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You have to carefully check for typos in the questions!
1.
4  z 2z  7

z 8 8 z
z-3
z-8
2. Jack usually mows his lawn in four hours. Marilyn can mow the same lawn in 3
hours How much time would it take for them to mow the lawn together?
1 5/7
(that’s 1 and 5/7)

3. 2 x  7  4 x 2  5x  8)

8x^3+ 51x + 38x^2 + 56
4.
Find the greatest common factor for the group of terms
 18a 2 ,3a 3
3a^2
5. Multiply and simplify
4c 2
2c  8

2
2c
2c  16c  32
2c
c-4
6. Use the quadratic formula to solve the equation
2 x 2  3x  6
You have to carefully check for typos in the questions!
7. Rationalize the denominator. Assume that all expressions under radicals represent
positive numbers.
u v
u v
8. 3x 2  5 x  5 (Evaluate the polynomial for x=0) When x=0, 3x 2  5 x  5 
Ans = 5
9.
Find all the numbers for which the rational expression is undefined
q 3  3q
q 2  36
-6, 6
10. In a right triangle, find the length of the side not given
b=2, c=
Ans = 5
29
The third side is?
11. Solve
w 2  4w  21  0
-3, 7
12. Find the vertex, line of symmetry, min/max value of
2 x^2  2 x  6
f(x)= You have another typo here…
X = 1/2
Y = 13/2
Symm: x = 1/2
Maximum is 13/2
You have to carefully check for typos in the questions!
13. Find the vertex, line of symmetry, min/max value of
1
f(x) = ( x  3) 2  5
2
vert: (-3, 5)
Symm: x = -3
Minimum is 5
14. Solve
3 / v  9 / v 1 / 5
30
15. Find the variation constant and an equation of variation where y varies directly as
x and y = 42 when x = 6
K=7
y = 7x
16. Find a polynomial for the perimeter and for the area d+8, d
Perim = 4d + 16
Area = d^2 + 8d
17. Television sets: What does it mean to refer to a 20 in tv set or a 25 in tv set? Such
units refer to the diagonal of the screen. A 25 in tv set also has a width of 20
inches. What is its height?
You have to carefully check for typos in the questions!
Height = 15
18. Add
2x
2
 
 
 9 xy  y 2   5x 2  4 xy  y 2  x 2  xy  3 y 2

-2x^2 – 12xy – 3y^2
19. Multiply
2 2  4 6 5 2 10 6 
-220



20. Factor the trinomial
r 3  5r 2  36r
r(r-9)(r+4)
21. Simplify
1
3 
27
-1/3
22. Find the x-intercepts for the graph of the equation
y  x 2  2x  3
(-3, 0), (1, 0)
23. If the sides of a square are lengthened by 8cm, the area becomes 169cm^2. Find
the length of a side of the original square.
Answer = 5
24. Factor completely
36a 2  49
(6a-7)(6a+7)
You have to carefully check for typos in the questions!
25. Factor completely
a 7
That’s not the question… I think it says to express with positive exponents.
But the answer is:
1
a^7
26. Multiply
1 
1

 v   v  
5 
4

v^2 + 9/20 v + 1/20
27. Multiply
a  p  a 2  ap  p 2 


a^3 + p^3
28. Solve
x^2 + 14x - 4 = 0
-7+√53, -7-√53
29. Simplify by removing factors of 1
2q 2  2q
18q 2  4q
q+1
9q+2
30. Convert to decimal notation
8.08 x 10^7
80800000
You have to carefully check for typos in the questions!
31. Solve
15 x 4  13x 2  2  0
32. Find the following
14  6
14
6
33. Multiply and simplify by factoring. Assume all expressions under radicals
represent non negative numbers
3
3y 5
3
y7
3
81y 8
3
34. Subtract the polynomials
 13a 2  7a  4  6a 2  4

 

-19a^2 + 7a
35. Solve
v  3v  18  0
-6, 3
2
36. Subtract. Simplify by collecting like radical terms if possible
2 12  2 3 
2√3
37. Divide and Simplify
2 z  16 2  8

77
49 z
14z
11
You have to carefully check for typos in the questions!
38. Solve
x  9x 17x  4  0
-9 < x < -4 or x > 17
39. Factor
40 14v  v^2
(v-10)(v-4)
40. Use rational exponents to simplify. Complete the expression
3
x12  0 (that is a three over the front of the square root symbol)
Answer is 4
41. Rewrite the following expression with positive exponents
(25xy)

2
5
1 / (25xy) ^ 2/5
42. Factor completely
6 x  30 x 4  42 x 3
5
6x^3 (x^2 – 5x + 7)
43. Factor
s 2  8s  16 =
(s+4)(s+4)
44. Identify the degree of each term of the polynomial and the degree of the
polynomial
3
 3x  6 x 2  2 x  6
First = 3, then 2, 1, 0, 3
You have to carefully check for typos in the questions!
45. Find the following. Assume that variables can represent any real number
a  12
|a+1|
(note the ||)
46. Multiply and simplify. Assume variables represent nonzero real numbers
a  a0
11
a^11
47. Divide and simplify
u7
u 19
1
u^12
48. Simplify by taking roots of the numerator and the denominator. Assume all
expressions under radicals represent positive numbers
3
64 x 5
y3
49. Solve 4x 2  8
Find the x-intercepts of
f(x)=4x 2 8
Sol: √2, -√2
Inter: (√2, 0), (-√2, 0)
50. Perform indicated operations and simplify
y  8 y  1 y  27


y  9 y  9 y 2  81
10
y+9
You have to carefully check for typos in the questions!
51. Rewrite with rational exponent
3
23
23 ^ 1/3
52. Multiply
 
(-3x) 2 2x 8
3
72x^26
53. Use rational exponents to write
1
4
1
6
x y z
1
7
84throot(x^21y^14z^12)
54. Write a quadratic equation in the variable x having the given numbers as solutions.
Type the equation in standard form,
ax 2  bx  c  0
Solution: 1, only solution
x^2-2x+1
55. If a pro basketball player has a vertical leap of about 30 inches, what is his hang
time? Use the hang time function V=48T^2
You left off the part where it says to round to the tenth…
0.8
56. Factor completely
63v 2  294vf  343 f 2 
7(3v+7f)(3v+7f)
57. For the following equation state the value of the discriminant and then describe
the nature of solutions
 7 x 2  6 x  5  0 Is there one or two real, or two imaginary solutions?
D = -104
Two imaginary
You have to carefully check for typos in the questions!
58. Add
5s
4

 4s 3  5s 2  14s  7  (s 5  8s 3  3s 2  5s  2)  (8s 4  s 2  4s  5)
Check VERY carefully for typos from mathlab…
s^5 + 13s^4 + 4s^3 + 9s^2 + 5s - 10
59. Solve for x
4x(x-1)-5x(x)=3
-3, -1
60. Use the FOIL method to find the product
( 4 x 8  2)( x 9  5)
4x^17 – 2x^9 – 20x^8 + 10
61. Add and simplify if possible
5r
r

2
r  25 r  5
r^2 + 10r
r^2 - 25
62. Simplify by factoring. Assume all exponents under radicals represent
nonnegative numbers
50a 2b
5a √2b
63. Simplify by removing factors of 1
s2  4
s  22
s-2
s+2


64. Divide 25b 3  10b 2  27b  31  5b  4
5b^2 -2b + 7 + 3/(5b+4)
You have to carefully check for typos in the questions!
65. Factor completely 9t 2 25  30t 
(3t-5)(3t-5)
66. Solve
x= 4
3x  24  x  2