Download 31. Number of cars in the United States: 143781202

Name ________________________________________
Honors Trig/PreCalc Summer Assignment
1. Completion of this summer assignment is a requirement of the course. You are responsible for
handing in the completed packet to your Honors Trig/Pre-Calculus teacher the first day of school. If
you do NOT have this completed by the first day of school, you will receive a zero for the assignment.
2.
The problems are designed as a review and to ensure the student’s readiness for Honors Trig/PreCalculus. If you do not know how to do some of these problems, utilize your resources and/or ASK
someone.
3. Allow several hours to complete this packet. Do not procrastinate.
4. You MUST SHOW ALL WORK under each problem and the work must be neat, organized and
completed in pencil to receive any credit. Circle all answers on your work.
5. It is important that you know how to do ALL of these problems.
6. You will have a test on these concepts the 1st week of school. Be prepared.
7. I will be checking my email throughout the summer. So if you have a question, email me at
[email protected]
Determine which numbers in the set are (a)
natural numbers, (b) integers, (c) rational
numbers, and (d) irrational numbers.
3
1
1. 22, , 31,  , 7,0.1234 

4
Determine the domain and the range of the
function. Write answers in interval notation.
5. f (x)  36  x2

3
7. Graph y 
9
4
2.  16, 57,  ,0,8.32, 

17
5
Evaluate the following.
3. If f (x)  x 2  10 , find f (5) and f (t )
1

 x  1 if x  2 
g( x )   3
 find g(10), and g(2)
4.
20
if x  2 
1
2
 x  2  7
2
6. h(x) 
x 1
x 2  7x  10
if x  0 

3x


2
2
x

1
if
x

0




8. Graph f (x)  
10. f (x)  1  x
In problems #9 & 10,
a) find f 1 (x)
b) graph f ( x ) and f 1 (x) on the same graph
1
3
9. f (x)  x  2
11. if f (x)  2  3x and g(x)  x find
a) ( f  g)(5)
b) (g f )(x)
12. Describe the transformation(s) that have been
done to f (x)  x to get g(x)  4 x  2
13. Describe the transformation(s) that have been
done to f (x)  x to get g(x)   x  7  6
14. Find the vertex and intercepts of the graph of
y  x2  4 x  3
15. The path of a ball is given by y  
1 2
x  3x  5 ,
20
 
25.  4 x 2/7  3x
1

7


1

26.  38 
3 4


3


where y is the height in feet and x is the horizontal
distance in feet.
a) Find the maximum height of the ball.

Simplify each expression with positive exponents
only.
9 u4v 2
812 u5v
b) What is the horizontal distance at the
maximum height?
27.
16. Divide by synthetic division (3x  4 x  1)  (x  1)
Is there a remainder? If so, what is it?
29. 
2
 x 4
 y
 x 
  4 
 y 
28.
2
4 3 m3n5
121 mn4
30.  x 3  y 2 
1
For problems # 31 & 32, write the number in
scientific notation.
Simplify each expression without a calculator.
Rationalize all radicals. Write all answers in
simplified radical form.
17. 2 12  3 48  5 27
18.
31. Number of cars in the United States:
143,781,202
28x 5  7x
32. Number of yards in 1centimeter:
0.010936133 yards
19.
2
2 x

4 xy 3
3
20. 4 50  5 90
Rewrite the expression by rationalizing the
denominator or numerator. Simplify your answer.
33.
21. 7  4(3)  10
23. 27

