Accelerated Math 2

Accelerated Math 2

Summer Work Packet

I. Linear Functions

A. Graph Linear Functions using slope, points, and intercepts

REMINDER: The slope-intercept form of a line is , where is the slope and is

the y-intercept.

A line crosses the x-axis when y = 0 and a line crosses the y-axis when x = 0. These

points are called the x- and y- intercepts.

Find the slope,x-intercept and y-intercept for each lineand the graph each line.

1. 2. 3.

4. 5. 6.

Write an equation for each line in slope-intercept form.

7. 8. 9.

B. Slope

REMINDER: The point- slope form of a line with slope m and containing the point is

Write the equation of the line containing each pair of the given points.

10. 11. 12.

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C. Special Types of Lines

REMINDER: Vertical lines have a slope that is undefined.

Horizontal lines have a slope of zero.

Parallel lines have the same slope.

Perpendicular lines have slopes that are negative reciprocals of each other.

Write the equation of the line containing each pair of the given points and describe the

slope.

13. (2, 7) and (-4, 7) 14. (-3, 8) and (-3, -2)

Write an equation in slope-intercept form for:

a) the line that contains the given point and is parallel to thegiven line

b) the line that contains the given point and is perpendicular to thegiven line.

15. 16.

17. 18.

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II. Function Families

Parent Graphs – Sketch the graphs of the following functions without using a graphing calculator. You should be familiar enough with these “parent” graphs to be able sketch them from memory.If you are unsure about how to graph the functions, make a “t”-chart of x- and y- values. Label the units on the graphs.

19. 20. 21.

22. 23. 24.

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B. Transformations of Basic Functions – Describe the transformations from the parent function,

to the function such as vertical shifts, stretches, and shrinks, as well as reflections

across the x- and y- axes) for each of the following functions.

25. 26.

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C. Characteristics of Graphs – For each of the following functions, state the:

domain and range
zeros
intercepts
intervals of increase and decrease
relative maximum and minimum values
end behavior.

27.28.

D. Writing Equations of Graphs

Write the equation for each of the following graphs:

29.30.

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III. Polynomials, Rationals, and Radicals

A. Add or Subtract

31. 32.

33. 34. 35.

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B. Multiply

36. 37. 38.

39. 40. 41.

42.

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C. Factor Polynomials

43. 44. 45.

46.

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D. Solve the Equation by Factoring

47. 48. 49.

E. Solve the Equation (round your solutions to the nearest hundredth)

50. 51. 52.

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F. Divide

53. 54. 55.

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IV. Lines, Reasoning, and Congruent Triangles

A. Distance and Midpoint Formulas

REMINDER: The distance between two points on a graph is given by:

The midpoint of a line segment is given by:

Find the distance between the two given points. Then find the midpoint of the segment.

56. (8, 6) and (9, 10)57. (- 8, 7) and (2, -5)

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B. Conditional Statements

Rewrite the statement in “if-then” form. Then write the converse, inverse, and

contrapositive.

58. A rose is a flower.59. All 90 angles are right angles.

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C. Linear Pairs, Right Angles, and Vertical Angles

Find the value of the variables and the measure of each angle in the diagram.

60.61.

3(2x+6) 12y (9y+5) (11y-5)

(14y-12) (7x+3) (13x+3) 2(7x-6)

62. 63.

(6x+12) (2x+10)

(5x-4)

D. Congruent Triangles

REMINDER: Triangles are congruent if:

a) Three sides of one triangle are congruent to three sides of another triangle.

b) Two sides and the included angle of one triangle are congruent to two sides and the

included angle of another triangle.

c) The hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg

of another right triangle.

d) Two angles and the included side of one triangle are congruent to two angles and the

included side of another triangle.

e) Two angles and a non-included side of one triangle are congruent to two angles and a

non-included side of another triangle.

Determine which, if any of the following triangles are congruent. State your reason.

64. 65.

66. 67.

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V. Triangle, Quadrilateral, and Polygon Relationships

A. Properties of Triangles

68. In , . Find all possible values of x. K

12 + x

20 - x

J 15 L

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69. In , , C is the midpoint of , and T is the midpoint of . Solve for x if

and .

C T

H S

70. In the figure at the left, which of the following statements is true?

B a) AB > CD b) AB < CD c) AB = CD

57 C

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71. In the diagram at the right, X is the centroid of . R

If WX = 12, determine the length of WT and TX.W

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72. In the diagram at the right, X is the circumcenter of .

