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MIDTERM REVIEW 2017 Date: ____________
Topics Covered on Midterm:
Chapter 1 Solving Equations and Inequalities
Apply Properties of Real Numbers
Evaluate and Simplify Algebraic Expressions
Solve Linear Equations
Rewrite Formulas and Equations
Solve Linear Inequalities
Rate of Change
Chapter 3 Systems of Equations
Solving a system by graphing
Solving a system by substitution or elimination
Solving a system of inequalities by graphing
Solving Systems Word Problems
Chapter 2 Functions
Functions, Relations, Vertical Line Test, Domain, Range
Function Operations, Composition
Finding Slopes of Lines, Parallel lines, Perpendicular lines
Graphing Equations of Lines, Parallel lines, Perpendicular lines
Scatter Plots (Linear Regression)
Chapter 3ish - Absolute Value Functions
Solving Absolute Value Equations and Inequalities
Graph an Absolute Value Function (vertex, x and y-intercepts, axis of symmetry)
Graph an Absolute Value Inequality
Find Domain and Range of various functions
Chapter 4 Quadratics (part 1)
Graphing Quadratics (vertex form)
Simplifying Radicals
The imaginary number and complex numbers ( EMBED Equation.3 )
Factoring Quadratic Expressions (grouping, difference of squares)
Chapter 4 Quadratics (part 2)
Solving Quadratic Equations
Taking Square Roots
Factoring
Quadratic formula (including discriminant)
Quadratic Equation Applications
Area of a Rectangle
Chapter 1: Solving Equations, Inequalities
Evaluate: EMBED Equation.3
Evaluate: EMBED Equation.3
Evaluate: EMBED Equation.3
Simplify the following expression: EMBED Equation.3
Solve the following inequality: EMBED Equation
Solve each equation.
6. EMBED Equation.3 7. EMBED Equation.3
Solve each inequality. Graph your solutions.
8. -9 EMBED Equation.3 -3x + 6 EMBED Equation.3 24
9. 4x + 2(x 1) < 11
Solve each absolute value equation or inequality.
Reminder: Absolute Value RULES
EMBED Equation.3 : EMBED Equation.3 or EMBED Equation.3
EMBED Equation.3 : EMBED Equation.3 or EMBED Equation.3
EMBED Equation.3 : EMBED Equation.3 or EMBED Equation.3
10. EMBED Equation.3 11. EMBED Equation.3 12. EMBED Equation.3
Solve the equation for x.
13. 2a + 8 = 4a + 12 14. EMBED Equation.DSMT4
15. EMBED Equation.DSMT4 16. EMBED Equation.DSMT4
Solve for the variable indicated.
17. EMBED Equation.DSMT4 ; solve for W 18. EMBED Equation.DSMT4 ; 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. EMBED Equation.DSMT4 20. EMBED Equation.DSMT4
21. EMBED Equation.DSMT4 22. EMBED Equation.DSMT4
23. Evaluate each function for the given values of x:
a. EMBED Equation.3 f(2) f(-1) f(x) = 0; solve for x.
b. EMBED Equation.3 g(-2) g(1/2) g(x) = -8; solve for x.
c. EMBED Equation.3 g(3) g(-10) 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 rockets 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. EMBED Equation.3 29. EMBED Equation.3 30. EMBED Equation.3
Solve the system by graphing.
31. EMBED Equation.3 32. EMBED Equation.3
Solve the systems using substitution.
33. EMBED Equation.3 34. EMBED Equation.3
Solve the following systems using elimination.
35. EMBED Equation.3 36. EMBED Equation.3
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 neighbors 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. EMBED Equation.DSMT4 42. EMBED Equation.3
43. EMBED Equation.3 44. EMBED Equation.DSMT4
Chapter 2: Functions/Linear Equations
45. Refer to the functions below to answer parts a d
EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4
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
x1249y-1-5-11-30
What is the equation for the line of best fit for this data? (hint: LinReg in calculator)
What is the correlation coefficient of this data?
