Math 2 Final Exam Packet Name ID: 1 - Weebly
Transcript of Math 2 Final Exam Packet Name ID: 1 - Weebly
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Math 2 Final Exam Packet
Part I
Name___________________________________ ID: 1
Date________________ Block____
-1-
Factor each completely.
1) p2 + 3p − 28
A) ( p + 7)( p + 4)B) Not factorableC) ( p + 7)( p − 4)D) ( p + 2)( p − 14)
2) r2 − 14r + 45
A) (r − 5)(r + 9)B) (r − 5)(r − 9)C) (r + 5)(r + 9)D) (r + 5)(r − 9)
3) 21k2 − 3kA) 3k(7k + 1)B) None of theseC) 21k(k − 1)D) 3k(7k − 1)
4) 21x3 + 177x2 + 72xA) 3(7x + 12)(x + 2)B) None of theseC) 3(x + 3)(7x − 8)D) 3x(7x + 3)(x + 8)
5) 7a3 − 55a2 + 42aA) Not factorableB) a(7a − 6)(a − 7)C) (7a + 6)(a − 7)D) None of these
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Solve each equation by factoring.
6) (4x − 1)(5x − 1) = 0
A) {1
4, 3} B) {1
4,
1
5}C) {− 1
4, −2} D) None of these
7) (5n + 4)(3n + 4) = 0
A) {1, −3
2} B) {−1, −3}
C) {− 4
5, −
4
3} D) {5
3, 4}
8) 6b2 − 84 = −30bA) None of these B) {3, 0}C) {6, 2} D) {4, −2}
9) n2 + 11n = −30
A) {5, 6} B) {−3, −6}C) {−5, −6} D) None of these
10) 15n2 − 18 = −3 + 16n
A) {− 3
5,
5
3} B) {7
5, 2}
C) {− 3
5, 4} D) {3
5, −
5
3}
11) 5x2 = 34x − 24
A) {− 4
5, −7} B) {8
7, −6}
C) {8
5, 4} D) {4
5, 6}
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Solve each equation by completing the square.
12) x2 + 14x + 33 = 0
A) {2.055, −16.055}B) None of theseC) {6, −10}D) {−3, −11}
13) a2 − 10a − 24 = 0
A) {8, −4}B) {12, −2}C) {9.099, −1.099}D) {21.136, −1.136}
14) r2 − 6r − 51 = −6
A) {8 + 3 17, 8 − 3 17}B) {3 + 3 6, 3 − 3 6}C) {16 + 345, 16 − 345}D) {5 + 2 22, 5 − 2 22}
15) r2 − 20r + 22 = −6
A) {20 + 2 93, 20 − 2 93}B) {4, −2}C) {10 + 6 2, 10 − 6 2}D) {2 + 2 3, 2 − 2 3}
16) x2 − 6x − 66 = 6
A) {12, −6}B) {8 + 115, 8 − 115}C) {6, −4}D) {−7 + 15, −7 − 15}
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Solve each equation with the quadratic formula.
17) n2 + 5n − 24 = 0
A) {4, −1} B) {1, −0.5}C) {0.618, −1.618} D) {3, −8}
18) 2x2 + x = 55
A) {−1 + 221
2, −1 − 221
2 }B) {5, −
11
2 }C) {7, −3}D) None of these
19) k2 = −9 + 6k
A) {1 + i 17
2,
1 − i 17
2 }B) {3}C) {−3}
D) {1 + 19
2,
1 − 19
2 }
Find the discriminant of each quadratic equation then state the number and type of solutions.
20) −3v2 + 6v − 9 = −6
A) 81; two real solutionsB) 0; two real solutionsC) 0; two imaginary solutionsD) 0; one real solution
21) −7x2 + 3x + 2 = 8
A) 177; two real solutionsB) None of theseC) −299; two real solutionsD) −159; one real solution
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22) −a2 − 3a − 1 = −aA) 0; one rational solutionB) 196; two rational solutionsC) 296; two irrational solutionsD) 52; two irrational solutions
23) 4b2 + 7b + 1 = −2bA) 97; two rational solutionsB) −143; two imaginary solutionsC) 65; two irrational solutionsD) 65; one rational solution
Simplify each expression.
24) (12p4 − 7p3 + 11p) − (6p3 − 8p4 + 7p)A) 34p4 − 13p3 + 4pB) 20p4 − 13p3 + 4pC) 34p4 + 11pD) 34p4 + 4p
25) (4p − 10p3 + 4) + (14p3 + 5p + 8)A) 15p3 + 9p + 12B) 15p3 + 5p + 22C) 4p3 + 9p + 12D) 15p3 + 5p + 12
Find each product.
26) (2v + 3)(5v + 8)A) 6v2 − 9B) 6v2 − 15v − 9C) 10v2 − v − 24D) 10v2 + 31v + 24
27) (−4n + 6)(−6n − 7)A) 24n2 − 42B) 16n2 − 4n − 20C) 24n2 − 64n + 42D) None of these
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Factor each completely.
28) 63xy + 147x2 + 18y + 42xA) 14x(3y + 2)B) 3(7x + 2)(3y + 7x)C) 3(7x + 2)(3y + 2)D) None of these
29) 28xy − 35x2 − 4y + 5xA) (7x + 1)(4y + 5x)B) None of theseC) 2x(4y + 1)D) (7x − 1)(4y − 5x)
Describe the end behavior of each function.
