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Name: _________________ Block: ____________ Date: ______________ Math 6: Study Guide 4 Properties, Exponents, Square Roots, Sequences, and Order of Operations Section 1: Properties Match the following properties with the examples. The answer choices can be used once, more than once, or not at all. Write your answer on the line with a CAPITAL letter. A Identity Property of Addition B Identity Property of Multiplication C Multiplicative Property of Zero D Inverse Property of Multiplication E Inverse Property of Addition 1.) ________ 3·0 = 0 2.) ________ 9x + 0 = 9x 3.) ________ 4.) ________ 5.) _______ 5 5 x1= 6 6 6.) ________ 4 5 x =1 5 4 7.) ________ 1=9x 45 1= 45 -7 + 7 = 0 1 9 Name: _________________ Block: ____________ Date: ______________ Fill in the blanks with the correct information to make the property true. 8.) 9.) 10.) 12 = 1 ________ 74 (____) = 0 2 X _____ = 1 7 11.) -17 + ____ = 0 12.) _____ + 0 = .34 Name: _________________ Block: ____________ Date: ______________ Section 2: Exponents Write each power (exponential form) as a product of factors. Then evaluate. 13. Exponential Form Product of Factors Evaluate 35 23 92 10 Write each product of factors in exponential form. Then evaluate. 14. Exponential Form Product of Factors 3×3×3 1×1×1×1 11 × 11 4×4×4×4×4 Evaluate Name: _________________ Block: ____________ Date: ______________ 15. Based on the pattern shown, what is the value of 55? 51 = 5 52 = 25 53 = 125 55 = __________ 16. Look at the given example: 33 = 32 = 31 = 30 = 3 × 3 × 3 = 27 3×3=9 3 =3 1 Now explain why 40 = 1 , using pictures, numbers or words. Name: _________________ Block: ____________ Date: ______________ Section 3: Perfect Squares and Square Roots 17. List the first 12 perfect squares in ascending order. ______ , _____ , _____ , _____ , _____ , _____ , ______ , ______ , _____ , _____ , _____ , _____ Evaluate: 18. √49 19. √121 20. √9 21. √81 22. What perfect square is between 121 and 169? Name: _________________ Block: ____________ Date: ______________ Section 4: Order of Operations (NO CALCULATOR) Apply order of operations to the following problems. Show each step clearly. 23. 53 – 32 × 5 24. (11 – 9)3 25. 36 ÷ 2 × 5 26. (12 + 49 – 52) × (7 + 0) Name: _________________ 27. Block: ____________ Date: ______________ (20 – 10 ÷10)2 – 82 + 5 28. Find the mistake in the given problem. Circle the mistake and explain what went wrong. (23 – 1 + 3) ÷ 2 + 32 (8 – 1 + 3) ÷ 2 + 32 (8 - 4) ÷ 2 + 32 (4) ÷ 2 + 32 4÷2+9 2+9 11 ___________________________________________________ ____________________________________________________