Algebra 2 Final Review
We will look at the Basic Algebra
Skills you need and the tests you’ve
taken throughout the year.
1. Solve: 4(x – 3) + x – 4 = 2(x + 2) – 4
7
8
16
16
a. 3
b. 3
c. 3
d. 5
2. What is the solution of 7x – 2 = 3(2x + 5)?
a. 1
b. 1
c. 3
d. 17
3. Solve the inequality:
a. x > -1
b. x > 3
2x – 5 < 3x + 1
c. x > -6
d. x < 1
4. What are the factors of a3 – b3?
a. (a – b)(a2 + ab + b2)
c. (a – b)(a + b)
b. (a + b)(a2 – ab + b2)
d. (a2 – b2)(a + b)
5. Factor: 25x2 – 20x + 4
a. (5x + 2)(5x – 2) b. (5x – 2)2
c. (25x – 4)(x – 1) d. (5x+ 2)2
6. Factor the following: 36x2 – 25y2
a. (36x + 25y)(36x – 25y)
b. (x – y)(36x + 25y)
c. (6x – 5y)(6x + 5y)
d. (6x – 5y)(6x – 5y)
7. Factor the following:
8x3 – 64y3
a. (2x + y)(4x2 – 4xy + y2)
b. (2x – 4y)(4x2 + 8xy + 16y2)
c. x3 – y3
d. cannot be factored
8. Which is a factor of 3x3 + 3x2 – 18x ?
a. (x + 2)
b. (x + 3)
c. (x – 3)
d. (x – 1)
9. Find the solution for the equation by factoring: 4x2 – 12x = 0
a. x = 0
b. x = -3
c. x = 0 and x = 3
d. x = 0 and x = -3
10. The expression (xm)n is equal to…
a. 2xmn
b. xmn
c. xm + n
d. xm - n
11. In the expression 12y-3, the y-3 is the same as…
a. (-y)(-y)(-y)
b.
1
y
3
1
c.
3
y
d. -3y
12. Simplify:
( 3 x y )(  2 xy )
2
a. -x3y4
4
b. -5x2y4
c. -6x3y5
d. 9x2y4
3
13.
m n
p
a.
2
written with all positive exponents is:
4
3
m n
p
4
2
b.
p
3
4
m n
c. m3n2p4
2
d. m-3n-2p-4
14. (3x2y3)3 can be written as…
a. 9x5y6
c. 6x5y9
b. 27x6y9
d. 27a5b6
15. (-2x-3y4)(-3x-5y) equals…
a. -5x-8y4
c. x3y4
b. 6x-8y5
d. 6x-8y4
16.
 a  a  , where a is a positive numbers, is equal to…
a.
a
b.
2a
c. a
2
d. a
17. Simplify:
a. 2 40
c. 20 2
80
b. 8 10
d. 4 5
18. Simplify:
a. 6x2y4
c. 18x2y4
36𝑥 4 𝑦 16
b. 6x2y8
d. 18x2y4
19. Add: 2 8𝑚3 + 3𝑚 2𝑚 − 5 50𝑚3
a. −18𝑚 2𝑚
c. 18𝑚2 2𝑚
b. 18 2𝑚
d. 7𝑚 2𝑚 − 2𝑚 5𝑚
20. Multiply: 3 6𝑥 ∙ 4 18𝑥
a. 12𝑥 108𝑥
c. 72𝑥 2 3
b. 36𝑥 3𝑥
d. 72𝑥 3
21. 2(x – 3) + 2x = 2x – 3 – 7
22. -3(2x + 1) – 5(x + 2) = 3(x – 4) + 3
23.
𝑥
3
5
𝑥
4
+6=2−3
24.
5𝑚
3
+3=
2𝑚
4
−4
25. -5(2p + 5) – (p + 3) ≤ -2p + 4
26. -2(5x – 3) – 4(2x + 3) ≤ -12(x + 4)
27. s – 4 + t = 5 for t
28. 6t = 8wm
for m
29. 12m3 – 4m2
30. 24x5 + 36x3 – 18x2
31. m3 + 1
32. x2 + x – 20
33. 3x2 + xy – 2
y2
34. −12e2 f 3 − 12e2 f 2 + 24e2
35. 3x3 – 12x2 – 45x
36. 5x3 + 15x2 – 20x
37. 5w – 1 – 25wx + 5x
38. x3 – 8y3
39. 4y2 – 9z2
40. 16m4n3 – 12m3n4 + 4m2n5
41. 6x2 = 5x + 4
42. 9x3 + 3x2 = 6x
43.
 2 a
2
b

3 4
 6x y
7
 3x y
3
4
44.
3
45. (-2m3n2)(3mn)
 36 a b
5
46.
5
16 a b
4
2
  3x 3 y 4
47.   4  2
 x y




2
48. (-2p-4q-2r3)-3
49. 12p-3q-4
50. -4m0n-6
  28 x  15 y  3 
51. 

5
4
 7x y

0
52. 4 2  3 2 
2
53.
2x
3
50 x
54.
4
81
55.
x
4
2y
8
56.
8
72 x y
16
57.
 3 m  2m m  6 m
3
3
58.
6m
8
30 m
5
59.
3𝑥
3
60. Take a look at the following work a student showed when solving a problem.
Do they have the correct solution? If not, circle their mistake and clearly explain
what the correct answer should be.
5 − 3𝑦 + 7 = 5𝑦 + 8
5 − 3𝑦 + 7 = 5𝑦 + 8
12 − 3𝑦 = 5𝑦 + 8
4 = 8𝑦
1
=𝑦
2