If side a=16 and angle A = 42°, find side b correct to two decimal places when angle B = 35°. (1) 13.7 (2) 7.48 (3) 34.25 (4) 36.15 (5) OMIT JUNE 2013 ALGEBRA 2 PART II Answer all 5 questions from this part. Show work in your notebook. [Four credits each] 31. Find the value of expression: β1π₯=β1(3π₯ β 7) NO OMITS ON THE PRACTICE FINALS!! 32. Using the formula π = ππ find the value of V for an investment of $5800 at an annual rate of 2.6% compounded continuously after 7 years. ππ‘ 15 33. Express 4ββ3 with a rational denominator, in simplest radical form. 34. Find the center and the radius of the circle with the equation: (π₯ β 3)2 + (π¦ + 7)2 = 169 8 3 5 35. Solve the fractional equation for x: π₯β2 + 4 = π₯β2 JUNE 2012 ALGEBRA 2 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 your notebook. [Each question selected is worth 10 points] 36. a) Solve 3x2 + 4x + 8 = 0 expressing the result in simplest a + bi form.[5 points] b) Solve for all values of x by factoring by grouping. [5 points] π₯ 3 + 5π₯ 2 β 16π₯ β 80 = 0 37. Answer both parts A and B a) The table below summarizes the average cost in thousands of dollars for annual tuition and fees at a public college. [5 points] Year Cost 1 12 2 12.6 3 13.1 4 13.4 5 13.9 6 14.2 7 14.6 8 15.2 9 15.5 10 16 1) Find the linear equation of best fit for the given data. Round decimals to three places. 2) Find the correlation coefficient βrβ correct to 4 decimal places for part a. 3) Use the equation of best fit in part a to estimate the cost of tuition and fees at the college in year 12. Round to the nearest dollar. b) St. Francis Prepβs soccer team has five games left in the season. The probability that the team will win a game is 0.75. What is the probability, to the nearest hundredth, that they will win at least four of the five games? [5 points] 38. a) Two forces have magnitudes of 46 pounds and 116 pounds respectively, and act upon a body at an angle of 73° between them. Find, to the nearest whole pound, the resultant force. [5 points] b) In βπ ππ, side π = 18.7, side π = 14.3, and the measure of angle π = 51° . Find to the nearest degree, the measure of angle S. [5 points] 39. Solve the equation below for all values of π on the interval 0° β€ π β€ 360° Round your answer to the nearest whole degree. [10 points] π‘ππ2 π β π‘πππ β 12 = 0 NO OMITS ON THE PRACTICE FINALS!! NAME:_________________________________________________________________ Final Review Packet Algebra 2 Final Exam Practice Final 4 June 2014 Algebra 2 Final Exam 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. Factor the expression 5π₯ 3 β 20π₯ 2 + 15π₯ completely: (1) (6π₯ 2 β 15π₯)(π₯ + 2) (2) 5π₯(π₯ 2 + π₯ β 3) (3) 5π₯(π₯ + 1)(π₯ β 3) (4) 5π₯(π₯ β 3)(π₯ β 1) (5) OMIT 2. If a function is defined by the equation y = πππ3 π₯, which equation represents the inverse of that function? (1) π¦ = (π₯)3 (2) π¦ = log(π₯ 3 ) (3) π¦ = 3π₯ (4) π¦ = ππππ₯ 3 (5) OMIT 3. The expression (3- 5i)2 is equivalent to (1) 9 + 25π 2 (2) β16 + 15π (3) β16 β 30π 1 4. The expression π₯1 π₯ (1) 1 +1 β1 (4) 34 + 30i (5) OMIT is equivalent to (2) 1 β π₯ 2 (3) 1+π₯ (4) 1βπ₯ π₯ 1βπ₯ 2 (5) OMIT 5. Which graph represents the solution set of |2π₯ + 3| < 9 (1) (3) (2) (4) (5) OMIT 6.Ten students measured their heights in inches. Their results were: 58,58,61,62,62,65,66,68,70,72 To the nearest tenth, what is the sample standard deviation for this set of data? (1) 64.2 (2) 4.6 (3) 4.8 (4) 61 (5) OMIT π₯β2 7. What is the domain of the function π(π₯) = 2π₯+10? (1) π₯ β β2 (2) π₯ β 2 (3) π₯ β β5 (4) π₯ β 5 (5) OMIT 8. . If π(π₯) = 4π₯ β 5 and π(π₯) = β2π₯ + 7, what is the value of π(π(5))? (1) -17 (2) -23 (3) 12 (4) 37 (5) OMIT 9. The expression 4π₯β20π₯ β 5β5π₯ 3 is equivalent to (1) βπ₯β25π₯ 3 (2) 3π₯β5π₯ (3) βπ₯β5π₯ (4) (4π₯ β 5)β15π₯ 2 (5)OMIT NO OMITS ON THE PRACTICE FINALS!! 