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Liberal Arts Math – Semester One Review A FLEX Produced Review

1. Simplify: 4(6$) ÷ 3 + 7

2. Simplify: 4[(−12 + 5) − 4/]

3. Simplify: 2[11 − (55 − 31) ÷ 4]

4. Evaluate 5𝑥$ + 16𝑦 for 𝑥 = 2 and 𝑦 = −3

5. Every weekend, Jaylon downloads interesting music on his phone from an app. He downloads 15 songs at $1.99 and 7 songs at $2.50. Write and simplify an expression to represent the cost of downloading the music.

6. A clock loses 2 minutes every 6 hours. At 3:00 pm, the clock is set to the correct time and allowed to run without interference.

a. What integer would describe the time loss after exactly 3 days?

b. What would the clock read at 3:00 pm three days later?

7. In golf, there is a number of strokes assigned to each hole, called the par for that hole. If you get the ball in the hole in fewer strokes than par, you are under par for that hole. If it takes you more strokes than par, you are over par for that whole. On the first 9 holes of gold, Avery had a par, 1 over par, 2 under par, 1 under par, 2 over par, 3 over par, 2 under par, 1 under par and another par. What is Avery’s overall score for the first 9 holes?

8. Simplify: 7(−5 + 𝑥)

9. Simplify: −3(3𝑥 + 2𝑦) − 5𝑦

10. Simplify:

14𝑚𝑛 + 6𝑚𝑛$ − 8𝑚𝑛 − 7𝑚$𝑛 + 5𝑚$𝑛

11. The profit Samantha’s company makes is given by the expression 0.1(1000 + 300𝑚) where m is the total number of sales. Rewrite the expression using the distributive property. What is the profit if her company sells 50 pieces of merchandise?

12. Simplify:

5𝑥 + 3𝑦 − 2𝑦 + 3𝑥𝑦 + 5𝑥𝑦 − 10𝑥


13. Solve for x: ;<== −9

14. Tianna mowed several lawns to earn money for a new phone. After she paid $17 for gas, she had $75 left over to pay towards the phone. Write and solve an equation to find how much money Tianna earned mowing lawns.

15. An ice cream sundae costs $1.75 plus an additional $0.35 for each topping. If the total cost is $2.80, how many toppings did the sundae have?

16. Solve for C: 6𝑐 − 1 − 4𝑐 = −49

17. Solve and graph:

−28 + 15 − 22𝑧 ≤ 31

18. When the sum of a number and 7 is multiplied by 4, the result is 16. What is the original number?

19. Solve for n: 3𝑛 + 2 = −2𝑛 − 8

20. Solve for b: 8𝑏 − 7 = 7𝑏 − 2

21. Solve and graph:

7(ℎ + 3) > 6(ℎ − 3)

22. Solve for x: 𝑚 = ;EFG


23. Edrik is looking into two different travel agencies to plan his vacation. ABC Travel has a plane ticket for $295 and a rental car for $39 per day. M&N Travel offers a plane ticket for $350 and a rental car for $33 per day. What is the minimum number of days that Edrik’s vacation should be for M&N Travel to have the better deal?

24. Solve for 𝑏H: 𝐴 =(KLEKM)

$ℎ

25. Concetta is going to have the exterior of her home painted. Colorful Painting charges $250 plus $14 per hour. Black and White Painting charges $22 per hour. How many hours would the job need to take for Colorful Painting to be the better deal?

26. Antonya is selling wind chimes from a booth at a flea market. She rents the space for $125 per day. The profit from each wind chime sold is $12. Her goal is to make $3500 in a work week. Which equation represents how many chimes she needs to sell in a week to meet her goal?