30) f (x) = −2x2 + 4x + 4
A) f (x) → +∞ as x → -∞f (x) → +∞ as x → +∞
B) f (x) → -∞ as x → -∞f (x) → -∞ as x → +∞
C) f (x) → +∞ as x → -∞f (x) → -∞ as x → +∞
D) f (x) → -∞ as x → -∞f (x) → +∞ as x → +∞
31) f (x) = x2 − 6x + 3
A) f (x) → +∞ as x → -∞f (x) → +∞ as x → +∞
B) f (x) → +∞ as x → -∞f (x) → -∞ as x → +∞
C) f (x) → -∞ as x → -∞f (x) → -∞ as x → +∞
D) f (x) → -∞ as x → -∞f (x) → +∞ as x → +∞
Simplify.
32) −5 36x3y3
A) −64x2 2yB) None of theseC) −30xy xyD) 48y 5x
33) 3 294ab4
A) 21b2 6a B) −10a2 3bC) 35a2b 2 D) −40a2b2 2
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34) 2 54 + 3 6 − 3 3
A) 9 6
B) 9 6 + 3 3C) None of theseD) 3 6
35) −2 45 − 5 + 2 8
A) −6 5 + 4 2
B) −7 5 + 4 2
C) −13 5 + 4 2
D) −19 5 + 4 2
36) 4 15(−3 10 + 6)A) 3 30 + 3
B) −60 6 + 12 10
C) 40 3D) 8
37) 5(2 + 4 5)A) 2 5 + 20 B) −29
C) −12 3 + 3 D) 10 5 + 3
Write each expression in exponential form.
38) ( 3x)3
A) (5x)3
2 B) (10x)5
3
C) (3x)3
2 D) (5x)7
4
39) 2n
A) (2n)1
2 B) n1
3
C) n5
6 D) None of these
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Write each expression in radical form.
40) v8
5
A) ( 5v)8
B) ( 2v)5
C) 7v D) ( 3v)4
41) r4
3
A) 4
r B) ( 3r)4
C) ( 34r)4
D) ( 3r)3
Identify the vertex, axis of symmetry, and min/max value of each.
42) f (x) = −x2 + 20x − 104
A) None of theseB) Vertex: (−8, 2)
Axis of Sym.: y = 2Min value = −8
C) Vertex: (10, −4)Axis of Sym.: x = 10Max value = −4
D) Vertex: (12, −5)Axis of Sym.: x = 12Min value = −5
43) f (x) = −x2 + 4x − 1
A) None of theseB) Vertex: (2, 3)
Axis of Sym.: x = 2Max value = 3
C) Vertex: (−3, −2)Axis of Sym.: y = −2Min value = −3
D) Vertex: (−2, 3)Axis of Sym.: y = 3Min value = −2
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Use the information provided to write the vertex form equation of each parabola.
44) f (x) = −x2 − 8x − 14
A) f (x) = −(x − 4)2 − 2
B) f (x) = −(x + 4)2 + 2
C) f (x) = −(x − 4)2 + 2D) None of these
45) f (x) = −x2 − 10x − 25
A) f (x) = −x2 + 5
B) f (x) = −(x + 5)2
C) f (x) = −(x + 8)2
D) f (x) = (x + 5)2
Use the information provided to write the standard form equation of each parabola.
46) f (x) = 1
13x2 + 4
A) None of these
B) f (x) = 4
13x2 + 4
C) f (y) = −1
13y2 +
8
13y −
16
13
D) f (x) = 2
13 ⋅ −x2 + 4
47) f (x) = −(x − 9)2
A) f (x) = x2 + 18x − 81B) f (x) = −x2 + 18x − 81C) f (x) = x2 − 18x + 81D) f (x) = 2x2 − 9
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Determine whether the scenario involves independent or dependent events. Then find theprobability.
48) A basket contains four apples and fourpeaches. You randomly select a piece offruit and then return it to the basket. Thenyou randomly select another piece of fruit. The first piece of fruit is an apple and thesecond piece is a peach.
A) Dependent; 7
26 ≈ 0.269
B) Dependent; 10
39 ≈ 0.256
C) Dependent; 4
15 ≈ 0.267
D) None of these
49) A cooler contains thirteen bottles of sportsdrink: five lemon-lime flavored, fiveorange flavored, and three fruit-punchflavored. You randomly grab a bottle. Then you return the bottle to the cooler,mix up the bottles, and randomly selectanother bottle. Both times you get alemon-lime drink.
A) Dependent; 3
11 ≈ 0.273
B) Independent; 36
169 ≈ 0.213
C) Independent; 25
169 ≈ 0.148
D) Independent; 1
4 = 0.25
Find the probability.
50) There are seven nickels and five dimes inyour pocket. Four of the nickels and twoof the dimes are Canadian. The others areUS currency. You randomly select a coinfrom your pocket. It is a nickel or isCanadian currency.
A) 5
6 ≈ 0.833 B)
3
4 = 0.75
C) 1 D) 7
9 ≈ 0.778
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Answers to Part I (ID: 1)1) C 2) B 3) D 4) D5) B 6) B 7) C 8) A9) C 10) A 11) D 12) D13) B 14) B 15) C 16) A17) D 18) B 19) B 20) D21) B 22) A 23) C 24) B25) C 26) D 27) D 28) B29) D 30) B 31) A 32) C33) A 34) C 35) B 36) B37) A 38) C 39) A 40) A41) B 42) C 43) B 44) B45) B 46) A 47) B 48) D49) C 50) B
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Math 2 Final Exam Packet
Part I
Name___________________________________ ID: 2
Date________________ Block____
-1-
Factor each completely.
