Advanced Alg Trig



When you are taking the exam, the first part will be taken with only the 4-function calculators in the classroom.

I will be clearing your calculators during this time and after the exam. Be sure to bring the calculator that you are familiar using. You will need a pencil, (#2), and an eraser to make it clear what your final answer is, as some this exam will not be hand graded, but will be graded with a computer.

Get plenty of rest the night before and come to the exam on time so that you have a full two hours.

Please bring you textbook at this time for collection purposes. I will glue any loose bindings, you will be fined for any lost pages or a lost cover.

Best of luck, do your best! If you can do the problems on this packet you will be prepared!

Advanced Alg Trig Name______________________________

Final Exam Practice

BE PREPARED! Bring your calculator, pencils, erasers. Don’t’ forget your textbook to hand in.

.Work out all the problems showing all steps. Note that some are non-calculator problems. These should be practiced without a calculator since the final exam will have a non-calculator part.

1. List the zeros of f(x) = x(x-3)3(x+5)2 , along with any multiplicities.

2. Use the Rational Zero Theorem to list all the possible rational zeros of the following. [pic]. Use the Remainder theorem to find the remainder when P(x) is divided by x – 1.

3. Divide: [pic], state the final answer.

4. Use the factor theorem to determine whether the given binomial is a factor of P(x).

a. [pic] b. [pic]

5. Determine the far right and far left behavior of the polynomials in 4.

6. Find all the real zeros by factoring:

[pic]

7. A certain manufacturer makes widgets. The cost C(x) to the manufacturer to produce x widgets is modeled by C(x) = .25x + 1300. If the manufacturer gets $5.00 for each widget, answer the following:

a) Determine the profit function.

b).How many widgets must be made and sold to break-even?

8. Given f(x) = x + 5 and g(x) = [pic], find each of the following

a. The domain of [pic] b. [pic]

c. [pic] d. [pic]

9. Given the line 2x – 3y = 6, find each of the following and state your answer as y=mx+b.

a. the line parallel which passes through (2,5)

b. The line perpendicular which passes through (0, -4)

10. Find the value for x in the domain of f(x) = 4 -3x for which f(x) = 7

11. Find the equation of the line that passes through (-3,2), and has slope = -4, leave answer in

y = mx + b.

12. Put the following in standard vertex form f(x) = [pic]. State the vertex, the axis of symmetry, the x- and – intercepts and graph.

13. Find the maximum or minimum value. State if it is a min or max. [pic]

14. Find the domain of each function:

[pic] b. [pic] c..[pic]

15. Given the piecewise function, find the values of f(3) , f(-2), and f(0).

F(x)=[pic]

16. Graph the piece wise function in 15.

G(x) =[pic]

17. Find the center and the radius of each circle.

a. [pic] b. [pic]

18. Find the distance between the two points, find the midpoint of the line segment which joins the two points.

a. (3, 5) and (2, 7) b. (-3, -5), and (-1, 3)

19. How do you determine if a graph is a function?

Is this a graph of a function? Why or why not?

a. b. c.

Write each of the following as a single log. NO Calculator.

20. [pic] 21. [pic]

22. Expand using the properties of logarithms. No Calculator.

a. [pic] b. [pic]

Solve each equation. No Calculator.

23. [pic] 24. [pic] 25. [pic]

Write each equation in logarithmic form. No Calculator.

26. [pic] 27. [pic] 28. [pic]

Write each equation in exponential form. No Calculator

29. [pic] 30. [pic] 31. [pic]

Evaluate. If decimals occur, round to the nearest hundredth.

32. [pic] 33. [pic] 34. [pic]

35. [pic] 36. [pic] 37. [pic]

Solve each equation.

38. [pic] 39. [pic] 40. [pic]

41. [pic] 43. [pic]

44. [pic] 45. [pic] (exact answer)

46. Find the pH of baking soda with H+ = 3.98 X 10-9 mole per liter.

47. Find the intensity of an earthquake that measures 6.7 on the Richter scale.

Find the balance of $4,500 invested in an account for 3 years, at an interest rate of 1.6%,

when: a. interest is compounded monthly

b. interest is compounded continually

48. If $4,500 is invested in an account that has an annual interest rate of 6%, how long will it take to double the amount in the account if the interest is compounded semiannually? Compounded continuosly?

49. Compare the intensities of the two earthquakes, earthquake of 1960 in Chile with a Richter scale magnitude of 9.5, and the 2012 earthquake in the Philippines with a Richter scale magnitude of 5.2.

50. If a chemical has a pH of 7.2, find the number of hydrogen ions in moles per liter.

51. A tree casts a 23 meter shadow on the ground and the angle of elevation to the top

of the tree is [pic]. Find the height of the tree.

[pic]

52. Find the exact value, show all work. No Calculator!

[pic]

53. Given the point (x, y) on the terminal side of an angle in standard position, find all six trigonometric ratios. If radicals occur, leave answers in simplest radical form. NO Calculator!

[pic]

a. (3, -4) b. (-2, 0)

|Sin θ |Csc θ |

|Cos θ |Sec θ |

|Tan θ |Cot θ |

|Sin θ |Csc θ |

|Cos θ |Sec θ |

|Tan θ |Cot θ |

[pic]

c. (0, 5) d. (6, -3)

|Sin θ |Csc θ |

|Cos θ |Sec θ |

|Tan θ |Cot θ |

|Sin θ |Csc θ |

|Cos θ |Sec θ |

|Tan θ |Cot θ |

54. Find the exact of each. NO Calculator!

a. sin 150˚ b. sec [pic] c. cot -225˚ d. cos [pic]

55. Find the complement and supplement of each. Answer in radians if given radians and in degrees if given degrees.

a. [pic] b. [pic] c. 25˚ d. [pic]

56. A central angle of 45˚ intercepts an arc. If the circle has a radius of 8 cm, what is the length of the arc?

57. If a wheel makes 200 revolutions per hour, how fast is the wheel turning in radians per second?

58. Given sin β = [pic] and 270˚ < β ................
................

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