H. Pre-Calculus ~ Semester One
Name___________________________________
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Exam Review
Evaluate each determinant.
1)
-5
2
4
1
2)
-2
-4
-5
-5
-4
-4
2
2
2
Simplify. Write "undefined" for expressions that are undefined.
3) -3
5)
-5
2
-2
-3
-2
4
1
-1
3
6 ×
2
3
-2
4
(
4)
-1
-1
-6
6
-3
-6
6)
0
-3
3
×
-5
8)
7
-10
-1
8
(
2
-3
)
1
1
×
1
3
-5
-4
1
-5
)
Find the inverse of each matrix.
7)
9
-1
-2
-8
Worksheet by Kuta Software LLC
-1-
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Use Cramer's Rule to solve each system.
9) -2x - 6 y = -30
-5x - 4 y = -20
10) -3 y - 5z = -14
-x - 2 y - 4z = -10
-5x + y - 5z = -7
Solve each system using the matrix method.
11) -12x - 9 y = 15
-2x + 8 y = 12
12) -x - 5 y + 2z = -2
5x + 6 y - z = 9
-3x - 6 y + 2z = -5
Worksheet by Kuta Software LLC
-2-
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13) Find the domain.
f(x) =
14) Find the domain.
2
x+3
5-x
f(x) =
x + 3x - 4
x+6
15) Graph. Find the domain and range.
f(x) =
x, x < -1
2 - x, -1 < x < 5
x + 3, 5 < x < 8
y
8
6
4
2
-8
-6
-4
-2
2
4
6
8 x
-2
-4
-6
-8
16) Find each.
D:
Ix:
R:
Iy:
Increasing:
AROC between 2 & 4 =
Decreasing:
Constant:
y
8
6
4
2
-8
-6
-4
-2
2
4
6
8 x
-2
-4
-6
-8
Worksheet by Kuta Software LLC
-3-
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Identify the domain of each. Is the function even, odd, or neither? Support your choice.
17) f ( x) =
-x 2 - 4x
x 2 - 3x
18) f ( x) =
x 3 - 5x 2 + 4x
4x 2 - 4x - 24
19) Graph using transformations. Find the domain and range.
f(x) = 3 -2x - 4+3
y
8
6
4
2
-8
-6
-4
-2
2
4
6
8 x
-2
-4
-6
-8
20) Graph using transformations. Find the domain and range.
f(x) = -2
1
x - 2 -3
2
y
8
6
4
2
-8
-6
-4
-2
2
4
6
8 x
-2
-4
-6
-8
Worksheet by Kuta Software LLC
-4-
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Perform the indicated operation.
21) f (n) = 4n - 3
g(n) = 2n - 1
Find ( f g)(n)
22) h(n) = n 3 - 4
g(n) = 3n + 3
Find (h + g)(n)
23) f (n) = -n 2 - 2
g(n) = -4n - 1
Find ( f g)(1)
24) h(n) = 2n + 1
g( n) = n 2 - 5
Find (h - g)(-4)
Use the information provided to write the transformational form equation of each parabola.
(
25) Vertex: (-6, -9), Focus: -6, -
17
2
)
26) Vertex: (7, -10), Directrix: x =
83
12
Identify the vertex, focus, axis of symmetry, and directrix of each. Then sketch the graph.
28) f (y) = -3 y 2 - 36 y - 112
1
2
16
27) f (x) = - x 2 + x 3
3
3
y
8
y
8
6
6
4
4
2
2
-8
-8
-6
-4
-2
2
4
6
-6
-4
-2
2
4
6
8 x
-2
8 x
-2
-4
-4
-6
-6
-8
-8
Worksheet by Kuta Software LLC
-5-
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Use the information provided to write the standard form equation of each circle.
29) Ends of a diameter: (-17, -5) and (-3, -3)
Identify the center and radius of each. Then sketch the graph.
30) x 2 + y 2 + 8x + 8 y + 31 = 0
31) x 2 + y 2 + 8x - 6 y + 21 = 0
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
Use the information provided to write the standard form equation of each ellipse.
32) Vertices: (5, -10), (-13, -10)
Foci: (-4 + 17, -10), (-4 -
17, -10)
33) Foci: (9 + 133, 9), (9 - 133, 9)
Co-vertices: (9, 15), (9, 3)
Worksheet by Kuta Software LLC
-6-
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Identify the center, vertices, co-vertices, and foci of each. Then sketch the graph.
34) x 2 + 4 y 2 - 2x - 24 y + 21 = 0
35) 25x 2 + 16 y 2 + 32 y - 384 = 0
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
Use the information provided to write the standard form equation of each hyperbola.
36) Vertices: (1 + 95, 9), (1 - 95, 9)
Foci: (1 + 255, 9), (1 - 255, 9)
37) Vertices: (12, -10), (2, -10)
Foci: (7 + 5 5, -10), (7 - 5 5, -10)
Identify the vertices and foci of each. Then sketch the graph.