1) x2 + 4x − 12
A) (x + 12)(x − 1)B) None of theseC) Not factorableD) (x + 2)(x + 6)
2) x2 + 5x − 36
A) Not factorableB) (x + 4)(x − 9)C) (x − 4)(x − 9)D) (x − 4)(x + 9)
3) 2x3 + 25x2 + 72xA) x(2x + 9)(x − 8)B) None of theseC) x(2x + 9)(x + 8)D) 2x(x + 4)(x + 9)
4) 28n4 − 136n3 + 96n2
A) 4(7n + 24)(n + 1)B) 4n2(n − 6)(7n + 4)C) 4n2(7n − 6)(n − 4)D) 4n2(7n + 6)(n − 4)
5) 3a2 + a − 10
A) (2a + 5)(a − 2)B) (3a − 5)(a − 2)C) (3a − 5)(a + 2)D) (3a + 2)(a − 5)
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Solve each equation by factoring.
6) (x − 4)(x − 3) = 0
A) {2, −3} B) {4, 3}
C) {2, 0} D) {− 4
5, 0}
7) (3m − 5)(m + 4) = 0
A) {− 1
3, 1} B) {5, −4}
C) {5
3, −4} D) {− 2
3, 3}
8) 2k2 − 48 = 4kA) {−2, 6} B) {−4, 6}C) {−8, 7} D) {1, −4}
9) b2 + 10 = −7bA) {−2, −5} B) {−5, 0}C) {−6, −4} D) {−5}
10) 30b2 + 122b + 117 = 5
A) {7
5,
8
3} B) {7
3, 2}
C) {− 7
5, −
8
3} D) {5
3, −3}
11) 15b2 + 114b + 175 = 4b
A) {− 2
7, 7} B) {4
7, 5}
C) {8
3, −1} D) {− 7
3, −5}
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Solve each equation by completing the square.
12) x2 − 4x − 60 = 0
A) {6.449, 1.551}B) {3.196, −7.196}C) {15.348, 0.652}D) {10, −6}
13) n2 − 10n − 46 = 0
A) {13.426, −3.426}B) {−4, −8}C) {11.123, 2.877}D) {16, −2}
14) x2 − 4x − 5 = −8
A) {−10 + 2 41, −10 − 2 41}B) None of theseC) {3, 1}D) {−4, −16}
15) b2 + 14b + 16 = 3
A) {6, −2}B) {3, −9}C) {−1, −13}D) {−6 + 3 7, −6 − 3 7}
16) r2 + 8r − 13 = 7
A) {−5 + 110, −5 − 110}B) {2, −10}C) {5, −7}D) {−8 + 2 21, −8 − 2 21}
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Solve each equation with the quadratic formula.
17) 2k2 − 5k − 25 = 0
A) {8, −3} B) {2.5, −5}C) {0.5, −1} D) {5, −2.5}
18) 10k2 = −3
A) {−1}B) {−1 + 2, −1 − 2}C) {1}
D) { i 30
10, −
i 30
10 }
19) 2n2 + 7 = 3n
A) {−1 + 41
2, −1 − 41
2 }B) {2, −
5
3}C) None of these
D) {1 + i 119
6,
1 − i 119
6 }
Find the discriminant of each quadratic equation then state the number and type of solutions.
20) −5x2 − 3x + 15 = 7
A) 169; two real solutionsB) 4; two imaginary solutionsC) 169; one real solutionD) −271; two imaginary solutions
21) −x2 + 6x − 1 = 7
A) 4; two imaginary solutionsB) 4; one real solutionC) 261; two real solutionsD) 4; two real solutions
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22) x2 + 9 = 10
A) 4; two imaginary solutionsB) 4; two rational solutionsC) −4; two imaginary solutionsD) −4; two rational solutions
23) −12r2 − 17r − 17 = −10r2 − 14 − 12rA) 1; one rational solutionB) None of theseC) 1; two rational solutionsD) 1; two irrational solutions
Simplify each expression.
24) (10x + 8x5 + 2x3) − (−9x5 + x3 + 5)A) −2x5 − 13x3 + 10x − 5B) 10x5 + x3 + 10x − 5C) 17x5 + x3 + 10x − 5D) −2x5 + x3 + 10x − 5
25) (−2x2 − 8x3 − 2x) + (−13 + 5x3 + 10x)A) −3x3 − 2x2 + 16x − 22B) −3x3 − 2x2 + 8x − 13C) None of theseD) −3x3 + 6x2 + 16x − 22
Find each product.
26) (−8n + 1)(−n − 6)A) 8n2 − 49n + 6B) 8n2 + 47n − 6C) 8n2 + 49n + 6D) 8n2 − 6
27) (7n − 5)(−5n + 4)A) 42n2 + 41n − 8B) −36n2 + 1C) −35n2 + 53n − 20D) −35n2 + 3n + 20
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Factor each completely.
