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Note: Many problems in this packet will be completed together in class during review time. Students are not expected to complete every single problem in the packet. They should complete several problems from each page-- in addition to studying the notes and past quizzes– in order to be fully prepared for test. TOPICS COVERED ON “The language of algebra” TEST : Order of Operations Evaluating Algebraic Expressions (substituting numbers for variables) Translating Algebraic Sentences Properties (Commutative, Associative, Distributive, Identity, Inverse, and Zero Properties) Vocabulary: Algebraic Expression v. Numeric Expression Constant Coefficient Variable NOTES SPACE/HELPFUL TIPS (to be filled out in class): Name: Date:

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Evaluate – (1) Parentheses, (2) Exponents, (3) Multiply or Divide, & (4) Add or Subtract: 1. 3(12 − 6) −82. 12 + 4(5 − 8)² 3. 12 + 4(5 − 8²)4. 1 + (- 2) − 2 ⋅ 27 ÷ 3 2 5. -4 2 + 14(-2)6. (-2 3 −2) 2 + 23 7. 3 + 8 – (6 ÷ 3 + 4 2 )8. -2 + 2(-8) 3(3)-3 (left to right) 2

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Evaluate the following by substituting the given #’s for each variable: 1. xy – y -- when x = -3 and y = -1 2. 4mp -- when m = 4 and p = -6 3. (x + y) 2 -- when x = -4 and y = 6 4. (x + y 2 ) -- when x = -4 and y = 6 5. -3(x + 4y) + 2 -- when x = -7 and y = -2 6. x³ + (y – x ÷ 2) -- when x = 2 and y = 7 7. 5(n + m 2 ) -- when m = 6 and n = 4 8. 72 ÷ y³ -- when x = 3 and y = -2 3

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Applying Properties: 1)Apply the Commutative Property in order to evaluate the following expression (give final answer as well): 3 + 13 + 10 = ______________________________ 2) Apply the Associative Property in order to evaluate the following expression (give final answer as well): (9 + 12) + 8 = ______________________________ 3) Apply the Distributive Property in order to evaluate the following expression (give final answer as well): 3(4 + 20) = ________________________________ 4) Apply the Inverse Property in order to evaluate the following expression (give final answer as well): 75( 2 / 5 ● 5 / 2 ) = _____________________________ Name the property represented by the following equations: 5)-35 + 35 = 0 ___________________________________________________________________________ 6)(½ xyz)(1) = ½ xyz____________________________________________________________________ 7)(¾ y)(0) = 0____________________________________________________________________________ 8)-50 + 0 = -50___________________________________________________________________________ Identify the properties used for EACH STEP in order to simplify the following expressions: 9) 50 + 100 + (-50) Step 1 = 50 + (-50) + 100_____________________________ Property of Addition Step 2 = [ 50 + (-50) ] + 100_____________________________ Property of Addition Step 3 = 0 + 100_____________________________ Property of Addition Step 4 = 100 _____________________________ Property of Addition 10) 4(6 + 7) + 6 Step 1 = 24 + 28 + 6 _____________________________ Property Step 2 = 24 + 6 + 28 _____________________________ Property of Addition Step 3 = (24 + 6) + 28 _____________________________ Property of Addition Step 4 = 30 + 28 Step 5 = 58 5

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1)________Which of the following is an algebraic expression? A. 8 + 2 B. -8 + 2 C. -8x + 2 D. 8 + -2 2) _________ Which of the following correctly lists the coefficients of the following expression? -9x + 6y – z + 4 A. x, y, and z B. -9, 6, and 1 C. -9 and 6 D. -9, 6, and -1 3) ________ For the following expression, which operation should be performed first? (10 – 8 + 3²) ÷ 9 + 3 8² A. 10 - 8 B. 3² C. 8 + 3 D. 8² 4)________ If x = -3, what is x² + x³ A. -36 B. -18 C. 18 D. 36 5)________Which property does the following equation represent? (2x)y = 2(xy) A. Commutative Property of Multiplication B. Inverse Property of Multiplication C. Associative Property of Multiplication D. Distributive Property 6)________For the following expression, which operation should be performed first? (5 – 2 + 4 )² A. 2 + 4 B. 5 – 2 C. 4² D. 2 + 4²

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