acp algebra ii midterm review - weebly

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ACP Algebra II Midterm Review

Section 1-1Solving Linear Equations

For additional practice go to pages 9-10 in textbook.

Write an algebraic expression to represent each verbal expression.

1. The difference between 8 and the quotient of a number and – 6 .

2. The product of the square of a number and 12.

Write a verbal sentence to represent the equation.

3. 3 8

122

x

Solve each equation. Check your solution.

4. 3 1

15 20 18 12 385 6

x x 5. 2 3

26 10

x x 6.

Solve each equation or formula for the specified variable.

7. 2E mc for c 8. for x

1-2 Solving Linear Inequalities


Solve each inequality. Then graph the solution set on a number line.

9. 5 35y 10.

9,8 , 1, 8

Define a variable and write an inequality for the problem. Then solve.

11. The quotient of three times a number and four is at least -16.

Section 1-3 Rate of Change and Slope


Find the slope of the line that passes through each pair of points.

12. 5,14 , 5, 8 13.

Graph each line.

14. 15.

Section 1-4 Writing Linear Equations


Write the equation in slope-intercept form for each graph.

16. 17.

Write the equation in slope-intercept form for the line described.

18. slope = 6

5 , passes through (3, - 7) 19. passes through (6, - 2) and (8, 3)

Write an equation in slope-intercept for the line that satisfies each set of conditions.

20. passes through (-6, -6), parallel to 2 3x y

21. passes through (10, 2), perpendicular to 4 6x y

Section 1-5 Graphing Linear Inequalities


Graph the inequality.

22. 2 3 12y x

Section 1-6 Solving Systems of Equations

For additional practice go to pages 47 - 49 in textbook.

Solve by graphing.

23. 3 6

2

x y

x y

24.

2 8

3 4 3

x y

y x

Solve the system using substitution. Solve the system using elimination.

25. 3 22

4 2 4

x y

x y

26.

8 3 11

5 2 3

x y

x y

1-7 Solving Systems of Inequalities by Graphing

For additional practice go to pages 55 - 57 in textbook.

27. 3 4

2 1

y x

y x

28.

2 4

3 3

y x

y x

Section 0-1 Representing Functions

State the domain and range of each relation in set-builder notation. Then determine whether the relation is a function.

Determine if it is one-to-one. Then state whether it is discrete or continuous.

29. 6,0 , 5,5 , 9, 2 , 2, 9

30.

Graph each equation, and determine the domain and range in set builder notation. Determine whether the equation is a

function. Determine if it is one-to-one. Then state whether it is discrete or continuous.

31. ( ) 4 2f x x 32. 7x 33. 22 1y x

Evaluate the function.

34. ( 3) if ( ) 4 8f f x x 35. (5 )g x if 2( ) 2 4 1g x x x 36. ( 1)h x if

2( ) 9h x x

Section 2-2 Linearity and Symmetry

For additional practice go to pages 100 in textbook.

State whether each function is a linear function. Write yes or no then explain.

37. 7

( )x

g xx

38. 12 4 8y x

Section 2-3 Extrema and End Behavior

For additional practice go to pages 107 – 109 in the textbook.

Describe the end behavior for each linear function using infinity notation.

39. 40.

41. The table below represents a continuous function. Determine the consecutive values of x between which the zeros

occur.

Use your graphing calculator to find the zeros, maxima and minima of the graph.

42. 3 2( ) 3 2 4 1f x x x x

Section 2-5 Graphing Special Functions

For additional practice go to pages 121 – 123 in textbook.

Graph each function. Identify the domain and range in interval notation.

43.

3 4

( ) 4 2

6 2

x

f x x x

x x

44.

8 1

( ) 2 1 4

4 4

x

g x x x

x x

Write a piecewise definition for the function shown.

45. 46.

( )g x

( )g x

47.

Section 2-6 Transformations of Functions

For practice problems go to pages 128 – 131 in textbook.

Graph each function. State the domain and range in interval notation.

48. 2( 3) 7y x 49.

1( ) 6 9

4h x x

Write an equation for each graph.

50. 51.

Section 3-1 Graphing Quadratic Functions


Complete parts a – d for each quadratic function.

a) Find the y-intercept, the equation of the axis of symmetry, and the vertex.

b) Make a table of values with 5 points including the vertex.

c) Use the information to graph the function.

d) State the domain and range in set-builder notation.

