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Name: ______________________ Class: _________________ Date: _________ ID: A STUDY GUIDE : Chapter 3 : Algebraic Expressions (ACC) Multiple Choice Identify the choice that best completes the statement or answers the question. Simplify the expression. 4. Which equation is true for all numbers a? a. a + 0 = a b. a + 1 = 1 c. a × 0 = a d. a × 1 = 1 1. 8 + 4c + 8.5 − c a. 3c + 16.5 b. 19.5c c. 19.5 + c d. −3c + 16.5 5. Sheryl earns money for college by walking dogs and by mowing lawns. She earns $3 for each dog she walks and $25 for each lawn she mows. Which expression can be used to determine the amount of money, in dollars, Sheryl earns from walking w dogs and mowing m lawns? a. 3w + 25m b. 3w + 25 c. 28 ( w + m ) d. 75 ( w + m ) 2. The steps Irena took to simplify an expression are shown below. What should Irena change in order to simplify the expression correctly? a. b. c. d. Multiply 48 and 24 by 12. Add 12 to(48 + 24) Divide 48 and 24 by 12. Multiply 24 by (48 + 12) Factor the expression using the GCF. 6. 8y − 6x a. 2(4y − 3x) b. 2(4y − 6x) c. 2(4y − 6x) d. 2y(4 − 3x) 3. An ice cream shop charges $3.39 for a dish of ice cream. A customer can also order toppings for $0.59 each. If x represents the number of toppings, which expression can be used to determine the total charge, in dollars, for a dish of ice cream with x toppings? a. 339x + 0.59 b. 3.39 + 0.59x c. 3.98 + x d. 3.98x 7. 10x + 20 a. 10(x + 2) b. 10(x + 20) c. 10(x + 4) d. 10x(1 + 2) 1 Name: ______________________ ID: A Evaluate the expression when a = 14, b = 10, and c = 8. 12. A symbol that represents one or more numbers a. algebraic expression b. terms c. variable d. coefficient e. constant f. equivalent expressions 8. 4a + 3 a. 60 b. 56 c. 57 d. 59 13. The numerical factor of a term that contains a variable a. algebraic expression b. terms c. variable d. coefficient e. constant f. equivalent expressions Name the word that matches the definition given. 9. A term without a variable a. algebraic expression b. terms c. variable d. coefficient e. constant f. equivalent expressions 14. Expressions with the same value a. algebraic expression b. terms c. variable d. coefficient e. constant f. equivalent expressions 10. An expression that contains numbers, operations, and one or more symbols a. algebraic expression b. terms c. variable d. coefficient e. constant f. equivalent expressions 15. Terms of an algebraic expression that have the same variables raised to the same exponents a. algebraic expression b. like terms c. factoring an expression d. coefficient e. constant f. equivalent expressions 11. The parts of an algebraic expression a. algebraic expression b. terms c. variable d. coefficient e. constant f. equivalent expressions 2 Name: ______________________ ID: A Write the phrase as an expression. 19. The expression 16 + x + 22 represents the perimeter of a triangle. Simplify the expression. a. 38 b. x + 38 c. 54 d. 38x 16. 16 multiplied by the quotient of a number n and 19 ÁÊ n ˜ˆ˜ ˜˜ a. 16 ÁÁÁÁ ÁË 19 ˜˜¯ 16 b. + 19 n ÊÁ 16 ˆ˜ ˜˜ 19 c. ÁÁÁÁ ˜ ÁË n ˜˜¯ d. Use the Distributive Property to write and simplify an expression for the area of the rectangle. 