Algebra Unit 2 Solving Equations and Inequalities
Name: ______Date: ______
Unit 2 Test Review
Find the solution of the linear system graphically. Write your solution in the blank provided.
______1. ______2.
Use substitution to solve the linear system. SHOW ALL WORK and write your solution in the space provided.
______3. ______4.
Use elimination to solve the linear system. SHOW ALL WORK and write your solution in the space provided.
______5. ______6.
Use any method to solve the linear system. SHOW ALL WORK and write your solution in the space provided.
______7.
Inequality Word Problems:
8. Bill wants to buy some CDs at the music store. Used ones sell for $4.99, and new ones sell for $13.99. He has $75 to spend that he got for his birthday.
a) Write a linear inequality (not a system) to represent the situation. ______
b) Can Bill by 4 used and 4 new CDs? Explain why or why not. ______
Systems of Linear Equations
9. A store sold 32 pairs of jeans for a total of $1050. Brand A sold for $30 per pair and Brand B sold for $35 per pair.
a) Write a system of equations to represent the situation. ______
b) How many of Brand A were sold? ______
work:
10. You are selling tickets for a basketball game. Student tickets cost $3 and general admission tickets cost $5. You sell 350 tickets and collect $1450.
a) Write a system of equations to represent the situation. ______
b) How many of each type of ticket did you sell? ______
work:
11. The football score for the home team’s last game was 27. They scored some field goals (worth 3 points each) and touchdowns (worth 7 points each – We are assuming they got all point after touchdowns and did not go for any two point conversions) . They scored 5 times and only had touchdowns or field goals.
a) Write a system of equations to represent the situation. ______
b) How many of each type did the team make? ______
work:
12. The sum of the weights of my two dogs is 160 pounds. Sarge weighs three times more than Jojo.
a) Write a system of equations to represent the situation. ______
b) How much does each dog weigh? ______
work:
Graph the systems of inequalities, and name one solution.
______13. ______14.
Systems of Linear Inequalities Word Problems:
15. Julia and Jackson are raising money for a Mother’s Day gift. They have a lemonade stand and are selling cups of lemonade for $2 each and cookies for $1.50 each. They must raise at least $150.
a) Write an inequality to express the income from the lemonade stand. ______
b) They expect to sell at least 3 dozen cookies. Write an inequality to represent this situation. ______
c) What is one solution for the system of inequalities? ______How do you know? ______
16. You are looking to buy a bouquet of flowers for your favorite math teacher. Lilies cost $3.00 each and roses cost $4.00 each. You have budgeted no more than $24 to spend on flowers. You want to buy at least 5 flowers.
a) Write a system of inequalities to represent the situation. ______
b) Graph a system of inequalities to illustrate how many of each type of flower you can purchase if you want to buy at least 5 flowers.
Equations and inequalities
17. Solve 3(2x + 5) = 8x – 5
18. Solve 4(2x – 4) = 5x + 3 + 3x
19. Solve, graph and write interval notation for the solution (Remember you will graph this on a number line NOT a coordinate plane)
20. Solve, graph and write interval notation for the solution (Remember you will graph this on a number line NOT a coordinate plane) 6 – 2x -12
Explain: (To get full points for explanation problems, you must have complete sentences with details.)
21. Does every system of equations have exactly one solution? ______Why or why not? ______
22. Does every system of inequalities have a range of solutions? ______Why or why not? ______
Sequences:
23. Write the recursive, explicit and function form of the sequence below. Then find the 100th term and the sum of the first 100 terms.
6, 10, 14, 18…… A1 = ______d= ______n = ______
Recursive: ______
Explicit: ______
Function: ______
A100: ______
S100: ______
Linear or not? ______
Type of sequence? ______
Functions, Domain and Range:
24. State the domain and range for the following graph. Use inequality and interval notation.
Domain inequality: ______
Domain Interval: ______
Range Inequality: ______
Range interval: ______
25. Given the function f(x) = 6x – 3, find f(-2). f(-2) = ______
If f(x) = 3, what is x? f(____) = 3
26. Solve for y: 2x – 5y = 30 ______
27. Solve for y: -6x + 8y = 22 ______
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