Algebra 2: 1st Semester Final Review
Name________________
1. Evaluate (2𝑎 + 𝑦)2 + 7y if a = 5 and y = –5.
2. Name the sets of numbers to which 0.21553… belongs.
3. Select the algebraic expression that represents the verbal expression the sum of a number and the product of 12 and
another number.
For questions 4 and 5, solve each equation.
4. -2(6x – 9) = 18x + 8
5. 3|2x + 5| = 36
For questions 6 - 9, solve each inequality.
6. –3w + 4 < -11
7. x – 4 ≤ 8 or 8 – x < 1
8. –5 ≤ 2y + 13 ≤ 14
9. |2x + 12| > 20
10. Graph: 2x – y < 8
11. Find the domain of the relation {(2, 3)(-5, 8)(2, -4)(0, 8)}. Then determine whether the relation is a function.
12. Find f (–2) if f (x) = –3x2– 4.
13. Give two
examples of a nonlinear equation.
14. Write y =
2
x – 4 in standard form.
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15. Find the x-intercept of the graph of 3x + 5y = 15.
16. Find the slope of the line that passes through (12, -6) and (–2, 8).
17. Write an equation in slope-intercept form for the line that passes through (0, 1) and is parallel to the line whose
equation is y = 5x – 6.
18. Graph: y  x  7
21. Solve the system of equations by using either substitution or elimination.
3 x  y  12
x y 8
2 x  4 y  5 z  18
22. Solve the system of equations by using either substitution or elimination. 3x  5 y  2 z  27
5 x  3 y  z  17
23. Graph:
26. Graph:
x y4
4 x  3 y  12
y  2x  3
x  3y  6
Use these matrices to find the following.
 4 5
P

 6 8
0 1 
R

5 3
 2 1 0 
S   4 5 10


 2 3 2 
28. Find 2P
29. Find P + 2R
30. Find PR
30. Find R + S
31. Find the value of the determinant
5
6
2 10
32. Graph f(x) = 𝑥 2 + 2x + 5
33. Write the quadratic equation with roots –5 and 2?
34. Solve: x2 + 6x – 4 = 0 by Quadratic Formula
35. What are the nature of the roots for: x2 – 5x + 2 = 0
36. Identify the y-intercept and the axis of symmetry for the graph of f(x) = 2x2 – 10x + 12
37. Determine whether f(x) = 3x2 – 6x +2 has a maximum or a minimum value and find that value.
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39. Identify the vertex, axis of symmetry, and direction of opening for y = 2 (𝑥 + 2)2 – 3
40. Write y = 𝑥 2 + 8x – 5 in vertex form.
42. Solve 5𝑥 2 + 20 = 0.
43. Simplify (5xy0)4(-3x4y2).
44. Simplify
2 x 4 y 6
. Assume that no variable equals 0.
8 xy 5
45. Simplify the expression (x – 2)(3x2 + x – 1)
46. Simplify (7m2 – 3m +6) – 2(m2 + 4m)
47. Simplify (x2 – 18x + 65) ÷ (x – 13)
48. Solve x4 – 10x2 + 24 = 0.
49. Use synthetic substitution to find f (-5) for f (x) = -x2 – 2x +5.
50. One factor of 3x3 + 20x2 +23x – 10 is x + 5. Find the remaining factors.
52. Simplify (3 + 2√5)(6 – √5).
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53. Write the expression x 3 in radical form.
2
54. Simplify the expression x 3 ( x 6 )
55. Solve √2𝑥 − 8 = 6.
58. Simplify
2
5 3
1
59. Simplify the expression
x3
5
x6
60. Simplify
4
64x 4 y 6