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Algebra 2/Trigonometry
Chapter 3 Examination:
Real Numbers and Radicals
Score:_______________
Name: __________________________________
Date: __________________________________
I.) Multiple Choice: Circle the best answer choice. Complete all calculations on the separate paper provided so that
I can see your work. Make sure to read all questions, relax, and good luck!
1. If x 0, the expression ( x )( 2 x ) is equivalent to
(1) 2x
(2) 2x
2. If a 0, then
(1) 7a
(2) 5 a
(3) x2 2
(4) x 2
9a2  16a2 equals
(3) 5a
(4) 7a
3. If 2 x  1  2  5, then x is equal to
(1) 1
(3) 5
(2) 2
(4) 4
4. What is the solution of the equation
(1) 42
(3) 3
(2) 39
(4) 6
2x  3  3  6 ?
5. What is the value of x in the equation
(1) 46
(3) 3
(2) 12
(4) 6
6. The solution set of the equation
(1) {–2,3}
(3) {3}
(2) {–2}
(4) { }
x  6  x is
7. What is the solution set of the equation
(1) {-1}
(3) {10}
(2) {9}
(4) {10, -1}
8. Which expression is equivalent to
12  4 2
7
12  4 2
(2)
11
(1)
12  4 2
7
12  4 2
(4)
11
(3)
3  x  5  2 ?
9 x  10  x ?
4
?
3 2
9. The expression
12
3 3
(1) 12  3
(2) 6  2 3
is equivalent to
(3) 4  2 3
(4) 2  3
10. The expression
(1) 1  3
(2) 1  3
11. The expression
3 2
7
21  2
(2)
7
2
is equivalent to
1 3
(3) 1  3
(4) 1  3
7
is equivalent to
3 2
(3) 3  2
(1)
(4) 3  2
12. The expression
 3 5
2
 3 5
(2)
2
(1)
13. The expression
5  13
3
5  13
(2)
3
(1)
11
is equivalent to
3 5
3 5
(3)
2
3 5
(4)
2
4
is equivalent to
5  13
2(5  13 )
(3)
19
2(5  13 )
(4)
19
14. Which expression is equivalent to
(1)
9
5
(2) -1
9  2 14
5
11  2
(4)
14
(3)
7 2
?
7 2
15. Which expression represents the sum of
2 33 2
6
2
(2)
5
(1)
(3)
(4)
1
1

?
3
2
3 2
3
3 2
2
II.) Free Response: The following are free response, where you are to show your work.
16. Simplify:
17. Solve for x:
50r 2 s 4
x  18  2  2
18. Solve for all values of q that satisfy the equation
3q  7  q  3.
19. The lateral surface area of a right circular cone, s, is represented by the equation
s   r r 2  h 2 , where r is the radius of the circular base and h is the height of the cone.
If the lateral surface area of a large funnel is 236.64 square centimeters and its radius is
4.75 centimeters, find its height, to the nearest hundredth of a centimeter.
20. The number of dogs, D, housed at a county animal shelter is modeled by the function
D  4 2 M  50, where M is the number of months the shelter has been open. How
many months will it take for 74 dogs to be housed at the shelter?