Download algebra 3 midterm - chapters 6

ALGEBRA 3 MIDTERM REVIEW
FACTORING, CHAPTERS 6 - 7
Name:__________________________________________
Date:_____/_____/_____
Match the polynomial in column A with its correct factored form in column B.
(1 Point Each)
Column A
___Column B
_____1. x2 – 12x + 32
A.
(x + 13)(x – 1)
_____2. x2 + 12x + 20
B.
(x + 2)(x – 14)
_____3. x2 – 12x – 28
C.
(5x – 2)(x + 1)
_____4. x2 + 12x – 13
D.
(x – 8)(x – 4)
_____5. x2 – 36
E.
(3x + 5)(x + 1)
_____6. 2x2 – 3x – 5
F.
(2x – 5)(x + 1)
_____7. 5x2 + 3x – 2
G.
(x + 10)(x + 2)
_____8. 3x2 + 8x + 5
H.
(x + 6)(x – 6)
In exercises 9 – 26, circle the correct multiple choice answer. Show your work!(2 Points Each)
9.
10.
Simplify: √a2
(A) -a
(B) a
(C) | a |
(D) - | a |
Simplify:
4
√(-3)4
4
(A) 3
(B) -3√3
(C) 81
(D) -3
11.
12.
13.
14.
15.
Simplify:
√30 · √15
(A) √450
(B) 15√2
(C) 450
(D) 2√15
Simplify:
7√2 + 2√3 – 4√2 + 6√3
(A) 3√2 + 8√3
(B) 11√2 + 8√3
(C) 3√2 – 4√3
(D) 11√5
Simplify:
(2√6 – √3)2
(A) 21
(B) 27 – 6√2
(C) 27 – 12√2
(D) 15 – 12√2
Find the conjugate of -1 – √3.
(A) -1 + √3
(B) √3 + 1
(C) 1 – √3
(D) -√3 – 1
Find the conjugate of 12.
(A) 2√3
(B) -2√3
(C) -12
(D) 12
16.
17.
18.
19.
20.
Simplify
6
.
3 + 2√3
(A) 6 + 4√3
(B) -6 + 4√3
(C) 6 – 4√3
(D) -6 – 4√3
6–x = 2.
Solve
(A) x = -2
(B) x = 2
(C) x = -4
(D) x = 4
Solve 3 – 2√x = 7 .
(A) x = -2
(B) x = 4
(C) x = -4
(D) No Solution
Solve for x: 3x2 + 14 = 8
(A) x = + 2i
(B) x = +√2
(C) x = + i√2
(D) x = + 2
Simplify
1 + 2i
1 – 2i
(A) 1 + 2i
(C)
3
/5 – 4i/5
.
(B) 1 – 2i
(D) - 3/5 + 4i/5
21.
22.
23.
24.
25.
Simplify (2 + 3i)(1 – i ).
(A) -1 + i
(B) 5 + i
(C) -1 + 5i
(D) -1
Which is a solution of the equation x2 = 8x – 20?
(A) -4
(B) -2
(C) 4 + 2i
(D) -4 + 2i
Determine the nature of the roots of the equation x2 + 5x + 6 = 0.
(A) Real, Unequal, Rational
(B) Real, Unequal, Irrational
(C) Real, Double Root
(D) Imaginary, Conjugate
Find the vertex of the function y – 3 = -2(x + 3)2 .
(A) V(-3, 3)
(B) V(3, -3)
(C) V(-3, -3)
(D) V(3, 3)
Find the equation of quadratic function with vertex V(3, 5) that passes through the
point (1, 2).
(A) y – 5 = ¾ (x – 3)2
(B) y + 5 = ¾ (x + 3)2
(C) y – 5 = - ¾ (x – 3)2
(D) y + 5 = - ¾ (x + 3)2
26. Find the maximum value of the function f(x) = -x2 – 2x + 8.
(A) -1
(B) 1
(C) -9
(D) 9
In exercises 27 - , simplify.
27.
√18
√3
28.
√27 · √15
29.
√24 · √63
30.
(3√5)2
31.
√45 · √(3/5)
32.
5
5
√243c
33. √45 + √20
35.
37.
39.
√18 – √6
√3
(√5 – 2)(√5 + 2)
1
4 – √15
3
34.
3
3
√24 – √56 + √81
36. √5(√5 – √10)
38.
40.
(3√2 + 1)(3√2 + 4)
√5 + 1
√5 – 3
In exercise 41, solve for x. Check your solution. Show all steps!
41.
3
2x – 5 = 3
In exercises 42 - 44, decide whether each statement is TRUE or FALSE.
42. 5π is an irrational number.
______________
43. The decimal 0.08 is equal to the fraction 8/99.
______________
44. -√-27 simplifies to -3√3.
______________
In exercises 45 – 46, write each decimal as a common fraction in lowest terms.
45.
0.1375
46.
2.36
In exercises 47 – 52, simplify each expression.
47.
18
3i
48.
√-45
49.
√-24 · √-63
50.
(9i)2
51.
√-8 + √-18
52.
i√4 · √-4
In exercises 53 – 54, solve for x.
53. x2 + 144 = 0
54.
3x2 + 40 = 4
In exercise 55 - 58, simplify the expression.
55. (12 – 2i) – (8 – 3i)
56. (3 + i√2)(3 + i√2)
57. 3i(2 – 3i)
58.
5
2+i
In exercises 59 – 60, solve each equation either by completing the square or using the
quadratic formula. SHOW ALL STEPS! If no real solution exists, express the result in
standard complex number form.
59.
x2 – 16x + 20 = 0
60.
3x2 + 9x = -8
In exercise 61, solve the equation using the substitution. SHOW ALL STEPS!
If no real solution exists, express the result in standard complex number form.(8 Points Each)
61.
x4 – 3x2 – 4 = 0
In exercises 62 – 63, identify the vertex and graph each parabola on the coordinate plane provided.
62.
y + 3 = 1/2 (x – 4)2
63. y = -x2 + 4x – 1
In exercise 64, use the vertex and given point to find the standard form of the
quadratic equation y – k = a(x – h)2. (4 Points Each)
64.
Vertex  (2, -4)
Point  (0, 6)