Algebra 2 Name: ______________________________________MIDTERM REVIEW 2014 Date: ____________

Topics Covered on Midterm:Chapter 1 – Solving Equations and Inequalities

a. Apply Properties of Real Numbersb. Evaluate and Simplify Algebraic Expressionsc. Solve Linear Equationsd. Rewrite Formulas and Equationse. Solve Linear Inequalitiesf. Solving Absolute Value Equations and Inequalitiesg. Rate of Change

Chapter 3 – Systems of Equationsa. Solving a system by graphingb. Solving a system by substitution or eliminationc. Solving a system of inequalities by graphingd. Solving Systems Word Problems

Chapter 2 – Functionsa. Functions, Relations, Vertical Line Test, Domain, Range

1. Function Operations, Compositionb. Finding Slopes of Lines, Parallel lines, Perpendicular linesc. Graphing Equations of Lines, Parallel lines, Perpendicular linesd. Scatter Plots (Linear Regression)e. Transformations (y = x2 and y = |x|)

Chapter 4 – Quadratics (part 1)a. Graphing Quadratics (standard form, vertex form)b. Simplifying Radicalsc. The imaginary number and complex numbers ( )d. Factoring Quadratic Expressions (Bust the B)

Chapter 4 – Quadratics (part 2)a. Solving Quadratic Equations

1. Taking Square Roots2. Factoring3. Quadratic formula (including discriminant)

b. Quadratic Equation Applications1. Max/Min Problems2. Pythagorean Theorem3. Area of a Rectangle

Chapter 1: Solving Equations, Inequalities

1. Evaluate:

2. Evaluate:

3. Evaluate:

4. Simplify the following expression:

5. Solve the following inequality:

Solve each equation.

6. 7.

Solve each inequality. Graph your solutions.

8. -9 -3x + 6 24

9. 4x + 2(x – 1) < 11

Solve each absolute value equation or inequality.

Reminder: Absolute Value RULES

: or : : or

10. 11. 12.

Solve the equation for x.

13. 2a + 8 = 4a + 12 14.

15. 16.

Solve for the variable indicated.

17. ; solve for W 18. ; solve for h

Identify AND correct where the mistake was made in each of the problems. If there were no mistakes were made state so.

19. 20.

21. 22.

23. Evaluate each function for the given values of x:

a. 1. f(2) 2. f(-1) 3. f(x) = 0; solve for x.

b. 1. g(-2) 2. g(1/2) 3. g(x) = -8; solve for x.

c. 1. g(3) 2. g(-10) 3. g(x) = 3; solve for x.

Rate of Change Word Problems

24. A climber is on a hike. After 2 hours he is at an altitude of 400 feet. After 6 hours, he is at an altitude of 700 feet. What is his average rate of change?

Independent Variable: ________________________________

Dependent Variable: __________________________________

Average rate of change: __________________

25. A scuba diver is 30 feet below the surface of the water 10 seconds after he entered the water and 100 feet below the surface after 40 seconds. What is the scuba divers rate of change?

Independent Variable: ________________________________

Dependent Variable: __________________________________

Average rate of change: __________________

26. A rocket is 1 mile above the earth in 30 seconds and 5 miles above the earth in 2.5 minutes. What is the rocket’s rate of change in miles per minute?

Independent Variable: ________________________________

Dependent Variable: __________________________________

Average rate of change: __________________

27. A teacher weighed 145 lbs in 1986 and weighs 190 lbs in 2007. What was the rate of change in weight?

Independent Variable: ________________________________

Dependent Variable: __________________________________

Average rate of change: __________________

Chapter 3: Systems of Equations

Vocab:Consistent Dependent System Consistent Independent System Inconsistent System

Solve by graphing in your calculator. Be sure to rewrite your equations in slope-intercept form.

28. 29. 30.

Solve the system by graphing.

31. 32.

Solve the systems using substitution.

33. 34.

Solve the following systems using elimination.

35. 36.

Set up a system and solve using the method of your choice.

37. There are 13 animals in the barn. Some are chickens and some are pigs. There are 40 legs in all. How many of each animal are there?

38. All 231 students in the Math Club went on a field trip. Some students rode in vans which hold 7 students each and some students rode in buses which hold 25 students each. How many of each type of vehicle did they use if there were 15 vehicles total?

39. Dennis mowed his next door neighbor’s lawn for a handful of dimes and nickels, 80 coins in all. Upon completing the job he counted out the coins and it came to $6.60. How many of each coin did he earn?