28) 8xy + x − 24y2 − 3yA) (x − 3y)(8y + 1)B) 5y(x + 1)C) 11y(x + 3y)D) 11y(x + 1)
29) 40xy + 16x + 25y + 10
A) (8x + 5)(5y + 2)B) None of theseC) 2(8x + 5)(4x − 1)D) 10(y + 1)(4x − 1)
Describe the end behavior of each function.
30) f (x) = −x2 + 8x − 11
A) f (x) → -∞ as x → -∞f (x) → -∞ as x → +∞
B) f (x) → +∞ as x → -∞f (x) → -∞ as x → +∞
C) f (x) → -∞ as x → -∞f (x) → +∞ as x → +∞
D) f (x) → +∞ as x → -∞f (x) → +∞ as x → +∞
31) f (x) = −x2 + 2xA) None of theseB) f (x) → +∞ as x → -∞
f (x) → -∞ as x → +∞C) f (x) → +∞ as x → -∞
f (x) → +∞ as x → +∞D) f (x) → -∞ as x → -∞
f (x) → +∞ as x → +∞
Simplify.
32) −6 150x4y3
A) 64x yB) −98x2y 2yC) None of theseD) −30x2y 6y
33) −3 72x2y4
A) −18y2x 2 B) −42y2 2xC) 40x2y 6y D) 16x2 3y
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34) 2 12 − 2 12 − 2 5
A) None of these B) −2 5
C) −2 5 + 4 3 D) 4 3
35) −3 12 − 3 − 12
A) None of these B) −11 3
C) −9 3 D) −15 3
36) −3 5(4 10 + 5)A) −15 5 + 30
B) 5 5 + 30C) None of theseD) −60 2 − 15 5
37) 15(2 + 6)A) 10 + 5 2
B) 2 15 + 3 10
C) 4 2 + 4
D) 5 5 + 5
Write each expression in exponential form.
38) 3
6p
A) p1
4 B) None of these
C) (6p)1
3 D) ( p3)1
4
39) 3
7b
A) (7b)3
2 B) (7b)1
3
C) None of these D) (6b2)1
3
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Write each expression in radical form.
40) (2v3)1
6
A) ( 6v)3B) ( 3
10v)5
C) None of these D) 6
2v3
41) (6n)3
2
A) ( 53n)7
B) 3
7n
C) ( 6n)3D) ( 4
5n)7
Identify the vertex, axis of symmetry, and min/max value of each.
42) f (x) = −x2 − 14x − 55
A) Vertex: (−7, −6)Axis of Sym.: y = −6Max value = −7
B) Vertex: (7, 6)Axis of Sym.: x = 7Max value = 6
C) Vertex: (−7, −6)Axis of Sym.: x = −7Min value = −6
D) Vertex: (−7, −6)Axis of Sym.: x = −7Max value = −6
43) f (x) = 1
3x2 +
4
3x +
7
3
A) Vertex: (−2, 1)Axis of Sym.: x = −2Min value = 1
B) Vertex: (−2, 1)Axis of Sym.: x = −2Max value = 1
C) Vertex: (−4, 3)Axis of Sym.: x = −4Max value = 3
D) Vertex: (−2, 1)Axis of Sym.: y = 1Min value = −2
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Use the information provided to write the vertex form equation of each parabola.
44) f (x) = x2 + 12x + 36
A) f (x) = (x + 6)2 − 3B) f (x) = x2 + 6
C) f (x) = (x + 6)2
D) f (x) = (2x + 7)2
45) f (x) = −6x2 − 108x − 494
A) f (x) = −6(x − 9)2 − 8
B) f (x) = −6(x + 7)2 − 8
C) f (x) = 1
2(x + 9)2 + 8
D) None of these
Use the information provided to write the standard form equation of each parabola.
46) f (x) = 3(x − 6)2 + 9
A) f (x) = 3x2 − 66x + 355B) f (x) = 3x2 + 36x + 99C) None of theseD) f (x) = 3x2 − 36x + 117
47) f (x) = 1
3(x + 7)2 + 3
A) None of these
B) f (x) = 1
3x2 +
18
3x +
56
3
C) f (x) = 1
3x2 −
14
3x +
58
3
D) f (x) = 1
3x2 +
14
3x +
58
3
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Determine whether the scenario involves independent or dependent events. Then find theprobability.
48) You roll a fair six-sided die twice. Thefirst roll shows a five and the second rollshows a two.
A) None of these
B) Independent; 20
169 ≈ 0.118
C) Independent; 1
36 ≈ 0.028
D) Dependent; 1
3 ≈ 0.333
49) A bag contains four red marbles and eightblue marbles. You randomly pick amarble and then pick a second marblewithout returning the marbles to the bag. Both marbles are red.
A) None of these
B) Independent; 16
49 ≈ 0.327
C) Independent; 1
4 = 0.25
D) Independent; 36
169 ≈ 0.213
Find the probability.
50) A spinner has an equal chance of landingon each of its six numbered regions. Afterspinning, it lands in region two or three.
A) 1
3 ≈ 0.333 B) None of these
C) 5
7 ≈ 0.714 D)
7
10 = 0.7
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Answers to Part I (ID: 2)1) B 2) D 3) C 4) C5) C 6) B 7) C 8) B9) A 10) C 11) D 12) D13) A 14) C 15) C 16) B17) D 18) D 19) C 20) A21) D 22) B 23) C 24) C25) B 26) B 27) C 28) A29) A 30) A 31) A 32) D33) A 34) B 35) C 36) D37) B 38) C 39) B 40) D41) C 42) D 43) A 44) C45) D 46) D 47) D 48) C49) A 50) A
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Math 2 Final Exam Packet
Part I
Name___________________________________ ID: 3
Date________________ Block____
-1-
Factor each completely.
