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c 2  6c  7  0 (use a comma to separate answers as needed)
1) Solve
Answer: -1,7
16 x 2
4 x  12
2) Multiply and simplify ( 2
)(
) (Type exponential notation
4x
4 x  24 x  36
with positive exponents)
4x
Answer:
x 3
3) Find the GCF for the group of terms  30a 3 ,5a 4
Answer: 5a3
4) Solve for x 4 x( x  2)  5 x( x  1)  2
Answer: -1,-2
5) Use Rational exponents to simplify 5 x15 = x ?
Answer: 3
6) Rewrite with a rational exponent 3 19
Answer: 191/3
7) Add (3b 4  5b 2  17b  9)  (b 5  12b 3  6b 2  5b  4)  (6b 4  b 2  7b  4)
simplify your answer
Answer: b5-3b4+12b3+12b2+5b-9
y  8 y  1 y  27



8) Perform the indicated operations and simplify
y  9 y  9 y 2  81
10
Answer:
y9
9) Rewrite the following expressions with positive exponents (49 xy) 3 / 7
1
Answer:
3/7
 49xy 
10) For the following equation, state the value of the discriminant and then describe
the nature of the solutions 9 x 2  2 x  15  0
a) The equation has two real solutions
b) The solution has one real solution
c) The equation has two imaginary solutions
11) Solve a) 5 x 2  15
b) Fine the x-intercepts f ( x)  5 x 2  15
Answer: a) -3, 3
b) (-3,0),(3,0)
12) Jack usually mows his lawn in 7hrs.Marilyn can mow the same yard in 3hrs. How
much time would it take for them to mow the lawn together?
( simplify by typing an integer, proper fraction, or mixed number)
Answer: 2 1/10 (Mixed number)
13) Multiply ( s  d )( s 2  sd  d 2 )
Answer: s3+d3
14) Factor b 2  14b  49  (b+7)(b+7 (Factor completely and type n if it is not
fortorable)
15)Find the vertex both x and y coordinates, the line of symmetry, the maximum and
minimum value of the quadratic function and graph the function f ( x)  2 x 2  2 x  5
Vertex is (1/2,11/2); line is x=1/2; maximum is 11/2
8x
x
x 2  14 x
16) Add and simplify if possible 2


x  36 x  6 x 2  36
p2  4 p  2
17) Simplify by removing factors of 1
=
( p  2) 2 p  2
18)Multiply and simplify by factoring. Assume that all expressions under radicals
represent nonnegative numbers
3
y 10 3 16 y 11 = 2 y 7 3 2
19) Solve c 2  5t  36  0
Answer: -9, 4
20) Find the polynomial for the perimeter and for the area w=n+9 , L=N
What is the perimeter, simplify and don’t factor
What is the area do not factor
Perimeter is 4n+18; area is n2+9n
1
21) Simplify 5 
( simplify the answer type a fraction or an integer)
3125
Answer: -1/5
22)Find the variation constant and an equation where y varies directly as x and y=36
when y=4
A)The variant constant of k is=9
B) The equation of variation is y=9x
23) Use the quadratic formula to solve the equation x 2  x  9 what is the solution set
{ } simplify your answer, type an exact answer using radicals as needed express
complex numbers in terms of t. Use integers or fractions for any numbers in the
expression use a comma to separate answers.
Answer:
1  35 i 1  35 i
,
2
2
24) Find the x-intercepts for the graph of the equation y  x 2  2 x  8
Answer: (-4,0) and (2,0)
25) Use the FOIL method to find the product of (7 x 2  6)( x 7  5)
Answer: 6x9-35x2-6x7+30
2 w  24 w  8
/
26) Divide and simplify
(simplify the answer using integers or fractions
4
10 w
for any number of expressions)
Answer:CHECK THIS QUESTION
27) Add
(2 x2  4 xy  y 2 )  (5x 2  5xy  y 2 )  ( x 2  xy  5 y 2 )
Answer: -2x2-5y2
28) Solve 3x  24  x  2 ( simplify and use a comma to separate answers as needed)
Answer: 4
29) Evaluate the polynomial for x=-1
3x 2  2 x  6
Answer: 11
30) If the sides of a square are lengthened by 6cm, the area becomes 225 cm^2. Find the
length of a side of the original square.
Answer: 9
2m 2  2m
31) Simplify by removing factors of 1
6m 2  4m
m 1
Answer:
3m  2
32) Factorize completely 45s 2  150 st  125t 2
Answer: 5(3s+5t)(3s+5t)
8 9 1
33) Solve
 