(a) What is the measure of ?

(b) If LM = 17, LR = 2x, and NM = 5x-18, what is the M P

length of LQ? X

L Q

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73. Which special triangle segment has as its point of concurrency the center of the inscribed

circle?

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B. Properties of Quadrilaterals

74. Points C (-3, 5), A (- 7, 6),T (-9, -2), and S(-5, -3) are the vertices of a quadrilateral.

Determine the most specific name for the quadrilateral and explain your answer.

______

75. (a) Solve for x and y. 127

(b) What is the most specific

name for this quadrilateral?

3y + 7

(2x - 1)

6y - 5

76. Complete the following chart by checking the box if the shape always has the given property.

Property / Parallelogram / Rectangle / Rhombus / Square / Kite / Trapezoid
Both pairs of opposite angles are
Both pairs of opposite angles are
Exactly one pair of opposite sides are
Exactly one pair of opposite angles are
Consecutive angles are supplementary
Exactly one pair of opposite sides are parallel
Diagonals bisect each other
Diagonals are perpendicular to each other

C. Properties of Polygons

REMINDER: The sum of the interior angles of a polygon is given as: .

The sum of the exterior angles of any polygon is 360.

77. If the sum of the interior angles of a convex polygon is 1440, how many sides does the

polygon have? Classify the polygon by the number of sides.

78. What is the measure of one interior angle of a regular nonagon?

79. How many sides does a regular polygon have if the measure of each exterior angle 12?

80. How many sides does a regular polygon have if the measure of one interior angle is 165?

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VI. Data Analysis and Probability

A. Permutations and Combinations

REMINDER:

The number of permutations of n objects is given by: .

The number of permutations of n objects taken r at a time is given by:

The number of combinations of n objects taken r at a time is given by:

81. Find the number of ways you can arrange (a) all of the letters and (b) 2 of the letters of the

word SPARTANS.

82. A bag contains 6 blue marbles and 10 red marbles. If you choose one marble at random,

and then another marble at random, what is the probability that both marbles are blue?

Evaluate the following expressions:

83. 84.

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B. Measures of Central Tendency

REMINDER:

The median of a numbered set of data is the middle number when the data is arranged in

numerical order.

The mode of a numbered set of data is the value that occurs most frequently.

The mean of a numbered set of data is the average value.

The range of a numbered set of data is the difference between the highest value and the

lowest value.

The deviation from the mean is the difference of a data value and the mean of a data set.

The mean absolute deviation of a numbered data set is given by:

85. Find the mean, median, mode, range and mean absolute deviation of the data set given by:

50, 47, 48, 49, 47, 52, 50

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VII. Complex Numbers

Simplify the following:

86. 87. 88. 89.

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VIII. Quadraticsand Special Functions

A. Quadratic Formula

REMINDER: To solve for x in a quadratic equation use the quadratic formula:

The discriminant is given as: and helps identify the nature of the

solutions to a quadratic equation.

1) For > 0, there are two real solutions.

2) For < 0, there are two non-real (imaginary) solutions.

3) For + 0, there is one real solution.

90. Find the discriminant for and determine the nature of the solutions.

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Solve each of the following equations:

91. .92.

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B. Quadratic Functions

REMINDER: The standard form for the equation of a quadratic function is:

The vertex from for the equation of a quadratic function is: ,

where are the coordinates of the vertex and is the equation for

the axis of symmetry.

The graph opens up if and opens down if .

93. Graph and label the vertex and axis of symmetry.

94. Write in standard form.

95. Write in vertex form (hint: use the method of completing the square) and state the

vertex.

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C. Piecewise Functions

96. Graph: 97. Graph: (hint: greatest integer function)

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IX. Circles and Spheres

A. Angle, Arc, Secant, Tangent, and Chord Measures

98. Find the measure of the indicated arc or angle in if and .

(a)

(b)

(d)

(e)

(f) P

(g)

C E

Solve the following for x.

99. 100.

x 3

156 x 32

4 9

101.102.

2x-1

110

x-2 x+7

4 98

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103. If the volume of a sphere is , what is the radius and surface area of the sphere?

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104. If the radius of a sphere is 12 cm and the length of the radius were halved, what would

be the relationship between:

(a) the surface area of the original sphere and the surface area of the smaller sphere?

(b) the volume of the original sphere and the volume of the smaller sphere?

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105. If the arc length of one sector of a circle that was divided into 12 equal sectors is 3,

what is the radius of the circle?