Name: Date: Period: Algebra 2 Unit 3 Test Review #1
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1 KEY Name: Date: Period: Algebra 2 Unit 3 Test Review #1 You are required to show all work in order to receive credit. 1. Graph the sstem of inequalities. 3x < 2x Using the sstem of inequalities graphed in problem #1, determine if the following points are solutions: a. (0,-2) b. (5, 3) c. (-3,1) NO YES NO 3. The graph of the sstem of two linear inequalities in two variables is shown below. Which sstem of inequalities can be used to represent the problem? A B 2x 3 > 6 2x + 2 2x 3 < 6 2x > x 2 3 2x + 2 C 3x 2 < 6 x D 2x 3 > 3 2x + 2
2 4. Which graph correctl shows the solution of the following sstem of inequalities? 2210 < x (A) 1 x (B) (C) (D) 5. Put the sstem in standard form and then write a matrix that could be used to solve the sstem. Solve. x + = 6-z 2x -3z = x +2-8 = ( 9, 5, 2)
3 6. Miss Croft made snack bags for the picnic that contain three tpes of snacks: packages of crackers, packages of cookies, and cand bars. A snack bag containing 6 of each tpe of snack costs $ A snack bag containing 8 packages of crackers, 5 packages of cookies, and 10 cand bars costs $ A snack bag containing 5 packages of crackers, 4 packages of cookies, and 7 cand bars costs $ If x represents packages of crackers, represents packages of cookies, and z represents cand bars, construct a sstem of equations that can be used to determine the price of each snack. 7. Using the sstem ou constructed in problem #7, solve for the price of each snack. $0.75 $ Package of Crackers: 1 Cand Bar: $ Package of Cookies: 8. Donald wants to produce two tpes of doughnuts: original glaze and chocolate delight. Donald onl has enough supplies to make no more than 12 doughnuts total. Donald sells his original glazed doughnuts for $4 and his chocolate delight doughnuts for $5. Donald wants to make at least $50 selling his donuts. Write a sstem on inequalities to represent this situation. g + c 12 4g + 5c 50
4 9. Solve the 3x3 sstem of equations b using Gaussian Elimination. x + + z = 3 x z = 5 2x z = R2 + R1 R2 (1, 1, 1) Solution: R1 + R3 R R2 + R3 R Is (1, -1, 2) a solution to x + + z = 2 3x + 2 z = 1 3x = 4? YES
5 11. Graph the sstem of inequalities. 2x x > 1 x + 2 < 3x Write the following sstem of equations as a matrix. Find the solution. x + + z = 0 2x + 2z = 8 x + 4z = 10 ( 2, 0, 2) 13. What is the next step in solving the sstem b Gaussian elimination? R + ( 2) R 1 2
6 14. What is the value of z in the following sstem of equations? x z =7 x =2 + 4z 2x + 4z = -3 z = Economics At a stock exchange there were a total of 10,000 shares sold in one da. Stock A had four times as man shares as Stock B. The number of shares sold for Stock C was equal to the sum of the numbers of shares sold for Stock A and Stock B. How man shares of each stock were sold? 16. Using the sstem ou constructed in problem #15, solve for the numbers of each stock sold. 17. Solve the following sstem of equations using an method (remember to show our work): 3x z = 1 x + + 2z = 8 6x 2 2z = 5 No Solution
7 18. At Fink Feed Store, Gerb purchased 7 pounds of cracked corn, 3 pounds of sunflower seed, and 8 pounds of mixed bird seed for $ Michael purchased 5 pounds of cracked corn, 4 pounds of sunflower seed, and 10 pounds of mixed bird seed for $ Jaleen purchased 4 pounds of sunflower seed and 12 pounds of mixed bird seed for $ If c represents cracked corn, s represents sunflower seeds, and b represents bird seed, write a sstems of equations that can be used to determine the price per pound of cracked corn, sunflower seed, and bird seed? 7c + 3s + 8b = 31 5c + 4s + 10b = s + 12b = Sand makes $2 profit on ever cup of lemonade that she sells and $1 on ever cupcake that she sells. Sand wants to sell at least 10 items per da. She wants to earn at least $25 per da. Write a sstem of inequalities to show and describe all the possible combinations of lemonade and cupcakes that Sand needs to sell to meet her goals. L + C 10 2L + C To help passengers stranded b bad weather one winter, an airport bought cots, tables, and chairs. In November the bought 10 cots, 40 chairs, and 10 tables for a cost of $1950. In December the bought 20 cots and 20 chairs for $1800. In Januar the bought 10 cots, 20 chairs, and 5 tables for $1350. What is the cost of a cot, a chair, and a table? Variables: C # of Cots H # of Chairs T # of Tables = = = Sstem: Work: $75 $15 $60 Solution: One cot costs One chair costs One table costs
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