16 19n 20. Write an expression for the problem. 17. You wash 30 cars in 3 hours. How many cars do you wash per hour? a. Cars washed per hour = 30 • 3 b. Cars washed per hour = 10 ÷ 3 c. Cars washed per hour = 30 ÷ 3 d. Cars washed per hour = 3 ÷ 30 18. A tortoise weighed 72 pounds two years ago. Today it weighs 89 pounds. How many pounds did the tortoise gain? a. Pounds gained = 72 + 89 b. Pounds gained = 89 – 72 c. Pounds gained = 72 • 89 d. Pounds gained = 2(89 – 72) a. b. c. d. x+3 3x + 9 3x + 3 3x + 6 a. b. c. d. 340 − 20x 340 − x 20 − 17x 340 − 17x 21. 3 Name: ______________________ ID: A Numeric Response Evaluate the expression when a = 4, b = 2, and c = 8. Evaluate the expression when x = 4 and y = 1. 1. a + 7 4. (x − 1)(y − 1) 2. bc 5. The running time (in minutes) of a TV episode is 30 – 0.5c where c is the number of commercials aired during the episode. What is the running time of an episode with 15 commercials? 3. A player’s score in the game of horseshoes is based on the number of “ringers” r and the numbers of horseshoes closest to the stake c that a player throws. Use the formula below to determine the score of a player who throws 4 ringers and 7 horseshoes closest to the stake. 3r + c Short Answer Identity the terms, coefficients, and constants of the expression. Complete the table. 5. 1. 5h + 9 x 1 3 5 2 2. a + 2 + 7b 4x – 1 Write the phrase as an expression. Write the expression using exponents. 3. r • r • r • r • r • r 6. the sum of 25 and 14 4. 4 • d • d • d 7. a number x multiplied by 3 8. 4 less than a number w 4 Name: ______________________ ID: A Tell which property the statement illustrates. 20. 6(8 – x) 9. 6 + (4 + x) = (6 + 4) + x Simplify the expression. 21. 2(6 + 3n) – 4 10. 5 • (3 • z) = (5 • 3) • z 22. 5a + 7 – 3a – 2 11. 0 + z = z 23. 6a + 2b + 3(a + b) 12. 3(x – 3) = 3x – 9 Factor the expression using the GCF. 13. 3 + z = z + 3 24. 24 – 9 14. 8(1) = 8 25. 54 – 30 15. (2 • 5)c = 2(5 • c) 26. 12y – 8 Simplify the expression. Explain each step. 27. 5x + 60y 16. 3.5 + (x + 2.7) Write the phrase as an expression. Then evaluate the expression when x = 3 and y = 6 17. 2 + (g + 5) 28. the product of 8 and a number x 18. 7(4p) 29. the quotient of a number y and 2 Use the Distributive Property to simplify the expression. 19. 7(x + 3) 5 Name: ______________________ ID: A 30. Complete the table. 31. To find the sales tax on an item, divide the price of the item by 20. a. Write an algebraic expression to find the sales tax on an item that costs d dollars. b. Find the sales tax on a television that costs $800. 6 ID: A STUDY GUIDE : Chapter 3 : Algebraic Expressions (ACC) Answer Section MULTIPLE CHOICE 1. ANS: NAT: MSC: 2. ANS: A PTS: 1 6.EE.2c | 6.EE.3 Knowledge A DIF: Level 1 REF: Section 3.4 KEY: simplify | expression Feedback A B C D Correct answer The student thinks that a number next to a quantity in parentheses represents the operation of addition. The student thinks that a number next to a quantity in parentheses represents the operation of division. The student thinks that the 24 should be distributed instead of the 