Directions : The purpose of this packet is to help you review the material you learned in previous math courses in preparation for Precalculus Regular. Please answer each question completely, showing all work to justify your solutions.
This packet is due on the first day of school and will be assessed for completion. There will be time for you to review any questions you may have with your teacher once the school year begins. You will be tested on these concepts on the first scheduled test day, Wednesday, August 26. We are looking forward to a very rewarding school year. Have a great summer and we will see you in the fall.
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PreCalculus Summer Packet 2015
Name___________________________________
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
State the name of the property illustrated.
1) 8 · (6 · 17) = 8 · (17 · 6) 1)
2) (5 ·
3) 6(x
11)
+ 5)
·
=
7 =
6x
5
+
·
6
(11
· 5
· 7)
Evaluate the algebraic expression for the given value or values of the variable(s).
6x
7x
+ xy
; x = 1 and y = 3
2)
3)
4)
Simplify the exponential expression.
5) ( 2x3y)( 7x5y4)
10
6) 16x
8x4
7) 20x
21y12
4x20y 10
5)
6)
7)
8) ( 10x3y8)2
9) 4x
4y3 z3
4
10) ( 2x6y
7)(4x 1y)
11) 12x
4y 2z3
3xy
2z 3
3
Solve and check the linear equation.
12) 7[7x 7 + 4(x + 1)] = 7x 7
13) 0.05(40) + 0.50x = 0.30(40 + x)
Solve the equation.
= x
3
+ 4
8)
9)
10)
11)
12)
13)
14)
1

15) x
+ 7
3
=
37
15
x 2
5
First, write the value(s) that make the denominator(s) zero. Then solve the equation.
16) 3
2
+ 3 = x
27
2
Solve the absolute value equation or indicate that the equation has no solution.
17) 4x 6 7 = 12
18) 3x + 6 = x + 3
Express the interval in set builder notation and graph the interval on a number line.
19) [ 9, 6)
15)
16)
17)
18)
19)
Use graphs to find the set.
20) (1, ) [17, ) 20)
Solve the linear inequality. Other than , use interval notation to express the solution set and graph the solution set on a number line.
21) 6x + 3 > 5x + 7 21)
22) 4(5x 3) < 24x + 28 22)
Solve the compound inequality. Other than , use interval notation to express the solution set and graph the solution set on a number line.
23) 4 < x 3 6 23)
Solve the absolute value inequality. Other than , use interval notation to express the solution set and graph the solution set on a number line.
24) |x 3| + 8 14 24)
2

Begin by graphing the standard absolute value function f(x) = x . Then use transformations of this graph to graph the given function.
25) g(x) = x 3 25)
Use the given conditions to write an equation for the line in slope intercept form.
26) Passing through (2, 3) and (7, 6)
Graph the line whose equation is given.
27) y = 2x 3
26)
27)
Solve.
28) A school has just purchased new computer equipment for $20,000.00. The graph shows the depreciation of the equipment over 5 years. The point (0, 20,000) represents the purchase price and the point (5, 0) represents when the equipment will be replaced. Write a linear equation in slope intercept form that models the value of the equipment, y, x years after purchase. Use the model to predict the value of the equipment after 3 years?
28)
3

Graph the inequality.
29) x + y < 6 29)
Solve the system of equations by the substitution method.
30)
3y = x
- 12
2x
+ 6 y = 0
Solve the system by the addition method.
31) 8x + 30y = 30
3x 6y = 6
30)
31)
Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets.
32) x + y =
5 x + y =
7
32)
33) 4x
+
+ y
3y
=
=
10
30
Graph the solution set of the system of inequalities or indicate that the system has no solution.
34) 3x y
6 x
+ 2 y 8
33)
34)
4

Solve the problem.
35)
Let A =
5
5
-1 2
6
9
and B =
2
-1
8
-3
4
5
. Find A + B.
36)
Let A =
8 8 7
4 9 2
8 1 7
and B =
1 5 1
4 3 2
7 5 2
. Find 4A 2B.
Find the product AB, if possible.
37)
A =
1 3 2
4 0 5
, B =
3 0
2 1
0 5
Evaluate the determinant.
38)
3 9
6 4
Find the inverse of the matrix, if possible.
39)
A =
6 3
3 1
Use Cramer's rule to solve the system.
40) 2x + 2y = 32
2x 3y = 3
35)
36)
37)
38)
39)
40)
Begin by graphing the standard quadratic function f(x) = x2 . Then use transformations of this graph to graph the given function.
41) h(x) = (x 7)2 + 7 41)
5

42) h(x) = (x + 6)2 7 42)
Find the coordinates of the vertex for the parabola defined by the given quadratic function.
43) f(x) = x2 6x + 1
Solve the problem.
44) A developer wants to enclose a rectangular grassy lot that borders a city street for parking.
If the developer has 344 feet of fencing and does not fence the side along the street, what is the largest area that can be enclosed?
Solve the equation by factoring.
45) x2 = x + 12
43)
44)
45)
46) 46) 7 7x = (4x + 9)(x 1)
Solve the equation by the square root property.
47) (2x 3)2 = 49
Perform the indicated operations and write the result in standard form.
48) (5 + 6i)(3 i) (1 i)(1 + i)
Solve the equation using the quadratic formula.
49) 9x2 + 7x + 2 = 0
Find the zeros of the polynomial function.
50) f(x) = x3 + x2 12x
47)
48)
49)
50)
51) f(x) = x3 + 7x2 x 7 51)
Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x axis or touches the x axis and turns around, at each zero.
52) f(x) = 5(x + 7)(x 6)2 52)
6

