2312 test 2 Fall 2010 Form B

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1 2312 test 2 Fall 2010 Form B 1. Write the slope-intercept form of the equation of the line through the given point perpendicular to the given lin point: ( 7, 8) line: 9x 45y = 9 2. Evaluate the function at the specified value of the independent variable and simplify. 3. Find the domain of the function. all real numbers all real numbers all real numbers 4. Find the difference quotient and simplify your answer.

2 5. Write an equation for the function that is described by the following characteristics: the shape of x-axis, but moved eight units down, two units to the left, and then reflected in the 6. Find. 7. Find the inverse function of f.

3 8. Compare the graph of with. 6 shifts right 6 units, shifts downward 6 units, and shrinks by a factor of. 6 shifts right 6 units, shifts upward 6 units, and shrinks by a factor of. 6 shifts left 36 units, shifts upward 6 units, and shrinks by a factor of. 6 shifts right 36 units, shifts upward 6 units, and shrinks by a factor of. 6 shifts left 6 units, shifts downward 6 units, and shrinks by a factor of. 9. Determine the vertex of the graph of the quadratic function.

4 10. Write the quadratic function in standard form. 11. Find all real zeros of the polynomial and determine the multiplicity of each. 12. Use long division to divid 13. Use synthetic division to divid 14. Write in the form when.

5 15. The graph of the function is shown below. Determine the vertical and horizontal asymptotes of its graph. horizontal: horizontal: horizontal: horizontal: horizontal: 16. The graph of the function is shown below. Determine the domain.

6 17. Determine the equations of the vertical and horizontal asymptotes of the graph of the function. horizontal: ; vertical: horizontal: ; vertical: horizontal: ; vertical: horizontal: ; vertical: horizontal: ; vertical: 18. Determine the domain of the function. Domain: all real numbers except Domain: all real numbers except Domain: all real numbers except Domain: all real numbers Domain: all real numbers except 19. Determine the domain of the function. Domain: all real numbers except Domain: all real numbers except Domain: all real numbers except Domain: all real numbers except Domain: all real numbers

7 20. Given slant: ; vertical: slant: ; vertical: slant: ; vertical: none slant: ; vertical: slant: ; vertical:, determine the equations of any slant and vertical asymptot 21. Which of the following functions is represented by the graph below? 22. The angle of elevation of the sun is. Find the length, l, of a shadow cast by a tree that is 44 feet tall. Round answer to two decimal places. feet feet feet feet feet 23. What is the value of the function at? Round to 3 decimal places

8 24. Identify the value of the function at. Round to 3 decimal places Solve the system by the method of substitution. ( 4, 23), (5, 14) no real solution ( 4, 25) ( 4, 25), (5, 16) ( 4, 15), (5, 24) 26. During one performance of a local arts council's presentation of Fiddler on the Roof, the box office sold 200 tickets and collected $1372. If adult tickets sold for $8 and children's tickets sold for $6, how many of each type of ticket were sold? adult tickets sold = 86; children's tickets sold = 114 adult tickets sold = 114; children's tickets sold = 86 adult tickets sold = 97; children's tickets sold = 125 adult tickets sold = 97; children's tickets sold = 99 adult tickets sold = 125; children's tickets sold = Given,, and, use the Law of Sines to solve the triangle for the value of Round answer to two decimal places. 28. Determine the area of a triangle having the following measurements. Round your answer to two decimal places.

9 24.72 sq. units sq. units sq. units sq. units sq. units 29. A straight road makes an angle, A, of with the horizontal. When the angle of elevation, B, of the sun is, a vertical pole beside the road casts a shadow 8 feet long parallel to the roa Approximate the length of the pol Round answer to two decimal places feet 9.04 feet feet 5.87 feet 4.78 feet 30. Given,, and, use the Law of Cosines to solve the triangle for the value of Round answer to two decimal places A vertical pole 29 feet tall stands on a hillside that makes an angle of with the horizontal. Determine the approximate length of cable that would be needed to reach from the top of the pole to a point 78 feet downhill from the base of the pol Round answer to two decimal places feet feet feet feet feet 32. Write the complex number shown below in trigonometric form.

