Name: __________________________

Date: __________________________

Unit Test – Linear equations and Inequalities

Directions: Select the best answer for the following questions. (2 points each) 7L

____1. The steps for solving ____ are: 1) Read the problem and label variables, 2) make an

appropriate equation, 3) solve for needed variables, 4) plug in the known number(s), 5)

answer the question, and 6) check your answer.

a. A system of linear equation b. A word problem c. An absolute value equation d. None of the above

____2. The steps for solving (a) _____ are: 1) Simplify both sides using the distributive property and

combining like terms, 2) Get all the variable terms to one side and constants on the other

side of the equation, 4) divide by the coefficient of the variable, and 5) check your answer.

a. Single variable inequality

b. Single variable linear equation

c. Two variable linear equation

d. Both A and B

____3. The steps for solving (a) ______ are: 1) Put all the variable on the same side of the equation

and in the same order, 2) multiply one equation by a constant, so that one variable in each

equation has the same or opposite coefficient, 3) Subtract one equation from the other or

add the equations together (depending of coefficient), 4) Solve equation for one variable, 5)

use the value found in step 4, and plug in to one of the original equations, 6) solve for

remaining variable, and 7) plug both values in and check answer.

a. Two variable linear equation

b. Two variable system of inequalities

c. Two variable system of linear equations

d. None of the above

Directions: Match the answers from Column B to the appropriate linear equation or inequality from

Column A. For problems 4 – 7 pick choices A-F and for problems 8-11 pick from choices G-L. Not all of

the answers will be used. MAKE SURE YOU SHOW YOUR WORK! (One point each)1M

Column A Column B

__E_ 4.

A. B. C. D. E. F. 6 __C_ 5.

__D_ 6.

__B_ 7.

G. H. I. J. K. L.

__L_ 8.

__J_ 9.

__H_ 10.

__I_ 11.

Directions: Select the correct equation for each of the following linear story problems. (2 points each).

2M

____12. Kim and Cyndi are starting a business tutoring students in math. They rent an office for

$400 per month and charge $40 per hour per student. Which is the correct equation for the

profit?

a.

b.

c.

d.

____13. Glenna wants to rent a car for a trip to Key West for one week. Mr. Kotter’s Rentals rents a

Cadillac Escalade for $99 for one week plus $0.11 per mile over 100 miles. Which is the

correct equation for the cost?

a.

b.

c.

d.

____14. A gardening company placed an order with a nursery. It was for 13 bushes and 4 trees, and

totaled $487. Which is the correct equation if X = Bushes and Y = trees.

a.

b.

c.

d.

____15. The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day,

2200 people enter the fair and $5050 is collected. Which is the correct equation for the

total income of the fair if C = children and A = adults?

a.

b.

c.

d. None of the above

Directions: Read the following inequality story problems and answer the question that follow. Must show

your work! (2 points each) 3M

18. The sum of two consecutive even integers is between 74 and 178. a. What is the equation for the statement above? Label your variable(s).

X= the first number

X+2 = Next Even consecutive number

b. What are the possible values for the set of integers (solve the inequality)? Does this make sense?

19. Bob wants to buy a car in two years, the least expensive car that he wants to buy it %15,000. He currently has $3,000 saved up, how much will he have to save per month over the next two year?

a. Write an equation for the statement above. (Label you variable(s)).

b. Solve the equation to find how much money Bob has to save per month.

____16. Two consecutive numbers have a sum of 91. Which is the correct equation

a.

b.

c.

d.

____17. Two consecutive even numbers have a sum of 40

a.

b.

c.

d. None of the above

20. John works at a restaurant and will make at least $75 tonight. If he works for 6 hours and makes $31.50 in tips, what hourly wages could he receive?

a. What is the equation for the statement above? (label variables)

b. What are the possible salaries John can earn?

