Algebra 2X
Name: ______________________
ALGEBRA 2X – MIDTERM EXAM REVIEW
1. What is the set of numbers that is described by R?
2. Solve: [pic]
3. Solve, write the solution as an inequality, and write the solution in interval notation: [pic]
4. Solve: [pic]
5. Write this set in interval notation: [pic]
6. Find the slope through the points (6, -3) and (10, 3).
7. Find the x-intercept of [pic]. Write the answer as a point.
8. Find the equation of the line (in slope-int. form) that goes thru (1, 4), and is perpendicular to [pic].
9. On the x- and y-axes, graph [pic].
10. Given the relation [pic], answer the following questions:
a. What is the domain of the relation?
b. What is the range of the relation?
c. Is the relation a function? How do you know?
d. If the relation is not a function, what could you change to make it a function? Explain.
OR
If the relation is a function, what could you change to make it only a relation? Explain.
11. Identify the domain and range of each graph below. Try to write the domain and range in as many different notations as possible (set notation, interval notation, inequality).
a. b.
[pic] [pic]
Domain: Domain:
Range: Range:
12. Let [pic], [pic], [pic], and [pic]. Evaluate the following:
a.) [pic] b.) [pic] c.) [pic]
d.) What is the vertex of the graph of [pic]?
e.) What is the leading coefficient of [pic]?
f.) Write the equation that would represent a translation of the graph of [pic] 3 units up and 5 units to the left.
13. Solve the system using Cramer's Rule, Substitution, and Linear Combinations (Elimination). You should also be comfortable solving on the calculator and identifying the intersection of the graphs.
[pic]
14. What does it mean if a system has no solution? What does this system look like graphically? What happens algebraically?
15. What does it mean if a system has many solutions? What does this system look like graphically? What happens algebraically?
16. Find the inverse of matrix A by hand, then check using the calculator. [pic]
17. The function [pic] models the height of a rocket launched straight up into the air from a height of 10 meters with an initial velocity of 200 meters per second. The variable t represents time (in seconds).
a.) After how many seconds will the rocket reach its maximum height?
b.) What is the maximum height reached by the rocket?
18. If [pic], what is [pic]?
19. Graph [pic] [pic]
20. What is the vertex of the graph of [pic]?
21. What is the y-intercept of the graph of [pic]?
22. Factor completely: [pic]
23. Factor completely: [pic]
24. Solve: [pic]
25. Find the zeros of [pic]
26. Solve: [pic]
27. Find the zeros of [pic]
28. Solve: [pic]
29. Solve: [pic]
30. Find the sum: [pic]
31. Find the product: [pic]
32. What is [pic] equal to in simplifies form?
33. Determine the remainder when [pic] is divided by (x – 1)
34. Multiply: [pic]
35. Solve: [pic]
36. If a quadratic function has 2 – 5i as one of its zeros, what is the other zero?
37. [pic] has three zeros, one of which is real. What is the function’s real zero? Use this real zero to find the other 2 zeros.
For 38-41, simplify each expression. Your answers should not have negative exponents.
38. [pic]
39. [pic]
40. [pic]
41. [pic]
42. Evaluate the following, if [pic] and [pic]:
a.) [pic]=
b.) [pic]
c.) [pic]=
43. Solve: [pic] 44. Solve: [pic] 45. Solve: [pic]
For 46-48, graph the functions using translations:
46. [pic] 47. [pic] 48. [pic]
[pic] [pic] [pic]
49. Solve, and write the solution in interval notation: [pic]
50. Solve, and write the solution in interval notation: [pic]
Answers!
1.) Integers 2.) x = 2 3.) [pic], [3, 7] 4.) x = 4, -10
5.) (-3, 9] 6.) [pic] 7.) (3, 0) 8.) [pic]
9.) Dotted, and shade left
[pic]
10.) a.) {-2, 3, 7, 5, 6}
b.) {0, -4, 2, 8}
c.) NO, inputs / x-values are repeated
d.) Change one of the 3’s in the x-coordinate so it is not repeated
11.) a.) Domain: [pic] OR [pic]
Range: [pic] OR [pic] OR [pic]
b.) Domain: [pic] OR [-4, 8] OR [pic]
Range: [pic] OR [-12, 4] OR [pic]
12.) a.) 12 b.) -3 c.) 27 d.) (3, 5) e.) 4 f.) [pic]
13.) Solution is (-2, 10)…did you solve it all 3 ways? You should have!
14.) No ordered pairs (x, y) work in both equations. Graphically, you get parallel lines. Algebraically, you get a false statement, like 17 = 0.
15.) Lots of ordered pairs (x, y) work in both equations (an infinite number). Graphically, you get the same line overlapping itself. Algebraically, you get a true statement, like 17 = 17.
16.) [pic]
17.) a.) 20.408 seconds b.) 2050.816 meters
18.) 51
19.)
[pic]
20.) (4, -14)
21.) (0, 4)
22.) [pic]
23.) [pic]
24.) [pic]
25.) [pic]
26.) [pic]
27.) [pic]
28.) [pic]
29.) [pic]
30.) 7 – i
31.) -5 + 10i
32.) 1
33.) 0
34.) [pic]
35.) [pic]
36.) 2 + 5i
37.) [pic] is the real root, [pic] are the other 2 (complex) roots
38.) [pic]
39.) [pic]
40.) [pic]
41.) [pic]
42.) a.) 6
b.) 48
c.) 27, since [pic], and [pic]
43.) x = 76
44.) [pic]
45.) [pic] (-3 is an extraneous root)
46.) 47.) 48.)
[pic] [pic] [pic]
49.) [pic]
50.) [2, 5]
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