40. At a high school championship basketball game 1200 tickets were sold. Student tickets cost $1.50 each and adult tickets cost $5.00 each. The total revenue collected for the game was $3200. How many student tickets were sold? How many adult tickets were sold?

Graph each system of linear inequalities.

41. 42.

43. 44.

Chapter 2: Functions/Linear Equations

45. Refer to the functions below to answer parts a – d

a) f(-2) = b) f(0) + h(-3) c) g(-4) =

d) if f(x) = -8, what is the value of x?46. Refer to the points below to answer a - b

x 1 2 4 9

y -1 -5 -11 -30

a) What is the equation for the line of best fit for this data? (hint: LinReg in calculator)

b) What is the correlation coefficient of this data?

47. Refer the equation

a) Rewrite the equation in slope intercept form.

b) What is the y-intercept of this equation?

c) What is the slope of this line?

d) What is the x-intercept of this line?

Let , , . Evaluate the following.

48. = ______________

49. = ______________

Let and . Find and evaluate the following.

50. 51.

52. 53.

Domain:

Let and and . Find the following.

54. 55.

56.

57. Answer the following using the relation: {(-7, 3), (0, 2), (4, 1), (-3, 1), (5, 2)}

a. Is the relation a function? Why or why not?

b. What is the domain of the relation?

c. What is the range of the relation?

Write the equation of the line that satisfies each condition.

58. m = 4, passes through (-3, 6) 59. m = undefined, passes through (1, -4)

60. passes through (0, 7) and (-3, -2) 61. passes through (4, 5) and (6, -7)

62. Refer to the linear equation y = -5x + 2 for a through d Determine whether each statement is true or false:

a. _____ The slope is -5

b. _____ The x intercept is at 2

c. _____ The line y = -5x – 4 is parallel to y = -5x + 2

d. _____ The line y = 5x + 3 is perpendicular to y = -5x + 2

63. Determine whether each statement is true or false in regards to functions:

a. _____ All functions pass the horizontal line test

b. _____ All functions have each x value corresponding to exactly 1 unique y value

c. _____ An equation with an undefined slope is also a function

d. _____ An equation with a slope of zero is also a function

64. Circle the points that satisfy the given inequality (hint: plug in x and y)

(0, -4) (2, 7) (0, -8) (-1, -10)

65. Write an equation that is parallel to , that passes through the point (4, 2)

66. Write an equation that is perpendicular to , that passes through the point (4, 2)

67. Refer to the absolute value function , to answer a through d.

a) Where is the vertex of the function?

b) Where is the y intercept of the function?

c) Where are the x-intercepts of the function?

d) Create a sketch of f(x) and label parts a – c

Write the coordinates of the vertex, and graph each function transformation.

68. f(x) = 69. f(x) =

vertex: ___________________ vertex: ____________________

70. f(x) = 71. f(x) =

vertex: ___________________ vertex: ____________________

Chapter 4: Quadratics

Solve each quadratic equation by factoring.

72. 73.

74. 75.

76. 77.

Set up a quadratic equation and solve each word problem.

78. The length of a rectangle is 3 centimeters more than its width. The area of the rectangle is 108 square centimeters. Find the dimensions of the rectangle.

79. One leg of a right triangle is 1 more than the other leg. The hypotenuse is 1 less than 2 times the shorter leg. Find the lengths of all the sides.

80. An object is projected upwards with an initial velocity of 40 ft/sec starting from a height of 4 feet. The object’s path follows the equation:

a.) When will the object be at its highest point and how high will it be at this time? (hint: maximum)

b.) When will the object hit the ground? (hint: x-intercept in calculator)

Find all the indicated information. Then sketch an accurate graph of the function. You may check your answers in a calculator.

81. 82.

Vertex: ___________ min or max? Vertex: ___________ min or max?

Axis of Symmetry: _______________ Axis of Symmetry: ________________

Opens up or down? Opens up or down?

y-intercept: ____________________ y-intercept: ______________________

zero(s): __________________________ zero(s): ____________________________

Simplify each expression.

83. 84. 85.

86. 87. 88.

Solve each quadratic equation using factoring and quadratic formula.

89.

Factoring: Quad Formula:

90.

Factoring: Quad Formula

Convert each function into vertex form. (hint: )

91. 92.

Find the discriminant. Determine the number and type of solutions. Do not solve.

93. 94.

95. 96.