Algebra 2
Final Exam Review Sheet 2013
Name:
Date:
Use Long Division to divide the polynomials.
1.
Period:
2.
Use Synthetic Division to divide the polynomials.
3.
4.
5.
Use the Remainder Theorem to find P(2) for
6.
The volume in cubic feet of a workshop’s storage chest can be expressed as the product of its
three dimensions:
. The depth is x + 1.
a. Find the other dimensions.
b. If the depth of the chest is 6 feet, what are the other dimensions?
Factor each polynomial.
7.
10. 15x2 – 16xy+ 4y2
13. 16j2 + 24j + 9
16. 49b2 – 36
8. 54c3d4 + 9c4d2
11.
14. 4x2 – 81y2
17. 6x4 – 9x3 – 36x2 + 54x
.
9. x2 – x – 42
12. 36y2 – 84y – 147
15. 3x3 + 3x2 + x + 1
Solve the equation using the Zero-Product Property.
18.
Solve the equation by Factoring.
19.
20.
21.
22.
The area of a playground is 336 yd2. The width of the playground is 5 yd longer than its length.
Find the length and width of the playground.
23.
The Sears Tower in Chicago is 1454 feet tall. The function
models the
height y in feet of an object t seconds after it is dropped from the top of the building.
a. After how many seconds will the object hit the ground? Round your answer to the nearest
tenth of a second.
b. What is the height of the object 5 seconds after it is dropped from the top of the Sears
Tower?
Order the group of quadratic functions from widest to narrowest graph.
24.
,
,
25.
Graph
and
. Compare the shape and position of the quadratic functions.
26.
Does
27.
Graph
28.
Identify the vertex and the y-intercept of the graph of the function
have a maximum or minimum point? State the Axis of Symmetry and Vertex.
. Label the Axis of Symmetry and Vertex.
.
29.
Graph
30.
.
Write the equation of the parabola in
vertex form.
y
y
8
8
6
6
4
4
2
2
–8
–6
–4
–2
O
2
4
6
8
–8 –6 –4 –2 O
–2
x
–2
–4
–4
–6
–6
–8
–8
2
4
6
8
31.
Rewrite
in Vertex Form.
32.
Rewrite
in Standard Form.
33.
A ball is thrown into the air with an upward velocity of 36 ft/s. Its height h in feet after t
seconds is given by the function
.
a. In how many seconds does the ball reach its maximum height? Round to the nearest
hundredth if necessary.
b. What is the ball’s maximum height?
34.
Dalco Manufacturing estimates that its weekly profit, P, in hundreds of dollars, can be
approximated by the formula
, where x is the number of units produced
per week, in thousands.
a. How many units should the company produce per week to earn the maximum profit?
b. Find the maximum weekly profit.
Find the discriminant and number of real number solutions for the equation.
35.
36.
Simplify the rational expression and state the restrictions.
37.
38.
Multiply and state the restrictions.
39.
40.
Divide and state the restrictions.
41.
42.
Add or subtract.
43.
44.
x
45.
46.
Simplify the complex fraction.
47.
48.
Solve each rational equation. Check for extraneous solutions.
49.
50.
51.
52.
Solve each radical equation. Check for extraneous solutions.
53.
54.
56.
57.
55.
Simplify the radical expression. Use absolute value symbols if needed.
58.
59.
60.
61.
-3
Multiply and simplify. Assume the variables are positive.
62.
63.
64.
65.
66.
67.
68.
(5 +
3 )(5 –
3)
69.
Divide and simplify. Assume the variables are positive.
70.
71.
72.
Rationalize the denominator of the expression.
73.
74.
75.
76.
77.
78.
Simplify.
79.
82.
80.
83.
81.
85.
86.
Simplify.
84.
87.
Write the exponential expression
88.
Write the radical expression
89.
Simplify
in radical form.
in exponential form.
. Write with rational exponents.
Solve. Check for extraneous solutions.
90.
91.
92.
93.
94.
Simplify
. Write with rational exponents.
Simplify each expression. Express each complex number in standard form.
95.
96. –6 –
97.
98.
99.
100.
101.
102.
103.
104.
105.
106.
107.
108.
109.
110.
Solve the equation using Square Roots.
111. 7 + 6 = 13
112.
113.
114.
115.
Find the value of n such that
Solve the equation by Completing the Square.
116.
118.
is a perfect square trinomial.
117.
119.
Solve the equation using the Quadratic Formula.
120.
121.
122.
123.
Find the length of the missing side. Leave your answer in simplest radical form.
125.
124.
15
5
6
c
14
Not drawn to scale
126.
A scuba diver has a taut rope connecting the dive boat to an anchor on the ocean floor. The
rope is 140 feet long and the water is 40 feet deep. To the nearest tenth of a foot, how far is
the anchor from a point directly below the boat?
127.
A grid shows the positions of a subway stop and your house. The subway stop is located at
(–5, 2) and your house is located at (–9, 9). What is the distance, to the nearest unit, between
your house and the subway stop?
Determine whether the given lengths can be sides of a right triangle.
128. 18 m, 24 m, 30 m
129.
m,
m,
130.
m
Find the exact perimeter of the triangle.
4x
x
131.
In the diagram
. Use the Pythagorean Theorem to find x. Do not round of estimate.
C
x
y
A
132.
1
D
5
Find the length of the hypotenuse.
45°
3 2
B
133.