52. 2 3 4y x x 53.

2( ) 2 8 5f x x x

Determine whether each function has a maximum or minimum VALUE, and find the value.

54. 2( ) 3 12f x x x 55.

2( ) 4 10 6f x x x

Section 3-2 Solving Quadratic Equations by Graphing

For additional practice go to pages 167 – 169 in the textbook.

Use the related graph of each equation to determine the solutions.

56. 2 2 3 0x x 57.

2 3 10 0x x 58. 2 8 16 0x x

Simplifying Radicals and Operations with Radicals

Not in textbook

Simplify

59. 1445 60. 4 192 61. 4 83 1280x y

62. 3 20 15 45 6 80 63. ( 6 2 7)( 13 6) 64. 450

65. 3 64 66. 10

12 67.

12 54 144x y

68. 8 20

12 6

69.

28

7 70.

2( 14 5)

71. (14 5 ) ( 8 19 )i i 72. ( 4 6 ) ( 3 12 )i i 73. 2(6 )( 4 )(7 )i i i

74. 3 2( 3 )( 7 )i i 75.

53i 76. 98i

77. 4

3 2i 78.

4 3

5 2

i

i

79.

12 6

5

i

i

80. 25 (8 4 15)i i i 81. (2 7 )(4 2 )i i 82.

2(9 10 )i

Sections 0-2 and 0-3 Multiplying Binomials and Factoring Polynomials

Find the product.

83. (3 2)(4 8)x x 84. 2(6 2)x

Factor completely.

85. 312 3x x 86.

26 2x y x 87. 27 51 14x x

88. 24 16x 89.

24 12 9a a 90. 210 2 5x xy xw yw

91. 327 64x 92.

3 327 125x y

Section 3-4 Solving Quadratic Equations by Factoring

For additional practice go to pages 184 – 186 in the textbook

Write a quadratic equation in standard form with the given root(s).

93. 8, 3 94. 2 4

,3 5

Solve each equation by factoring.

95. 212 2 2x x 96.

2 3 28 0x x

3-5 Solve Quadratic Equations by Square Root Property and Completing the Square


Solve each equation by completing the square.

97. 2 3 21 0x x 98.

22 8 5x x

Solve each equation using the square root property..

99. 24 32 0x 100.

2 36 0x

Write each function in vertex form. Identify the vertex.

101. 2 6 11y x x 102. 10242)( 2 xxxf

Section 3-6 The Quadratic Formula and the Discriminant


Find the discriminant. Describe the number and type of roots.

103. 22 3 7x x 104.

23 10 10 0x x

Use the Quadratic Formula to solve each equation.

105. 25 3 3x x 106.

29 6 19x x

Quadratic Word Problems

For additional practice see the word problems in sections 3-4, 3-5, and 3-6 in textbook.

Model each situation with a quadratic equation. Solve the equation and answer the question.

107. The length of a rectangle is 7 inches more than the width. The area is 120 inches2. Find the length and width of the

rectangle.

108. A framed picture has a length of 35 inches and a width of 25 inches. The picture itself has an area of 375 inches2.

How far is it from the edge of the picture to the edge of the frame if the distance is uniform around the picture.

109. Steve throws a baseball upward with an initial upward velocity of 64 ft/sec. The ball is five feet above the ground

when it leaves Steve’s hand. How many seconds does it take the baseball to reach its’ maximum height? What is the

maximum height?

110. Hugh Betcha launches a model rocket with an initial velocity of 88 ft/sec. After how many second will the rocket be

40 feet high?

111. Joe has been eating at a square card table until he bought a rectangular dining table. The new table is 2 feet longer

and 1 foot wider than the card table. It has an area of 24.75 ft2. How long was a side of his old card table?

112. Juliet was standing on a balcony with her arms outstretched 5 meters above the ground. Romeo, standing on the

ground below, tosses a rose up to her. It leaves his hand 2 meters above the ground with a velocity of 8 m/sec. How many

chances will Juliet have to catch the rose? When will she have these chances?

113. To celebrate the 4th of July, the town has hired Pyro Tech Inc. to launch fireworks from an 80-foot tower in town.

The rockets being fired have an initial velocity of 64 ft/sec. How long will it take the rocket to reach its’ maximum

height? How high will the rocket go? How long after launching will debris hit the ground?

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