Download Precalculus Summer Enrichment Assignment

Summer Mathematics Enrichment Packet
For Incoming Precalculus Scholars
(2016-2017 School Year)
This packet must be turned into your Precalculus teacher by the second day of instruction in
August 2016! Failure to turn in this packet will result in a grade penalty of 10 points per day.
Every problem in the packet must be completed with work shown where applicable. If you fail
to show work the packet will not be accepted and you will automatically receive a 10 point
deduction along with the advice to turn in the packet the next school day. On the third day of
instruction you will take your first Precalculus Quiz, make sure you are prepared by
completing this packet and understanding how to perform all operations without the aid of a
video, teacher, friend, etc…
No Exceptions, No Excuses, & No Sad Stories!
Inside this mathematics packet you will find a wide range of concepts. If you believe these
concepts are too difficult it is your responsibility to find help prior to the packet due date. Ask
your Algebra II or future Precalculus teacher for help or look for video tutorials online. There
are an abundance of self-help videos. Your Precalculus teacher will not accept that you are
unable to find assistance.
Incoming Precalculus
Name___________________________________
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Summer Mathematics Assignment
Period____
Solve each equation.
1) 6(2m + 3) = 3(8m + 2)
3) 8 -4 - 2k - 3 = 13
2)
( )
13
7
83 1
k- =+ k
3
5
20 2
4) 1 - 2 v + 1 = -19
Solve each compound inequality. Express the solution using inequality notation, interval notation,
and graphically.
5) 8 £ n + 10 < 20
6)
-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12
a
9
> 1 or a + 10 £ 6
-8 -6 -4 -2
0
2
4
6
8
10 12 14
Sketch the graph of each line.
7) x-intercept = -3, y-intercept = 2
8) 2 x + y = -3
y
y
6
5
4
3
2
1
-6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
6
5
4
3
2
1
1 2 3 4 5 6 x
-6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
1 2 3 4 5 6 x
Worksheet by Kuta Software LLC
-1-
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9) y = 6 x - 2
10) 0 = - x - 3 y - 6
y
y
6
5
4
3
2
1
6
5
4
3
2
1
-6 -5 -4 -3 -2 -1
1 2 3 4 5 6 x
-1
-2
-3
-4
-5
-6
-6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
1 2 3 4 5 6 x
Write the slope-intercept form of the equation of each line.
11)
y
4
2
-5 -4 -3 -2 -1
1 2 3 4 5 x
-2
-4
Write the slope-intercept form of the equation of each line given the slope and y-intercept.
4
3
12) Slope = , y-intercept = 5
Write the slope-intercept form of the equation of each line.
13) 13 x + y = 8
Write the slope-intercept form of the equation of each line.
14) y - 1 =
1(
x + 5)
5
Worksheet by Kuta Software LLC
-2-
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Write the slope-intercept form of the equation of the line through the given point with the given
slope.
15) through: (1, -4), slope = -1
Write the slope-intercept form of the equation of the line through the given points.
16) through: (-2, -4) and (0, 3)
Write the slope-intercept form of the equation of the line described.
1
2
17) through: (-2, 2), parallel to y = - x
Write the slope-intercept form of the equation of the line described.
1
2
18) through: (-4, 3), perp. to y = x - 5
Graph each equation.
19) y = x + 3 + 3
20) y = - x - 3 + 1
y
y
6
5
4
3
2
1
-6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
6
5
4
3
2
1
1 2 3 4 5 6 x
-6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
1 2 3 4 5 6 x
Worksheet by Kuta Software LLC
-3-
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Simplify.
21) (-6 + 5i) - (7 - 5i)
23)
22) (-7 - 2i)(4 - 2i)
-5 + 2i
4i
24)
6 - 10i
-7 + 7i
Sketch the graph of each function.
