Name: _________________________________ Date: _____________________ Period:____________
Algebra II
1. Solve the system of equations by graphing.
𝑥+ 𝑦=3
{
𝑥 + 3𝑦 = 6
2. Solve the system of equations by using
Substitution.
Semester 2 Exam Review
4. The senior classes at High School A & High
School B planned separate trips to New
York City. The senior class at High School A
rented & filled 16 vans & 8 buses with 752
students. High School B rented & filled 5
vans & 5 buses with 380 students. Each van
& each bus carried the same number of
students. How many students can a van
carry? How many students can a bus carry?
5. Identify the axis of symmetry of the
parabola 𝑓(𝑥) = −3𝑥 2 + 12𝑥 − 10
4𝑥 + 2𝑦 = 10
{
𝑥 − 𝑦 = 13
6. Give the vertex of the parabola 𝑓(𝑥) =
2(𝑥 + 9)2 + 8
7. State the domain & the range of 𝑓(𝑥) =
−4(𝑥 − 3)2 + 6
3. Solve the system of equations by using
Elimination.
−2𝑥 + 3𝑦 = 15
{
−6𝑥 + 6𝑦 = 18
8. Give the 𝑥 − &𝑦 −intercepts of 𝑓(𝑥) =
𝑥 2 − 9𝑥 + 8
9. Factor & solve 𝑥 2 − 16𝑥 = −63
17. Find the exact solution to 3𝑥 2 = 7𝑥 − 6 by
using the Quadratic Formula.
10. Factor & solve 𝑥 2 − 5𝑥 − 14 = 0
11. Simplify: 𝑖 31
18. State the discriminant, & describe the
number & type of roots of 𝑥 2 = 3𝑥 − 8
12. Simplify: (2 + 4𝑖) + (3 + 7𝑖)
13. Simplify: (8 − 11𝑖) − (−7 + 2𝑖)
19. Does 𝑓(𝑥) = 2(𝑥 + 6)2 + 7 open upwards
or downwards? How do you know that by
looking that the equation?
14. Simplify (5 + 3𝑖)(9 − 6𝑖)
20. Graph 𝑓(𝑥) = 𝑥 2 − 6𝑥 + 5
15. Find the value of c that makes 𝑥 2 + 12𝑥 +
𝑐 a perfect square.
16. Solve 𝑥 2 + 8𝑥 − 10 = 0 by completing the
square.
21. Identify the vertex, axis of symmetry, &
direction of opening for 𝑓(𝑥) = −𝑥 2 +
4𝑥 − 6
22. Write a formula for a quadratic function
that has its vertex at (-3, 5) & opens
downwards.
23. Graph 𝑓(𝑥) > 𝑥 2 + 2𝑥 − 2
24. Graph 𝑓(𝑥) ≤ 𝑥 2 + 6𝑥 + 10
26. Use synthetic division to divide 𝑥 3 −
10𝑥 2 + 20𝑥 + 26 by 𝑥 − 5.
27. Factor 𝑥 3 − 𝑥 2 − 14𝑥 + 24 completely,
given that 𝑥 − 3 is already a factor.
28. Write a polynomial equation with zeros
3, −4, 2, & − 1.
29. Write a polynomial equation with zeros 3,
& − 4.
25. State the number of possible zeros, draw a
sketch, & state the end behavior of
𝑓(𝑥) = 𝑥 3 − 2𝑥 2 .
𝑓(𝑥) = 2𝑥 − 3
𝑔(𝑥) = 𝑥 2 − 7
1
{ ℎ(𝑥) = 2 𝑥 + 4
30. (f + g)(x)
31. (g – h)(x)
32. (f · g)(x)
33. (𝑔) (𝑥)
ℎ
41. Simplify: 3√81 + 4√27 − √75
34. 𝑓(ℎ(𝑥))
35. (𝑔 ° 𝑓)(𝑥)
36. 𝑓 −1 (𝑥)
37. 𝑔−1 (𝑥)
42. Simplify: 7√18𝑎3 𝑏7 ∙ √10𝑎5 𝑏4
38. ℎ−1 (𝑥)
3√2
4√6
43. Simplify:
39. Graph 𝑓(𝑥) = √𝑥 − 4 − 2
4
2
44. Simplify: 𝑥 3 ∙ 𝑥 5
1
45. Simplify:
254
3
57
40. Graph 𝑓(𝑥) = 2√𝑥 + 3 − 5
13
46. Rewrite √79 using rational exponents.
7
47. Rewrite 62 in radical form.
3
48. Solve √6𝑥 + 5 = 11
56. Graph log 4 (𝑥 − 5) + 6
49. Solve √4𝑥 − 7 = 8
50. Rewrite as a logarithmic function: 𝑒 32 = 𝑥
57. Solve 35𝑥−6 = 81𝑥+4
51. Rewrite as an exponential function:
log 4 64 = 3
52. Solve 3log 8 (𝑥) − log 8 (2) = log 8 (4)
53. Solve log 7 (343) = 𝑥
58. Solve log 8 𝑥 = 4
59. Rewrite & round to the nearest hundredth:
log 5 18
54. Solve ln 𝑥 − ln 5 = 7
55. Graph 𝑓(𝑥) = 2𝑥+4 + 4
60. Rewrite & round to the nearest hundredth:
log 2 61
61. The initial number of bacteria in a culture is
67. The culture doubles each day. How
many days will it take for the culture to
reach 137,216?
62. Simplify:
𝑛+3
𝑛+2
÷
(𝑛−1)(𝑛+3)
(𝑛−1)(𝑛−4)
5
8
63. Simplify:
−
69. If 𝑦 varies inversely as 𝑥, & 𝑦 = 24 when
𝑥 = 4, find 𝑦2 when 𝑥 = 12.
7
3𝑥+4
7
70. Solve 12 +
𝑥2
64. Simplify 4
−
5
9
𝑥−4
=
55
48
4
𝑎
65. Graph 𝑓(𝑥) =
1
𝑥−3
− 2
71. Write the formula for the sequence
5, −6, −17, −28 …
72. Write the formula for the sequence
−1
, 2, −8, 32, …
2
73. Denote the series in Sigma Notation: 2 −
4 + 6 − 8 + 10.
66. Graph 𝑓(𝑥) =
2
𝑥+4
+1
74. Denote the series in Sigma Notation: 216 +
72 + 24 + 8 +
8
3
+ …
75. Given 𝑎1 = 7 & 𝑑 = −4, find 𝑎13 .
76. Given 𝑎1 = 6 & 𝑟 = 3, find 𝑎7
67. Suppose 𝑦 varies jointly as 𝑥 & 𝑧. Find 𝑦
when 𝑥 = 2 & 𝑧 = 8, if 𝑦 = 70 when 𝑥 =
10 & 𝑧 = 4.
68. If 𝑦 varies directly as 𝑥 & 𝑦 = −20 when
𝑥 = 4, find 𝑦 when 𝑥 = −6.