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end behavior to match the function with its graph.
53) f(x) = 2x2 + 2x 3
A) falls to the left and falls to the right B) falls to the left and rises to the right
53)
C) rises to the left and rises to the right D) rises to the left and falls to the right
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Determine the maximum possible number of turning points for the graph of the function.
54) f(x) = 2x6 + 5x5 + 6x 22 54)
Divide using long division.
55) (15x3 28x2 + 30x 5) ÷ (5x 1)
Divide using synthetic division.
56)
3x3 11x2 + 24x + 20 x + 5
55)
56)
Find all zeros of the function and write the polynomial as a product of linear factors.
57) f(x) = x3 x2 + 9x 9 57)
7

Graph the polynomial function.
58) f(x) = x3 2x2 5x + 6 58)
Use the Binomial Theorem to expand the binomial and express the result in simplified form.
59) (4x + 2)3
Use the product rule to simplify the expression.
60) 14x2 · 28x
Add or subtract terms whenever possible.
61) 10 27 4 147 4 243
Simplify using properties of exponents.
62) (10x3/2)(5x2/3)
Simplify by reducing the index of the radical.
15
63) 8x3
For the given functions f and g , find the indicated composition.
64) f(x) = 3x + 2, g(x) = 2x + 9
(g f)(x)
65) f(x) = 13x2 4x, g(x) = 17x 6
(f g)(10)
Find the inverse of the one to one function.
66) f(x) = 6x + 5 66)
59)
60)
61)
62)
63)
64)
65)
8

Use the graph of f to draw the graph of its inverse function.
67)
Graph the rational function.
68) f(x) =
2x2 x2 25
67)
68)
Graph the function.
69) Use the graph of f(x) = 2x to obtain the graph of g(x) = 2x
2.
69)
9

70) Use the graph of f(x) = ex to obtain the graph of g(x) = ex + 3.
70)
Graph the functions in the same rectangular coordinate system.
71) f(x) = 5x and g(x) = log5x 71)
Evaluate the expression without using a calculator.
72) 7 log 7 13 72)
73) log 6 6 73)
Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.
74) log 2 (7 · 11) 74)
75) ln e
5
2
75)
76) log 2 x8 76)
Solve the equation by expressing each side as a power of the same base and then equating exponents.
77) 4(1 + 2x)
= 64 77)
10

Solve the exponential equation. Express the solution set in terms of natural logarithms.
78) 2 x
+ 8
= 5 78)
Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer.
79) log 2 (x + 3) + log 2 (x 3) = 4 79)
80) log 3 (x + 6) + log 3 (x 6) log 3 x = 2 80)
81) 81) ln x + 8 = 5
Use the graph of the rational function shown to complete the statement.
82) 82)
As x 2
-
, f(x) ?
Find the vertical asymptotes, if any, of the graph of the rational function.
83) g(x) = x + 4 x(x + 1)
Find the horizontal asymptote, if any, of the graph of the rational function.
84) f(x) =
8x
2x2 + 1
83)
84)
85) g(x) =
6x2
2x2 + 1
85)
Simplify the rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression.
86) 2x
2
x -
10x
1
+ 8
86)
Multiply or divide as indicated.
87) 2x
2
·
6x + 3
5
87)
11

88) (y
5)2
6
÷ 6y
30
36
Add or subtract as indicated.
89) 2
3
x
4
3
Simplify the complex rational expression.
7 x
+ 1
90)
7 x
1
88)
89)
90)
Write the first four terms of the sequence whose general term is given.
91) an =
3 n2
91)
Write the first four terms of the sequence defined by the recursion formula.
92) a1 = 4 and an = 4an 1 4 for n 2
Find the common difference for the arithmetic sequence.
93) 13, 18, 23, 28, . . .
92)
93)
Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the sequence with the given first term, a1, and common difference, d.
94) Find a 33 when a1 = 3 , d = -
3
4
.
94)
Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.
44
95) (5i 8) i = 1
95)
Find the indicated sum.
96) Find the sum of the first 48 terms of the arithmetic sequence: 2, 4, 6, 8, . . .
96)
If the given sequence is a geometric sequence, find the common ratio.
97) 4, 12, 36, 108, 324 97)
Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r.
98) Find a12 when a1 = 6, r = 2.
98)
Use the formula for the sum of the first n terms of a geometric sequence to solve.
99) Find the sum of the first 11 terms of the geometric sequence: 5, 10, 20, 40, 80, . . . .
99)
12

Find the sum of the infinite geometric series, if it exists.
100) 3 +
3
4
+
3
16
+
3
64
+ . . .
Find the standard form of the equation of the ellipse and give the location of its foci.
101)
100)
101)
Graph the ellipse.
102) (x
+ 1)2
9
+
(y + 2)2
16
= 1 102)
Find the foci of the ellipse whose equation is given.
103) (x
1)2
36
+
(y 3)2
9
= 1
Find the vertices and locate the foci for the hyperbola whose equation is given.
2
y2
64
= 1
103)
104)
13

Find the standard form of the equation of the hyperbola.
105) 105)
Find the standard form of the equation of the parabola using the information given.
106) Focus: (15, 0); Directrix: x = 15 106)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Match the equation to the graph.
107) (x + 2)2 = 6(y 1)
A) B)
107)
C) D)
14

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
108) In how many ways can 7 players be assigned to 7 positions on a baseball team, assuming that any player can play any position?
108)
109) How many 3 letter codes can be formed using the letters A, B, C, D, and E? No letter can be used more than once.
109)
Use the formula for nCr to evaluate the expression.
110) 12C4
Find the probability.
111) A bag contains 6 red marbles, 4 blue marbles, and 1 green marble. What is the probability of choosing a marble that is not blue when one marble is drawn from the bag?
112) A card is drawn from a well shuffled deck of 52 cards. What is the probability of drawing an ace or a 8?
113)
110)
111)
112)
113)
What is the probability that the arrow will land on 3 or 5?
15