1) x2 − 3x + 2
A) (x + 2)(x − 1)B) None of theseC) (x + 2)(x + 1)D) Not factorable
2) x2 − 9x + 18
A) (x + 3)(x − 6)B) (x + 2)(x + 1)C) (x − 3)(x − 6)D) (x − 3)(x + 6)
3) 20x2 + 36xA) 4x(5x − 9) B) 4x(5x + 9)C) 4x(5x + 1) D) 20x(x + 9)
4) 15v2 + 6v + 42
A) 3(5v + 2)(v − 10)B) 3(5v2 + 2v + 14)C) 15(v + 2)2
D) 3(5v − 2)(v − 10)
5) 5r2 + 14r − 24
A) (5r + 24)(r − 1)B) (5r + 4)(r − 6)C) (5r − 6)(r + 4)D) 2(5r + 2)(r + 3)
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Solve each equation by factoring.
6) (r − 4)(r − 1) = 0
A) None of these B) {4, −2}
C) {4, 1} D) {5
2,
1
2}
7) (x − 1)(5x + 1) = 0
A) {4, −1
5} B) {−4, −5}
C) {1, −1
5} D) None of these
8) 6b2 − 54b = −84
A) {−7, −8} B) {2, 7}C) {2, −5} D) {−7, 7}
9) v2 = −8 − 6vA) None of these B) {−4, −7}C) {−3, 7} D) {3, 0}
10) 27x2 − 19x − 17 = −5 + 6x2
A) {− 5
2, −2} B) None of these
C) {4
3, −
3
7} D) {− 1
7, −5}
11) 11x2 − 3 = 8x2 + 8x
A) {− 3
7, −3} B) {5
4, −3}
C) {− 1
3, 3} D) {7
2,
4
7}
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Solve each equation by completing the square.
12) x2 + 10x − 24 = 0
A) {11.083, −1.083}B) None of theseC) {4.124, −12.124}D) {10, 2}
13) m2 + 14m − 50 = 0
A) None of theseB) {6, −8}C) {5.55, −9.55}D) {2.95, −16.95}
14) n2 + 20n + 87 = 3
A) {1 + 67, 1 − 67}B) {−6, −14}C) {−10 + 2 46 , −10 − 2 46}D) {−5 + 67, −5 − 67}
15) n2 − 18n − 70 = −7
A) {2 + 2 3, 2 − 2 3}B) {21, −3}C) None of theseD) {7 + 95, 7 − 95}
16) m2 + 8m + 10 = 3
A) {−1, −7}B) {−3, −13}C) {4 + 3, 4 − 3}D) None of these
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Solve each equation with the quadratic formula.
17) n2 − 5n − 24 = 0
A) {8, −3} B) {6, −4}C) {1.646, −3.646} D) {4, −6}
18) 7m2 + 1 = 4mA) None of these
B) {1 + i 7
4,
1 − i 7
4 }C) {2 + i 3
7,
2 − i 3
7 }D) {1 + i 3
2,
1 − i 3
2 }
19) 3x2 + 2x = 33
A) None of these
B) {−1 + 7i 2
3, −1 − 7i 2
3 }C) {1 + 7i 2
3,
1 − 7i 2
3 }D) {3, −
11
3 }
Find the discriminant of each quadratic equation then state the number and type of solutions.
20) −3k2 + 3k − 11 = −2
A) 117; one real solutionB) −99; two imaginary solutionsC) 117; two real solutionsD) −99; one real solution
21) n2 − 6n + 12 = 3
A) 0; one real solutionB) −284; two real solutionsC) 105; two real solutionsD) 0; two real solutions
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22) 14x2 − 5x − 5 = −14x − 6 + 13x2
A) 77; one rational solutionB) 77; two imaginary solutionsC) −35; two imaginary solutionsD) 77; two irrational solutions
23) −13x2 − 5x + 14 = 2xA) 777; two imaginary solutionsB) 777; two irrational solutionsC) −679; two imaginary solutionsD) 777; one rational solution
Simplify each expression.
24) (11 − 3n + 6n2) + (−14 − 14n2 − 9n3)A) −16n3 − 8n2 − 3n − 2B) −9n3 − 8n2 − 3n − 3C) −22n3 − 8n2 − 3n − 3D) None of these
25) (5a2 − a3 + a4) − (11a2 − 9a3 − 12a4)A) 13a4 − 10a3 − 6a2
B) None of theseC) 13a4 − 6a3 − 6a2
D) 13a4 + 2a3 − 6a2
Find each product.
26) (8x − 7)(4x − 5)A) 32x2 + 12x − 35B) 32x2 − 12x − 35C) 32x2 + 35D) None of these
27) (7n − 7)(3n − 4)A) 21n2 − 7n − 28B) −21n2 − 41n − 10C) −21n2 + 29n + 10D) None of these
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Factor each completely.
28) −21uv − 18u2 + 4v2
A) (3u + 4v)(v − 6u)B) 9u(3u − 4v)C) −3u(3u + 4v)D) None of these
29) 8xy − 14x2 + 4y − 7xA) (2x + 1)(4y + 1)B) (2x + 1)(4y + 7x)C) None of theseD) 9x(2x − 1)
Describe the end behavior of each function.