10. Which relation IS a one-to-one function? (1) {(2,3), (-4, 5), (2, -6), (9, 11)} (2) {(6, 0), (-3, 9), (3, 9), (8, -6)} (3) {(-10, 2), (6, 1), (9, -5), (8, 12)} (4) {(0,7), (2, -1), (8, 3), (11, -1)} (5) OMIT 11. In βABC, πβ π΄ = 71° , side b = 23 and side c = 14. What is the area of βABC to the nearest tenth of a square inch? (1) 154.5 (2) 152.2 (3) 52.4 (4) 304.5 (5) OMIT 12. Which graph does not represent a function? (1) (2) (3) (4) (5) OMIT 13. The expression πππ6 216 is equivalent to (1) 1/3 (2) 36 (3) 3 (4) 4 (5) OMIT 14. Express (1 β cos π₯)(1 + cos π₯) as a single trigonometric function. (1) sin2 π₯ (2) β cos 2 π₯ (3) sec 2 π₯ (4) tan2 π₯ (5) OMIT 15.What change will be made to the graph of the equation π¦ = π₯ 2 if the equation is changed to π¦ = (π₯ β 2)2 + 6? (1) shift left 2, down 6 (3) shift up 2, left 6 (2) shift right 4, up 6 (4) shift right 2, up 6 (5)OMIT 16. What are the sum and product of the roots of the equation: π₯ 2 β 4π₯ + 8 = 0? (1) sum = -8; product = -4 (3) sum = 4; product = 8 (2) sum = -4; product = -8 (4) sum = 8; product = 4 (5)OMIT 9 17. If cos π₯ = 41, what is sin(2π₯)? 1519 (1) β 1681 1519 (2) 1681 18 (3) 41 720 (4) 1681 (5) OMIT 18. What is the solution of the equation log 5 (π₯ + 4) = 1? (1) 1 (2) 9 (3) -3 (4) 5 (5) OMIT 19. A circle has a radius of 10 feet. In feet, what is the length of the arc intercepted by a central angle of 2 radians? (1) 5 (2) 8 (3) 12 (4) 20 (5) OMIT 20. What are the values of π in the interval 0° β€ π < 360° that satisfy the equation 2cos π + β2 = 0? (1) 45o, 315o (2) 135o, 315o (3) 135o, 225o(4) 225o, 315o(5) OMIT NO OMITS ON THE PRACTICE FINALS!! 21. What is the equation of the axis of symmetry of the graph of: π¦ = 4π₯ 2 β 8π₯ + 5 5 5 (1) π₯ = β1 (2) π₯ = 1 (3) π₯ = β 8 (4) π₯ = 8 (5) OMIT 22. Which formula can be used to determine the total number of different 10 letter arrangements that can be formed using the letters in the word SMARTBOARD? 10! 10! 10! (1) 10! (2) 4! (3) 2!2! (4) 2!+2! (5) OMIT 23. The solution set of |3π₯ β 4| + 7 = 15 is β4 (1) {4} (2) {-4, 4} (3) { 3 , 4} 19 (4) { 3 } (5) OMIT 24. The graph at the right represents which of the following equations? (1) π¦ = 2π ππ2π₯ (2) π¦ = 2πππ 2π₯ (3) π¦ = 2π πππ₯ (4) π¦ = π ππ2π₯ (5) OMIT 25. What is the fourth term in the expansion of (π₯ + 4)6 ? (1) 24π₯ 4 (2) 24π₯ 3 (3) 64π₯ 3 (4) 1280π₯ 3 26) Simplify the expression 4π₯ 8 (1) 7π¦ 5 4π¦ (2) 7π₯ 2 20π₯ 5 π¦ β3 35π₯ 3 π¦ 2 4π¦ 2 (5) OMIT and only use positive exponents. (3) 7π₯ 5 4π₯ 2 (4) 7π¦ 5 (5) OMIT 27. Factored completely the expression 3π₯ 2 β 10π₯ β 8 is equivalent to (1)(3π₯ + 2)(π₯ β 4) (2)(3π₯ β 2)(π₯ + 4) (3)(3π₯ + 4)(π₯ β 2) (4)(3π₯ β 4)(π₯ + 2) 28. The solution set of β3π₯ β 5 + 6 = 8 is: (1) {2} (2) {23} (3) {3} (4) {-26} (5) OMIT (5) OMIT 29. Given the equation cos(3π₯ β 4)° = sin (5π₯ + 14)° solve for the value of x (1) 80 (2) 10 (3) 30 (4) 60 (5) OMIT 30. If side a=23 and angle A = 61°, find side b correct to two decimal places when angle B = 40°. (1) 16.90 (2) 31.30 (3) 36.34 (4) 37.08 (5) OMIT JUNE 2014 ALGEBRA 2 PART II Answer all 5 questions from this part. Show work in your notebook. [Four credits each] 31. Find the center and the radius of the circle with the equation: (π₯ + 15)2 + (π¦ + 1)2 = 196 32. Solve the fractional equation for x: 10 4 2 + = π₯β3 3 π₯β3 26 33. Express 7+β5 with a rational denominator, in simplest form. NO OMITS ON THE PRACTICE FINALS!! 34. Find the value of the expression: βπ₯=7 π₯=4(5π₯ β 12) 35. Using the formula π = ππ ππ‘ find the value of V for an investment of $5200 at an annual rate of 4.1% compounded continuously after 12 years. 