Algebra 2: Spring Final Exam Study Guide
Name:________________________________Period:_____ Score:__________/100
There are approximately 20 free response questions and 20 multiple choice questions on the
actual two hour final exams.
My final exam is: _____________________________________
Directions: Simplify each expression. SHOW ALL YOUR WORK. Circle your final answer.
1)
3

64x 2 3 m1 2 y2 5
4
2)
81m3 y 20 k 17
3
10
125
4)
7)
24x 7 m5 k 9
5)

12
8)

3)
8x 9
27m12

1252 3 • 16 3 4
50
63
6)

9)
4
x•8 x• x
4
16m

12 3 56 3
k x
Directions: For the given function, do the following analytically:
a) Identify the vertex and write it as an ordered pair. Underline the x coordinate and circle the y
coordinate within the quadratic equation.
b) Find the equation of the axis of symmetry.
c) Find the minimum or maximum function value and the x-value at which it occurs.
d) Use interval notation to describe the domain and range of the function. Label your answer!!
e) Use the quadratic formula to find the x intercepts. Write your answers as simplified roots.
f) Find the y intercept of the function analytically. Write this as an ordered pair.
g) Sketch the graph of the function on the graph provided labeling parts (a), (b), (e), and (f).
SHOW YOUR WORK FOR PARTS A-F BELOW. LABEL EACH PART SO I CAN CLEARLY SEE YOUR WORK.
10) y = -2(x - 1)2 + 5
10
8
6
4
2
-10
-5
5
-2
-4
-6
-8
-10
A)_______________________
B)_______________________
C)_______________________
D)_______________________
E)_______________________
F)_______________________
10
Directions: For each equation A) identify the vertex B) show the orientation C) state if it has a
stretch, compression or neither D) show direction and value of any shifts.
11) y  4  x  7   2
2
A:_________________________
B:_________________________
C:_________________________
D:_________________________
12) y 
1
2
 x  8  6
5
A:_________________________
B:_________________________
C:_________________________
D:_________________________
13) Directions: For the given function, do the following: (A) Write the equation for the
parabola in vertex form. (B) Write the equation in standard form. (C) Use interval notation to
describe the domain and range of the function.
Directions: Answer the following analytically. BE SURE TO SHOW ALL YOUR WORK.
14) Write the equation of a parabola that has a vertex at (-4, -19) and the point (5, 8) on it.
15) Write the equation of a parabola that has a vertex at (7, 55) and the point (2, -20) on it.
Directions: Solve for x. SHOW ALL YOUR WORK. Circle your final answer.
16)
x  3 1 x  4
17)
2x 1 3  7  5
18)
8  4 x  1  11
Directions: Rewrite each exponential equation as a logarithmic equation.
3
19) 4  64
20) 10
2.57
x
x
21) 3  5
Directions: Rewrite each logarithmic expression using the change of base formula. When possible,
evaluate the expression. SHOW ALL YOUR WORK.
22) log 3 15
23) log 8 128
24) log 4 512
Directions: Expand each logarithm.
25) log 5
3
xm 4
26)
 6x 3 
log 7  5 
 n 
Directions: Write each logarithmic expression as a single logarithm.
1
log9 m  3log9 w
27) 2
28)
1
4 log x  5 log k  log w
3
Directions: Solve for x showing all your work. When necessary, round your answer to the nearest
thousandth. Circle your final answer.
29)
5
2 ln x  ln e  15
32) log 7 4x  23  18
6
35)
105x9  75
11
30) log 5 125x  47
33)
2 3x5  1611
36) 2ln x  3ln2  5
31)
log16 4 x 
5
16
34) 5e x  7  27
37) 4 x  7  25
38)
log 2 .03125  x
41) log 25x   log 2  3
44)
log3 x  8  log3 x  2  3
40) ln 1 2x   3
39) e4 x7  507
42)
37 4 x1  1253
43) 27 8x  9 x7
45)
log3 11 x   log3 x  25  5
Directions: Solve each problem showing all your work.
46) Henry invested $1200 in a 6 year CD at a 5.25% interest rate. The interest is compounded
monthly. How much money will Henry have when his CD matures?
47) Katherine invests $1000 in a 5 year CD that compounds interest continuously. She was thrilled
to lock in at a 5.73% interest rate. How much money will Katherine have when her CD matures?
48) How long will you have to invest $500 if you earn 3.74% compounded continuously and you want
to double your money?
Directions: Use Pascal’s Triangle or the binomial theorem to expand the binomials.
5
49)
 3x  2 
 5m  3x 
50)
4
Directions: Evaluate each series.
51)
10
  n  3
52)
n 1
1


