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1. Simplify (simplify your answer. Type a fraction or an integer. Type N if the root
is not a real number.)
1
3 
8
2. Rewrite with a rational exponent. (Simplify the answer)
7
23
3. Multiply and simplify by factoring. Assume that all expressions under radicals
represent nonnegative numbers. (Simplify the answer. Type in radical form.)
3
y 13 3 81y 14
4. Solve. (Use comma to separate answers. Type N if the solution is not a real
7 x  46  x  4
number.)
5. Rewrite the following expression with positive exponents (11xy) 7 / 9
Choose the correct equivalent expression.
A) (11xy) 7 / 9  (11xy) 9 / 7 B) (11xy) 7 / 9  (11xy) 7 / 9 C) (11xy) 7 / 9 
(11xy) 7 / 9 
1
(11xy) 9 / 7
D)
1
(11xy) 7 / 9
6. Find the following. (Simplify the answer. Type N if the root is not a real number.)
16
( 6)16 
7. Solve for x. (Simplify the answer. Use a comma to separate answers. Type N if
there is no solution.) 4x(x-2)-5x(x-1)=2
8. Multiply. (Simplify the answer. Type and exact answer, using radicals as needed.)
(3 2  6 6 )(5 2  10 6 )
9. Solve. (Simplify your answer. Type and exact answer, using radicals as needed.
Rationalize all denominators. Use as comma to separate answers as needed Type N if
there is no solution.) 4x 4 12 x 2  5  0
The solution is x=
10. Subtract. Simplify by collecting like radical terms if possible (Simplify the answer,
Type and exact answer using radicals as needed.)
3 75  4 3 
11. Use rational exponents to simplify (Simplify the answer.)
3
x9
12. Find the following. Assume that variables can represent any real number.
(a  9) 2 
13. Solve. (Use comma to separate answers. Type N if there is no solution.)
b 2 6b  40  0
The solution is b =
14. In a right triangle, find the length of the side not given. (Simplify the answer.
Type an exact answer, using radicals as needed.)
B=1, c= 17
The length of the third side is
15. Find the vertex, the line of symmetry, the maximum or minimum value of the
quadratic function, and graph the function.
F(x) =- 2x 2 2 x  8
The x-coordinate of the vertex is
The y-coordinate of the vertex is
The equation of the line of symmetry is x =
The maximum/minimum of f(x) is
1 17
The value, f ( )  is ?
2
2
Minimum
Maximum
16, For the following equation state the value of the discriminant and then describe
the nature of the solutions. 8x 2 8 x  2  0
What is the value of the discriminant?
Which one of the statements below is correct?
A) the equation has two imaginary solutions
B) the equation has two real solutions
C) the equation has one real solution
17. Rationalize the denominator. Assume that all expressions under
radicals represent positive numbers. (Simplify the answer. Type and
x y
exact answer, using radicals as needed.)
x y
18. Solve. (Use at least one inequality or compound inequality to express
your answer. For answers with more than one inequality, separate
the inequalities by a comma or the word type R if the answer is all
real numbers. Type N if there is no solution.)
19. Simplify by taking roots of the numerator and the denominator.
Assume that all expressions under radicals represent positive
numbers. (Type an exact answer, using radicals as needed. Type N if
the root is not a real number)
3
343 x 5
y3
20. 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
The solution 1, only solution
The equation is
=0
21. 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 30in TV
set also has a width of 24 inches. What is it height?
What is the height of a 30 in TV?
Inches
22. a) Solve 2x 2  10
b) Find the x-intercepts of f(x) =2x 2 10
a) What is the solutions? X =
(Type an exact answer, using radicals as needed. Rationalize all
denominators. Express complex numbers in terms of i. Use a comma to separate
answers as needed.)
b) What are the x-intercepts?
(Type and ordered pair, Type and exact answer. Using radicals as
needed. Rationalize all denominators. Express complex numbers in terms of i. Use a
comma to separate answers as needed. Type N if there is no x-intercepts.)
23. Use rational exponents to write x 1 / 4  y1 / 6  z 1 / 8 as a single radical
expression. Choose the correct expression below
A)
24
x 6 y 4 z 3 B)
192
xyz C) 24 xyz D)
24
(xyz)13
24. Find the vertex, the line of symmetry and the maximum or
minimum value of f(x). Graph the function.
1
F(x) = ( x  7) 2  6
2
The vertex is
(Type an ordered pair.)
The line of symmetry is x =
What is the maximum/minimum value of f(x)?
Is the value, f (-7) =6 a minimum or maximum?
Minimum
Maximum
25. If a pro basketball player has a vertical leap of about 20 inches what
is his hand time? Using the hand-time function V=48T 2
His hang time is
seconds. (Simplify the answer. Type and
integer or a decimal. Round to the nearest tenth.)
26. Solve. (Simplify your answer. Use a comma to separate answers.
Type exact answers, using radicals as needed. Type N if there is no
solution.)
x 2 18 x  4  0
The solution is x =
27. Use the quadratic formula to solve the equation. (Simplify your
answer. Type exact answers, using radicals as needed. Express
complex solutions in terms of i. Use commas to separate answers.)
2x 2 3 x  10
The solution set is {
}
28. Simplify by factoring. Assume that all expressions under radicals
represent non-negative numbers. (Type an exact answer, using
radicals as needed)
32a 2 b