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 your notebook. [Each question selected is worth 10 points] 36. Answer BOTH parts a and b: a) Solve π₯ 2 β 6π₯ + 34 = 0 expressing the result in simplest a + bi form. [5 points] b) Solve for all values of x by factoring by grouping. [5 points] 2π₯ 3 β 10π₯ 2 β 18π₯ + 90 = 0 37. Answer BOTH parts a and b: a) The table below represents the average cost in thousands of dollars for automobiles in the USA. [5 points] Year 1 2 3 4 5 6 7 8 9 10 Cost 18 19.6 23.1 23.4 23.9 24.2 24.6 25.2 25.5 26 1) Find the linear equation of best fit for the given data. Round decimals to three places. 2) Find the correlation coefficient βrβ correct to 4 decimal places for part a. 3) Use the equation of best fit in part a to estimate the cost of an automobile in year 12. Round to the nearest dollar. b) A New York baseball team has six games left in the season. The probability that the team will win a game is 0.63. What is the probability, to the nearest hundredth, that they will win at least five of the six games? [5 points] 38. Answer BOTH parts a and b. a. Two forces have magnitudes of 42 pounds and 65 pounds respectively, and act upon a body at an angle of 40° between them. Find, to the nearest pound, the resultant force of these two forces. b. In βPQR, side p = 16.4, side q = 12.7, and the measure of angle P = 68°. Find, to the nearest degree, the measure of angle Q. 39. Solve the equation below for all values of π on the interval 0° β€ π β€ 360°. Round your answer to the nearest whole degree. [10 points] π‘ππ2 π β 4π‘πππ β 12 = 0 NO OMITS ON THE PRACTICE FINALS!! Answers to Practice Final 1 Part I Part II 1. 3 2. 2 3. 1 4. 3 5. 3 6. 4 7. 1 8. 1 9. 1 10. 2 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 3 1 3 4 2 1 4 3 1 1 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 1 1 4 1 3 3 2 4 1 2 31. 105 32. $10,805.78 33. 54+9β2 17 34. πΆ = (8, β1) π = 9 35. π₯ = 3 Part III 36. a) π₯ = β3 4 ± πβ31 4 or 3±πβ31 b) π₯ = β6, π₯ = 5, π₯ = β5 4 37 a. 1) π¦ = 0.347π₯ + 17.533 2) π = 0.9980 3) 23 *Make sure your calculator has diagnostics on *2nd ο 0β¦ Scroll to βDiagnostics onβ (You will be reminded of this on test day) b. 0.56 38. a) π = 127 πππ’πππ b) πππππ π΅ = 77° 39. π = 68°, 127°, 248°, 307° NO OMITS ON THE PRACTICE FINALS!! Answers to Practice Final 2 Part I 1. 1 2. 3 3. 1 4. 1 5. 1 6. 1 7. 3 8. 1 9. 2 10. 4 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 3 1 4 4 2 3 4 3 2 4 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 2 1 3 3 3 1 3 2 2 4 Part II 31. 90 32. $14,264.18 63β9β5 33. 22 34. πΆ = (β12, β5) π = 11 35. π₯ = β6 5 Part III 1 36. a) π₯ = 2 ± β11 π 2 β¦orβ¦ π₯= 1±πβ11 2 b) π₯ = 1, π₯ = 7, π₯ = β7 37. a) 1) π¦ = .298π₯ + 9.997 b) 0.66 38. a) π = 151 πππ’πππ b) πππππ π΅ = 41 39. π = 60°, 300° 2) π = .9918 3) 15 Answer Key 1)3 2) 1 3) 2 4) 4 5) 3 6) 2 7) 3 8) 3 9) 2 10) 4 Practice Final 3 11) 2 12) 4 13) 4 14) 2 15) 1 16) 3 17) 1 18) 3 19) 4 20) 3 21) 3 22) 4 23) 2 24) 1 25) 1 26) 2 27) 1 28) 2 29) 4 30) 1 31. -21 32. $6957.76 60+15β3 33. 13 34. center (3, -7) r = 13 35. x = -2 β2±2πβ5 36. A) x = B) x = ±4, β5 3 37. A) 1) y = .428x+11.693 B) .63 2) r = .9981 3) y = 17 38. A) 137 lbs B) 36o 39. {76, 108, 256, 288} 19 (June 2013) Answers to Practice Final 4 (June 2014 Final) 1) 4 2) 3 3) 3 4) 3 5) 3 6) 3 7) 3 8) 2 9) 2 10) 3 11.) 2 12) 3 13) 3 14) 1 15) 4 16) 3 17) 4 18) 1 19) 4 20) 3 21) 2 22) 3 23) 3 24)4 25) 4 26) 4 27) 1 28) 3 29) 2 30) 1 31. center (-15, -1) r = 14 32. x = -3 91β13β5 33. 22 34. 62 35. $8505.04 36. A) 3 + 5i B) x = -3, 3, 5 37. A) 1)y = .774x + 19.093 2) r = .9045 3) 28 B) .28 38. A) 101 lbs B) 57o 39. 81, 117, 261, 297 20