Download Algebra II Midterm Part II

Algebra II Midterm REVIEW
Name________________
12-13
1. Find the value of 3 + 4 [10 – (4+ 2)]
a. 28
b. -19
2. Find the graph of y 
a.
c. 19
2
x4
3
b.
c.
3. Simplify: 1/2(12x – 6) + 1/4(24x + 8)
a. 5
b. 12x-1
c. 12x+1
4. Simplify: (3x + 2)²
a. 9x² - 4
c. 9x² - 12x + 4
d. -28
d. 1/2)(x+2)
b. 9x² - 6x + 4
d. 9x² + 12x + 4
5. If x²+ 6x + c is a perfect square trinomial, what is the value of c?
a. 3
b. 9
c. 36
d. 12
e. 4
6. Simplify:  8 
a. 8
b. | 8|
2
c. 8i
Solve each equation:
7. 2(6  3x)  12  4(x  2)
a. 4
b. -4
c. 1/4
d. -64i
d. -1/4
d.
8. 16= 2|3x – 4|
a. 4, -4/3
b. 4/3, 4
c. 4, -4
d. 1
9. Find the graph of 2x – y < 3
a.
b.
10. |2x – 4|≤ 10
a. x≤ 7
b. -3≤ x ≤ 7
11. Find the graph of f (x)  
a.
c.
c. -7≤ x ≤ 3
d. All real numbers
1
x
3
b.
12. Determine how many real and imaginary solutions the equation
2x² + 3x - 8 = 0 has?
a. 2 real, no imaginary b. 1 real , no imaginary
c. 1 real, 1 imaginary
d. no real, 2 imaginary
13. Solve: | x – 4| ≤ -8
a. All real numbers
c. no solution
d.
b. x = -4, -12
d. x = -4, 12
c.
d.
14. Give the domain of h = { (-3, 4), (1, 5), (4, 5)} tell if h is a function.
a. { 4, 5}; h is a function
b. { -3, 1, 4}; h is not a function
c. { -3, 1, 4}; h is a function
d. { 4, 5}; h is not a function
15. If g(x)  2x 3  3x 2  x  4 find g(-3).
a. 74
b. -74
c. -53
d. -53
e. 12
16. What type of polynomial function is f (x)  5x 4  3x 3  2x  1 ?
a. constant
b. linear
c. quadratic
d. cubic
e. quartic
17.Find the slope and y-intercept of 4x+ 6y = 12?
2
2
2
a.  , (0,-2)
b. , (0,-2)
c. , (0,2)
3
3
3
2
d.  , (0,2)
3
18.Find the graph of f (x)  x(x  4)2
a.
b.
c.
What is the x intercept of the line whose equation is
6x + 4y = 3?
a. -2
b. 1/2
c. 2
d.
19.
20.
a.
Find the graph of f (x)  x  3  2
b.
d.-1/2
c.
d.
21.
What is the slope intercept form of the equation of a line that passes through (6, 1) and is perpendicular to the line whose
equation is
y = 3x - 2?
1
1
a. y   x  3
b. y   x  2
3
3
1
c. y = - 3x  3
d. y  x  2
3
22. For which equation is the graph a vertical line?
a. x = 2
b. y = 4
c. x = y
d. y = |x|
23. For which pair of equations are the lines parallel?
a. 4x + 2y = 8 and 8x + 16y = 4
b. x + 3y = 4 and x = 3y + 8
c. y = 1/4x + 2 and y = 4x + 1
d. y = 2x and y = -1/2 x
24.
a.
Find the graph of y  3x 2  7x  4
b.
25. Subtract 3x 3  4x 2  8x 1 from 4x 3  7x 2  2x  3
a. x 3  3x 2  10x  4
b. x 3  3x 2 10x  4
c.
d.
c. x 3  3x 2  10x  4
d. x 3  3x 2 10x  4
26. What is the vertex of the graph of y = 3(x – 2)² - 8 ?
a. ( 2,8)
b. (3,-8)
c. (-2, -8)
27. What is the correct factorization of 6x² - 5x – 4 ?
a. (3x - 4)(2x +1)
b. ( 3x –1)(2x+ 4)
d. ( 2x + 4)(3x – 1)
e. ) (2x – 2)( 3x + 2)
28. What are the zeros of y = x² + 10x + 16 ?
a. -2, -8
b. -2, 8
c. 2, -8
29.
d. (2, -8)
c. (6x + 4)( x – 1)
d. 4, 8
e. 2, 8
You want to eliminate x by the addition method in the system:
3x – 4y = 5
-2x + 5y = 8 If you multiply each side of the top
equation by 2, by which number would you
multiply each side of the bottom equation?