30) f (x) = x2 − 4x − 2
A) f (x) → +∞ as x → -∞f (x) → -∞ as x → +∞
B) f (x) → -∞ as x → -∞f (x) → +∞ as x → +∞
C) f (x) → +∞ as x → -∞f (x) → +∞ as x → +∞
D) None of these
31) f (x) = x2 − 6
A) f (x) → +∞ as x → -∞f (x) → -∞ as x → +∞
B) f (x) → -∞ as x → -∞f (x) → -∞ as x → +∞
C) f (x) → -∞ as x → -∞f (x) → +∞ as x → +∞
D) f (x) → +∞ as x → -∞f (x) → +∞ as x → +∞
Simplify.
32) 4 112xy2
A) −16xy 2
B) −14y2x 5xC) −112xy 2yD) 16y 7x
33) −2 108u4v
A) −12u2 3v B) 8v 7uvC) 64uv 6u D) −24v 7u
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34) −2 27 − 24 − 3
A) −8 3 B) None of theseC) −7 3 D) −7 3 − 2 6
35) −2 3 − 3 3 + 3 3
A) −5 3 B) −2 3
C) −3 3 D) 0
36) 6(5 + 2)A) −15 5 + 5
B) 5 6 + 2 3C) None of theseD) −25 2 + 4 3
37) 3(−3 5 + 5)A) 44
B) −20 2 + 10 5
C) −3 15 + 5 3
D) 30 + 5
Write each expression in exponential form.
38) ( 4v)5
A) None of these B) v5
4
C) v4
5 D) v1
2
39) ( 6m)3
A) m3
2 B) (6m)3
2
C) (2m)6
5 D) (4m)2
3
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Write each expression in radical form.
40) (2k)7
5
A) ( 5k)7
B) ( 510k)6
C) ( 52k)8
D) ( 52k)7
41) (7p)2
3
A) p B) ( 32p)4
C) ( 53p2 )2
D) ( 37p)2
Identify the vertex, axis of symmetry, and min/max value of each.
42) f (x) = x2 + 12x + 27
A) Vertex: (−9, 6)Axis of Sym.: x = −9Min value = 6
B) Vertex: (−6, −9)Axis of Sym.: x = −6Min value = −9
C) Vertex: (6, 9)Axis of Sym.: x = 6Max value = 9
D) Vertex: (−6, −9)Axis of Sym.: y = −9Min value = −6
43) f (x) = x2 − 16x + 71
A) None of theseB) Vertex: (8, 7)
Axis of Sym.: x = 8Min value = 7
C) Vertex: (−8, 7)Axis of Sym.: y = 7Max value = −8
D) Vertex: (−7, −8)Axis of Sym.: x = −7Min value = −8
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Worksheet by Kuta Software LLC-9-
Use the information provided to write the vertex form equation of each parabola.
44) f (x) = −2x2 − 20x − 55
A) None of theseB) f (x) = −2(x + 5)2 − 5
C) f (x) = 2(x − 5)2 + 5
D) f (x) = 2(x − 7)2 − 4
45) f (x) = −4x2 − 16x − 10
A) f (x) = 4(x + 2)2 + 6
B) f (x) = −4(x − 2)2 + 6
C) f (x) = −4(x + 2)2 + 6
D) f (x) = −4(x + 6)2 + 2
Use the information provided to write the standard form equation of each parabola.
46) f (x) = −6(x + 7)2 − 10
A) f (x) = 6x2 + 84x + 284B) f (x) = 9x2 − 84x + 305C) f (x) = −6x2 − 84x − 304D) None of these
47) f (x) = −(x + 9)2 − 8
A) f (x) = −x2 − 18x − 89B) f (x) = −x2 + 18x − 89C) f (x) = 0 + 21x − 89D) f (x) = 2x2 + 36x + 154
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Determine whether the scenario involves independent or dependent events. Then find theprobability.
48) A box of chocolates contains five milkchocolates and seven dark chocolates. You randomly pick a chocolate and eat it. Then you randomly pick another piece. Both pieces are milk chocolate.
A) Independent; 1
4 = 0.25
B) Dependent; 5
33 ≈ 0.152
C) Dependent; 5
18 ≈ 0.278
D) None of these
49) You flip a coin twice. The first flip landstails-up and the second flip landsheads-up.
A) Independent; 1
36 ≈ 0.028
B) Independent; 1
16 ≈ 0.063
C) Independent; 1
4 = 0.25
D) Dependent; 15
91 ≈ 0.165
Find the probability.
50) A spinner has an equal chance of landingon each of its four numbered regions. After spinning, it lands in region two orthree.
A) 1
3 ≈ 0.333 B)
2
3 ≈ 0.667
C) None of these D) 9
14 ≈ 0.643
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Answers to Part I (ID: 3)1) B 2) C 3) B 4) B5) C 6) C 7) C 8) B9) A 10) C 11) C 12) B13) D 14) B 15) B 16) A17) A 18) C 19) D 20) B21) A 22) D 23) B 24) B25) B 26) D 27) D 28) A29) C 30) C 31) D 32) D33) A 34) D 35) B 36) B37) C 38) B 39) B 40) D41) D 42) B 43) B 44) B45) C 46) C 47) A 48) B49) C 50) C
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Math 2 Final Exam Packet
Part I
Name___________________________________ ID: 4
Date________________ Block____
-1-
Factor each completely.