y y 11
Answer: 11
34) Subtract the polynomials (10a 2  9a  2)  (7a 2  2) =-17a2+9a
35) Television sets. What does it mean to refer to a 20in TV set or a 25 in TV set ? Such
units refer to the diagonal of the screen . A 30 in TV set also has a width of 24 inches .
What is it’s height.
Answer: 18
36) Factor the trinomial s 3  2 s 2  63s
Answer: s(s-9)(s+7)
( factor completely)
37) Find the following 12 (4)12 (simplify your answer)
Answer: 4
38) Identify the degree of each term ( 1,2,3,4) and degree of the polynomial
 7 x 3  8x 2  5x  3
3,2,1,0, degree of polynomial: 3
39) If a pro basketball player has a vertical leap of about 30 inches, what is his hang
time? Use the function V=48T^2 ( time in seconds)
Answer: 0.8
40) Use rational exponents to write x1 / 5 . y 1 / 8 .z 1 / 4 as a single radical exprexssion.
Answer:
40
x8 y 5 z10
41) Find all numbers for which the rational expression is undefined
t 3  9t
t2  4
(use
comma to separate answers)
Answer: CHECK THIS QUESTION
42) Factor completely 16c 2  25  40c
Answer: (4c-5)(4c-5)
43) Write a quadratic equation in the variable x having the given numbers as solutions.
Type the equation form,
ax 2  bx  c  0
Solution 7, only solution.
The equation is? = 0
Answer: x2-14x+49
44)Convert to decimal notation 8.98 x10 7
Answer: 89,800,000
( simplify by typing an integer or decimal)
45) Solve 6 x 4  13 x 2  6  0 ( type an exact answer, using radicals as needed,
Rationalize all denominators. Use a comma to separate answers as needed)
6 6
6 6
,
,
,
Answer: 
2 2
3 3
46) Multiply and simplify. Assume variables represent nonzero real numbers a 12 .a 0
Answer: a12
47) Factor completely 2 x 8  16 x 7  4 x 6 ( type an answer in factored form)
Answer: 2x6(x2-8x+2)
48) Multiply (5 x  3)( 2 x  5 x  9) simplify your answer
Answer: CHECK THIS
49) Solve x 2  18 x  4  0 ( Simplify and use a comma to separate answers, type an
exact answer using radicals as needed)
Answer: -9+85, 9-85
50) Multiply (4n) 2 (3n 2 ) 2
Answer: 144n6
51) Multiply (5 7  10 2 )( 4 7  8 2 ) ( simplify, type an exact answer using
radicals as needed)
Answer: -20
52) Express using a positive exponent n 2
1
Answer: 2
n
53) Subtract. Simplify by collecting like terms if possible 6 27  9 3
54)
55)
56)
57)
Answer: 9 3
Factor completely 16b 2  81 ( type N if the binomial is not factorable)
Answer: (4b-9)(4b+9)
Factor 80  18v  v 2 =(v-10)(v-8)
1
h3
Divide and simplify 14 = 11
h
h
Solve ( x  18)( x  6)( x  5)  0
a) The solution is x 18  x  5 or x  6 ( use at least one inequality or
compound inequality to express your answer if possible separate with a
comma or the word “or”)
b) The solution is all real numbers
c) There is no solution.
58) Simplify by taking roots of the numerator and denominator. Assume that all
expressions under radicals represent positive numbers.
3
8x11 2 x3 3 x 2

y3
y
1
1
59) Multiply (v  )(v  )  ( simplify your answer)
5
2
7
1
Answer: v 2  v 
10
10
60) Find the following. Assume that variables can represent any real
number (a  2) 2
Answer: |a+2|
61) Simplify by factoring. Assume that all expressions under radicals represent
nonnegative numbers 18a2b  3a 2b =
62) Divide (36b 3  6b 2  42b  33) /(6b  3)
Answer: 6b2-2b+8+ 9/(6b+3)
7  z 8z  9 7 z  2


z 3 3 z
z 3
64) In a right triangle, find the length of the side not given side b= 2, side c = 29
what is the length of side C=5
65) Find the vertex , line of symmetry, and maximum and minimum value of f(x)
1
Graph the function. f ( x)  ( x  7) 2  6 also is the value f(-7)=6, a max or
2
min value.
Answer:Vertex is (-7,6); line: x=-7; minimum is 6; minimum
63) Subtract ,simplify if possible
66) Rationalize the denominator, Assume that all expressions under radicals
c d
represent positive numbers
c d
c  d  2 cd
Answer:
cd