12. PTS: NAT: MSC: 3. ANS: 1 DIF: Level 2 6.EE.3 | 6.EE.4 Comprehension B REF: Ch 3 Standards Assessment KEY: Distributive Property Feedback A B C D The student writes an expression that multiplies the cost of a dish of ice cream by the number of toppings and represents the cost per topping as a one-time charge. Correct answer The student adds the charges for a dish of ice cream and one topping and then adds the number of toppings to this sum. The student adds the charges for a dish of ice cream and one topping and then multiplies this sum by the number of toppings. PTS: 1 NAT: 6.EE.2a DIF: Level 2 REF: Ch 3 Standards Assessment KEY: algebraic expression MSC: Application 1 ID: A 4. ANS: A Feedback A B C D Correct answer. The student misapplies the multiplication property of one to the operation of addition, thinking that one added to any number equals one. The student misapplies the addition property of zero to the operation of multiplication, thinking that any number multiplied by zero equals the number itself. The student misapplies the multiplication property of one, thinking that any number multiplied by one equals one. PTS: NAT: KEY: MSC: 5. ANS: 1 DIF: Level 2 REF: Ch 3 Standards Assessment 6.EE.3 Multiplication Property of Zero | Multiplication Property of One | Addition Property of Zero Comprehension A Feedback A Correct answer B The student does not multiply the earnings per lawn by the number of lawns mowed, representing the earnings per lawn as a one-time charge. The student adds the earnings per dog and the earnings per lawn and then multiplies this sum by the sum of the number of dogs and the number of lawns. The student multiplies the earnings per dog by the earnings per lawn and then multiplies this product by the sum of the number of dogs and the number of lawns. C D 6. 7. 8. 9. 10. 11. 12. PTS: NAT: ANS: NAT: KEY: MSC: ANS: NAT: KEY: MSC: ANS: NAT: ANS: TOP: ANS: TOP: ANS: TOP: MSC: ANS: TOP: 1 DIF: Level 2 REF: Ch 3 Standards Assessment 6.EE.2a KEY: algebraic expression MSC: Application A PTS: 1 DIF: Level 1 REF: Extension 3.4 6.EE.3 | 6.NS.4 factor | greatest common factor | GCF | numerical expression | Distributive Property Knowledge A PTS: 1 DIF: Level 1 REF: Extension 3.4 6.EE.3 | 6.NS.4 factor | greatest common factor | GCF | numerical expression | Distributive Property Knowledge D PTS: 1 DIF: Level 1 REF: Section 3.1 6.EE.2c KEY: evaluate | expression | variable MSC: Knowledge E PTS: 1 DIF: Level 1 REF: Section 3.1 Vocabulary KEY: constant MSC: Knowledge A PTS: 1 DIF: Level 1 REF: Section 3.1 Vocabulary KEY: algebraic expression MSC: Knowledge B PTS: 1 DIF: Level 1 REF: Section 3.1 Vocabulary KEY: terms (of an algebraic expression) Knowledge C PTS: 1 DIF: Level 1 REF: Section 3.1 Vocabulary KEY: variable MSC: Knowledge 2 ID: A 13. ANS: TOP: 14. ANS: TOP: 15. ANS: TOP: 16. ANS: NAT: MSC: 17. ANS: NAT: 18. ANS: NAT: 19. ANS: NAT: MSC: 20. ANS: NAT: MSC: 21. ANS: NAT: MSC: D PTS: 1 DIF: Level 1 REF: Section 3.1 Vocabulary KEY: coefficient MSC: Knowledge F PTS: 1 DIF: Level 1 REF: Section 3.3 Vocabulary KEY: equivalent expressions MSC: Knowledge B PTS: 1 DIF: Level 1 REF: Section 3.4 