1) m2 + m − 30
A) (m − 5)(m + 6)B) (m + 5)(m + 6)C) (m − 5)(m − 6)D) (m + 5)(m − 6)
2) v2 + 2v − 8
A) (v − 9)(v + 1)B) (v − 2)(v − 4)C) (v + 2)(v − 4)D) (v − 2)(v + 4)
3) 7n4 + 4n3
A) 6(5n − 7)(n + 10)B) n3(7n + 4)C) 3n3(3n + 7)D) n3(7n + 1)
4) 10n2 − 48n + 32
A) 2(n − 4)(5n + 4)B) (n − 4)(5n − 4)C) 2(5n − 4)(n − 4)D) 2(5n + 8)(n + 2)
5) −5v2 + 8v − 3
A) −(5v + 3)(v + 1)B) −(5v − 3)(v − 1)C) Not factorableD) −(v − 3)(5v + 1)
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Solve each equation by factoring.
6) (x + 3)(x − 3) = 0
A) {−3, 3} B) {− 2
3, −3}
C) {− 5
4,
2
3} D) {1, 2
5}
7) (3n + 2)(n − 4) = 0
A) None of these B) {2
3, −2}
C) {1, 0} D) {− 2
3, −3}
8) x2 + 7x = 8
A) {1, 0} B) {1, −8}C) {5, 8} D) {1, 5}
9) m2 − 8m = 0
A) {8, 0} B) {2, −6}C) None of these D) {−5, 0}
10) 4b2 − 3b + 12 = 8b + 6
A) None of these B) {3
4, 2}
C) {5
7, −3} D) {3
5, −
2
5}
11) 3a2 − 24 = a
A) {− 3
7, −
5
3} B) None of these
C) {− 8
3, 3} D) {− 3
2,
1
2}
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Solve each equation by completing the square.
12) v2 − 10v − 39 = 0
A) {−1, −9}B) None of theseC) {−5, −7}D) {−0.461, −19.539}
13) x2 + 14x − 51 = 0
A) {0.292, −10.292}B) {3, −17}C) {−0.31, −9.69}D) {−0.151, −19.849}
14) n2 − 10n + 16 = −5
A) {7, 3} B) {9, −1}C) None of these D) {7, −11}
15) m2 + 8m − 76 = −4
A) None of theseB) {−1, −9}C) {−4 + 2 22, −4 − 2 22}D) {4, −18}
16) b2 + 18b + 82 = 10
A) {−2 + 22, −2 − 22}B) {2 + 74, 2 − 74}C) {−6, −12}D) {14, 4}
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Solve each equation with the quadratic formula.
17) n2 + 5n + 6 = 0
A) {1, −2} B) {3, −5}C) {−2, −3} D) {6, −1}
18) 2m2 − 6m = −10
A) {−3 + i, −3 − i}
B) {3 + 29
2,
3 − 29
2 }C) {5
2,
1
2}D) None of these
19) 4a2 − 12 = 8aA) {3, −1}B) {1, −1}C) {1 + i 2, 1 − i 2}
D) {2 + 7
2,
2 − 7
2 }
Find the discriminant of each quadratic equation then state the number and type of solutions.
20) k2 − 2k + 6 = 5
A) 8; two real solutionsB) 0; one real solutionC) −320; two imaginary solutionsD) 9; two real solutions
21) 4x2 − x − 4 = −8
A) −63; two imaginary solutionsB) 160; two real solutionsC) −15; two imaginary solutionsD) −63; two real solutions
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22) −2k2 − 6k + 3 = −8k2 + 7kA) −167; two imaginary solutionsB) None of theseC) −20; two rational solutionsD) 97; two irrational solutions
23) −11b2 − 11 = 6bA) −448; two rational solutionsB) −448; two irrational solutionsC) −448; two imaginary solutionsD) 520; one rational solution
Simplify each expression.
24) (−14p − 7p2 + 2p5) − (−6p2 + 4p5 − 6p3)A) −2p5 + 6p3 − p2 − 14pB) −4p5 + 6p3 − p2 − 14pC) −4p5 + 2p3 + 13p2 − 14pD) −4p5 + 2p3 − p2 − 14p
25) (−13n5 − 9n − 8n4) + (12n5 − 8n4 − 13n)A) −n5 − 5n4 − 24nB) None of theseC) −n5 − 16n4 − 22nD) 9n5 − 5n4 − 24n
Find each product.
26) (8a + 1)(a − 6)A) −12a2 + 7a + 49B) 8a2 − 47a − 6C) −12a2 + 49a − 49D) 8a2 − 6
27) (3n + 1)(−8n − 3)A) −42n2 + 50n − 12B) −24n2 − n + 3C) None of theseD) −24n2 − 17n − 3
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Factor each completely.
28) 7uv + 2u + 42v + 12
A) (7v + 6)(u − 2)B) (u + 6)(7v + 2)C) None of theseD) (u + 6)(7v + 6)
29) 120uv − 168u + 280v − 392
A) None of theseB) 8(3u − 7)(5v + 7)C) 8(3u + 7)(5v − 7)D) (3u − 7)(5v − 7)
Describe the end behavior of each function.
