Midterm Review 2012-2013

ALGEBRA 2 HONORSSemester 1 Exam Review

The following chapters and sections will be covered on the exam:

Chapter Sections

11, 4 – 6

*interval & set notation

22 – 4

*piecewise functions, transformations

4 2, 6, 10

51 – 4, 6, 7

*imaginary & complex numbers, quadratic inequalities

6

2 – 5, 8 – 12, 14*graphing exponential & logarithmic functions, e & ln, solving exponential & logarithmic equations, compound

interest

7 & 10 7.3 – 7.6, 10.3 & 10.4

8 2 – 5

FunctionsFunction Operations (+, -, x, ÷), Compositions, Domain,

Inverses

The first semester exam is scheduled for the following times:

1st Hour: Tuesday, January 22, 20132nd Hour: Tuesday, January 22, 20136th Hour: Thursday, January 24, 2013

No questions will be answered after Monday, January 21 st .

No graphing calculators are allowed on the exam. You may use a scientific calculator.

*Please remember that I have a very limited number of calculators. Make sure that you have a calculator to use on the exam.

Be sure to review all handouts and material not presented in the text.

Please remember that the problems on this review make up a small sampling of what we have covered in class this semester. Make sure you complete some additional problems (from the book, notes, previous homework assignments, quiz/test review sheets, etc.) for extra practice with the concepts we covered.

Simplify each expression.

1. 2. 3.

4. 5. 6.

7. 8. 9.

10. 11. 12.

13. 14. 15.

Solve each equation.

16. 17. 18.

19. 20. 21.

22. 23. 24.

25. 26. 27.

28. 29. 30.

31. 32.

Solve each inequality.

33. 34. 35.

Determine whether or not each relation is a function. State the domain and range of each.

36. 37. 38.

39. Write in vertex form. Identify the vertex and the x- and y-intercepts.

40. Write the equation of the quadratic function that passes through the points (1, 4), (-3, 32) and (4, 25).

Graph. State the domain and the range.

41. 42. 43.

44. 45. 46.

47. 48. 49.

Graph each system of inequalities.

50. 51.

Given , , and , determine each of the following values.

52. 53.

54. 55.

Graph each piecewise function.

56. 57.

58. The Pythagorean Sea has a depth that varies quadratically with its width. The width of the sea is 1000 meters. Two hundred meters from shore, the depth is 20 meters.

a) Write the equation of this function expressing depth in terms of width.

b) What is the maximum depth of the Pythagorean Sea?

59. You invest $800 at 4.05% annual interest. Calculate the amount you would have after 18 years if the interest rate is compounded as follows:

a) quarterlyb) monthlyc) continuously

60. If you deposit $250 into an account earning 3% annual interest compounded continuously how long will it take to triple your money?

61. The value of a $65000 car decreases by 7.5% each year. What will the car be worth in 3 years?Determine the inverse of each function.

62. 63. 64.

Factor completely.

65. 66.

67. 68.

Multiply/Divide.

69. 70.

71. a) List all possible rational roots of .

b) Could there be other roots? Explain.

c) How many roots does f(x) have?

72. Write a polynomial equation of the lowest degree with roots of 5 and 1 – 6i.

73. Given and , determine the value of each of the following.

a) b) c)

d) Determine and state the domain.

74. Given and , complete the following.

a) Determine and state the domain of the composition.

b) Determine and state the domain of .