ALGEBRA 2 ASSESSMENT
Variable Expressions
1. Evaluate the expression for x = 8.
x+6=
2. Evaluate the expression for j = -4.
4j =
3. Evaluate the expression for g = -1.
10g – 6 =
4. Evaluate the expression for n = -16 and p = -20. Simplify your answer.
p
=
n–p
5. Evaluate the expression for m = 0.4 and n = 7.
Write your answer as a decimal or whole number.
mn + m =
6. Evaluate the expression for f = -16. Simplify your answer.
f
=
2
7. Evaluate the expression for b = -1.
Write your answer as a decimal or whole number.
Algebra 2 | 1
-5.9b
– 13.9 =
8. Simplify the expression:
-4
+ (v + 6) =
9. Simplify the expression:
-3
+ (z + -6) =
10. Simplify the expression:
(-5y)(-3) =
Equations
11. Solve for y.
5 – 15y = -4 – 16y
y=
12. Solve for z.
-15z
= -16z – 10
z=
13. Solve for c.
16c = 20 + 12c
c=
Algebra 2 | 2
14. Oliver can grow 2 plants with every seed packet. How many seed packets does
Oliver need to have a total of 4 plants in his backyard?
15. Solve for q.
8 = |4q|
Write your answers as integers or as proper or improper fractions in simplest form.
q=
or q =
16. Solve for t.
-6
= -3|t|
Write your answers as integers or as proper or improper fractions in simplest form.
t=
or t =
17. Solve for z.
|-3z| = 0
Write your answers as integers or as proper or improper fractions in simplest form.
z=
or z =
18. Solve for s.
|s + 3| = 3
Write your answers as integers or as proper or improper fractions in simplest form.
s=
or s =
Algebra 2 | 3
19. Solve for w and graph the solution.
4 =|w–4|
20. Solve for t and graph the solution.
|t+4|=1
Inequalities
21. Graph. x>6
22. Graph. x<2
23. Graph. x ≥4
24. Graph this inequality:
y>x–4
25. Graph this inequality:
y < -x + 3
Write a compound inequality like 1 < x < 3 or like x < 1 or x > 3.
Use integers, proper fractions, or improper fractions in simplest form.
25. Solve for t.
|t|+4≤7
26. Solve for s.
|-2s|≤6
27. Solve for d.
|d|–8>-2
Functions
Algebra 2 | 4
28. Use the following function rule to find f(-4).
F(x)=2x+9
f(-4) =
29. Use the following function rule to find f(64).
F(x)=
64
+12
x
f(64) =
30. Use the following function rule to find f(12).
f(x)=7x–3
f(12) =
31. Use the following function rule to find f(2).
f(x)=12–
32
x
32. Graph this function using intercepts:
6x–y=6
33. Graph this line:
slope=3, y-intercept= -3
34. Graph this equation:
x= -7
35. Graph this line using the slope and
y-intercept: y= x+6
Systems of Equations
36. Is (1, 3) a solution to this system of equations?
Algebra 2 | 5
y = 10x + 2
y=x+2
37. Is (1, 1) a solution to this system of equations?
7x + 8y = 15
x + 12y = 13
38. Is (4, 5) a solution to this system of equations?
x+y=9
2x + 2y = 18
39. Is (2, 2) a solution to this system of equations?
3x + 3y = 12
3x + y = 8
Solve this system of equations by graphing. First graph the equations, and then type the
solution.
40. y= -12x –3x = 4
41. y= -13x +2y = 1
42. y= -x +7x = 3
Systems of Inequalities
43. Is (8, 4) a solution to this system of inequalities?
x>6
x + y ≤ 12
44. Is (1, 9) a solution to this system of inequalities?
2x + 2y ≥ 20
x + y > 18
45. Is (3, 10) a solution to this system of inequalities?
y>x+4
x≥3
46. Is (1, 5) a solution to this system of inequalities?
Algebra 2 | 6
y < 3x + 2
y<x+5
Complex Numbers
Use the imaginary number 𝑖 to rewrite the expression below as a complex number.
Simplify all radicals.
47. √−16
48. √−9
49. −√−100
50. √−49
Simplify. Write your answer in the form a+bi
51. -𝑖–5𝑖
52. -4–5𝑖
53. -2𝑖+5𝑖
54. -9𝑖+3𝑖
Find the complex conjugate of the given number. Write your answer in the form a+b𝑖
55. -10–2𝑖
56. -2–4𝑖
57. -5–6𝑖
58. -8+3𝑖
Simplify.
59. 5𝑖·3
5𝑖
60. −4𝑖
61. -3𝑖·4
Algebra 2 | 7
−𝑖
62. −3𝑖
63. -2(3+4𝑖)
64.
−10𝑖
−9𝑖
Find the absolute value. Simplify all radicals in your answer.
65. | -8𝑖|
66. | 6𝑖|
67. |3|
68. |8+6𝑖|
Compute.
69. 𝑖 3
70. 𝑖 2
71. 𝑖 4
Factoring
Factor out the greatest common factor.
72. 6𝑐 3 + 9𝑐 2
73. 3𝑏 3 + 6𝑏 2
Factor.
74. 𝑗 2 − 13𝑗 + 22
75. 12𝑦 3 − 9𝑦 2 + 8𝑦 − 6
76. 𝑛2 − 8𝑛 + 7
Polynomials
Add, subtract or multiply.
77. (9c+7) + (c+7)
78. (8u+4) – (3u+3)
Algebra 2 | 8
79. (9h4 )(−7h4 )
80. −3𝑡(−𝑡 2 – 2t)
.
Algebra 2 | 9
Algebra 2 | 10