Vocabulary KEY: like terms MSC: Knowledge A PTS: 1 DIF: Level 1 REF: Section 3.2 6.EE.2a | 6.EE.6 KEY: write an expression Knowledge C PTS: 1 DIF: Level 1 REF: Section 3.2 6.EE.2c KEY: write an expression MSC: Comprehension B PTS: 1 DIF: Level 1 REF: Section 3.2 6.EE.2c KEY: write an expression MSC: Comprehension B PTS: 1 DIF: Level 2 REF: Section 3.4 6.EE.2b | 6.EE.3 | 6.EE.4 KEY: addition | properties | simplify Application B PTS: 1 DIF: Level 2 REF: Section 3.4 6.EE.2b | 6.EE.3 | 6.EE.4 KEY: Distributive Property | write an expression | simplify | area Application D PTS: 1 DIF: Level 2 REF: Section 3.4 6.EE.2b | 6.EE.3 | 6.EE.4 KEY: Distributive Property | write an expression | simplify | area Application NUMERIC RESPONSE 1. ANS: 11 PTS: 1 DIF: Level 1 KEY: evaluate | algebraic expression 2. ANS: 16 REF: Ch 3 Quiz 1 MSC: Knowledge NAT: 6.EE.2c PTS: 1 DIF: Level 1 REF: Ch 3 Quiz 1 NAT: 6.EE.2c KEY: evaluate | algebraic expression MSC: Knowledge 3. ANS: 19 Common error: The student makes an order of operations error by first adding 4 and 7 and then multiplying 3 by this sum to get 3(4 + 7) = 33 PTS: 1 NAT: 6.EE.2 4. ANS: 20 DIF: Level 2 REF: Ch 3 Standards Assessment KEY: algebraic expression | evaluate MSC: Application PTS: 1 DIF: Level 1 KEY: evaluate | algebraic expression REF: Ch 3 Test B NAT: 6.EE.2c MSC: Knowledge 3 ID: A 5. ANS: 22.5 minutes PTS: 1 DIF: Level 2 KEY: algebraic expression | evaluate REF: Ch 3 Test A NAT: 6.EE.2a | 6.EE.6 MSC: Application SHORT ANSWER 1. ANS: terms: 5h, 9 coefficient: 5 constant: 9 PTS: 1 DIF: Level 1 REF: Ch 3 Quiz 1 NAT: 6.EE.2c KEY: algebraic expression | terms (of an algebraic expression) | coefficient | constant MSC: Knowledge 2. ANS: terms: a 2 , 2, 7b coefficients: 1, 7 constant: 2 PTS: 1 DIF: Level 1 REF: Ch 3 Quiz 1 NAT: 6.EE.2c KEY: algebraic expression | terms (of an algebraic expression) | coefficient | constant MSC: Knowledge 3. ANS: 6 r PTS: 1 DIF: Level 1 KEY: algebraic expression 4. ANS: 3 4d REF: Ch 3 Quiz 1 MSC: Knowledge NAT: 6.EE.2c PTS: 1 DIF: Level 1 KEY: algebraic expression 5. ANS: REF: Ch 3 Quiz 1 MSC: Knowledge NAT: 6.EE.2c x 1 3 5 4x – 1 3 11 19 PTS: 1 DIF: Level 2 KEY: algebraic expression | evaluate 6. ANS: 25 + 14 PTS: 1 DIF: Level 1 KEY: numerical expression REF: Ch 3 Quiz 1 NAT: 6.EE.2c MSC: Comprehension REF: Ch 3 Quiz 1 MSC: Knowledge 4 NAT: 6.EE.2a ID: A 7. ANS: x•3 PTS: 1 DIF: Level 1 KEY: algebraic expression 8. ANS: w– 4 REF: Ch 3 Quiz 1 MSC: Knowledge NAT: 6.EE.2a PTS: 1 DIF: Level 1 KEY: algebraic expression 9. ANS: Associative Property of Addition REF: Ch 3 Quiz 1 MSC: Knowledge NAT: 6.EE.2a PTS: 1 DIF: Level 1 REF: Ch 3 Quiz 2 KEY: Associative Properties of Addition and Multiplication 10. ANS: Associative Property of Multiplication NAT: 6.EE.3 MSC: Knowledge PTS: 1 DIF: Level 1 REF: Ch 3 Quiz 2 KEY: Associative Properties of Addition and Multiplication 11. ANS: Addition Property of Zero NAT: 6.EE.3 MSC: Knowledge PTS: 1 DIF: Level 1 KEY: Addition Property of Zero 12. ANS: Distributive Property REF: Ch 3 Test A NAT: 6.EE.3 MSC: Knowledge PTS: 1 DIF: Level 1 KEY: Distributive Property 13. ANS: Commutative Property of Addition