26) y = -3 x 2 - 18 x - 24
25) y = 2( x + 4) 2 - 2
y
y
7
4
6
2
5
4
-4
3
-2
2
4
6
8
x
-2
2
-4
1
-7 -6 -5 -4 -3 -2 -1
1
-6
2 x
-1
-8
-2
-10
-3
Factor each completely.
27) p 2 - 1
28) x 2 + 18 x + 81
29) u 2 - uv - 42v 2
30) v 2 + 7v - 30
Worksheet by Kuta Software LLC
-4-
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31) 3m 3 - 14m 2 - 80m
32) -2a 2 - 3a + 5
33) 30n 2 + 55n - 35
34) -10n 2 - 63n - 18
Solve each equation by taking square roots.
35) b 2 = 25
36) a 2 + 7 = 32
37) 9m 2 + 2 = 326
38) 2 x 2 + 2 = -29
Solve each equation by factoring.
39) (a - 6)(a - 7) = 0
40) x 2 - 14 x + 49 = 0
41) x 2 - x - 14 = 6
42) 3 x 2 = -3 - 10 x
Solve each equation with the quadratic formula.
43) 5m 2 - 5 = 3m
44) -n 2 + 12n + 6 = -8n 2
Worksheet by Kuta Software LLC
-5-
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Name each polynomial by degree and number of terms.
45) - x 5 - 2
46) 6 - 2k 2 + 2k 4 - 6k
Simplify each sum.
47) (2n 2 + n + 5n 4 ) + (8n 4 + n + 6n 2 )
Simplify each expression.
48) (n 2 - 4n 4 - 2n) - (n + 5n 4 + 4n 2 ) + (4n 4 - 5n)
Find each product.
49) (5m - 3)(8m + 5)
50) (7 x - 6)(3 x 2 + 7 x + 3)
State if the given binomial is a factor of the given polynomial.
51) (n 4 - 3n 3 - 47n 2 + 40n - 12) ¸ (n + 6)
Divide.
52) (7n 3 - 14n 2 - 14n - 29) ¸ (n - 3)
Worksheet by Kuta Software LLC
-6-
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Evaluate each function.
53) h(n) = 4n - 3; Find h(2)
55) k(a) = a 2 + 3; Find k(-5)
57) f (n) = 3n - 5; Find f (n - 2)
7
4
()
54) h(a) = 2a - ; Find h
1
2
56) g(a) = 4a + 1; Find g(6)
6
5
( )
4
3
58) g( x) = x 3 - x; Find g - x
Perform the indicated operation.
59) h(n) = 3n 3 + 1
g(n) = 4n - 4
Find (h + g)(n)
60) f ( x) = x 2 + x
g( x) = -3 x - 3
Find ( f - g)( x)
61) g( x) = x + 3
f ( x) = 4 x - 2
Find ( g × f )( x)
62) g( x) = 2 x + 2
f ( x) = 2 x - 4
g
( x)
Find
f
63) g(n) = 3n - 5
Find ( g g)(n)
64) g( x) = x 2 + 2
h( x) = -3 x + 4
Find ( g h)(0)
()
Worksheet by Kuta Software LLC
-7-
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65) g( x) = 4 x + 3
f ( x) = 4 x + 4
Find ( g f )(9)
66) g(n) = -2n + 1
h(n) = -n 3 + 3n 2
Find ( g h)(n - 1)
Find the inverse of each function. Then graph the function and its inverse.
67) f (n) = -4n - 20
1
3
68) f (n) = 2 + n
y
6
5
4
3
2
1
-6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
y
6
5
4
3
2
1
1 2 3 4 5 6 x
-6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
1 2 3 4 5 6 x
Find the inverse of each function.
69) g( x) =
3
71) f (n) =
4n - 16
7
x+2 -1
70) f ( x) =
5
72) f ( x) = -
x-2 +2
4
+3
x-2
Worksheet by Kuta Software LLC
-8-
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Simplify.
