CP Algebra 2 Final Exam Review
Name:_________________________Period:_____
4
𝑦8
1. Simplify ( 𝑧 6 )
2. Simplify (𝑠 2 𝑡 6 )5
3. Simplify
4𝑥 3
𝑦3
∙
𝑦 −4 𝑥 −5
12𝑥 −2
4. Multiply (𝑥 + 7)(𝑥 2 + 𝑥 + 6)
5. Factor completely: 4𝑥 3 − 4𝑥 2 + 16𝑥
6. Factor: 25𝑦 2 − 16
7. Factor completely: 4𝑥 3 − 8𝑥 2 + 3𝑥 − 6
8. Find (4𝑥 4 − 12𝑥 3 − 48𝑥 − 60) ÷ (𝑥 − 4)
9. Find all real zeros of the function 𝑓(𝑥) = 2𝑥 3 − 𝑥 2 − 10𝑥 + 5
10. Find all the zeros of the function 𝑔(𝑥) = 5(3𝑥 + 8)(−4𝑥 − 6)(3𝑥 − 7)
11. Write a polynomial function that has zeros 5, −2, 𝑎𝑛𝑑 2 with a leading coefficient of 1.
12. Find all the zeros of the function 𝑓(𝑥) = 15𝑥 4 − 19𝑥 3 − 9𝑥 2 + 19𝑥 − 6
13. If a student tosses a nickel and a dime, what is the probability of returning a nickel tail and
a dime tail?
14. Let 𝑓(𝑥) = 8 − 𝑥 2 and 𝑔(𝑥) = 5 − 2𝑥. What is 𝑓(𝑥) − 𝑔(𝑥)?
2
15. What is the inverse of the function 𝑓(𝑥) = 4𝑥 + 3 ?
16. Solve the equation. Check for extraneous solutions. √𝑥 + 20 = 𝑥
3
17. Solve the equation. Check for extraneous solutions. √𝑥 − 8 = −2
3
18. Solve the equation. Check for extraneous solutions. 3𝑥 4 = 192
19. Solve the equation. Check for extraneous solutions. √𝑥 2 + 5 = 3 − 𝑥
20. Divide
(𝑥 2 +10𝑥+21)
𝑥 2 −9
2𝑥−3
21. Simplify (𝑥+3)2 ∙
7
𝑥+7
÷ 𝑥−7
𝑥 2 +4𝑥+3
4𝑥 2 −9
6
22. Find 𝑥+2 + 𝑥−2
3𝑥−5
4
23. Simplify 𝑥 2 −25 − 𝑥−5
24. Simplify
9
𝑥−5
6
+7
𝑥
𝑥2
9
25. Solve 𝑥+2 = 𝑥+2
26. Express as a single logarithm: 𝑙𝑜𝑔𝑏 7 + 𝑙𝑜𝑔𝑏 35
27. Expand 𝑙𝑜𝑔𝑎
1
7𝑥𝑦 3
𝑧4
28. Solve 9 = 818𝑥−5
1
1
29. What is 8 (53 ) + 6 (53 ) ?
30. Solve the equation 75𝑙𝑜𝑔9 𝑥 = 62
1
1
31. What is 62 ∙ 65 ?
32. You have 7 t-shirts, 4 pairs of pants, and 8 hats. How many different outfits can you wear?
33. What is the solution of 𝑙𝑜𝑔7 (4𝑥 + 5) = 3
34. What is the solution of ln(8𝑥 − 7) = ln(𝑥 − 14) ?
35. What is the solution of 44𝑥 = 64𝑥+1 ?
36. If 𝑓(𝑥) = 𝑥 2 + 3𝑥 − 1 and 𝑔(𝑥) = 𝑥 + 5, what is 𝑓(𝑔(𝑥))?
5
𝑥5
37. What is the simplified form of √𝑦 35?
1
38. What is the value of −643 ?
39. Factor 𝑥 3 + 27.
7𝑥 −3
−2
40. What is the simplified expression of (5𝑦 −6 ) ?