Algebra 2 Honors Final Exam StudyGuide

Transcription

1 Name: Algebra 2 Honors Final Exam StudyGuide Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Simplify Asume that all absolute value symbols are present 1 of 22 5/23/12 12:43 PM

2 5. 6. Asume that all absolute value symbols are present 7. Solve the given triangle. Round the measures of sides to the nearest tenth and measures of angles to the nearest degree. 8.,, a.,, c.,, b.,, d.,, Find the value of the given trigonometric function of 22 5/23/12 12:43 PM

3 Solve the given equation. 10. a. n = c. n = 1 b. n = d. n = 11. a. The solution set is (, ). c. The solution set is (, ). b. The solution set is (, ). d. The solution set is (, ). 12. a. n = 1 c. n = b. n = d. n = Factor the polynomial completely Find for the following functions. 3 of 22 5/23/12 12:43 PM

4 a., c., b., d., 17. Use a calculator to approximate the value of to three decimal places. a c b d Solve the following system of equations by graphing. a. (1, 18) c. (4, 17) b. (2, 18) d. (18, 2) 19. Write an equation for the parabola whose vertex is at and which passes through 20.. Simplify the given expression. Assume that no variable equals of 22 5/23/12 12:43 PM

5 22. Evaluate the determinant using expansion by minors a. 2 c. 18 b. 58 d. 58 Estimate the x-coordinates at which the relative maxima and relative minima occur for the function. a. The relative maximum is at, and the relative minimum is at. b. The relative maximum is at, and the relative minimum is at. c. The relative maximum is at, and the relative minimum is at. d. The relative maximum is at, and the relative minimum is at. 25. Write an equation in slope-intercept form for the line that satisfies the following condition. slope 8 and passes through (4, 29) a. y = c. y = b. y = d. y = Simplify the given expression. 5 of 22 5/23/12 12:43 PM

6 26. a. b. c. d Simplify the expression using long division. a. quotient and remainder 0 c. quotient and remainder 32 b. quotient and remainder 16 d. quotient and remainder Find one angle with positive measure and one angle with negative measure coterminal with an angle of 158. a. 248, 68 c. 518, 68 b. 512, 22 d. 518, Use synthetic substitution to find and g ( 5) for the function. a. 475, 3,603 c. 479, 3,693 b. 547, 482 d. 151, Find and for the function. a. 21; 1,383 c. 43; 1,405 b. 25; 53 d. 38; 1, Find for the following functions. 33. The workers in a factory earn $25 an hour. Every week, 20% of each worker s total pay is deducted for taxes. If each worker wants a take-home salary of at least $620 a week, solve the inequality to determine how many hours each worker must work. a. at the most 31 c. at least 31 b. at least 3.1 d of 22 5/23/12 12:43 PM

7 34. Two boys are on opposite sides of a tower. They sight the top of the tower at 33 and 24 angles of elevation respectively. If the height of the tower is 100 m, find the distance between the two boys. a m c m b m d m As a receptionist for a hospital, one of Elizabeth s tasks is to schedule appointments. She allots 60 minutes for the first visit and 30 minutes for a follow-up. The doctor cannot perform more than eight follow-ups per day. The hospital has eight hours available for appointments. The first visit costs $120 and the follow-up costs $70. Let x be the number of first visits and y be the number of follow-ups. 35. Write a system of inequalities to represent the number of first visits and the number of follow-ups that can be performed. 36. What is the maximum income that the doctor receives per day? a. $1920 c. $970 b. $960 d. $ Graph the system of inequalities showing the feasible region to represent the number of first visits and the number of follow-ups that can be performed. 7 of 22 5/23/12 12:43 PM

8 38. Determine the number of first visits and follow-ups to be scheduled to make the maximum income. a. 4 first visits and 8 follow-ups c. 4 first visits and 7 follow-ups b. 16 first visits and 0 follow-ups d. 8 first visits and 0 follow-ups 39. Find and. 40. Find the coordinates of the vertices of the figure formed by each system of inequalities. a. ( 2.5, 4.5), (8, 6), (34, 27) b. ( 2.5, 4.5), ( 24, 22), ( 34, 27) c. ( 2.5, 27), ( 34, 6), (8, 4.5) d. ( 2.5, 4.5), (8, 6), ( 34, 27) Rewrite the radian measure in degrees. 8 of 22 5/23/12 12:43 PM

9 41. Graph the quadratic inequality. 42. Find the value of the determinant of 22 5/23/12 12:43 PM

10 a. 26 c. 34 b. 50 d. 29 Find the exact solution of the following quadratic equation by using the Quadratic Formula Find for the following functions. Write a quadratic equation with the given roots. Write the equation in the form, where a, b, and c are integers and 4 Evaluate the expression. Express the result in scientific notation. 47. Rewrite the degree measure in radians of 22 5/23/12 12:43 PM

11 Given a polynomial and one of its factors, find the remaining factors of the polynomial. Some of the factors may not be binomials. 49. ; a. ( )( ) c. ( ) b. ( )( ) d. ( ) 50. Find and. a. b. c. d. Perform the indicated matrix operation The formula to calculate the volume of a cylinder is. Write an expression to represent the volume of the cylinder. 11 of 22 5/23/12 12:43 PM

