Download Junior Summer Assignment, Part II

Borst, Pre-calculus IB, [email protected]
Name___________________________________
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Junior Summer Assignment, Part II
Solve each equation.
1) 26 + v = 6(1 + 2v) - 2
3) -
2) 29 - 6x = -5 - 2(1 - 6x)
419 7
10
5
+ x= x+ -2
336 4
7
6
21
19 19
2
v=
+1 v
5
6 10
3
4)
5) 3 x + 5 = 36
8n + 5
=5
3
6)
Solve each inequality.
7) 40 + 5v > -8(1 - 4v) - 3v
9) 3
8) 3x + 3 £ 3(1 + 8x)
b
<7
3
10)
-9x
£2
9
Sketch the graph of each line.
11) -x + 2 y = -6
12) -5 y = 5 - 3x
y
y
6
6
5
5
4
4
3
3
2
2
1
1
-6 -5 -4 -3 -2 -1
1
2
3
4
5
6 x
-6 -5 -4 -3 -2 -1
1
-1
-1
-2
-2
-3
-3
-4
-4
-5
-5
-6
-6
2
3
4
5
6 x
Write the slope-intercept form of the equation of the line through the given points.
13) through: (1, -1) and (4, 3)
14) through: (-5, 1) and (-4, 4)
Worksheet by Kuta Software LLC
-1-
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Graph each equation.
15) y = - x - 2
16) y = x - 2 + 3
y
y
6
6
5
5
4
4
3
3
2
2
1
1
-6 -5 -4 -3 -2 -1
1
2
3
4
5
6 x
-6 -5 -4 -3 -2 -1
1
-1
-1
-2
-2
-3
-3
-4
-4
-5
-5
-6
-6
2
3
4
5
6 x
Solve each system by elimination.
17) 10x - 10 y = 10
-2x - 5 y = -2
18) -24x + 6 y = -24
-4x + y = -4
Simplify. Your answer should contain only positive exponents.
19)
21)
y
-3
20)
(2x y 2) 2
(
2m
4
2
2m × nm
2
23)
4 2
×x y
yx × x
-4
)
-2
22)
-3 2
2x y
0 -1
)
(2m 0) 4 × 2mn -1
4 2
mn
3
(2x 3) -2
(
3 4
2x y × x y
24)
(2x -1 y -2) 0
2
3 -1
2y × x y
Worksheet by Kuta Software LLC
-2-
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Sketch the graph of each function.
f ( x) = -2 ×
25)
()
1
2
x
26) f ( x) = 5 × 2
x
y
20
y
-6
-4
-2
2
4
6
18
x
-2
16
-4
14
-6
12
-8
10
-10
8
-12
6
-14
4
-16
2
-18
-6
-4
-2
2
4
6
x
-20
Factor the common factor out of each expression.
27) 6n 5 + 18n + 8
28) 24x 2 - 40x + 4
Factor each completely.
29) m 2 + 7m - 30
30) b 2 - 5b + 4
Sketch the graph of each function.
31) f ( x) = x 2 - 8x + 15
1
32) f ( x) = - x 2 + 2x - 8
4
y
5
y
1
4
3
-1
1
2
-1
1
-2
2
3
4
5
6 x
-3
1
2
3
4
5
6
7 x
-1
-4
-2
-5
-3
-6
-7
Worksheet by Kuta Software LLC
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2
2
33) f ( x) = ( x - 4) + 3
34) f ( x) = -2( x + 3) - 1
y
y
8
-8
-7
-6
-5
-4
-3
-2
-1
1
2 x
-1
7
-2
6
-3
5
-4
4
-5
-6
3
-7
2
-8
1
-9
-1
1
2
3
4
5
-10
6 x
Solve each equation by factoring.
35) m 2 - 5m = -4
36) m 2 - 32 = -4m
Solve each equation with the quadratic formula.
37) 11n 2 = 7
38) 4m 2 - 4m = 35
Find the value of c that completes the square.
39) r 2 - 16r + c
40) x 2 - 18x + c
Solve each equation by completing the square.
41) v 2 - 4v - 2 = 2
42) n 2 + 8n - 73 = -9
Simplify.
43)
45n
44)
175 p 4
Find the distance between each pair of points.
45) (-5, -5), (1, 6)
46) (-5, 4), (-6, 7)
Worksheet by Kuta Software LLC
-4-
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Find the midpoint of the line segment with the given endpoints.
47) (1, -6), (-4, 6)
48) (7, 8), (-3, 10)
Simplify.
49) 3 24 - 3 8 - 3 8
51)
53)
15 ( 6 + 4)
5
50) 2 3 + 2 8 -
52)
15 (3 6 + 2 10 )
2
54)
4 2-
-5 - 2 2
2
5
Solve each equation. Remember to check for extraneous solutions.
55) -15 = -3 v - 2
56) 4 =
49k - 3
Simplify each and state the excluded values.
57)
27n
27n 2 + 72n
58)
6v + 4
6
Simplify each expression.
59)
1
6a 2 - 2a
×
24a 2 - 8a
5
60)
a 2 + 5a - 50 a + 9
×
8a - 40
a + 10
61)
4p
5p
p+6
p-3
62)
5
2
k-2
k-1
Solve each equation. Remember to check for extraneous solutions.
63)
2
1
3
+ 2= 2
3a a
2a
64)
1 3 2
+ =
v 5 v
Worksheet by Kuta Software LLC
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Find the value of each trigonometric ratio.
65) sin X
66) sin X
X
X
24
Y
13
5
10
26
Y
Z
12
67) cos C
B
Z
68) tan Z
9
Y
A
32
24
X
40
Z
40
41
C
Find the measure of the indicated angle to the nearest degree.
69)
70)
11
7
?
8
14
71)
?
72)
30
35
?
9
?
41
Find the missing side. Round to the nearest tenth.
73)
20
74)
15
28°
x
x
75)
60°
76)
x
17
42°
62°
x
16
Worksheet by Kuta Software LLC
-6-
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