1. What properties of real numbers are used in each step of the following simplification?
a.
1
1
(3 4)  (4 3)
4
4
1
b. 
4
________________________________

4  3 ___________________________________

c. 1 3 ____________________________________
d. 3 ____________________________________
2. Evaluate:
6( x  2)  4( x  1)
3x  1
3. Simplify:
1 2
( x  6 y)  (4 y  x 2 )
2
for x  3
4. The expression 19.95  0.20x models the daily cost of renting a car. In the expression, x represents the number of
miles the car is driven. Find the cost of renting a car for a day when the car is driven 50 miles.
1
7
5. Solve the equation: 3( x  )  5( x  )  4 x  1
2
2
6. Solve the equation: 7(a  5)  12  3(a  2)
7. Solve each equation for x and state the restrictions:
a. tx  ux  3t
b.
x 3
3 a
6
c. 5 x  7a  ax  9
8. Solve each formula for the indicated variable:
1
a. R  (r1  r2 )
2
b. P  2l  2w solve for l
solve for r2
9. The length of a rectangle is 5 cm greater than its width. The perimeter is 106 cm. Write an equation and find the
dimensions of the rectangle.
10. Evaluate the expression
11. Evaluate the expression
b2 c2
ad
when a = −4, b = .08, c = 5, and d = 15.
j2 −3h2 k
j3 +2
when h = 4, j = −1, and k = .5.
12. Forensic scientists use the equation h = 2.6f + 47.2 to estimate the height h of a woman given the length in
centimeters of her femur bone. Suppose the equation has a margin of error of +3 centimeters. Write an inequality to
represent the height of a woman given the length of her femur bone.
13. Marine biologists often have to transplant a dolphin from its natural habitat to a pool. Dolphins prefer the
temperature of water to be at least 22℃ but no more that 29℃. The acceptable temperature of water t for
dolphins can be described by what compound inequality.
3
14. Solve and graph: 4a  3(a  1)  (7  a)
2
15. Solve and graph: 6[5 y  (3 y  1)]  4(3 y  7)
16. Solve: 3x  1  5 or 2 x  4  6
17. Solve: 3  2 x  5  5
18. Solve: 4 | 2 x  3| 7  13
19. Solve:
20. Solve: 5 | 3x  7 | 4  29
21. Solve: | 3x  2 | 10  5
22. For the following relation, answer the following questions:
 2, 1 ,  4,5 , 1,7  ,  2, 3,  1,2
1
| 2 x  5 | 3x  4
3
a. Find the domain & range
b. Is the relation a function? Why/why not?
c. Make a mapping of the function
23. Find the domain & range of the following functions:
a.
b.
24. Suppose f ( x)  3x  4 and g ( x) | x | 3 . Find each value:
3
a. f ( )
4
1
b. f ( )  g (2)
3
c.
f (1)
g (1)
25. Find the slope and y-intercept of 3x  5 y  15
26. Write the equation of a line in Standard Form that:
1
b. has a slope of 6 and passes through ( , 2)
2
a. passes through (4,1) and (2, 2)
c.
passes through (6, 1) and is perpendicular to y 
3
1
x
2
4
d. passes through (1, -5) and is parallel to 6 x  3 y  7
27. Graph:
e. slope is undefined and passes through (-9, 17)
3
a. y   x  1
4
b. y | x  2 | 3
3
c. y   | x | 4
2
e. 2 x  3 y  6
f. 1  y | 2 x  1|
g. y  3 | 3x | 1
d. y  3x –12  1
28. Find the equation/inequality describing the graph:
a.
b.
29. Classify the system without solving:
x  5   y
a. 
2 y  10  2 x
2 x  y  7
b. 
 y  2x  8
6 x  2 y  2
c. 
 3 x  7 y  17
30. Solve the system using substitution:
 y  2x  8
a. 
 3 x  y   1
 4 x  6 y  15
b. 
 x  2 y  5
2
7
 x  y  1
c.  3
3
14 x  4 y  6
 2 x  5 y  17
b. 
 5 x  7 y  10
6
11
 4
 x  y 
c.  5
5
5
6 x  9 y  3
 2 x  4 y  4
31. Solve the system using elimination: a. 
3 x  5 y   3
 x  y  2
32. Solve the system by graphing: 
2 x  2 y  1
33. A citrus fruit company plans to make 13.25 lb gift boxes of oranges and grapefruits. Each box is to have a retail
value of $21. Each orange weighs 0.5 lb and has a retail value of $.75, while each grapefruit weighs 0.75 lb and
has a retail value of $1.25. How many oranges and grapefruits should be included in the box?
34. Tickets for your school’s play are $3 for students and $5 for non-students. On opening night, 937 tickets are sold
and $3943 is collected. How many tickets were sold to students?
35. You have a collection of nickels and quarters. There are a total of 20 coins and their value is $3.20. How many of
each coin do you have?
36. Graph:
y  x  5
a. 
3 x  y  2
y  x  2
b. 
 y | x  3 | 1
37. Graph the system of constraints. Find all vertices and evaluate the objective function to find the minimum value
 2 x  y  30

