Download midterm review File

Advanced Algebra II
Midterm Review
Name_________________________
Summer Review Packet (i.e. Keystone Test Topics)
1. Evaluate 4x + 5 – 3y for x = 2 and y = -4
2. Given the linear equation 5x - 4y = 20
a) Find the slope of the line.
b) What is the slope of the line perpendicular to this line?
3. Find the slope of the line through (-4,3) and (-6,-4).
4. Six more than eight times a number is the same as sixteen less than ten
times the number. Find the number.
5. Find the equation in slope-intercept form of the line containing the
point (-3,2) with a slope of 1/3.
6. Find an equation in slope-intercept form of the line parallel to 2x - y = 3
and containing the point (-4,8).
7. Find the intercepts of equation 2x + 5y = 10,
8. Graph and label both lines on the graph below
a) x = 5
b) y = -3
Chapter 4
1. Solve by graphing
-2x + y = 1
3x + y = -4
2. Solve by substitution
x+y=6
y=x+2
4. Solve by linear combination (not matrices)
2x – y + z = 7
x + 2y + 2z = 3
7x – 3y – 3z = 4
3. Solve by linear
combination
2x + 7y = 2
3x + 5y = -8
Graph
5. 3x – 5y  15
6.
y 3
x+y<3
x > -1
y  -3
7. The difference between two numbers is 11. Three times the larger number
is nine times the smaller. What are the two numbers?
8. In triangle ABC, the measure of angle B is 2º more than three times the
measure of angle A. The measure of angle C is 8º more than the
measure of angle A. Find the angle measures.
What type of systems are these? (Consistent or Inconsistent? Dependent or
Independent?)
9. x + 2y = 6
2x = 8 – 4y
10. y – x = 4
x + 2y = 2
11. 3y = x – 2
3x = 6 + 9y
12. One day a store sold 30 sweatshirts. White ones cost $9.95, and yellow
ones cost $10.50. In all, $310.60 worth of sweatshirts were sold. How
many of each color were sold?
Chapter 5
Collect like terms
13. 6x2 – 7x2 + 3x
14. –2y - 5x + 7y
15. 5x2y – 2y +3xy2 – 4x2y + 6y + xy2
Add or Subtract
16. (3x + 4y – 5) + (2x – 4y +3)
17. (3x + 4y – 5) – (2x – 4y +3)
Multiply
18. (-8x2y)(4xy2)
19. (3x2 – 2x + 5) (-3x + 4)
20. (x + 2)2
Factor
23. 4a2 + 2a
21. (x + 3)3
24. 49y2 – 81
22. (3x – 2y)(x - y)
25. 4y2 + 20y – 56
26. 12x2 + 12x + 3x + 3
28. y2 +36 –12y
31. 75x 4 y  60 x 3 y  12 x 2 y
33. x2 + 3x –28 = 0
27. x2 + 4x + 4
29. 8x2 + 50 + 40x
30. 27x3 – 64y3
32. 6x2 – 5x – 25
34. 2x2 + 9x = -4
35. (x –6)2 = 81
36. Four times the square of a number is 21 more than eight times the
number. What is the number?
37. The square of a number plus the number is 156. What is the number?
38. The sum of the squares of two consecutive odd positive integers is 202.
Find the integers.
39. Thirty-Five square yards of linoleum are laid in a rectangular room.
The length of the room is 3 yd less than 2 times the width. What are the
dimensions of the room?
Chapter 6
40. In the expression
x
(3x  2) x , which values are not acceptable
replacements for x:
x  2 x2  x  6

41.
equals
x4
x4
42.
z 5
4

equals
( z  3)( z  2) z  3
1 1

2x y
2
2
43. The complex fractional expression x  y can be simplified by
2 xy
multiplying the numerator and denominator by:
1 1

x y
44. 2
equals
2
x y
xy
45. (72x5 –24x3 + 36x2)  12x2 equals
46. (12x2 – 28x + 3)  (3x + 2) has a remainder of:
47. Solve
1
x
3

x 3 x 3
48. It takes one worker 5 hours to do the same job that it takes another worker
12 hours to do. If they work together how long will it take for the job to be
done?
49. Y varies directly as the square of x. If y = 20 when x = 2, what is the value
of y when x = 4?
Chapter 7
50. If r represents any real number, then
51. The product of
3
52.
54.
256 y 11
3

4y
2
144r 2 equals
38 and 12 in simplified form is
equals
53.

2
6  5 equals
56. A solution for
x  3  12
55.
is
24  54  150 equals
3  2i
equals
3  2i
57. Solve
x  9  x  5 is
58. (1 + 3i)(6 – i) equals
59.
4i
equals
2  5i
Chapter 8
60. Determine the nature of the solutions of
3x2 = 9x + 8.
61. Given
2y2 - 9y = 18 are
a) What is the discriminant
b) find the solutions of the equation
62. Solve by completing the square
3x2 + 12x – 52 = 0
63. Solve using the quadratic equation
3x2 – 4x + 8 = 0
64. Solve
x4 – 10x2 + 25 = 0
65. The width of a dock is 4 meters less than the length. The area is 12 m2.
What are the dimensions of the dock?
66. Solve for the indicated letter
A = πr + πrh ; for r
67. Use the formula h(t) = -9.8t2 + v0t + h0
An object is dropped from a height of 500m. with an initial velocity
of 12 m/s.
a) How long does it take to reach
b) How far will it fall in 5
the ground?
sec.?
68. Y varies directly as the square of x, and y = 27 when x = 3.
Find y when x = 2
Chapter 13
69. What are the dimensions of this matrix? _________________
1 9  6 8 
12 11 3  1


5 7  8 10 
b) Assume the values represent the coefficients of an equation, find the
solution matrix.
70. What is N – 2M?
Given M =
and N =