a. 2
b. -2
c. 3
d. -3
31. What does d equal in the solution of the system : 2c + d = 5
c-d=1
a. 1
b. -1
c. 2
`
32. For which system are there infinitely many solutions?
a. 2x + 6y = 7
b. x – 2y = 8
4x + 12y = 14
5x = -10y + 40
d. -2
c. 2x – y = 8
2x + y = -8
d. 3x - y = 4
y = 3x – 4
33. Simplify: ( 2 + i ) – ( 5 – 2i)
a. -3 – 3i
b. -3 + 3i
35. Simplify :
a. 5i 3
c. 3 – 3i
d. 3 + 3i
75
b. 3i 5
c. 25i 3
d. 5i 5
36. What are all the solutions of 5(x – 2)² - 4 = 21 ?
a. 4
b. 7
c. 2  5
d. -2, -4
37. Simplify : 2 8  50
a. 9 2
b. 2
c.
d.  2
2
38. Factor : 9x² - 1 = 0
a. ( 3x – 1)²
c. ( 3x + 1) ( 3x + 1)
e. 2  5
b. ( 3x – 1)( 3x + 1)
d. ( 3x – 1)( 3x - 1)
39. Factor: 3x² + 18x + 27 = 0
a. 3( x+3)²
b. 3(x – 3)²
c. ( 3x – 9)²
d. (3x + 3)²
40. What does (x+3)(x-4)(x-1) equal?
a. x 3  2x 2  11x  12
b. x 3  2x 2  11x  12
41. Find the product of ( -8 + 4i)(2 – i).
a. -12 + 16i
b. -12 – 16i
d. 20
e. -20– 16i
42.  2 is
a. rational
b. irrational
43. If
a. 1
1 = i,
b. -1
c. -20
c. real
d. imaginary
then i² = ______.
c.
1
44. Find the graph of y  (x  2)2  1
c. x 3  2x 2  11x  12
d.
1
d. x 3  2x 2  5x  12
a.
b.
45. What are the solutions of x² = 25 ?
a. 5
b. -1, -25
c. 5, -5
46. The graph of y = x is a
a. circle
b. line
c. parabola
c.
d. 0, 25
d. rectangle
47. Which polynomial has the factorization: ( 3x + 2) ( 9x² - 6x + 4)
a. 27x³ - 8
b. 9x³ - 4
c. 9x³ + 8
d. 27x³ + 8
e. 27x³ + 4
48. What is the quotient of ( 6x³ - 8x² - 2x – 3) ÷ ( x – 2) ?
a. 6x³ + 4x² + 6x + 9
b. 6x² + 4x + 6 + 9
c. 6x² + 4x + 6 + __ 9__________ d. 6x² + 4x + 6 + __9__
6x³ - 8x² - 2x – 3
x–2
e.
6x² - 4x + 6 - __15__
X- 2
49. What are all the rational zeros of f(x) = x³ +2x² - 5x - 6
a. -2, -1, -3
b. 2, 3, 1
c. 2, -3, -1
d. -2, 1 ,3
e. -2, -3, 1
50. How many zeros does the function f(x) = -2x4 + 3x + 4 have ?
a. 0
b. 1
c. 2
d. 3
e.4
51.
Which function is graphed?
d.
a. F(x) = (x+2)(x – 3)(x – 1)
c. f(x) = -x(x+2)(x-3)
52.
b. f(x) = x(x-1)(x + 3)
d. f(x) = x(x+1)(x+3)
Find the graph of y  (x  2)(x  4)
a.
b.
c.
d.
53.
Write the polynomial function with the solutions 4, -5i.
a. f(x) = (x - 4)(x + 5i)(x – 5i)
b. f(x) = (x + 4)(x – 5i)(x + 5i)
c. f(x) = (x - 4)(x + 5i)
d. f(x) = (x + 4)(x + 5i)
54.
Solve: x 4  5x 2  36  0
a.
3,2i
b. 3,i
c. 3,i,2i
d. 3i,2
55.
1
Describe the translation of the parent function f ( x)  x 2 to obtain the graph of f (x)   (x  3)2  2 .
2
a.
b.
c.
d.
56.
Vertical shift -2, Horizontal shift -3, shrink 2, reflect over x-axis
Vertical shift -2, Horizontal shift -3, stretch 2, reflect over x-axis
Vertical shift -3, Horizontal shift 3, stretch 2, reflect over y-axis
Vertical shift 3, Horizontal shift -3, shrink 2, reflect over x-axis
Find the graph of y  (x  2)(x  1)(x  3) .
a.
b.
c..
d.
On the back of your answer card show your work for each of the following questions and circle your answers.
57.
Solve x 2  5x  2  0 .
58.
Write y  4x 2  16x  3 in vertex form.