Algebra 2: Spring Final Exam Study Guide
Name:________________________________Period:_____ Score:__________/100
My final exam is: _____________________________________
Directions: Simplify each expression. SHOW ALL YOUR WORK. Circle your final answer.
1)
3
7
24x m k
3
4)
5 9
8x 9
27m12
2)
5)

4
3
20 17
81m y k

1252 3 • 16 3 4

50
63
3)
4
6)
16m

12 3 56 3
k x
Directions: Simplify each expression. SHOW ALL YOUR WORK!!
x5
x

7) 2x  1 x  3
x 2  6x  5
49x 2  9
• 2
2
10) 7x  4x  3 x  7x  10
x5 x7

6x
8) 8x
9)
7
5

3x 3 6x 2
6x 2  47x  8
36x 2  1
 4
4
3
2
4x  8x 3
11) x  6x  16x
Directions: Solve for x. Be sure to show all your work.
7
2

12) 4x  5 2x  4
13)
4
2

5x  3 7x  6

x3
x
x
 2

14) x  2 x  4 x  2
15)
26
35 56


x5 x
x
Directions: Graph each of the following functions, first identifying the specified information.
𝑥−1
𝑥+2
2𝑥
16) 𝑓(𝑥) = 𝑥+3
17) ℎ(𝑥) = (𝑥−3)(𝑥−2)
18) 𝑔(𝑥) = 𝑥 3 −𝑥
Vertical asymptote:
Vertical asymptote:
Vertical asymptote:
Holes:
Holes:
Holes:
Horizontal asymptote:
Horizontal asymptote:
Horizontal asymptote:
x-intercept(s):
x-intercept(s):
x-intercept(s):
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!!!
19)
f (x)   2x  6
12
10
8
6
4
2
-10
-5
5
10
5
10
-2
-4
-6
-8
-10
-12
20)
w(x)  x  2  1
12
10
8
6
4
2
-10
-5
-2
-4
-6
-8
-10
-12
Directions: Rewrite each exponential equation as a logarithmic equation.
3
21) 4  64
22) 10
2.57
x
x
23) 3  5
Directions: Rewrite each logarithmic expression using the change of base formula. When possible,
evaluate the expression. SHOW ALL YOUR WORK.
24) log 3 15
25) log 8 128
26) log 4 512
Directions: Expand each logarithm.
27) log 5
3
xm 4
28)
 6x 3 
log 7  5 
 n 
Directions: Write each logarithmic expression as a single logarithm.
1
log 9 m  3log 9 w
2
29)
30)
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.
31)
2 ln x  ln e5  15
34)
105x9  75
32) log 7 4x  23  18
6
35) 2ln x  3ln2  5
33) 5e x  7  27
36)
log3 x  8  log3 x  2  3
𝑟
Directions: Solve each problem showing all your work. Use the equations 𝐴 = 𝑃(1 + 𝑛)𝑛𝑡 or 𝐴 =
𝑃𝑒 𝑟𝑡 , as appropriate.
37) 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?
38) 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?
39) How long will you have to invest $500 if you earn 3.74% compounded continuously and you want
to double your money?
Directions: Simplify each expression showing all your work.
15!
40) 11!7!
41) 6! - 0!
10!3!
42) 8!
43) 5! + 4!
44) There are twelve students trying out for the debate team. Only four students can be selected.
How many different groups of four can be formed?
45) There are fourteen different pizza toppings from which I can choose. If I want a seven topping
pizza, how many different pizzas can I order?
46) Thirteen people have entered a math contest. How many different ways can these thirteen
people place first, second, or third?
47) I plan to order a deli sandwich for lunch. There are nine different items from which I can choose
to include on my sandwich. If I want a four item sandwich, how many different sandwiches can I
order?
Directions: Use Pascal’s Triangle or the binomial theorem to expand the binomials.
5
48)
 3x  2 
49)
 5m  3x 
4
50) What is the 3rd term of (2 x  5)7 ?
Directions: Convert each angle from degrees to radians.
51) 170
52) 510
Directions: Convert each angle from radians to degrees.
2
9
53)
54)
7
5
Directions: Sketch each angle.
55) –135
56)
9
4
57) Give two angles coterminal to the angle
7
6
58) Find the six trigonometric functions of  in the right triangle below.

9
7
59) What is the value of  in the triangle above in degree measure, to the nearest tenth?
60) Directions: Complete the blank unit circle with degrees, radians and coordinates.
Directions: Evaluate the expression without using a calculator. Leave all answers as fractions or
whole numbers. Put all answers in rationalized form.
2
61) sin
62) cos (-300)
63) tan 840
3
64) sec
4
3
67) csc 120
65) tan

66) cos(150)
3
68) cos( )
69) sin
Directions: Verify each identity.
1
70) sec 𝑥 − tan 𝑥 sin 𝑥 = sec 𝑥
71) sec  csc tan
72) tan   cot   sec csc
73)
1−cos2 x
cosx
15
4
= sinxtanx
73)
csc 𝜃
cot 𝜃
− tan 𝜃 = 1
sin 𝜃
csc 𝑥 cos 𝑥
74) cos 2 𝑥 = tan 𝑥+cot 𝑥
tan2 𝑥
74) tan2 𝑥+1 = sin2 𝑥
sint
cost
75) tant + cott = sint + cost
Directions: Use sum and difference formulas to find the exact value of the following.
76) sin 15°
77) tan 75°
78) cos 105°
79) sin 265°
Directions: Sketch at least one period of each of the following functions.
80) 𝑦 = 3 cos 𝑥
81) 𝑦 = cos 2𝑥 + 1
𝜋
82) 𝑦 = 2 sin(𝑥 − 2 )
𝑥
83) 𝑦 = − sin 2