2
3
22. 321  3(8 15) 
24.
50x8b7
5
3 7
34.
7
5 2
For problems # 35-38, perform the operations.
Write the result in standard form.
35.   4 x2  6 x    3  6 x 
37. (2x  9)(7 x  6)
49. 2 x 
3
2(x  4)
50.
3
4 x2  5
 2
x  2 2 x  3x  2
36. 9y  4 y 2   5y  10  
38. (4 x  5)3
Simplify the complex fraction.
For problems # 39-46, factor completely.
39. 2x2  14 x  16
40. 8 x 3  343
41. 12x2  67x  50
42. 4x4  21x2  27
43. x 3  4 x2  3x  12
44. y 4  16
45. 2x2  13x  7
46. 4ax  14ay  10bx  35by
For problems 47-50, write the rational expression
in simplest form. State any domain restrictions.
47.
1 4

y2 x2
51.
x
2y
3
y
x
6
1

52. x  2 x  15 x  3
1
1
x5
2
For problems # 53-56, solve the equation (if
possible) and check your solution. Put all answers
in reduced fraction form.
53. 3x  2(x  5)  10
54. 4(x  3)  3  2(4  3x)  4
55. .5(x  3)  2(x  1)  5 56. 4 x  2(7  x)  5
4x  6
x 2  3x
1 x 1
 2
48.  2
2
(x  1) x  2 x  3
x x 1
For problems # 57-65, use any method to solve the
equation (if possible).
57. 2 x  3(4  x)  5
58.
5
2
13

 2
t 1 t 2 t t 2
59. 4y 2  8y  2  0
60.
61. 3 x  2x  1  0
62. 2x  1  5  6
63. x2  6 x  3  0
65.
x  5  x 1
71.
x 5 4
2 x  5  3x  2
72.
73. 4 x  30  2x
74.
75.  x  2  3  36  0
76. 64 x 3  125  0
77. 2x  3  7
78. 2 4  x  6  18
5
x 5 9 7
64. 20  4 x  3x2  0
y 5
1
3


y2  y  2 y  2 y  1
2
66. Solve by completing the
square: x2  6 x  247  0
For problems #67-79, find all solutions of the
equations. Check for extraneous solutions.
67. 4 x 3  6x2  0
68. 3x2  6 x  9
79.
69. x 4  5x2  6  0
70. x 3  3x2  4 x  12  0
1
5
6


x  4 x  2 x2  2x  8
5
2
80. Simplify. Use positive exponents only.
8(4 x  3)1  10(5x  1)(4 x  3)1
88. 3  4 x  3  19
For problems # 81 – 91, solve each linear,
compound, or absolute value inequality. Use
interval notation to express the solutions sets.
90. 3(x  1)  2  20
81. 2  3(x  4)  13
82.
1
3

x x 5
91. 12  2x  6  3
83. 4(x  1)  2  3x  6
84.
3x
1 x
1  
10
5 10
2
3
89. 3  x  5  1
85.
4x  3
2x  1
2 
6
12
86. 1  2x  x  7  3x  1
87.
3 3 x  5  8 x  7  53(x  6)  2(3x  5)  2(4 x  3)
For problems # 92 & 93, find the midpoint of the
line segment joining the points and the distance
between the two points.
92. (3,5),(7, 4)
93. (11,3),(1,9)
94. A total of 200 feet of fencing are available to
enclose a rectangular area with 4 subdivisions, as
show below. Find the maximum possible area that
can be enclosed.
99. A car radiator contains 20 liters of 40%
antifreeze solution. How many liters will have to
be replaced with pure antifreeze if the resulting
solution is to be 50% antifreeze?
95. For what value of k will the graph of
kx  7y  10  0 be perpendicular to the graph of
100. Suppose you work in a lab. You need a 15%
acid solution for a certain test, but your supplier
only ships a 10% solution and a 30% solution.
Rather than pay the hefty surcharge to have the
supplier make a 15% solution, you decide to mix
10% solution with 30% solution, to make your own
15% solution. You need 10 liters of the 15% acid
solution. How many liters of 10% solution and 30%
solution should you use?
8 x  14 y  3  0
96. For what value of k is the graph of
kx  7y  10  0 parallel to the graph of
8 x  14 y  3  0
97. Find a 4th degree polynomial in standard form
that has -1, -1, and 3i as zeros.
98. A biologist introduces 1000 ladybugs into a
crop field. The population P of the ladybugs is
approximated by the model P 
1000(1  4t)
where
6t
t is the time in days. Find the time required for
the population to increase to at least 2000
ladybugs.