REF: Ch 3 Test A NAT: 6.EE.3 MSC: Knowledge PTS: 1 DIF: Level 1 REF: Ch 3 Test B NAT: 6.EE.3 KEY: Commutative Properties of Addition and Multiplication MSC: Knowledge 14. ANS: Multiplication Property of One PTS: 1 DIF: Level 1 KEY: Multiplication Property of One 15. ANS: Associative Property of Multiplication REF: Ch 3 Test B NAT: 6.EE.3 MSC: Knowledge PTS: 1 DIF: Level 1 REF: Ch 3 Test B NAT: 6.EE.3 KEY: Associative Properties of Addition and Multiplication MSC: Knowledge 5 ID: A 16. ANS: 3.5 + (x + 2.7) = 3.5 + (2.7 + x) = (3.5 + 2.7) + x = 6.2 + x Commutative Property of Addition Associative Property of Addition Add 3.5 and 2.7. PTS: 1 DIF: Level 1 REF: Ch 3 Quiz 2 NAT: 6.EE.3 KEY: Associative Properties of Addition and Multiplication | Commutative Properties of Addition and Multiplication MSC: Knowledge 17. ANS: 2 + (g + 5) = 2 + (5 + g) Commutative Property of Addition = (2 + 5) + g Associative Property of Addition =7+g Add 2 and 5. PTS: 1 DIF: Level 1 REF: Ch 3 Test A NAT: 6.EE.3 KEY: Associative Properties of Addition and Multiplication | Commutative Properties of Addition and Multiplication MSC: Knowledge 18. ANS: 7(4p) = (7 • 4)p Associative Property of Multiplication = 28p Multiply 7 and 4. PTS: 1 DIF: Level 1 REF: Ch 3 Test A NAT: 6.EE.3 KEY: Associative Properties of Addition and Multiplication MSC: Knowledge 19. ANS: 7x + 21 PTS: 1 DIF: Level 1 KEY: Distributive Property 20. ANS: 48 – 6x REF: Ch 3 Quiz 2 MSC: Knowledge NAT: 6.EE.2b | 6.EE.3 PTS: 1 DIF: Level 1 KEY: Distributive Property 21. ANS: 8 + 6n REF: Ch 3 Quiz 2 MSC: Knowledge NAT: 6.EE.2b | 6.EE.3 PTS: 1 DIF: Level 1 KEY: Distributive Property | like terms 22. ANS: 2a + 5 REF: Ch 3 Quiz 2 MSC: Knowledge NAT: 6.EE.3 | 6.EE.4 PTS: 1 DIF: Level 1 KEY: Distributive Property | like terms 23. ANS: 9a – 5b REF: Ch 3 Quiz 2 MSC: Knowledge NAT: 6.EE.3 | 6.EE.4 PTS: 1 DIF: Level 1 KEY: like terms | algebraic expression REF: Ch 3 Test B NAT: 6.EE.3 | 6.EE.4 MSC: Knowledge 6 ID: A 24. ANS: 3(8 – 3) PTS: 1 DIF: Level 1 REF: Ch 3 Quiz 2 NAT: 6.EE.3 | 6.EE.4 | 6.NS.4 KEY: Distributive Property | greatest common factor | GCF | factor MSC: Knowledge 25. ANS: 6(9 – 5) PTS: 1 DIF: Level 1 REF: Ch 3 Test A NAT: 6.EE.3 | 6.EE.4 | 6.NS.4 KEY: Distributive Property | greatest common factor | GCF | factor MSC: Knowledge 26. ANS: 4(3y – 2) PTS: 1 DIF: Level 1 REF: Ch 3 Test A NAT: 6.EE.3 | 6.EE.4 | 6.NS.4 KEY: Distributive Property | greatest common factor | GCF | factor MSC: Knowledge 27. ANS: 5(x + 12y) PTS: 1 DIF: Level 1 REF: Ch 3 Test B NAT: 6.EE.3 | 6.EE.4 | 6.NS.4 KEY: Distributive Property | greatest common factor | GCF MSC: Knowledge 28. ANS: 8x; 24 PTS: 1 DIF: Level 1 KEY: algebraic expression | evaluate 29. ANS: y ;3 2 REF: Ch 3 Test A NAT: 6.EE.2a | 6.EE.6 MSC: Knowledge PTS: 1 DIF: Level 1 KEY: algebraic expression | evaluate 30. ANS: 2, 5, 8, 11, 14 REF: Ch 3 Test A NAT: 6.EE.2a | 6.EE.6 MSC: Knowledge PTS: 1 DIF: Level 2 KEY: algebraic expression | evaluate 31. ANS: d a. 20 b. $40 REF: Ch 3 Test A NAT: 6.EE.2c MSC: Comprehension PTS: 1 DIF: Level 2 KEY: algebraic expression | evaluate REF: Ch 3 Test A NAT: 6.EE.6 | 6.EE.2a MSC: Application 7