Download Quarter 2 Review

Algebra 2
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Quarter 2 Review
Date________________ Period____
Simplify.
1) (7 - 4i) - (2 + 7i)
3)
2) (3 - 2i)(6 + 5i)
1 + 8i
10 + i
Find the discriminant of each quadratic equation then state the number and type of solutions.
4) -4n 2 - 8n + 1 = 5
Solve each equation by any method you choose.
5) 6r 2 + 7 = -77
Worksheet by Kuta Software LLC
-1-
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Simplify each expression.
6)
p+7
p2 + p - 2
×
p2 + 6 p - 7
p+4
Describe the end behavior of each function.
7) f ( x) = x 2 - 8x + 12
Divide.
8) (v 4 - v 3 - 10v 2 + 14v + 14) ¸ (v - 2)
State the possible rational zeros for each function.
9) f ( x) = 2x 3 - 15x 2 - 40x + 25
Identify the vertex and axis of symmetry of each.
10) f (x) = -
1
( x - 4)( x + 2)
4
Worksheet by Kuta Software LLC
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Simplify.
11) (8 - 6i) - (6 + 7i)
13) (5 - 2i)
15)
12) 3 - (-2 + i) - 5
2
14)
4 5
16)
2 45
10i
-2 + 10i
5 5
4 3
Simplify. Your answer should contain only positive exponents.
4 -1
17) 4a b
19) nm × (2mn
4
-4 -4
× 4a b
-2 -4 -3
18) ( x y
3 -4
)
× 2x y
-3
2 2
)
20)
-2x y
4 0
-2x y
Simplify completely.
21) -4 10 (2 -
2)
Simplify.
22) -3 225xy 4 z 2
Worksheet by Kuta Software LLC
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Factor each completely.
23) 10x 3 - 35x 2 + 12x - 42
24) 125x 3 + 216 y 3
Solve each equation by any method you choose.
25) 28v 2 - 96 = 52v
26) 6n 2 - 3 = 147
27) -5m 2 - 7 = -3m
Sketch the graph of each function.
2
28) y > -2( x + 2) + 1
2
1
-9
-8
-7
-6
-5
-4
-3
-2
-1 0
-1
1
-2
-3
-4
-5
-6
-7
-8
Worksheet by Kuta Software LLC
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Use Reminder Theorem to Evaluate given function at the given value.
29) f (x) = -x 4 + 36x 2 - x + 2 at x = -6
Sketch the graph of each function.
30) f (x) = 2x 2 - 16x + 28
5
4
3
2
1
-1 0
-1
1
2
3
4
5
6
7
8
-2
-3
-4
-5
Describe the end behavior of each function.
31) f (x) = -x 4 + x 2 - 3
Simplify each expression.
32) (-6k 3 - 5k 4 - 5) - (6k 3 + 6k 4 ) + (-3k 4 + 3k 3 - 7)
Find each product.
33) ( x + 2)(5x 2 - 7x - 3)
Worksheet by Kuta Software LLC
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Solve each equation by completing the square.
34) n 2 + 16n + 77 = -5
35) 3x 2 - 12x + 62 = -4
Divide.
36) ( x 3 + 6x 2 + 15x + 25) ¸ ( x + 3)
37) (4x 3 + 31x 2 + 9x - 8) ¸ (4x + 3)
Find all roots. One root has been given.
38) x 3 + 6x 2 - 7x - 60 = 0; -5
Factor completely. One factor has been given.
39) x 3 + 4x 2 - 17x - 60 = 0; x + 3
Worksheet by Kuta Software LLC
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40. Evaluate:
i 50
i11
i0
i103
41. The graph of g(x) is shown. Determine all of the information below.
d) The equation of parabola in vertex form
e) The equation of parabola in standard form
a) Vertex:
____________
b) Axis of Symmetry:
____________
c) x-intercepts = roots = zeros = solutions:
f) The equation of parabola in intercept form
g) The interval where f(x) is increasing
h) The interval where f(x) is decreasing
i) Does this function have a min or a max?
What is it’s value?
j) The interval(s) where f(x) > 0
1
2
42. Solve: - - (x +6)2 - 8 = 14
43. Find all the following information for the given function:
# of Turning Points _______
Lowest Degree ______
Real Zeros: ________
y-intercept: ________
Relative maximum(s): _______________
Relative minimum(s): _______________
As x→ +∞, f(x) → ______ is _________ end behavior
As x→ -∞, f(x) → ______ is _________ end behavior
44. Write equation of the function of the best fit for given data (remember to check whether linear or
quadratic works better!):
x
5
6
7
8
9
y
173 250 339 445 560
Linear or Quadratic?
Equation: _________________________