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: Order of Operations Evaluating Algebraic Expressions Verbal Math Sentences (translating) Properties  Commutative  Associative  Distributive  Identity  Inverse  Zero Property Sequences (Arithmetic and Geometric) Vocabulary (study the below)  Expression– math sentence that does NOT contain an equals (=) symbol  Equation– math sentence that MUST contain an equals (=) symbol  Term-- parts of a math sentence separated by either plus signs or minus signs  Variable– letter used in a math sentence that represents a number  Coefficient– the number “with” a variable (3x – “3” is the coefficient)  Constant– a number that stands alone (2x + 5 – “5” is the constant) Name:____________________________________________________________________________________Date:_____/_____/__________ Study guide/ practice Unit 3 Test, “The Language of Algebra” On the back of this cover page is the Unit 3 “Quick Guide” – for your reference.

2. Unit 3, “The Language of Algebra” Quick Guide “Seven less than a number is five” x – 7 = 5 “Seven less a number is five” 7 – x = 5 AddSubtractMultiplyDivide SumDifferenceProductQuotient totalless less than twice (x2)split

3. 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) 3

4. 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 4

5. 5 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.

6. 6 Be able to identify the following properties! Study, study, study!! Circle ALL of the choices that represent the following property: 1.Commutative of Multiplication 2.Inverse of Addition 4x(-5) = -5(4x)x + y = y + x4(xy) = (4x)y 2 ½ = 1(-2)(x + 3) = (x + 3)(-2)5(0) = 0 5 + (-3 + 3) = 5 + 04(0) = 0 4x + (-4x) = 02 – 2 = 0

7. 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 7

8. Sequence Rule (Common Diff. or Ratio) What Comes next? Arithmetic or Geometric? Variable Expression 1) -5, -3, -1, 1, 3... 2) 1, 3, 9, 27... 3) 16, 8, 4, 2, 1, ½... 4) 2, -6, 18, -54... 5)10, 6, 2, -2, -6... 1) Which of the following sequences is a geometric sequence? A.1, -4, 16, -64... B.2, 4, 6, 8... C.2, -2, -6, -10... 2) What would be the 6 th term of the following arithmetic sequence? 4, 1, -2, -5... A.-8 B.-11 C.8 3)Which variable term describes what would come next in the following sequence? 6, 2, -2, -6... A.x + 4 B.4x C.x – 4 4)What is the common difference in the following arithmetic sequence? 1, -4, -9, -14... A.-5 B.5 C. 1 / 5 5)What is the common ratio in the following geometric sequence? 50, 10, 2, 2 / 5... A. 5 B.-5 C. 1 / 5 Fill-in-the-Blanks: An arithmetic sequence is a sequence where the next term is found by either adding or __________________________________ by the SAME #, and the “rule” for determining what comes next is described as the common _______________________________. A geometric sequence is a sequence where the next term is found by either multiplying or __________________________________ by the SAME #, and the “rule” for determining what comes next is described as the common _______________________________. Multiple Choice:

9. 1.Which of the following is an algebraic expression? A. 8 + 2 B. -8 + 2 C. -8x + 2 D. 8 + -2 2.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 3.If x = -3, what is x² + x³A. -36 B. -18 C. 18 D. 36 4.Which property does the following equation represent? A. Commutative Property of Multiplication B. Commutative Property of Addition C. Associative Property of Multiplication D. Distributive Property 5.Which choice 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

10. 6.Bob was given: -45 + 17 + 45 + 3 Bob re-wrote the expression as: (-45 + 45) + (17 + 3) When evaluating, which properties will Bob use? A.the associative property and the distributive property B.the commutative, associative, and inverse properties C.the commutative, associative, inverse, and identity properties D. the commutative and zero properties 7. 8.Which property is shown in the following number sentence? ( ½ xy + 8 ) + 0 = ( ½ xy + 8) A. multiplicative inverse property B. additive identity property C. multiplicative identity property D. additive inverse property 9.Kate evaluated -3 2 + 11, and got 20 as her answer. Is this correct? Why or why not? A.Yes, because she correctly followed the order of operations, and her calculations are correct. B.No, because -3 2 is -9, therefore, “2” should be the correct answer. C.Yes because Kate always gets the right answer. D.No, because she did not follow the order of operations. 10.Which variable expression describes the following sequence? 48, 24, 12, 6, 3...