1. 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. Equation Constant Coefficient Variable NOTES SPACE/HELPFUL TIPS (to be filled out in class): Name:__________________________________________________________________________________Date: _____/_____/__________

2. 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

3. Evaluate the following by substituting the given #’s for each variable: 1. xy – y -- when x = -3 and y = -1 2. 4(m)(p) 2 -- when m = 4 and p = -3 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. x 2 + (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

4. 4 Translate the following verbal expressions/ sentences into algebraic sentences. 1) Forty less than a number is five. 2) Forty less a number is five. 3) the product of triple a number and eight 4) the difference of twice a number and two 5) The total of double a number and six is fifty. 6) the quotient of a number and ten 7) twice the sum of a number and four 8) Triple the difference of a number and six is twelve. 9) Five less than a number divided by two is four. 10) the quotient of a number squared and two 11) the product of nine and a number cubed 12) Double the sum of a number squared and two is thirty-six.

5. 5 Be able to identify the following properties! Study, study, study!!

6. 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 6

7. 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