Study Island
Copyright © 2015 Edmentum - All rights reserved.
Generation Date: 03/13/2015
Generated By: Robert Dilliplane
1. Simplify the following.
A.
B.
C.
D.
2. Simplify the following expression.
A.
B.
C.
D.
3. Simplify the following.
A.
B.
C.
D.
4. Simplify:
+
A.
B.
C.
D.
5. Evaluate the following expression when n = 2.
|2n - 5| + |-5|
A. 6
B. -4
C. 4
D. -6
6. Simplify the following.
A.
B.
C.
D.
7. Evaluate the following expression when r = 2 and t = 3.
(3 × rt)-2
A.
B.
C.
D.
8.
A.
B.
C.
D.
9. Simplify the following expression.
A.
B.
C.
D.
10. Evaluate the following expression when r = 2 and t = 3.
8r t + 38
A. 118
B. 102
C. 70
D. 46
11. Simplify: (|-5 - 2| + 12)2
A. 19
B. 165
C. 141
D. 361
12.
A.
B.
C.
D.
13. Simplify the following expression.
A.
B.
C.
D.
14. Evaluate the following expression when n = 9.
|n - 6| - |5 - n|
A. 7
B. -4
C. 6
D. -1
15. Simplify:
A.
+
B.
C.
D.
-
First Set of Problems (Answers)
1. D
2. A
3. B
4. D
5. A
6. A
7. D
8. B
9. A
10. B
11. D
12. A
13. C
14. D
15. C
Explanations
1. Order of Operations:
1. Parentheses or Brackets from the inside out.
2. Exponents and Roots
3. Multiplication and Division from left to right.
4. Addition and Subtraction from left to right.
2. If the bases are different but the exponents are the same, then multiply the bases and keep the
exponent.
3. Order of Operations:
1. Parentheses or Brackets from the inside out.
2. Exponents and Roots
3. Multiplication and Division from left to right.
4. Addition and Subtraction from left to right.
4. Use the Product Property of Radicals to simplify.
5. Absolute value is the magnitude of a number irrespective of its sign.
Evaluate the given expression piece-by-piece, using order of operations:
|2n - 5| = |2 × 2 - 5| = |4 - 5| = 1
|-5| = 5
1+5=6
6. Order of Operations:
1. Parentheses or Brackets from the inside out.
2. Exponents and Roots
3. Multiplication and Division from left to right.
4. Addition and Subtraction from left to right.
7.
8.
9. Any number raised to a power of 0 is equal to 1.
Therefore,
.
A sample verification is shown below.
10. Plug the numbers into the equation and solve.
8r t + 38 =
=
=
=
8 × 23 + 38
8 × 8 + 38
64 + 38
102
11. Use the order of operations to simplify the expression.
(|-5 - 2| + 12)2 = (|-7| + 12)2
= (7 + 12)2
= (19)2
= 361
12.
13. If the bases are different but the exponents are the same, then divide the bases and keep the
exponent.
14. Absolute value is the magnitude of a number irrespective of its sign.
Evaluate the given expression piece-by-piece, using order of operations:
|n - 6| = |9 - 6| = |3| = 3
|5 - n| = |5 - 9| = |-4| = 4
3 - 4 = -1
15. Expand and simplify the expression.