Review for Test #2

Name: ______Date: ______Mr. Art Period: ______Review for Test #2

Properties, Order of Operations, Laws of Exponents, Scientific Notation

Part I: Match each property with an example that represents it. a. Commutative property of addition 1. ______¼ ∙ 4 = 1 b. Commutative property of multiplication 2. ______(x + 2y) + z = x + (2y + z) c. Associative property of addition 3. ______15 + 0 = 15 d. Associative property of multiplication 4. ______x ∙ y = y ∙ x e. Distributive property 5. ______2x + 3y = 3y + 2x f. Addition property of zero (Additive Identity) 6. ______(2 ∙ a) ∙ b = 2 ∙ (a ∙ b) g. Multiplication property of zero 7. ______x ∙1 = x h. Symmetric property 8. ______3(x +4y) = 3x + 12y i. Multiplication property of one 9. ______5+2 = 0 and 0 = 5+2 (Multiplicative identity) 10. ______9 ∙ 0 = 0 j. Multiplicative Inverse

11. Two students simplified the following expressions. Which student is correct and why? Alexa Joe

15 - 4∙ 3 + 2

15 – 12 + 2 15 – 12 + 2 3 + 2 15 - 14 5 1

1 12. Kevin uses the below steps to simplify the expression.

 Step 1:

 Step 2:

 Step 3:

 Step 4: 75 – 30

 Step 5: 45

The teacher finds an error in Kevin’s work. Which step contains the error? Explain using complete sentences. ______13. Simplify each expression. Leave all answers in exponential form. Where necessary, write all answers that contain negative exponents to an equivalent answer with a positive exponent. a. 158 152 ______f. (43)2 ______

b. x12 ∙ x 3 ______g. 23 ∙ 34 ______

c. 102 105 ______h. (64)3 ______

d. 2 5 ______i. ______

e. ______j. ______

2 (Show all work for questions 14 - 26) 14. Simplify: │7 - 12│

15. Simplify: -│5│ - │-3│

16. Find the value of 4-2

17. Find the value of 2-3

18. Multiply: (6 x 104) (2 x 102)

19. Divide:

20. Multiply: (5.9 x 104) (3.7 x 105)

21. Divide:

3 22. What is the additive inverse of -4? ______

23. What is the multiplicative inverse of -4? ______

24. Is ab = ba an example of the commutative property? Explain your answer. ______

25. Write in scientific notation: a. 198,000,000 ______b. 56,200 ______c. 0.006 ______d. 0.0008722 ______e. 8,040,000,000,000 ______f. 0.0000000203 ______

26. Write in standard decimal form. a. 3.76 x 10 5 ______b. 7.0 x 106 ______c. 4.5 x 10 -3 ______d. 6.88 x 10-5 ______

4 Multiple Choice Practice Section: Mixed Review

1. What is the value of the following 2. Which of the following represents expression: 8.32 x106? (12 + 4) ∙ 2 – 3 ∙ 4 a) 12 c) 20 a) 832,000 c) 83,200,000 b) 16 d) 30 b) 8,320,000 d) 832,000,000

4. There are about 9 million people living in 3. Simplify ? NYS. Write this number in scientific notation?

-6 5 40 13 a) 1.9 x 10 c)19 x 10 a) 3 c) 3 7 6 b) 33 d) 312 b) 1.9 x 10 d)1.9 x 10 5. Baby kangaroos are very tiny when they are 6. Which is greatest? born. One born at the Prospect Park Zoo in Brooklyn weighted 3.5 x 10-2 ounces. How do you write this in standard form? a) 0.0035 c) 350 a) 3.3 x 103 c)3.3 x 105 b) 0.035 d) 3,500 b) 3.3 x 104 d)3.3 x 10

7. What is the value of the following 8. Which is an example of the distributive expression: property? 22 + 21 – 7 – (3 ∙ 4) a) 2(cd) = (2cd) b) 2(c + d) = 2c + 2d a) 24 c) 37 c) 2(cd) = (2c)d b) 13 d) 88 d) 2( c+d) = (2 + c) x (2+d)

9. Which property is illustrated by the 10. Which one of the following statements equation: illustrates the associative property of addition? -8 + 0 = -8?

a) 5(20 + 3) = 5(20) = 5(3) b) 5(20 + 3) = (20 + 3)(5) a) Additive inverse c) Additive identity c) 5 + (20 + 3) = (5 + 20) + 3 b) Distributive d) Symmetric property d) 5 + 0 = 5

5 11. Which expression is equivalent to x-6 ? 12. The expression 45 ∙ 4∙ 43 is equivalent to

9 7 a) c) -6x a) 4 c) 4 b) 649 d)647 b) x6 d) 0

13. What is the first step in simplifying the 14. Which number is rational? expression (3 ∙ 4 + 7 – 4)2? a) Square 4 c) Subtract 4 from 7 a)П c) 87 b) Add 4 and 7 d) Multiply 3 by 4 b) d)

15. Which of the following is a perfect square? 16. The expression -│7 - 12│is equivalent to a) 44 c) 121 a) -5 c) 19 b) 87 d) 180 b) 5 d) -19

17. Simplify 18. What is the value of ?

6 5 a) 12 c) 1 a) 4 c) 1 5 7 b) 12 d) 12 b) 0 d) 2