38) -x 2 + y 2 - 25 = 0
39) x 2 - 4 y 2 + 2x + 16 y - 31 = 0
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
Worksheet by Kuta Software LLC
-7-
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Factor each completely.
40) 18u 2 v 2 + 24uv 3 - 64v 4
41) 50 y 2 x 2 - 50 y 3 x
42) 18a 3 - 26a 2 b + 8b 2 a
43) 18x 2 - 136xy - 64 y 2
44) 90x 4 - 48x 2 + 6
45) 15a 4 + 38a 2 + 7
46) 48 p 2 u + 8 p 2 v + 288qu + 48qv
47) 40mn - 60m - 50n + 75
48) 343xy - 196x 2 - 196ny + 112nx
49) 56 pc 2 - 35 pd + 448qc 2 - 280qd
50) 100x 2 - 36 y 2
51) 18x 2 - 50 y 2
52) 20u 2 + 20uv + 5v 2
53) 45x 2 + 120xy + 80 y 2
54) 648u 3 - 3
55) 81x 3 - 3
Expand completely.
56) (3v + 4u)
4
57) (m 3 - 5n)
3
Worksheet by Kuta Software LLC
-8-
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Divide.
58) (b 5 - 16b 4 + 59b 3 + 14b 2 - 56b + 41) ¸ (b - 6)
59) (14r 5 + 39r 4 + 10r 3 + 63r + 9) ¸ (7r + 2)
State the possible rational zeros for each function. Then factor each and find all zeros.
60) f ( x) = 4x 3 - 8x 2 + 5x - 1
61) f ( x) = 5x 3 + 9x 2 + 3x - 1
Worksheet by Kuta Software LLC
-9-
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62) f ( x) = 4x 3 - 9x 2 + 6x - 1
63) f ( x) = 3x 3 + 7x 2 + 5x + 1
State the possible rational roots for each equation. Then factor each and find all roots.
64) 4x 5 + 6x 4 - 14x 3 - 21x 2 + 6x + 9 = 0
65) 3x 5 - 9x 4 - x 3 + 3x 2 - 4x + 12 = 0
Worksheet by Kuta Software LLC
-10-
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H. Pre-Calculus ~ Semester One
Name___________________________________
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Exam Review
Evaluate each determinant.
1)
-5
2
4
1
2)
-13
-2
-4
-5
-5
-4
-4
2
2
2
2
Simplify. Write "undefined" for expressions that are undefined.
-3
-2
4
1
3) -3
4)
11
-13
5)
-5
2
-2
(
-6
6
-3
-6
)
11
-4
-1
3
6 ×
2
3
-17
18
0
-1
-1
-2
4
6)
0
-3
3
×
-5
0
-15
6
20
16
(
33
-13
2
-3
1
1
×
1
3
-5
-4
1
-5
)
-24
49
Find the inverse of each matrix.
7)
9
-1
-2
-8
4
37
1
74
8)
1
37
9
74
7
-10
4
23
5
23
-
-1
8
1
46
7
46
Worksheet by Kuta Software LLC
-1-
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Use Cramer's Rule to solve each system.
9) -2x - 6 y = -30
-5x - 4 y = -20
(0, 5)
10) -3 y - 5z = -14
-x - 2 y - 4z = -10
-5x + y - 5z = -7
(
1 5
-1, ,
2 2
)
Solve each system using the matrix method.
11) -12x - 9 y = 15
-2x + 8 y = 12
(-2, 1)
12) -x - 5 y + 2z = -2
5x + 6 y - z = 9
-3x - 6 y + 2z = -5
(1, 1, 2)
Worksheet by Kuta Software LLC
-2-
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13) Find the domain.
f(x) =
14) Find the domain.
2
x+3
5-x
f(x) =
0
x + 3x - 4
x+6
0
15) Graph. Find the domain and range.
f(x) =
x, x < -1
2 - x, -1 < x < 5
x + 3, 5 < x < 8
y
8
6
4
2
-8
-6
-4
-2
2
4
6
8 x
-2
-4
-6
-8
0
16) Find each.
D:
Ix:
R:
Iy:
Increasing:
AROC between 2 & 4 =
Decreasing:
Constant:
y
8
6
4
2
-8
-6
-4
-2
2
4
6
8 x
-2
-4
-6
-8
0
Worksheet by Kuta Software LLC
-3-
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Identify the domain of each. Is the function even, odd, or neither? Support your choice.