73)
3
72 p 2 qr 3
74)
3
76) -3 64 p 7 q 6 r 8
75) 2 162m 5 p 3 q 8
64 x 2 yz 6
3
Simplify. Your answer should contain only positive exponents.
77) 4 y 3z 2 × 3 x -2 y 4z -3
(
xz 4 × 2 x 3z 4
79)
x -3
)
(
78) p 4q 3 × (2mpq -3)
-1
80)
-3 4
)
(n 2 p -1) 3
2 m 0n 0 p 3 × m 3 p 2
Solve each equation. Remember to check for extraneous solutions.
81)
2a - 2 = 2
82) -4 b - 1 = -8
Worksheet by Kuta Software LLC
-9-
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Identify the domain and range of each. Then sketch the graph.
83) y = 2 x + 2 - 4
84) y = -2 x + 4 + 4
y
-8
-6
-4
y
8
8
6
6
4
4
2
2
-2
2
4
6
8 x
-8
-6
-4
-2
2
-2
-2
-4
-4
-6
-6
-8
-8
4
6
8 x
6
8 x
Identify the center and radius of each. Then sketch the graph.
85) x 2 + y 2 = 9
86) ( x + 2) 2 + ( y - 3) 2 = 3
y
-8
-6
-4
y
8
8
6
6
4
4
2
2
-2
2
4
6
8 x
-8
-6
-4
-2
2
-2
-2
-4
-4
-6
-6
-8
-8
4
Evaluate each expression.
87) log 7 343
89) log 4
1
64
88) log 3 27
90) log 2 -32
Worksheet by Kuta Software LLC
-10-
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Find the inverse of each function.
91) y = log x 5
93) y =
10 x
4
92) y = ln ( x - 1)
x
94) y = e
2
Expand each logarithm.
95) log 3 (a × b × c 4)
Condense each expression to a single logarithm.
96) 12 log 8 x - 4 log 8 y
Solve each equation.
97) 10 2 - 5n + 10 = 60
98) -5 × 3 10a - 6 - 7 = -62
99) log 13 -4n = log 13 (-5n - 5)
100) log 13 (9 - a 2 ) = log 13 -8a
101) log 2 (-2 x - 1) - log 2 7 = 1
102) log 4 (2 - 4 x 2 ) + log 4 2 = 1
Worksheet by Kuta Software LLC
-11-
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Identify the points of discontinuity of each.
103) f ( x) = -
4
x+2
104) f ( x) = -
1
2
x +x-6
Identify the vertical asymptotes of each.
105) f ( x) =
1
+3
x-3
106) f ( x) =
x2 + 3x + 2
-3 x - 9
Identify the horizontal asymptote of each.
107) f ( x) = -
1
x
-3
x3 - 9x
109) f ( x) = 2
3x + 3x - 6
x2 + 4
108) f ( x) = 2
x + 2x - 3
110) f ( x) =
2
x+2
Worksheet by Kuta Software LLC
-12-
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Identify the x-intercepts of each.
111) f ( x) =
3
+1
x-2
112) f ( x) =
2x2 - 2x
x2 - 4x + 3
Identify the holes of each.
113)
4
f ( x) =
+1
x+2
114)
x3 + x2 - 2x
(
)
f x =
2
3x + 6x
Identify the domain of each.
115) f ( x) =
2
+2
x+1
116) f ( x) = -
2
-2
x+2
Worksheet by Kuta Software LLC
-13-
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Assume that the rate at which a cricket chirps varies linearly with the temperature. Crickets make
70 chirps per minute at 60°F and 100 chirps per minute at 80°F.
117) State the independent variable.
118) State the dependent variable.
119) Write a linear equation that expresses this
relationship.
120) What is the temperature-intercept?
121) What does the temperature and chirp
relationship tell you about the affect
temperature has on cricket chirps?
122) What is the slope of the temperature and
chirp relationship?
123) Interpret the meaning of the slope as a rate
of change.
Worksheet by Kuta Software LLC
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