Unit 1 Test Review. Be able to justify each step in a two-step equation. (HS.A-REI.A.1)

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1 Name: Period: Date: Unit 1 Test Review Be able to justify each step in a two-step equation. (HS.A-REI.A.1) 1. Solve the equation x 3 = 4. Write a reason for each numbered 2 step. x 3 = 4 2 Given [1] 2 x 2 = 2 7 [2] x = 14 a. [1] Addition Property of Equality [2] Division Property of Equality b. [1] Subtraction Property of Equality [2] Division Property of Equality c. [1] Addition Property of Equality [2] Multiplication Property of Equality d. [1] Subtraction Property of Equality [2] Multiplication Property of Equality 2. Solve the equation 3x + 2 = 11. Write a reason for each numbered step. 3x + 2 = 11 Given 2 2 [1] 3x [2] 3 = 9 3 a. [1] Addition Property of Equality [2] Division Property of Equality b. [1] Subtraction Property of Equality [2] Division Property of Equality c. [1] Addition Property of Equality [2] Multiplication Property of Equality d. [1] Subtraction Property of Equality [2] Multiplication Property of Equality

2 3. A classmate has just solved an equation without checking the answer. Unfortunately, the solution has several mistakes. Without redoing the entire problem, go through each step and explain how the step was obtained. If the step is incorrect, explain the error and the procedure that should have been followed (6x + 18) = 3x x + 6 = 3x x + 6 = 3x x + 6 = 12 3x = 6 x = 1 2 Interpret algebraic expressions in terms of a situation. (HS.A-SSE.A.1) 10. How many terms are in the algebraic expression 3x 2y + 4xz 8? a) 4 b) 7 c) 8 d) What are the factors of the term 4x 2 yz 3? a) 4, x, x, y, z b) 4, x, y, z c) 4, x, x, y, y, y, z, z, z d) 4, x, x, y, z, z, z 12. What is the coefficient of y in the expression 3x 2y + 4xz 8? a) -8 b) -2 c) 3 d) 4 2

3 13. Write an algebraic expression that represents five less than four times a number. a) 4(x 5) b) 5 4x c) 4x 5 d) 5x Write an algebraic expression that represents the three times the sum of a number and 2. a) 3(x + 2) b) 3x + 2 c) 2(x + 3) d) 2x Laurie rents 14 movies a month from her local video store for m months in a row. Write an expression to show how many movies Laurie watched in all, then find the number of movies Laurie watched for 12 months. a) 14 m; 2 movies b) 14 + m; 26 movies c) 14m; 168 movies d) 14 ; 168 movies m 16. At a movie theatre tickets for a matinee show are $7.25 each. At the concession stand, drinks are $3.50 each, popcorn costs $5.50 each and candy costs $2.25 per box. If Sammie and Tim go to a matinee and purchases d drinks, p popcorns, and c boxes of candy, the amount of money m they spend can be represented by m = 3.5d + 5.5p c Which of the following are correct interpretations for parts of this equation? (there may be more than one answer) a) 3.5d represents the cost of the movie tickets b) 3.5d represents the cost of the popcorn c) 3.5d represents the cost of the drinks d) 3.5d represents the cost of the candy e) 5.5d represents the cost of the movie tickets f) 5.5d represents the cost of the popcorn g) 5.5d represents the cost of the drinks h) 5.5d represents the cost of the candy 3

4 At a supermarket, the apples cost $1.29 per pound, oranges cost $0.79 per pound and grapes cost $2.99 per pound. Let a be the pounds of apples purchased, r represent the pounds of oranges purchased and g be the pounds of grapes purchased. Match the algebraic expressions with their appropriate interpretations in this context. a) The cost of four people purchasing a pounds of apples. b) The cost of purchases g pounds of grapes and r pounds of oranges with a 25% off coupon. c) The cost per person if four people split a pounds of apples, g pounds of grapes and r pounds of oranges. d) The cost of purchasing a pounds of apples, g pounds of grapes and r pounds of oranges. e) The cost of purchasing g pounds of grapes and r pounds of oranges. f) The cost of purchasing a pounds of apples. g) The cost of purchasing a pounds of apples and r pounds of oranges g r (2.99g r) a a g r 4 Create and solve equations and inequalities in one variable. (HS.A-REI.B.3) (A) Write an equation or inequality to represent each situation. (B) Solve it. 21. Keith spent half of his allowance going to the movies. He washed the family car and earned 6 dollars. What is his weekly allowance if he ended with 16 dollars? 22. Oceanside Bike Rental Shop charges 16 dollars plus 8 dollars an hour for renting a bike. Time paid 88 dollars to rent a bike. How many hours did he pay to have the bike checked out? 4

5 23. Mike bought 8 new baseball trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 29 cards left. How many cards did Mike start with? 24. You want to rent a limousine for a trip to the city. The limo costs $700 for the night and $0.15 per mile. You have $750 to spend. Write an inequality that represen ts this scenario. How many miles can the limo travel on your budget? 25. Tom bought 8 candy bars and a soft drink. The soft drink cost 3 dollars. He spent a total of 19 dollars. How much did each candy bar cost? 26. Tim sold half of his comic books and then bought 7 more. He now has 16. How many did he begin with? 27. Sara goes to Fredonia University. She has $900 in her savings account. She needs to buy a small laptop computer before the next semester. The laptop costs $600. Every 2 weeks she withdraws $60 from her savings account for food. How many times can Sara withdraw money for food? Write an ineqaulity to represent this situation. 28. Skateland charges $50 flat fee for birthday party rental and $5.50 for each person. Joann has no more than $100 to spend on her birthday party. Write an inequality to represent this and determine how many people she can include. 5

6 Solve each equation. 29. n+4 5 = = 3 + r a = a (4p 1) 4(1 2p) = (x + 8) = 6(x 2) + 7x n 2 = 10 6

7 Solve and graph each inequality < r n v < 7 3m ( 6x 7) < n 20 or n x 2(11 + 3x) 42. 6x or 8x + 3 > (m 4) < 3( 7 + 5m) 6m 44. 7k + 1 < 62 or 5k 3 < 33 7

8 Solve a literal equation for a specified variable. (HS.A-REI.B.3) Solve for the indicated variable. 45. I = prt, for r 46. A = 2(L + W), for W 47. 2x 3y = 8, for y 48. ax + by = c, for y 49. V = LWH, for L 50. x+y = 5, for y x 4y = 20, for y 52. A = 1 h(b + c), for c C = 2πr, for r 54. A = r 2L, for L 8