10 33. Find the standard form of the complex number shown below. 34. Use DeMoivre's Theorem to find the indicated power of the following complex number.

11 4, , Find all solutions to the following equation. 36. Use fundamental identities to simplify the expression below and then determine which of the following is not equivalent. 37. Which of the following is equivalent to the given expression? 38. Solve the following equation.

12 39. Solve the multiple-angle equation. 40. Use inverse functions where needed to find all solutions (if they exist) of the given equation on the interval. solution does not exist 41. Find the exact value of the given expression.

13 42. Write the given expression as the sine of an angl 43. Find the exact value of given that and. (Both u and v are in Quadrant II.) 44. Let Q represent a mass of radioactive radium ( 226 Ra) (in grams), whose half-life is 1599 years. The quantity of radium present after t years is Determine the quantity present after 200 years. Round to the nearest hundredth of a gram g 0.13 g 1.83 g 0.00 g 0.92 g 45. Rewrite the exponential equation in logarithmic form.

14 46. Evaluate the function at. Round to 3 decimal places. (You may use your calculator.) undefined Use the One-to-One Property to solve the following equation for x Condense the expression to the logarithm of a single term. 49. Determine the quadrant in which an angle,, lies if. 2nd quadrant 4th quadrant 1st quadrant 3rd quadrant 50. Rewrite the logarithmic equation in exponential form.

15 51. Find the point on the unit circle that corresponds to the real number. Use your results to evaluate. 52. Rewrite the logarithm in terms of the common logarithm (base 10). 53. Sketch the graph of the function below, being sure to include at least two full periods.

16 54. An initial investment of $7000 grows at an annual interest rate of 5% compounded continuously. How long will it take to double the investment? Use, P- principal, r - rate, t- time 1 year years years years years 55. The point is on the terminal side of an angle in standard position. Determine the exact value of.

17 56. Identify the graph of the function.

18 57. Determine the exact value of Use an inverse function to write as a function of x.

19 59. Find the exact value of, using the triangle shown in the figure below, if. 60. Given the equation below, determine two solutions such that. 61. Condense the expression to the logarithm of a single term.

20 62. Write an algebraic expression that is equivalent to. 63. Find the angle, in radians, in the figure below if and.