 n  1

n 1  2
4
53)
n 
6
2
n2
Directions: Write the summation notation for each series.
54) 7  14  21  28  35
56) 1  1  1  1  1
3
4
5
6
7
55) 144  169  196  225
Directions: Graph each function, identify the domain and range, find its inverse, identify its domain
and range, and graph it. LABEL ALL YOUR ANSWERS APPROPRIATELY!!!
57)
f (x)   2x  6
12
10
8
6
4
2
-10
-5
5
10
5
10
-2
-4
-6
-8
-10
-12
58)
g(x)  2 x
12
10
8
6
4
2
-10
-5
-2
-4
-6
-8
-10
-12
59)
h(x)  (x  4)2  3
12
10
8
6
4
2
-10
-5
5
10
5
10
-2
-4
-6
-8
-10
-12
60)
w(x)  x  2  1
12
10
8
6
4
2
-10
-5
-2
-4
-6
-8
-10
-12
Directions: Graph each conic. Identify which type of conic is represented by the equation. If the
equation is a circle, identify the coordinates of the center and the length of the radius. If the conic is
an ellipse, identify the coordinates of the center, the coordinates of the foci, and the major and minor
axis. If the conic is a hyperbola, identify the coordinates of the center, the coordinates of the vertices
and foci, and the equations of the asymptotes. LABEL ALL YOUR ANSWERS APPROPRIATELY!!!
61)
 x  5
2
 9  y  3  36
2
12
10
8
6
4
2
-10
-5
5
10
5
10
-2
-4
-6
-8
-10
-12
62)
x 2   y  5  16
2
12
10
8
6
4
2
-10
-5
-2
-4
-6
-8
-10
-12
63)
x 2 y2

1
36 64
12
10
8
6
4
2
-10
-5
5
10
5
10
-2
-4
-6
-8
-10
-12
64)
9y2  x 2  36
12
10
8
6
4
2
-10
-5
-2
-4
-6
-8
-10
-12
Directions: Write the equation of each conic section and sketch its graph.
65) circle with center at (-3, 1) and radius 3
-10
66)
ellipse with center (1, -4), vertices
at (1, 1) and (1, -9) and co-vertices at
(-1, -4) and (3, -4)
12
12
10
10
8
8
6
6
4
4
2
2
-5
5
10
-10
-5
5
-2
-2
-4
-4
-6
-6
-8
-8
-10
-10
-12
-12
10
67) hyperbola has a vertical transverse axis with its center at the origin and central rectangle with a
base of 6 units and a height of 14 units
12
10
8
6
4
2
-10
-5
5
-2
-4
-6
-8
-10
-12
10
Directions: Write each equation in standard form. Identify which type of conic section it represents.
2
2
68) 4y  2x  24y  20x  15  7
69) 5x 2  10x  y2  6y  29
Directions: Simplify each expression. SHOW ALL YOUR WORK!!
x5
x

70) 2x  1 x  3
x 2  6x  5
49x 2  9
• 2
2
73) 7x  4x  3 x  7x  10
x5 x7

6x
71) 8x
72)
7
5

3x 3 6x 2
6x 2  47x  8
36x 2  1
 4
4
3
2
4x  8x 3
74) x  6x  16x
Directions: Solve for x. Be sure to show all your work.
x 5x

3
75) 9 18
7
2

76) 4x  5 2x  4
77)
4
2

5x  3 7x  6

x3
x
x
 2

78) x  2 x  4 x  2
79)
50 16 64


x3 x
x
80)
26
35 56


x5 x
x