17) f ( x) =
-x 2 - 4x
x 2 - 3x
18) f ( x) =
Domain: All reals except 3, 0
x 3 - 5x 2 + 4x
4x 2 - 4x - 24
Domain: All reals except 3, -2
19) Graph using transformations. Find the domain and range.
f(x) = 3 -2x - 4+3
y
8
6
4
2
-8
-6
-4
-2
2
4
6
8 x
-2
-4
-6
-8
The dot next to the choice indicates that it is the answer.
20) Graph using transformations. Find the domain and range.
f(x) = -2
1
x - 2 -3
2
y
8
6
4
2
-8
-6
-4
-2
2
4
6
8 x
-2
-4
-6
-8
0
Worksheet by Kuta Software LLC
-4-
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Perform the indicated operation.
21) f (n) = 4n - 3
g(n) = 2n - 1
Find ( f g)(n)
22) h(n) = n 3 - 4
g(n) = 3n + 3
Find (h + g)(n)
n 3 + 3n - 1
8n - 7
23) f (n) = -n 2 - 2
g(n) = -4n - 1
Find ( f g)(1)
-27
24) h(n) = 2n + 1
g( n) = n 2 - 5
Find (h - g)(-4)
-18
Use the information provided to write the transformational form equation of each parabola.
(
25) Vertex: (-6, -9), Focus: -6, 2 ( y + 9 ) = ( x + 6)
17
2
)
26) Vertex: (7, -10), Directrix: x =
2
83
12
1
( x - 7) = ( y + 10) 2
3
Identify the vertex, focus, axis of symmetry, and directrix of each. Then sketch the graph.
28) f (y) = -3 y 2 - 36 y - 112
1
2
16
27) f (x) = - x 2 + x 3
3
3
y
y
Vertex: (1, -5)
23
Focus: 1, 4
Axis of Sym.: x = 1
17
Directrix: y = 4
8
(
6
4
2
-6
-4
-2
2
4
6
(
6
)
4
2
-8
-8
Vertex: (-4, -6)
49
Focus: - , -6
12
Axis of Sym.: y = -6
47
Directrix: x = 12
8
-6
-4
-2
2
4
6
)
8 x
-2
8 x
-2
-4
-4
-6
-6
-8
-8
Worksheet by Kuta Software LLC
-5-
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Use the information provided to write the standard form equation of each circle.
29) Ends of a diameter: (-17, -5) and (-3, -3)
( x + 10) 2 + ( y + 4) 2 = 50
Identify the center and radius of each. Then sketch the graph.
30) x 2 + y 2 + 8x + 8 y + 31 = 0
31) x 2 + y 2 + 8x - 6 y + 21 = 0
y
-8
-6
-4
y
Center: (-4, -4)
Radius: 1
8
6
6
4
4
2
2
-2
2
4
6
Center: (-4, 3)
Radius: 2
8
8 x
-8
-6
-4
-2
2
-2
-2
-4
-4
-6
-6
-8
-8
4
6
8 x
Use the information provided to write the standard form equation of each ellipse.
32) Vertices: (5, -10), (-13, -10)
Foci: (-4 + 17, -10), (-4 -
( x + 4) 2
81
+
( y + 10) 2
17, -10)
33) Foci: (9 + 133, 9), (9 - 133, 9)
Co-vertices: (9, 15), (9, 3)
( x - 9) 2
169
+
( y - 9)
36
=1
64
Worksheet by Kuta Software LLC
-6-
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Identify the center, vertices, co-vertices, and foci of each. Then sketch the graph.
34) x 2 + 4 y 2 - 2x - 24 y + 21 = 0
y
6
4
2
-6
-4
-2
y
Center: (1, 3)
Vertices: (5, 3)
(-3, 3)
Co-vertices: (1, 5)
(1, 1)
Foci: (1 + 2 3, 3)
(1 - 2 3, 3)
8
-8
35) 25x 2 + 16 y 2 + 32 y - 384 = 0
2
4
6
Center: (0, -1)
Vertices: (0, 4)
(0, -6)
Co-vertices: (4, -1)
(-4, -1)
Foci: (0, 2)
(0, -4)
8
6
4
2
8 x
-8
-6
-4
-2
2
-2
-2
-4
-4
-6
-6
-8
-8
4
6
8 x
Use the information provided to write the standard form equation of each hyperbola.
36) Vertices: (1 + 95, 9), (1 - 95, 9)
Foci: (1 + 255, 9), (1 - 255, 9)
( x - 1) 2
-
( y - 9) 2
95
37) Vertices: (12, -10), (2, -10)
Foci: (7 + 5 5, -10), (7 - 5 5, -10)
( x - 7) 2
=1
-
( y + 10) 2
25
160
=1
100
Identify the vertices and foci of each. Then sketch the graph.