12 a. b. c. d. 53. Find all of the zeros of the function. a., 2, 12 c., 2, 12 b., 2, 12 d., 12 Find the exact values of the remaining five trigonometric functions of θ. 54. Suppose θ is an angle in the standard position whose terminal side is in Quadrant II and. a.,,,, b.,,,, c.,,,, d.,,,, 55. Suppose θ is an angle in the standard position whose terminal side is in Quadrant I and. 12 of 22 5/23/12 12:43 PM

13 a.,,,, b.,,,, c.,,,, d.,,,, 56. Solve by using the measurements,, and. Round measures of sides to the nearest tenth and measures of angles to the nearest degree. a.,, c.,, b.,, d.,, For the given graph, a. describe the end behavior, b. determine whether it represents an odd-degree or even-degree polynomial function, and c. state the number of real zeros. 13 of 22 5/23/12 12:43 PM

14 57. a. The end behavior of the graph is as and as. It is an even-degree polynomial function. The function has four real zeros. b. The end behavior of the graph is as and as. It is an even-degree polynomial function. The function has five real zeros. c. The end behavior of the graph is as and as. It is an odd-degree polynomial function. The function has four real zeros. d. The end behavior of the graph is as and as. It is an even-degree polynomial function. The function has four real zeros. 58. Find the value of f( 9) and g(9) if and. a. f( 9) = 11 g(9) = b. f( 9) = 29 g(9) = c. f( 9) = 43 g(9) = d. f( 9) = 36 g(9) = Simplify. Solve the given equation. Check your solution. 14 of 22 5/23/12 12:43 PM

15 60. a. {1.98, 3.03} b. { 1.98, 3.03} c. { 1.98, 3.03} d. {39.5, 3.03} 61. Solve Find for the following functions. a., c., b., d., 63. Determine whether the given triangle has no solution, one solution or two solutions. Then solve the triangle. Round measures of sides to the nearest tenth and measures of angles to the nearest degree.,, a. one solution; ; ; b. one solution; ; ; c. no solution d. one solution; ; ; Write the following quadratic function in vertex form. Then, identify the axis of symmetry. 15 of 22 5/23/12 12:43 PM

16 64. a. The vertex form of the function is The equation of the axis of symmetry is. b. The vertex form of the function is The equation of the axis of symmetry is. c. The vertex form of the function is The equation of the axis of symmetry is. d. The vertex form of the function is The equation of the axis of symmetry is. Write a verbal expression to represent the given equation. 65. a. The quotient of a number and 25 is 3. b. The difference of a number and 25 is 3. c. The sum of a given number and 25 is 3. d. The difference of 25 and a number is Write an equation in slope-intercept form for the line that satisfies the following condition. passes through (18, 5), perpendicular to the graph of y = x + 15 a. y = x + c. y = x + ( ) b. y = x + d. y = x + Solve the given inequality. Graph the solution set on a number line. 67. or a. b. c. 16 of 22 5/23/12 12:43 PM

17 d. 68. A 15-m long ladder rests against a wall at an angle of with the ground. How far is the foot of the ladder from the wall? a m c. 7.5 m b. 30 m d m 69. Find the inverse of the given function Simplify the expression using synthetic division. a. quotient and remainder 93,170 b. quotient and remainder 0 c. quotient and remainder 102,487 d. quotient and remainder 18,282 Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located. 17 of 22 5/23/12 12:43 PM

18 a. Thec. solution set is. The solution set is. b. Thed. solution set is. The solution set is. 72. The formula for the surface area A of a sphere with diameter d is c = 4. Write an expression to represent the surface area of the sphere. a. b. c. d. 18 of 22 5/23/12 12:43 PM

19 Solve the system of inequalities by graphing. 73. x > 3 y > Graph the given function. State its domain and range. 19 of 22 5/23/12 12:43 PM

20 The domain is x and the range is The domain is x and the range is b. y 1. d. y 1. The domain is x and the range is The domain is x and the range is y 1. y Find the value of if n = 4, b = 4, and a = 40,000. a b c. 10,000 d Find the values of the six trigonometric functions for angle θ, when and. a. sin θ =, cos θ =, csc θ =, sec θ =, tan θ =, and cot θ =. b. sin θ =, cos θ =, csc θ =, sec θ =, tan θ =, and cot θ =. c. sin θ =, cos θ =, csc θ =, secθ =, tan θ =, and cot θ =. d. sin θ =, cos θ =, csc θ =, secθ =, tan θ =, and cot θ =. 20 of 22 5/23/12 12:43 PM

21 77. List all of the possible rational zeros of the following function. a.,,,,,,, b.,,,,,,, c. 1, 2, 4, 5, 10, 20, 25, 50 d. 1, 2, 4, 5, 10, 20, 25, 50, Graph the inequality. 79. Consider the quadratic function. Find the y-intercept and the equation of the axis of symmetry. a. The y-intercept is + 2. The equation of the axis of symmetry is x =. b. The y-intercept is. The equation of the axis of symmetry is x = of 22 5/23/12 12:43 PM

22 c. The y-intercept is. The equation of the axis of symmetry is x = 2. d. The y-intercept is 2. The equation of the axis of symmetry is x =. Evaluate the logarithmic expression of 22 5/23/12 12:43 PM