A. 12𝑐 − 625 = 3500 B. 5(12𝑐) − 125 = 3500 C. 5(12𝑐 + 125) = 3500 D. 5(12𝑐 − 125) = 3500

27. Solve and graph the compound inequality:

5 < 𝑘 − 2 < 11


6𝑏 − 1 > 41 or 2𝑏 + 1 < 11


3 < 2𝑝 − 3 ≤ 12


9 − 𝑐 < 2 or −3𝑐 > 15


31. Solve the absolute value equation:

5|𝑝 − 6| = 25

32. Solve the absolute value equation:

|𝑥 − 8| = −16

33. Solve and graph the absolute value inequality:

|4𝑎| ≥ 32

34. Solve and graph the absolute value inequality:

4|2𝑥| + 1 < 5

35. Which of the following represent a function? (Select all that apply)

a. {(−3, 2), (6, −1), (8, 2), (−3, 2), (0, 5)} b. {(0, 7), (−2,−1), (3, 0), (−1, 8), (−2, 3)} c.

d.

e.

f.

g.

x 4 4 4 4 4 y 1 7 9 0 3

h.

x 0 4 6 8 9 f(x) 0 5 9 2 8

−3

−1

0

2

−7

−5

−3

3

−4

−2

0

1

−5


36. What is the domain and range of the given set?

{(−3, 9), (2, 5), (−1,−1), (0, 5), (−6, 9)}

Domain: _________________________________

Range: ___________________________________

37. What is the domain and range of the graph?

Domain: _______________________________

Range: _________________________________

38. Find 𝑓(−2) if 𝑓(𝑥) = −5𝑥 + 10

39. Find 𝑓(4) if 𝑓(𝑥) = −2𝑥$ + 18

40. If 𝑓(𝑥) = 5𝑥 + 22, find the value for x when 𝑓(𝑥) = 7

41. Write the equation in slope-intercept form: 5𝑥 − 4𝑦 = −20

42. Write the equation in slope-intercept form: 𝑥 + 7𝑦 = 42

43. Find the x- and y-intercept of the linear function: 3𝑥 − 5𝑦 = −15 X-Intercept: __________ Y-Intercept: __________

44. Find the x- and y-intercept as coordinates of the linear function: 6𝑥 + 7𝑦 = −42 X-Intercept: __________ Y-Intercept: __________


45. Use the graph provided to graph the function: 𝑦 = − =

1𝑥 − 5

46. Use the graph provided to graph the function: 𝑦 = 6𝑥 + 1

47. Write the equation of the line that passes

through the point (−1,−4) and has a slope of 7.

48. Write the equation of the line that passes through the point (3, 3) and has a slope of 1

=.

49. Write the equation of the line that passes through the points (1, −1) and (0, 5).

50. Write the equation of the line that passes through the points (−4, 5) and (0, −1).

51. A tire has a pressure of 36 PSI in the morning. While driving, a nail punctures the tire and begins to lose 2 PSI per hour. Write an equation to represent the total PSI left in the tire, P after h hours.


52. Maigan spends her summer working at as a camp counselor. She makes $1800 and wants to use it to buy a new phone. The phone she wants will cost $50 per month. Write an equation that represents the relationship between total money left, T and months, m.

53. Colin joins a gym across the street from his house. The gym charges an initial fee of $15 for the key card plus $20 per month. Write a relationship between total cost, C and number of months, m.

54. Marijah wants to start saving money as a New Year’s resolution. She starts with $125 and decides to save $15 per week from her part-time job. Write an equation to represent the total money saved, T after w weeks.

55. Solve the system:

X 𝑦 = 𝑥 − 17𝑥 − 8𝑦 = 6


X2𝑥 − 2𝑦 = 16𝑦 = −2𝑥 + 10


X 𝑦 = −3𝑥 + 3−3𝑥 − 𝑦 = −6


X2𝑥 − 𝑦 = −19−2𝑥 − 5𝑦 = −11



X−5𝑥 − 2𝑦 = 14−5𝑥 − 2𝑦 = 14


X9𝑥 + 10𝑦 = 85𝑥 + 𝑦 = 9


X7𝑥 − 9𝑦 = 283𝑥 + 2𝑦 = 12

62. DeShawn and Shawna each improved their yards by planting hostas and ivy. They bought their supplies from the same store. DeShawn spent $144 on 12 hostas and 5 pots of ivy. Shawna spent $54 on 6 hostas and 1 pot of ivy. How much does one hosta cost?