30) f (x) = −x2 − 8x − 10
A) f (x) → -∞ as x → -∞f (x) → -∞ as x → +∞
B) f (x) → +∞ as x → -∞f (x) → +∞ as x → +∞
C) f (x) → -∞ as x → -∞f (x) → +∞ as x → +∞
D) f (x) → +∞ as x → -∞f (x) → -∞ as x → +∞
31) f (x) = 2x2 + 8x + 2
A) f (x) → +∞ as x → -∞f (x) → -∞ as x → +∞
B) f (x) → +∞ as x → -∞f (x) → +∞ as x → +∞
C) f (x) → -∞ as x → -∞f (x) → +∞ as x → +∞
D) f (x) → -∞ as x → -∞f (x) → -∞ as x → +∞
Simplify.
32) 3 392xy
A) −40y2x 2 B) 42 2xyC) −84y x D) 24x2y2 3
33) −3 100u3v3
A) 24uv uB) −7u2v2 5
C) −30uv uvD) None of these
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34) −3 54 + 2 27 − 3 24
A) −27 6 + 6 3
B) −15 6 + 6 3
C) −30 6 + 6 3
D) −21 6 + 6 3
35) − 45 − 6 + 3 45
A) 6 5 − 6B) None of theseC) 15 5 − 2 6
D) 15 5 − 6
36) 15(− 6 + 3)A) 25 B) 14
C) 5 3 + 4 D) None of these
37) 15(3 + 3)A) 4 3 − 5 30
B) 30 + 4
C) 3 15 + 3 5
D) −8 3 + 2
Write each expression in exponential form.
38) ( 5b)2
A) (4b)2
3 B) (10b)3
4
C) (6b)2
3 D) b2
5
39) 3a
A) (6a)1
3 B) a4
5
C) (3a)1
2 D) None of these
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Write each expression in radical form.
40) n5
3
A) 4
2n B) ( n)5
C) ( 3n)5
D) ( 53n)4
41) (7v)1
3
A) None of these B) ( 53v)7
C) 3
7v D) ( 410v)5
Identify the vertex, axis of symmetry, and min/max value of each.
42) f (x) = −6x2 − 96x − 391
A) Vertex: (7, 8)Axis of Sym.: x = 7Max value = 8
B) Vertex: (−8, −7)Axis of Sym.: x = −8Max value = −7
C) Vertex: (−8, −7)Axis of Sym.: y = −7Min value = −8
D) Vertex: (8, 7)Axis of Sym.: x = 8Max value = 7
43) f (x) = −2x2 − 24x − 73
A) Vertex: (−6, −1)Axis of Sym.: y = −1Min value = −6
B) Vertex: (−5, −3)Axis of Sym.: y = −3Min value = −5
C) None of theseD) Vertex: (−6, −1)
Axis of Sym.: x = −6Max value = −1
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Use the information provided to write the vertex form equation of each parabola.
44) f (x) = −3x2 + 60x − 297
A) f (x) = 3(x − 10)2 − 3
B) f (x) = −3(x − 10)2 + 3
C) f (x) = −3(x + 3)2 + 10
D) f (x) = 3(x − 10)2 + 3
45) f (x) = x2 + 2x − 2
A) f (x) = 2(x + 1)2 − 3
B) f (x) = (x + 1)2 − 3
C) f (x) = −(x + 1)2 − 3D) None of these
Use the information provided to write the standard form equation of each parabola.
46) f (x) = 1
2(x − 1)2 − 3
A) f (x) = 1
1x2 − x −
5
3B) None of these
C) f (x) = −1
2x2 − 3x −
11
2
D) f (x) = 1
2x2 − x −
5
2
47) f (x) = (x + 8)2 − 5
A) f (x) = x2 + 16x + 59B) f (x) = 2x2 + 32x + 123
C) f (x) = 1
2x2 + 8x + 27
D) f (x) = −x2 − 16x − 69
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Determine whether the scenario involves independent or dependent events. Then find theprobability.
48) A bag contains three red marbles and fiveblue marbles. You randomly pick amarble and then pick a second marblewithout returning the marbles to the bag. The first marble is red and the secondmarble is blue.
A) Independent; 20
169 ≈ 0.118
B) Dependent; 15
56 ≈ 0.268
C) Independent; 1
4 = 0.25
D) Dependent; 2
33 ≈ 0.061
49) You flip a coin twice. The first flip landstails-up and the second flip also landstails-up.
A) Independent; 56
225 ≈ 0.249
B) Dependent; 5
18 ≈ 0.278
C) Independent; 1
4 = 0.25
D) None of these
Find the probability.
50) A litter of kittens consists of two graykittens, two black kittens, and threemixed-color kittens. You randomly pickone kitten. The kitten is gray ormixed-color.
A) 7
10 = 0.7 B)
9
10 = 0.9
C) 2
13 ≈ 0.154 D)
5
7 ≈ 0.714
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Answers to Part I (ID: 4)1) A 2) D 3) B 4) C5) B 6) A 7) A 8) B9) A 10) B 11) C 12) B13) B 14) A 15) C 16) C17) C 18) D 19) A 20) B21) A 22) D 23) C 24) A25) C 26) B 27) D 28) B29) C 30) A 31) B 32) B33) C 34) B 35) A 36) D37) C 38) D 39) C 40) C41) C 42) B 43) D 44) B45) B 46) D 47) A 48) B49) C 50) D