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Semester 1 Final Exam Review Packet
Algebra IIA
Name_________________________
1. Select the algebraic expression that represents the verbal expression five increased by seven times a number.
2. Evaluate (𝑎 – 𝑦) 2 + 2 𝑦 3 if a = 2 and y = –3.
3. Evaluate – |a – 3b| if a = –2 and b = 6.
180(𝑛 − 2)
4. The formula A =
relates the measure A of an interior angle of a regular polygon to the number of sides n. If
𝑛
an interior angle measures 120°, find the number of sides.
1
5. Simplify (6x + 3) – 4(3x – 2).
3
For Questions 6 –9, solve each equation.
2
3
6. 5𝑦 = 14
7. 3|x – 5| = 12
8. 3(5x – 1) = 3x + 3
9. |y – 8| + 6 = 15
10. Yoshi is 12 years older than his sister. Six years from now, the sum of their ages will be 32. Find Yoshi’s present
age.
For Questions 11 –15, solve each inequality.
11. –3(r – 11) + 15 ≥ 9
12. –2 < 4z + 10 ≤ 12
14. 3|m – 4| > 6
16. Solve and graph 8.5 > 6.1 + 0.6 y.
15. |3w – 7| ≤ 2
13. 2x – 5 ≤ 10 or 33 – 4x < 5
17. Find the range of the relation {(–1, 4), (2, 5), (3, 5)}. Then determine whether the relation is a function.
18. Find f(-1) if f(x) =
𝑥 2 −6𝑥
𝑥+2
.
19. Find f(a) if f(t) = 2𝑡 2 – t – 2.
20. Which equation is linear?
A. x = –2
B. y = 3𝑥 2 + 1
C. y < 5x – 2
1
D. 𝑦 2 = 𝑥 + 3
2
21. Find the slope of a line that passes through (2, 4) and (-7, 8).
22. What is the slope of the line x = –2?
23. What is the slope of a line that is parallel to the graph of 2x – 3y = 6?
24. The graph of the line through (2, 3) that is perpendicular to the line with equation x = –1 also goes through which
point?
25. Write an equation in slope-intercept form for the line that has a slope of 3 and passes through (–1, 2).
26. Write an equation in slope-intercept form for the line that passes through (–1, –2) and (3, –7).
27. Write an equation in slope-intercept form for the line that passes through (0, –2) and is parallel to the line whose
equation is 3x + 5y = 3.
28. The table below shows the relationship between the number of hours practiced and the number of free throws made
for 5 players. Use a scatter plot to draw a line of fit and then describe the correlation.
Hours Practiced
1 3 4
7
12
Free Throws Made 0 4 6
16
19
29. Identify the domain of y = 3⎪x + 2⎥ .
30. Write the inequality that describes the situation when Bob has at least 3 pets?
31. The system of equations y = 2x – 3 and y = 4x – 3 has
In 32 – 33 solve, and identify as:
A. consistent and independent
B. inconsistent
C. consistent and dependent
D. inconsistent and dependent
32. x + 2y = 7
33. 2x + 3y = 10
3x – 2y = 5
4x + 6y = 20
34. Solve.
6x – 5y = 21
4x + 7y = 15
36. Solve by graphing.
35. Solve.
2x + y = 2
3x – y = 4
2x + 5y = 16
8x – 4y = 10
37. Graph the system of inequalities? 2x + y > –5
3x – 2y ≥ 9
For Questions 38-41, use the matrices to find the following.
3 1
P=[
]
−4 0
0
Q=[
1
38. the first row of RS.
−0.25
]
0.75
4 −5 2
R=[
]
8 −1 3
3 1
S = [ 0 2]
−4 5
39. the first row of 5P – 4Q 40. the inverse of matrix Q. 41. the determinant of P
42. Solve the matrix equation [
𝑚
2
7 −3
] ⋅ [ ] = [ ] by using inverse matrices?
𝑛
6
1 1
43. Identify the y-intercept and the axis of symmetry for the graph of f(x) = –3𝑥 2 + 6x + 12.
44. Determine whether f(x) = –5𝑥 2 – 10x + 6 has a maximum or a minimum value and find that value.
45. Solve 𝑥 2 = 4x by graphing. If exact roots cannot be found, state
the consecutive integers between which the roots are located.
46. Solve 𝑥 2 – 3x = 28 by factoring.
1 + 2𝑖
48. Simplify 2 − 3𝑖 .
.
47. Simplify (15 – 13i) – (–1 + 17i).
49. Solve 4𝑥 2 – 28x + 49 = 25.
50. Write the quadratic equation 𝑥 2 – 18x = –106 in vertex form.
For Questions 51 and 52, use the value of the discriminant to determine the number and type of roots for each equation.
51. 3𝑥 2 – x – 12 = 0
52. 𝑥 2 + 10 = 3x – 3
53. Identify the vertex, axis of symmetry, and direction of opening for y = –8(𝑥 + 2)2 .
54. Write y = 𝑥 2 – 18x + 52 in vertex form.
55. Graph each quadratic inequality.
a. y ≤ (x – 3)(x + 1)
b. y > (x + 3)(x – 1)
56. Solve 2x + 3 ≥ 𝑥 2 .