21 2312 test 2 Fall 2010 Form B Answer Section 1. ANS: C PTS: 1 REF: 1 OBJ: Find equation of line perpendicular to another line through given point 2. ANS: B PTS: 1 REF: 12 OBJ: Evaluate functions 3. ANS: B PTS: 1 REF: 16 OBJ: Find domain of functions 4. ANS: D PTS: 1 REF: 18 OBJ: Find difference quotients 5. ANS: B PTS: 1 REF: 45 OBJ: Write equations for transformations of common functions 6. ANS: D PTS: 1 REF: 54 OBJ: Find compositions of functions 7. ANS: C PTS: 1 REF: 61 OBJ: Find inverse of functions 8. ANS: E PTS: 1 REF: 68 OBJ: Compare transformed graph to base graph 9. ANS: B PTS: 1 REF: 70 OBJ: Determine vertex of quadratic function 10. ANS: B PTS: 1 REF: 75 OBJ: Write quadratic function in standard form 11. ANS: E PTS: 1 REF: 92 OBJ: Determine zeros and multiplicity 12. ANS: E PTS: 1 REF: 98 OBJ: Divide polynomials using long division 13. ANS: D PTS: 1 REF: 103 OBJ: Divide polynomials using synthetic division of polynomial 14. ANS: A PTS: 1 REF: 107 OBJ: Rewrite polynomial: quotient and remainder 15. ANS: A PTS: 1 REF: 155 OBJ: Determine vertical and horizontal asymptotes 16. ANS: B PTS: 1 REF: 156 OBJ: Determine the domain of a rational function 17. ANS: B PTS: 1 REF: 159 OBJ: Determine vertical and horizontal asymptotes 18. ANS: E PTS: 1 REF: 160 OBJ: Determine the domain of a rational function 19. ANS: C PTS: 1 REF: 161 OBJ: Determine the domain of a rational function 20. ANS: A PTS: 1 REF: 195 OBJ: Determine equation of slant asymptote 21. ANS: C PTS: 1 OBJ: Determine function given graph 22. ANS: E PTS: 1 OBJ: Application: Angle of elevation 23. ANS: C PTS: 1 OBJ: Evaluate exponential functions 24. ANS: C PTS: 1 OBJ: Evaluate logarithmic function 25. ANS: E PTS: 1 OBJ: Solve systems of equations in two variables by substitution 26. ANS: A PTS: 1 OBJ: Solve systems of equations in two variables 27. ANS: E PTS: 1 OBJ: Solve triangles using the Law of Sines (ASA) 28. ANS: E PTS: 1 OBJ: Find the area of an oblique triangle 29. ANS: B PTS: 1 OBJ: Application: Law of Sines 30. ANS: A PTS: 1 OBJ: Solve triangles using the Law of Cosines (SAS) - no figure 31. ANS: D PTS: 1 OBJ: Application: Law of Cosines 32. ANS: D PTS: ANS: A PTS: 1

22 34. ANS: D PTS: ANS: D PTS: ANS: B PTS: 1 OBJ: Use fundamental identities to determine equivalent expression 37. ANS: D PTS: 1 OBJ: Use fundamental identities to determine equivalent expression 38. ANS: A PTS: 1 OBJ: Solve trig equations 39. ANS: A PTS: 1 OBJ: Solve multiple-angle equations 40. ANS: D PTS: 1 OBJ: Solve trig equations by factoring 41. ANS: C PTS: 1 OBJ: Find exact value of expression using sum formula 42. ANS: B PTS: 1 OBJ: Rewrite an expression using a sum or difference formula 43. ANS: C PTS: 1 OBJ: Find exact value of expression using sum or difference formula with constraints 44. ANS: C PTS: 1 OBJ: Application: Exponential functions 45. ANS: D PTS: 1 OBJ: Express exponential equation in logarithmic form 46. ANS: B PTS: 1 OBJ: Evaluate logarithmic function 47. ANS: B PTS: 1 OBJ: Solve exponential equations using one-on-one property 48. ANS: C PTS: 1 OBJ: Condense logarithmic function using the properties of logs 49. ANS: D PTS: 1 OBJ: Determine in which quadrant an angle lies 50. ANS: E PTS: 1 OBJ: Express logarithmic equation in exponential form 51. ANS: C PTS: 1 OBJ: Evaluate trig function using unit circle 52. ANS: B PTS: 1 OBJ: Convert logarithmic expression from one base to another 53. ANS: D PTS: 1 OBJ: Sketch graphs of trig functions 54. ANS: B PTS: 1 OBJ: Solve exponential equations 55. ANS: C PTS: 1 OBJ: Determine value of trig function given point on terminal side 56. ANS: C PTS: 1 OBJ: Identify graph of exponential function 57. ANS: A PTS: 1 OBJ: Determine exact trig value of angle 58. ANS: D PTS: 1 OBJ: Rewrite theta as an inverse function involving x 59. ANS: A PTS: 1 OBJ: Determine trig value from diagram 60. ANS: E PTS: 1 OBJ: Solve trig equations 61. ANS: A PTS: 1 OBJ: Condense logarithmic function using the properties of logs 62. ANS: A PTS: 1 OBJ: Rewrite inverse trig expression as an algebraic expression 63. ANS: C PTS: 1 OBJ: Find measure of central angle given radius and arc length

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