ACP Algebra 2 Final Exam Review
1. Write in standard form −5𝑥 3 (−4𝑥 3 + 2𝑥 2 − 4𝑥 + 7)
2. Factor.
4𝑥 4 − 48𝑥 3 + 128𝑥 2
𝑥 3 + 3𝑥 2 − 28𝑥
3. What are the zeros? What are their multiplicities?
𝑓(𝑥) = 𝑥 5 − 7𝑥 4 + 6𝑥 3
𝑓(𝑥) = 𝑥 4 − 10𝑥 3 + 25𝑥 2
4. What are the real or imaginary solutions?
𝑥 4 − 16𝑥 2 = 225
5. Divide.
(3𝑥 4 + 𝑥 3 − 6𝑥 2 − 9𝑥 + 12) ÷ (𝑥 + 1)
𝑥 4 − 45𝑥 2 + 324 = 0
(12𝑥 3 − 71𝑥 2 + 57𝑥 − 10) ÷ (𝑥 − 5)
6. Is (𝑥 − 3) a factor of 𝑃(𝑥) = 6𝑥 3 − 17𝑥 2 − 4𝑥 + 3? If yes, write 𝑃(𝑥) as a product of 2
factors.
7. Multiply and simplify.
√10 ∙ √8
3
3
√10 ∙ √5
√2𝑦(√𝑦 − 4√2
3
3
8. Simplify.
√12𝑥 3 𝑦 4 𝑧 5
3
√16
3
√2
√24𝑥 4 𝑦 6
5
3
√5𝑥 8 ∙ √6𝑥 9
5
5√7𝑥 + 9√7𝑥
7√3𝑥 − 10√3𝑥
√12 + √18 − √20
9. (3 − √5)(4 + √5)
1
(7 − √3)(7 + √3)
2
303 ∙ 303
2
10. Write in radical form 4𝑦 3 .
11. If you invest $3000 at an annual interest rate of 6.25%. How much will you have after 6
years?
12. Write in log form.
43 = 64
34 = 81
13. Write in exponential form.
log 5 25 = 2
1
log 10 = −1
14. Evaluate log 2 64
15. Write as a single log.
4log 𝑥 𝑤 + 3log 𝑥 𝑦
5log 3 𝑥 + 4log 3 𝑦
16. Expand the log.
𝑥
log 𝑎 𝑥𝑦
log 4 5
17. Use Change of Base to evaluate:
log 6 50 =
log 3 243 =
18. Solve
102𝑥 = 32
log(2𝑥 + 50) = 3
19. 𝑦 varies directly with x and inversely with z and 𝑦 = 35, 𝑥 = 40, 𝑧 = 5. Write an equation
that models this information. Then find 𝑦 when 𝑥 = 24 and 𝑧 = 6.
6
20. Write an equation for the translation of 𝑦 = 𝑥 with asymptotes 𝑥 = −3 and 𝑦 = 5.
21. Name the vertical asymptotes and holes if they exist.
𝑦=
(𝑥 − 2)(𝑥 + 4)
(𝑥 + 6)(𝑥 − 2)
22. Simplify.
𝑡 2 − 𝑡 − 30
𝑡 2 − 7𝑡 + 6
23.
𝑡 2 + 14𝑡 + 48
𝑡+6
24. Find the product and state the restrictions.
𝑥 2 𝑥 2 + 5𝑥 + 6
∙
𝑥+2
𝑥 2 + 3𝑥
25. Find the quotient and state the restrictions.
𝑎+3
𝑎+1
÷ 2
𝑎 − 10 𝑎 − 7𝑎 − 30
26. Find the sum or difference.
6
5
+ 2
𝑥 + 4 𝑥 − 16
𝑛2 − 10𝑛 + 24
9
−
𝑛2 − 13𝑛 + 42 𝑛 − 7
27. Simplify.
2
1
−
3𝑥 2𝑦
5
3
+
12𝑦 2𝑥
28. Solve.
3 5
+
=7
𝑥 2𝑥
29. Write the equation of a circle with center (−4, 5) and radius = 6.
30. Write the equation of a circle 𝑥 2 + 𝑦 2 = 25 translated 2 units right and 3 units down.
31. What is the center and radius of the following circles.
(𝑥 − 6)2 + (𝑦 − 7)2 = 4
𝑥 2 + 𝑦 2 + 14𝑥 − 12𝑦 = −69
33. Write the equation of an ellipse with a center at the origin, co-vertex (−4, 0) and vertex
(0, −6).
35. Graph.
(𝑥 − 5)2 + (𝑦 + 3)2 = 9
𝑦=
3
+4
𝑥−2
𝑥2 𝑦2
+
=1
25 16
𝑥2 𝑦2
−
=1
16 25
𝑥2 + 𝑦2 = 4