Download Alg II Study Guide for 1 st Semester Final

Alg II Study Guide for 1st Semester Final
Evaluate the expression for the given values:
1.
( 7 + y) ¸10x
when x = 2 and y = 43
Solve each equation:
x x
+ =5
2. 2 4
1
3. 4 ( 3y + 2 ) = 7
4. 6x + 34 -10x = 24 - 6(2x +1)
6. Solve for t in the equation:
5.
-9 =
2x 5 9
+ =
3 6 4
t
+ 4s
3
Solve each problem:
7. You are selling pizza for a fund raiser. Slices of plain pizza sell for $1 a slice. Pepperoni pizza sells for $2 a
slice. At the end of the evening, you find you have collected a total of $30. You sold 10 slices of plain
pizza. How may slices of pepperoni pizza did you sell?
8. A rectangle is 6 feet longer than it is wide. The perimeter of the rectangle is 32 feet. What is the width of
the rectangle?
Solve and write in interval notation:
9. 5x - 7 £ 3(x - 7)
10. 10x-12 < -32 or -26x £ -78
11. -10<4n-10<10
Solve each absolute value equation (make sure to check for extraneous solutions):
12. 2x - 5 = 1
13. 3x - 4 = x - 8
Solve then write in interval notation:
14. 3b-15 < 6
Find f(-5) for questions 15 and 16:
15. 𝑓(𝑥) = 5 − 𝑥
f (x) = x4 + 3
16.
17. Which is a linear function? Be able to explain why.
f (x) = -6 x + 5
f (x) =
3
a.
18a.
b.
19
+ 2x - 8
x
c.
f (x) = 3x2 + 5
d. f (x) = 2x - 9
If the relations are a function then find the domain and range of the relation.
{(−6, 2), (-4, 3), (−7, −7) (-6,2)}
18b.
If the relations are a function then find the domain and range of the relation.
{(12, 3), (-5, 3), (3, 3) (12-3)}
19a .
If the relations are a function then find the domain and range of the relation.
{(10, 3), (-5, 1.7), (3, 7) (12-3) (5, 3)(5,6) (7, 1.2)}
19b.
If the relations are a function then find the domain and range of the relation.
{(-10, 3), (-5, 7), (3, 7) (12-3) (5, 3) (-10,2)}
Use graph for questions 20 and 21:
20. What is the domain?
21. What is the range?
Use graph for questions 20a and 21a:
20a. What is the domain?
21a. What is the range?
Use graph for questions 20b and 21b:
20b. What is the domain?
21b. What is the range?
22. Find the slope of the line passing through the points (4, – 3) and (4, – 4).
22. Find the slope of the line passing through the points (5, – 3) and (6, – 3).
22. Find the slope of the line passing through the points (-6, – 3) and (4, – 5).
−1
23. Graph function 𝑓(𝑥) = 2 𝑥 − 3?
23. Graph function 3𝑥 − 6𝑓(𝑥) = 12
23. Graph function 𝑓(𝑥) =
−1
5
24a. Find the slope of the line.
(-2,8)
𝑥 + 6?
24b. Find the slope of the line.
24c. Find the slope of the line.
25. Line 1 contains (7, 2) and (3, 4). Line 2 contains (-3, –4) and (2, 6). Compare the lines
26a. Line 1 contains (3, -2) and (1, 4). Line 2 contains (1, –5) and (–2, 4). Compare the lines:
26b. Line 1 contains (2, 2) and (6, 5). Line 2 contains (1, –1) and (–2, 3). Compare the lines:
27a. Line 1 contains (– 6, 5) and (–4, –3). Line 2 contains (0, 8) and (2, 0). Compare the lines
27b. Line 1 contains (– 4, -3) and (–2, –2). Line 2 contains (1, 1) and (0, 3). Compare the lines
Graph the equation that goes with each graph:
3
a. 28 a. y   x  1
4
29 a.  5 x  4 y  12
28 b. x=3
29 b. y=-2
2
30b. y   x  1
3
30a. 4 x  5 y  25
31a. Write the equation of a line has slope –8 and y-intercept –12?
31b. Write the equation of a line has slope 4 and y-intercept –10?
31c. Write the equation of a line has slope –2 and y-intercept –6?
32. Write the equation of a line passes through (−1, −1) and (1, 4)?
32. Write the equation of a line passes through (4, −4) and (-1, 6)?
32. Write the equation of a line passes through (−1, −2) and (1, 4)?
33. Which equation of a line is perpendicular to 𝑦 =
through (−6, −2)?
33. Which equation of a line is perpendicular to 𝑦 =
through (−4, −1)?
33. Which equation of a line is perpendicular to 𝑦 =
through (−3, −1)?
Graph the equation:
2
3
1
2
1
3
𝑥 − 6 and passes
𝑥 + 3 and passes
𝑥 + 6 and passes
1
34a. 𝑦 = |𝑥 + 4| − 3
34b. y = 4 |𝑥 − 4|
1
34 c. y = 3 |x-3|
34 d.
y = −2|𝑥 − 4|
35. Sketch the graph of the function. Label the vertex and two other points on the graph.
1
a) y  x  2  1
b) y =  x  4  3
c) y =  x  1  1
2
Solve the system.
36.
x  2 y  z  2
37.
3x  3 y  z  1
2 x  3z  9
2x  3y  z  2
z 5
x yz 3
38. Telethon During a recent telethon, people pledged $10 or $20. Four times as many people pledged $20
as $10. Altogether, $900 was pledged. How many people pledged $10? How many people pledged $20?
(Show the equations used, define their variables, and solve the equations to get your answer)
Simplify the following:
39. (15  3i )  (4  3i )
40. 5i  5(8  9i )
42. i 15
43.
41. (2  4i )(9  7i )
4  5i
8i
44.
 2  11i
5  6i
Solve the following equation
45. 3x 2  18  9 x  2 x 2
46. 9 x 2  45 x
48. 4 x 2  49  0
49. 10 x 2  35  65 x
50.
2
 x  5 2  8
3
52. 3x 2  8 x  1  0
53. 4 x 2  8  9 x
51.
47. 3 x 2  8 x  16
x2
 6  26
5
Instructions: Graph the following polynomial functions with all characteristics listed/labeled for each problem.
For full credit, all characteristics must be listed.
54. f ( x)  x 4  4 x 2
55. f ( x)   x 3 ( x  4)( x  2)
56. f ( x)  x 4  13x 2  36
57. f ( x)  2 x( x  1)( x  2) 2
58. f ( x)  x 5  3x 3  2 x 2  4 x (hint: use T-chart) 59. f ( x)  ( x  2)( x 2  2 x  2)
60. Find the quotient of
61. Find all solutions of
62. Given
(5x4 - 2x3 - 7x2 - 39) ¸ (x2 + 2x - 4)
x5 + 27x2 = 0
f (x) = 2x3 -15x2 + 34x - 21 and one of its zeros = 1 . find all of its zeros.
63a. Write the equation in standard and factored form. Write the equation in standard and factored
form.
63b.
.
64. Which polynomial(s) are of the least degree with rational coefficients that has the given roots.
a) 2,3,4
b) 3,4,3i
c) 1+2i, -3
65. Divide (x3 -13x -12) ¸ (x - 4)
66. Solve : m3 +6m2 - 3m= 18
67. Solve:
4 x 7  64 x 3  0
68. Find the zeros: f ( x)  2 x3  15x 2  34 x  21; x  3 is a factor of the function
69. Write the polynomial function in factored form of the graph below.