Pre-Test Name Date 1. The equation 3x 2 4 5 11 is solved as shown. Describe the inverse operations used in each step. 3x 2 4 5 11 Step 1: 3x 2 4 1 4 5 11 1 4 3x 5 15 Step 2: 3x 5 15 3 3 x 5 5 Solve each equation. 2. 2x 2 7 5 19 3. 2 x 2 4 5 1 1 3 4 4. Determine if there is one solution, no solution, or an infinite number of solutions. 2(3x 1 4) 2 (x 2 8) 5 3(4x 1 2) 2 7x 1 10 5. Monica bought 3 types of fruit for a fruit salad. She paid twice as much for blueberries as for oranges, and $1.50 less for strawberries than for blueberries. a. Define a variable and write algebraic expressions to represent the amount she spent on each type of fruit. Chapter 1 Assessments 1069
Pre-Test page 2 b. If the total cost was $12.25, how much did Monica spend on each type of fruit? Solve and check each equation. 6. 6(2x 2 1) 5 218 5 7. 22(5x 1 4) 5 23(3x 1 2) 2 7 3 3 1070 Chapter 1 Assessments
Post-Test Name Date 1. The equation 4x 1 5 5 17 is solved as shown. Describe the inverse operations used in each step. 4x 1 5 5 17 Step 1: 4x 1 5 2 5 5 17 2 5 4x 5 12 Step 2: 4x 5 12 4 4 x 5 3 Solve each equation. 2. 3x 2 6 5 15 3. 3 x 2 2 5 1 1 5 3 4. Determine if there is one solution, no solution, or an infinite number of solutions. 22(3x 1 4) 2 x 1 6 5 25x 2 2(x 1 1) 1 5 5. Anna bought 3 types of fruit for a fruit salad. She paid three times as much for blueberries as for pears and $2.50 less for strawberries than for blueberries. a. Define a variable and write algebraic expressions to represent the amount she spent on each type of fruit. Chapter 1 Assessments 1071
Post-Test page 2 b. If the total cost was $13.25, how much did Anna spend on each type of fruit? Solve and check each equation. 6. 7(3x 2 2) 5 214 4 7. 23(2x 1 1) 5 3(x 1 4) 1 3 4 4 1072 Chapter 1 Assessments
End of Chapter Test Name Date 1. A submarine is 575 feet below sea level. It is descending at a rate of 325 feet per minute. a. How many feet below sea level will the submarine be in 5 minutes? b. How many feet below sea level will the submarine be in 8 minutes? c. Define a variable for the amount of time the submarine descends. Then use the variable to write an expression that represents the number of feet below sea level the submarine is, given the number of minutes it has been descending. d. In how many minutes will the submarine be 2850 feet below sea level? Explain your reasoning. e. Write an equation that you can use to determine after how many minutes the submarine will be 1875 feet below sea level. Then, determine the value of the variable that will make the equation true. 2. Solve 5.6 5 211.2 2 2z. Chapter 1 Assessments 1073
End of Chapter Test page 2 3. Consider the equation 3(x 1 1) 1 x 1 2 5 2(2x 1 1) 1 3. a. Solve the equation. b. Is the resulting equation from part (a) always true, sometimes true, or never true? Explain your reasoning. c. Use a graphing calculator to graph the left side of the equation as y 1 and the right side of the equation as y 2. Sketch the graph on the coordinate grid shown. y 10 8 6 4 2 10 8 6 4 2 2 4 6 8 10 x 2 4 6 8 10 d. Interpret the graph in terms of a value of x for which these expressions are equal. 4. Determine if 3(x 1 1) 1 4 5 2(x 2 1) 1 x has no solution, one solution, or an infinite number of solutions. 1074 Chapter 1 Assessments
End of Chapter Test page 3 Name Date 5. A charity organization is collecting change to raise money. They have collected twice as many dimes as quarters, 22 more nickels than dimes, and 3 times as many pennies as nickels. a. Define a variable for the number of quarters collected. b. Use your defined variable to write algebraic expressions to represent the number of quarters, dimes, nickels, and pennies collected. c. If they have collected a total of 2134 coins, how much many of each coin have they collected? Check your work. Chapter 1 Assessments 1075
End of Chapter Test page 4 Solve each equation. Check your work. 6. 2 (4x 1 9) 5 18 5 7. 3 (x 1 8) 5 3 (x 1 5) 1 1 8 4 8 1076 Chapter 1 Assessments
Standardized Test Practice Name Date 1. Which is the solution to the equation 3 (3x 1 9) 5 6? 4 a. 2 1 3 b. 12 1 3 c. no solution 2. How many solutions does an equation have when you isolate the variable and it equals a constant? a. 0 b. 1 c. 2 3. Melissa bought 3 loaves of freshly baked bread at a specialty bread shop. She paid twice as much for the whole grain bread as for the French bread, and $2.50 more for the cinnamon raisin bread than for the whole grain bread. She spent a total of $11.25 for the 3 loaves. If f represents the price of a loaf of French bread, which equation describes this situation? a. f 1 f 1 (f 1 2.50) 5 11.25 b. f 1 2f 1 (f 1 2.50) 5 11.25 c. 2f 1 2.50 5 11.25 d. f 1 2f 1 (2f 1 2.5) 5 11.25 4. A neighborhood pool charges $22 for a pool membership plus an additional $2 for each visit to the pool. If Elliot visited the pool 16 times, how much did he pay to use the pool? a. $10.00 b. $54.00 c. $350.00 d. $352.00 5. Which is the solution to the equation 23(2x 1 5) 5 23? 5 a. 21 b. 0 c. no solution Chapter 1 Assessments 1077