38) -x 2 + y 2 - 25 = 0
39) x 2 - 4 y 2 + 2x + 16 y - 31 = 0
y
6
-8
-6
-4
y
Vertices: (0, 5)
(0, -5)
Foci: (0, 5 2 )
(0, -5 2 )
8
6
4
4
2
2
-2
2
4
6
Vertices: (3, 2)
(-5, 2)
Foci: (-1 + 2 5, 2)
(-1 - 2 5, 2)
8
8 x
-8
-6
-4
-2
2
-2
-2
-4
-4
-6
-6
-8
-8
4
6
8 x
Worksheet by Kuta Software LLC
-7-
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Factor each completely.
40) 18u 2 v 2 + 24uv 3 - 64v 4
41) 50 y 2 x 2 - 50 y 3 x
2v 2 (3u - 4v)(3u + 8v)
42) 18a 3 - 26a 2 b + 8b 2 a
50 y 2 x( x - y)
43) 18x 2 - 136xy - 64 y 2
2a(a - b)(9a - 4b)
44) 90x 4 - 48x 2 + 6
2( x - 8 y)(9x + 4 y)
45) 15a 4 + 38a 2 + 7
6(3x 2 - 1)(5x 2 - 1)
46) 48 p 2 u + 8 p 2 v + 288qu + 48qv
(5a 2 + 1)(3a 2 + 7)
47) 40mn - 60m - 50n + 75
8( p 2 + 6q)(6u + v)
48) 343xy - 196x 2 - 196ny + 112nx
5(4m - 5)(2n - 3)
49) 56 pc 2 - 35 pd + 448qc 2 - 280qd
7(7x - 4n)(7 y - 4x)
50) 100x 2 - 36 y 2
7( p + 8q)(8c 2 - 5d )
51) 18x 2 - 50 y 2
4(5x + 3 y)(5x - 3 y)
52) 20u 2 + 20uv + 5v 2
5(2u + v)
2(3x + 5 y)(3x - 5 y)
53) 45x 2 + 120xy + 80 y 2
2
54) 648u 3 - 3
5(3x + 4 y)
2
55) 81x 3 - 3
3(6u - 1)(36u 2 + 6u + 1)
3(3x - 1)(9x 2 + 3x + 1)
Expand completely.
4
56) (3v + 4u)
81v 4 + 432v 3 u + 864v 2 u 2 + 768vu 3 + 256u 4
3
57) (m 3 - 5n)
m 9 - 15m 6 n + 75m 3 n 2 - 125n 3
Worksheet by Kuta Software LLC
-8-
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Divide.
58) (b 5 - 16b 4 + 59b 3 + 14b 2 - 56b + 41) ¸ (b - 6)
b 4 - 10b 3 - b 2 + 8b - 8 -
7
b-6
59) (14r 5 + 39r 4 + 10r 3 + 63r + 9) ¸ (7r + 2)
2r 4 + 5r 3 + 9 -
9
7r + 2
State the possible rational zeros for each function. Then factor each and find all zeros.
60) f ( x) = 4x 3 - 8x 2 + 5x - 1
61) f ( x) = 5x 3 + 9x 2 + 3x - 1
1
2
Possible rational zeros: ± 1, ± , ±
Factors to: f ( x) = ( x - 1)(2x - 1)
1
Zeros: 1, mult. 2
2
{
1
4
Possible rational zeros: ± 1, ±
2
1
5
Factors to: f ( x) = (5x - 1)( x + 1)
1
Zeros: , -1 mult. 2
5
}
{
2
}
Worksheet by Kuta Software LLC
-9-
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62) f ( x) = 4x 3 - 9x 2 + 6x - 1
63) f ( x) = 3x 3 + 7x 2 + 5x + 1
1
2
Possible rational zeros: ± 1, ± , ±
Factors to: f ( x) = (4x - 1)( x - 1)
1
Zeros: , 1 mult. 2
4
{
1
4
Possible rational zeros: ± 1, ±
2
1
3
2
Factors to: f ( x) = ( x + 1) (3x + 1)
1
Zeros: -1 mult. 2, 3
}
{
}
State the possible rational roots for each equation. Then factor each and find all roots.
64) 4x 5 + 6x 4 - 14x 3 - 21x 2 + 6x + 9 = 0
65) 3x 5 - 9x 4 - x 3 + 3x 2 - 4x + 12 = 0
Possible rational roots:
Possible rational roots:
1 3 9 1 3 9
± 1, ± 3, ± 9, ± , ± , ± , ± , ± , ±
2 2 2 4 4 4
1 2 4
± 1, ± 2, ± 3, ± 4, ± 6, ± 12, ± , ± , ±
3 3 3
Factors to: (2x + 3)( x 2 - 3)(2x 2 - 1) = 0
3
2
2
Roots: - , 3, - 3,
,2
2
2
{
Factors to: ( x - 3)( x 2 + 1)(3x 2 - 4) = 0
2 3 2 3
Roots: 3, i, -i,
,3
3
}
{
}
Worksheet by Kuta Software LLC
-10-
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