47. Refer the equation EMBED Equation.3
Rewrite the equation in slope intercept form.
What is the y-intercept of this equation?
What is the slope of this line?
What is the x-intercept of this line?
Let EMBED Equation.3 , EMBED Equation.3 , EMBED Equation.3 . Evaluate the following.
48. EMBED Equation.3 = ______________
49. EMBED Equation.3 = ______________
Let EMBED Equation.3 and EMBED Equation.3 . Find and evaluate the following.
50. EMBED Equation.3 51. EMBED Equation.3
52. EMBED Equation.3 53. EMBED Equation.3
Domain:
Let EMBED Equation.3 and EMBED Equation.3 and EMBED Equation.3 . Find the following.
54. EMBED Equation.3 55. EMBED Equation.3
56. EMBED Equation.3
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:
_____ The slope is -5
_____ The x intercept is at 2
_____ The line y = -5x 4 is parallel to y = -5x + 2
_____ The line y = 5x + 3 is perpendicular to y = -5x + 2
63. Determine whether each statement is true or false in regards to functions:
_____ All functions pass the horizontal line test
_____ All functions have each x-value corresponding to exactly 1 unique y value
_____ An equation with an undefined slope is also a function
_____ An equation with a slope of zero is also a function
64. Circle the points that satisfy the given inequality EMBED Equation.DSMT4 (hint: plug in x and y)
(0, -4) (2, 7) (0, -8) (-1, -10)
65. Write an equation that is parallel to EMBED Equation.3 , that passes through the point (4, 2)
66. Write an equation that is perpendicular to EMBED Equation.3 , that passes through the point (4, 2)
67. Refer to the absolute value function EMBED Equation.3 , to answer a through d.
Where is the vertex of the function?
Where is the y intercept of the function?
Where are the x-intercepts of the function?
d) Create a sketch of f(x) and label parts a c
Find the domain and range of each graph. Determine whether or not the graph shows a function.
68. 69.
Domain: __________________ Domain: ____________________
Range: ___________________ Range: ______________________
Function? Yes or No Function? Yes or No
70. 71.
Domain: __________________ Domain: ____________________
Range: ___________________ Range: ______________________
Function? Yes or No Function? Yes or No
Chapter 4: Quadratics
Solve each quadratic equation by factoring.
72. EMBED Equation.3 73. EMBED Equation.3
74. EMBED Equation.3 75. EMBED Equation.3
76. EMBED Equation.3 77. EMBED Equation.3
Solve each equation by taking the square root.
78. EMBED Equation.3 79. EMBED Equation.3
80. EMBED Equation.3 81. EMBED Equation.3
Set up a quadratic equation and solve each word problem.
82. 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.
83. The length of a rectangle is 3 inches less than twice its width. The area of the rectangle is 104 square inches. Find the dimensions of the rectangle.
Find all the indicated information. Then sketch an accurate graph of the function.
84. EMBED Equation.3 85. EMBED Equation.3
Vertex: ___________ min or max? Vertex: ___________ min or max?
Axis of Symmetry: _______________ Axis of Symmetry: ________________
y-intercept: ____________________ y-intercept: ______________________
zero(s): __________________________ zero(s): ____________________________
D: ___________ R: ________________ D: ___________ R: ________________
Simplify each expression.
86. EMBED Equation.3 87. EMBED Equation.3 88. EMBED Equation.3
89. EMBED Equation.3 90. EMBED Equation.3 91. EMBED Equation.3
Solve each quadratic equation using factoring and quadratic formula.
92. EMBED Equation.3
Factoring: Quad Formula:
93. EMBED Equation.3
Factoring: Quad Formula
Find the discriminant. Determine the number and type of solutions. Do not solve.
94. EMBED Equation.3 95. EMBED Equation.3
96. EMBED Equation.3 97. EMBED Equation.3
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