Standardized Test Practice page 2 6. How many solutions does an equation have when the variable adds out and the final sentence is false? a. 0 b. 1 c. 2 d. infinite 7. A concert hall has three sections: the main floor, the balcony, and the gallery. For a recent concert, 1020 tickets were sold. There were twice as many balcony tickets sold as gallery tickets, and 225 more main floor tickets than balcony tickets. If g represents the number of gallery tickets sold, which expressions represents this situation? a. Gallery: g Balcony: g Main Floor: g 1 225 b. Gallery: g 1 g 1 225 Balcony: 2g Main Floor: g c. Gallery: g Balcony: g 1 225 Main Floor: 2g 1 225 d. Gallery: g Balcony: 2g Main Floor: 2g 1 225 8. The art club is raising money to go to an art museum. So far they have raised $50 by selling chalk drawings for $5 each. If they need to raise a total of $400, how many more drawings do they need to sell? a. 10 b. 70 c. 80 d. 90 1078 Chapter 1 Assessments
Standardized Test Practice page 3 Name Date 9. Which is the solution to the equation 4(x 2 8) 5 22(3x 1 1) 1 2 5 5? a. 12 17 b. 16 c. no solution 10. How many solutions does an equation have when the variable adds out and the final sentence is true? a. 0 b. 1 c. 2 d. infinite 11. A charity group is holding a formal dinner as a fundraiser. They are selling tickets for the dinner for $50 per person. So far they have raised $1000. How many more tickets would the charity group need to sell to raise a total of $5000? a. 20 b. 80 c. 100 d. 120 12. Ben is the youngest of four children. Bob is 5 years older than Ben, Bridget is twice as old as Bob, and Brian is 3 years younger than Bridget. If Ben is 2 years old, how old is each of his siblings? a. Bob: 7, Bridget: 4, Brian 1 b. Bob: 7, Bridget: 4, Brian 3 c. Bob: 7, Bridget: 14, Brian 3 d. Bob: 7, Bridget: 14, Brian 11 Chapter 1 Assessments 1079
Standardized Test Practice page 4 13. Heidi has $1500 in a savings account. She wants to go on a trip to Costa Rica that costs $2300. If she earns $8 per hour at a part-time job, how many hours does she need to work to have enough money for her trip? a. 100 b. 150 c. 187.5 d. 287.5 14. Which is the solution to the equation 1 (9x 1 2) 5 4 1 2 (6x 1 4)? 3 3 a. 26 b. 6 c. no solution 15. What will the display of a graphing calculator look like if you graph the left side of an equation with an infinite number of solutions as y 1 and the right side of the same equation as y 2? a. The graph of the lines will intersect at exactly 1 point. b. The graph of the lines will intersect in exactly 2 points. c. The graph of the lines will be the same. d. The graph of the lines will never intersect. 16. Javier wants to buy a new video game that costs $62.00. Last week he saved $20 for the game. If he earns $9 per hour at his part-time job, which equation can be used to find the number of hours, h, Javier needs to work to have enough money to buy the video game? a. 9h 5 62 b. 20 5 62 h c. 9h 2 20 5 62 d. 20 1 9h 5 62 1080 Chapter 1 Assessments
Standardized Test Practice page 5 Name Date 17. All eighth grade students can choose to take one of the following elective courses: art, chorus, band, or woodworking. There are 20 more students enrolled in chorus than art. Band has 3 4 the enrollment as chorus. Woodworking has 5 fewer students enrolled than band. Which expressions represent this situation? a. art: a, chorus: a 1 20, band: 3 (a 1 20), woodworking: 3 (a 1 20) 2 5 4 4 b. art: a, chorus: a 1 20, band: 3 a 1 20, woodworking: 3 a 1 15 4 4 c. art: a, chorus: a 1 20, band: 3 (a 1 20), woodworking: 3 a 1 15 4 4 d. art: a 1 20, chorus: a, band: 3 (a 1 20), woodworking: 3 (a 1 20) 2 5 4 4 18. Which is the solution of the equation 2(2x 2 1) 1 2x 5 6(x 2 1)? a. 1 2 b. 0 c. no solution 19. Which is the solution of the equation 1 (3x 2 1) 5 2x 2 2 4 3? a. 5 6 b. 1 3 c. no solution 20. Which is the solution of the equation 4(x 1 2) 1 x 1 1 5 2x 2 3 1 3(x 1 4)? a. 21 b. 1 c. no solution Chapter 1 Assessments 1081
1082 Chapter 1 Assessments