Algebra 2
1st Semester Final Review
Find the domain and range of the following
1. 𝑦 = √𝑥 − 2 + 5
2. 𝑦 = √𝑥 + 4 + 7
State the translation for the following.
3. 𝑦 = √𝑥 + 5 − 6
4. 𝑦 = √𝑥 − 1 + 9
Solve the following. Check for extraneous solutions
6. √𝑥 2 + 7 = √𝑥 + 7
5. √𝑥 2 − 6 = √𝑥 − 6
Solve the following. Check for extraneous solutions
8. √2𝑥 + 8 = 𝑥
7. √5𝑥 + 6 = 𝑥
Simplify
9. √2 (√10 + 2)
Simplify.
Simplify
10. √5(√15 + 5)
20𝑥 3 𝑦 4 𝑧 11
54𝑥 5 𝑦 3
11. √
12. √
2𝑥 2 𝑦
Simplify
3
4
13. (16𝑦12 𝑧17 )
2
14. (8𝑥 12 𝑦 25 )3
𝑥4𝑦6𝑧8
Algebra 2
1st Semester Final Review
Solve and graph.
1
15. 3 |4𝑥 + 1| − 5 < −2
Solve and graph.
1
16. 4 |3𝑎 + 1| − 6 < −2
Write an equation of a line in slope-intercept form that is parallel to the following line and goes through the given
point.
2
1
17. 𝑦 = − 𝑥 + 3; (−14, 2)
18. 𝑦 = − 𝑥 − 6; (−9, 1)
7
Write an equation for the following graph.
19.
20.
3
Describe all the transformation(s) that relates y = 𝑥 2 .
21. 𝑦 = −(𝑥 − 5)2 − 3
22. 𝑦 = − (𝑥 + 2)2 − 5
Write an equation in point-slope form for the following points
23. (-2, 3) & (2, 9)
24. (-2, -3 ) & (2, -1)
Algebra 2
1st Semester Final Review
25. Lisa goes to the mall one day and buys four shirts and
three pairs of pants for $85.50. She returns the next day
and buys three shirts and five pairs of pants for $115.00.
What is the price of each shirt and each pair of pants?
26. At a restaurant the cost for a taco and a small glass of
milk is $2.10. The cost for 2 tacos and 3 small glasses of
milk is $5.15. What is the price for a taco and a glass of
milk?
Solve the following system. State whether the system is consistent, inconsistent, dependent, and independent. And
state the number of solutions.
27. 2x + 8y = 6
28. −6x + 5y = 1
−5x − 20y = −15
6x + 4y = −10
Graph the following inequalities.
29. 𝑦 < 1 2 𝑥 + 4
𝑥 − 2𝑦 ≥ 6
30. xy
xy
Algebra 2
1st Semester Final Review
Identify the vertex, axis of symmetry and the number of solutions for the following quadratics.
31. 𝑦 = −𝑥 2 + 2𝑥 + 3
32. 𝑦 = −3𝑥 2 + 18𝑥 − 27
Find the zeros for the following.
33. 𝑥 2 − 10𝑥 = −16
34. 𝑥 2 + 2𝑥 = 63
Solve the function.
35. 2𝑥 2 − 3𝑥 = −7
36. 4𝑥 2 − 5𝑥 = −6
State whether the leading coefficient is positive or negative. Also the degree of the polynomial.
37.
38.
Algebra 2
1st Semester Final Review
Find the zeros of the given polynomial function.
39. f(x) = x3 – 5x2 + 2x + 8
40. f(x) = x3 + x2 - 17x + 15
Divide the expression by using long division.
41. (50k 3 + 10k 2 − 35k − 7) ÷ (5k − 4)
42. (12v 3 + 38v 2 - 16v - 20) ÷ (6v – 5)
State whether the following is a factor of the polynomial 𝑝(𝑥) = 𝑥 3 + 3𝑥 2 − 10𝑥 − 24
43. x + 4
44. x + 6