for C  x  4 y .  x  y  20
 x  0, y  0

38. Which point gives the minimum value for P = 3x + 2y and lies within the system of restrictions?
1  x  6

2  y  5
 x  y  10

A. (1, 2)
B. (0, 0)
C. (5, 5)
D. (1, 5)
39. a)
b)
1 0
 7
 4 1 7 
 2
40. Simplify: 3 

5
 8 6 2 
 3 5
3x 2   4 0   16 2 
41. Solve for x & y: 


0 
 1 8   7 8  y
42. Write the piecewise-defined function shown in each graph.
a)
b)
43. State the degree of the polynomial x5y + 9x4y3 – 2xy
44. State the degree of the polynomial 18x – 12x2 + 6x3
45. Simplify.
46. Simplify
47. Simplify.
48. Simplify.
49.
a)
b) If c(x) = x3 −2x and d(x) = 4x2 −6x + 8, If find:
50. Use both long and synthetic division to find the following:
51. Use both long and synthetic division to find the following:
52. Solve the inequality both algebraically and graphically.
a) 0 > x2 + 5x – 6
b) −x2
53. Graph: a. y  3x2  12x  11
b. y  2 x2  12 x  3
54. Find the vertex and axis of symmetry: a. y 
55. Factor: a. 5x2  80
e. 4a 2  16  9a3  36a
56. Solve by factoring:
1 2
1
x  6 𝑦 = 2 𝑥2 − 6
2
b. 32 x2 +16 x  2
c. 6 x 2  9 x  5
f. 2d 2  12d  16
g. 6 x2 y 2  36 xy 2
a. 8 x 2  6 x  5
57. Solve by taking square roots: a.
b. y   x2  7 x  2
58. Solve using completing the square:
59. Solve using quadratic formula:
c. 16n2  32  0
b. 2 y 2  4 y  8   y 2  y
3 2
x  17  22
4
d. 7 y8  7
b. 26  5 x 2  50
a. 2 x 2  6 x  1  0
b. 7k 2  10k  100  2k 2  55
c. 2 x2  9 x  7  0
d.
q 2 9q 2

 18
4
20
a. 16 x2  20 x2  24 x  5
b. 7h2  2h  9  0
c. 3.5 y 2  2.6 y  8.2  0.4 y 2  6.9 y
d. 8x2  4 3x  1
60. Evaluate the discriminant of each equation. How many real solutions does it have?
a. 2 x2  5x  4  0
b. 16 x2  8x  1  0
a. i  (8  2i)  (5  9i)
61. Simplify:
d. | 9  6i | |−9 + 6𝑖|
c. 2(3  10i)2
g.
62.
c. 3x2  4 x  3  0
 4i  2i i i 
3
5
11
19
h.
i i i i i 
9
27
14
10
8
b.
7 2
3
1 1
i   4(6  i)  ( i  3)
3 5
2
3 4
e.
5  3i
4i
f.
6  2
6  2
i. ( 9  2)( 4  1) j. √−24 ∙ √−12
A ball is thrown upward from ground level. Its height, h, in feet, above the ground after t seconds is
h  48t  16t 2 . Find the maximum height of the ball. When will the ball reach the maximum height? When will
the ball land on the ground?
63. Suppose a parabola has a vertex in Quadrant IV and a < 0 in the equation y  ax2  bx  c . How many real
solutions will the equation ax 2  bx  c  0 have?
64. Solve:
a.
2 x  3 3x  4

x5
x7
b.
.
2x +1
x
65. Solve: a. ( x  1)( x2  5x  6)  0
b. x3  10 x 2  16 x  0
Area = 105
c. x3  3x2  54 x  0