Find the lengths of the missing sides in the triangle. Write your answers as decimals rounded
to the nearest tenth.
y
7
45°
x
134.
Find the value of the variable. If your answer is not an integer, leave it in simplest radical
form.
45°
x
5
Not drawn to scale
135.
The area of a square garden is 50 m2. How long is the diagonal?
Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form.
137.
136.
6
x
x
y
30°
60°
20
12
Not drawn to scale
138.
Find the value of x and y rounded to the nearest tenth.
x
34
45°
30°
y
139.
The length of the hypotenuse of a 30°-60°-90° triangle is 4. Find the perimeter.
140.
A piece of art is in the shape of an equilateral triangle with sides of 7 in. Find the area of the
piece of art. Round your answer to the nearest tenth.
141. a. Graph the relation s and its inverse. Use open circles to graph the points of the inverse.
b. Describe the relationship between the line y = x and the graphs of s and its inverse.
x
0
4
9
10
y
3
2
7
–1
142.
Consider the relation s given by the values in the table.
x
–5
–3
–1
1
y
–6
–2
–2
–6
a. Is the relation s a function? How do you know?
b. Find the inverse relation s if it exists. Support your answer.
143.
Find the inverse of each function if it exists.
2
a. y  x  5
b.
f  x   x2  4
3
c.
f  x  5
d.
g  x  x  3
144.
Graph y  4 x . Then state the equation of the asymptote, y-intercept, x-intercept, domain and
range of the function.
145.
Graph y  log6 x . Then state the equation of the asymptote, y-intercept, x-intercept, domain and
range of the function.
146.
Rewrite the equation in exponential form: log6 1296  4 .
147.
Rewrite the equation in logarithmic form: 125
148.
Solve.
a.
log x 64  6
b.
log9 3  x
4
3
 625 .
Algebra 2 - Final Exam Review 2013
Answer Section
–38/(x+6)
1.
2.
4.
5.
3.
4
6. a. height, x – 1; width, x – 3 b. height, 4 ft; width, 2 ft
7. 2x(x2 + 2x + 4)
8. 9c3d2(6d2 + c)
10. (3x – 2y)(5x – 2y)
11. 2(5x – 2)(2x + 3)
13. (4j + 3)2
14. (2x + 9y)(2x – 9y)
16.
(7b + 6)(7b – 6)
17.
19.
c = 0 or c = 4
20.
22.
length = 16 yd, width = 21 yd
24.
25.
,
3x(x2 – 6)(2x – 3)
9.
12.
15.
18.
(x – 7)(x + 6)
3(2y – 7)(6y + 7)
(x + 1)(3x2 + 1)
1
n = 0 or n =
10
21.
23.
a. 9.5 seconds b. 1,054 ft
,
graph for
has the same shape as
, but it is shifted up 4 units
y
5
4
3
2
1
–4 –3 –2 –1
–1
1
2
3
4
x
–2
–3
–4
–5
–6
–7
–8
–9
y
6
26.
27.
minimum; axis of symmetry:
; vertex:
Axis of symmetry:
Vertex:
4
2
see graph on the right hand side
–6
–4
–2
2
–2
–4
–6
4
6
x
28.
vertex: (–2, 5); y-intercept: –7
30.
33.
1.13 s; 29.25 ft
31.
34.
36.
-3; no solutions
37.
39.
;
42.
;
29.
1,000 units; $1300
;
40.
;
32.
35.
72; 2 solutions
38.
;
41.
;
43.
44.
45.
46.
47.

48.
49.
x=
50.
x=8
52.
14
53.
5
3
10
1
2
51.
x=
54.
55.
56.
57.
–6
5 is a solution to the original equation. The value –8 is an extraneous solution.
0 and 7 are solutions of the original equation.
x = 22
58.
59.
60.
63.
61.
64.
62.
65.
66.
67.
68.
69.
70.
71.
72.
73.
74.
75.
76.
77.
78.
81.
not possible to simplify
79.
82.
80.
83.
84.
3
85.
not possible
87.
90.
16
88.
–1
91.
22
86.
89.
–5, 11
92.
7
6
93.
94.
95.
97. -1
100.
103. -63
106.
98. 1
101.
104. -25
107.
108.
109.
110.
111.
112.
113.
4 4
 i, i
3 3
114.
115.
116.
5, –1
117.
118.
119.
121.
122.
96.
99.
102.
105.
120.
8
–36
9, 14
123.
361
4
124.
3 21 cm
125.
14.9
8
128.
yes
2 13
126.
134.2 ft
127.
129.
yes
130.
132.
6
133.
x = 9.9, y = 7
135.
138.
141.
10 m
x = 24.0, y = 46.4
a.
136.
139.
137. x = 30, y =
140. 21.2 in.2
6+2
b. If you reflect each point of s over the line y = x, you get
the inverse of s.
y
131.
134.
8
4
–8
–4
4
8
x
–4
–8
142.
143.
a. yes; passes the vertical line test; no domain value is used more than once
b. no; the relation s fails the horizontal test; the range of s is used more than once
3x  15
a. y 1 
b. no inverse exists c. no inverse exists d. g 1  x   x 2  3x  9
2
144.
Equation of the asymptote: y  0 y-intercept:  0,1
x-intercept: none domain: all real numbers range: y  0
145.
Equation of the asymptote: x  0 y-intercept: none
x-intercept: 1,0  domain: x  0
range: all real numbers
146.
64  1296
147.
log125 625 
148.
a.
x2
4
3
b.
x
1
2