21. Your school is sponsoring a pancake dinner to raise money for a field trip. You estimate that 200 adults and 250 children will attend. Let x be the cost of an adult ticket and let y be the cost of a child ticket.

a. Write an equation to find out what price to make the adult and child ticket if we want to raise at least $3800.

b. Using the equation above, if the cost of an adult ticket is $10 what was the cost of child ticket? Does this make sense?

22. You are running a concession stand at the basketball game. You sell hot dogs for $1 and sodas for $0.50. At the end of the night, you estimate you made less than or equal to $200. Let x represent the number of hotdogs sold and y represent the number of sodas sold.

a. Write an equation that can be used to find out how many hot dogs and sodas were sold.

b. Using the equation above, if you sold 100 hotdogs how many sodas were sold? Does this

answer make sense?

23. John is an insurance salesman who works on commission. Each time he gets a new client, who purchases car insurance, he earns $100 in commission. Each time he gets a client who purchases homeowners insurance, he earns $50 in commission. Let x represent the number of clients who purchase car insurance and let y represent the number of clients who purchase homeowners insurance.

a. Write an equation that you could use to find out how many clients, for each type of insurance, John would sell to earn more than $3000 in commission.

b. Using the equation above, if he had 40 clients that purchased homeowners insurance, how many have car insurance? Does this answer make sense?

Directions: Fill in the following blanks with the correct answer for each of the system of linear equations. MUST SHOW WORK! (2 pts each) 4M

24. Solve the following system of linear equations:

X= _-1 _ and Y= _ 2 _

25. Solve the following system of linear equations:

X= _

_ and Y= _

_

26. Solve the following system of linear equations:

X= _ -5 _ and Y= __

____

27. Kristin spent $131 on shirts. Fancy shirts cost $28 and plain shirts cost $15. If she bought a total of 7 then how many of each kind did she buy?

Fancy shirts= __2__ and Plain shirts=__5__

28. All 231 students in the Math Club went on a field trip. Some students rode in vans which hold 7students each and some students rode in buses which hold 25 students each. How many of each type of vehicle did they use if there were 15 vehicles total?

Vans= __8__ and Buses=__7__

29. There are 13 animals in the barn. Some are chickens and some are pigs. There are 40 legs in all. How many of each animal are there?

Chickens = __6__ and Pigs =__7__

Directions: Examine the following system of inequality graphs and answer the questions that correspond

to them. Show work! (Points labeled on problem) 5M

Graph 1:

30. Explain what the dotted and solid lines mean, in relationship to the points on that line. (1pt)

The Dotted line means that the line is not included and

the solid like means it is included in the region.

31. Which point(s) listed below is part of the system in Graph 1? (1pt)

a. (0,1)

b. (0, -2)

c. (2,0)

d. (3.4)

32. What is the system of inequalities that correspond to Graph 1? (2pt)

Graph 2:

33. Which point(s) listed below is part of the system in Graph 2? (1pt)

a. (0,0)

b. (2,3)

c. (3,3)

d. Both B and C

34. What is the system of inequalities that correspond to Graph 2? (2pt)

Graph 3:

35. Write an inequality system for the shaded region in Graph 3. (3pts)

Graph #4:

36. What is the system of inequalities that correspond to Graph 4? (2 pt)

Directions: Label the following absolute value equation and inequality statements as correct or incorrect.

If answer is incorrect, solve the equation and give the correct answers. Show Work! (2 points each ).6M

37. _Incorrect _

38. _Correct _

39. _Correct _

40. _Incorrect _

41. _Incorrect _

42. _Correct _

Directions: Describe how to solve the following problem as if you were explaining it to a new student who has never seen this before (i.e. by reading your description they should be able to correctly answer the problem). One easy way to describe how to complete the problem is to actually compute the answer. You may use a picture or diagram to help you describe what you’re doing. Make sure you give your solution to the problem at the end. (12 points)7H

43.

Target Meets Expectations Need improvements

The student description is easy to follow and is presented in a logical manner.

The students know the steps on how to obtain the correct answer.

If the description was given to a student who has never seen this before they could follow the directions and get the correct answer.

The student finds the correct number for each variable.