63. A coin bank has 250 coins, dimes and quarters, worth $39.25. How many of each type of coin are there?

64. You are running a concession stand at a basketball game. You are selling hot dogs and sodas. Each hot dog costs $1.50 and each soda costs $0.50. At the end of the night, you made a total of $88.50. You sold a total of 93 hot dogs and sodas combined. How many sodas were sold?


65. Camila started a coin collection. Currently, she has a total of 23 nickels and dimes. There is a total amount of $1.95 in her coin collection. Which two of the following systems could be used to find how many nickels and dimes Camila has in her collection?

A. Y 𝑁 + 𝐷 = 1.955𝑁 + 10𝐷 = 23 B. Y 𝑁 + 𝐷 = 23

5𝑁 + 10𝐷 = 195

C. Y 𝑁 + 𝐷 = 230.05𝑁 + 0.10𝐷 = 1.95 D. Y 𝑁 + 𝐷 = 195

0.05𝑁 + 0.10𝐷 = 23

66. Which inequality represents the graph? A. 𝑦 > 𝑥 − 3

B. 𝑦 > 3 − 𝑥

C. 𝑦 < 𝑥 − 3

D. 𝑦 < 3 − 𝑥

67. Which graph represents the linear inequality?

𝑦 ≥ −2𝑥 + 3

A.

B.

C.

D.

68. Match the absolute value functions with its corresponding graph.

A. 𝑓(𝑥) = |𝑥 − 3| B. 𝑓(𝑥) = |𝑥 + 3| C. 𝑓(𝑥) = |𝑥| − 3 D. 𝑓(𝑥) = |𝑥| + 3

Graph I ____

Graph II ____

Graph III ____

Graph IV ____

69. Solve the system by graphing.

\𝑦 = 3𝑥 − 4

𝑦 = −12𝑥 + 3


70. Which graph represents the system of linear inequalities?

X 2𝑥 − 𝑦 ≤ 2𝑦 ≥ −2𝑥 + 2

A.

B.

C.

D.

71. Graph the linear inequality

]𝑦 <

32𝑥 + 1

𝑦 ≥12𝑥 − 1

72. The graph below shows the equation 𝑦 = 2𝑥 + 4.

How would the graph change if the 2 in the equation became a 3? A. The graph would become steeper. B. The graph would translate one unit up. C. The graph would translate on unit down. D. The graph would become less steep.

73. A lawn care service charges a $15 equipment

fee plus $10 per hour. For x number of hours, they charge 𝑦 = 10𝑥 + 15. Susan found a coupon for this company that gave her a discount off the equipment fee. How will this change the graph of the equation?

A. The line will be translated down. B. The line will be translated up. C. The line will be steeper. D. The line will be less steep.

74. Which of the following functions matches the graph?

A. 𝑦 = 3𝑥$

B. 𝑦 = ^H=_;

C. 𝑦 = 3; D. 𝑦 = 3𝑥


75. Determine if each function represents exponential growth or decay.

A. 𝑦 = 2(1.5); _________________

B. 𝑦 = ^H$_; __________________

C. 𝑦 = 4(0.3); __________________

D. 𝑦 = 4; __________________

76. Which of the following scenarios is the best fit for the graph?

A. The value of a $100 stock that decreases in

value by 10% each year. B. A bank account that starts with $100 and

doubles each month. C. The population of a small town that is

decreasing by 10% a year. D. A population of 100 deer that increases at a

rate of 10% each year.

77. Graph the parent function of a quadratic 𝑓(𝑥) = 𝑥$. Graph each transformation listed in the table below. Extra graphs provided on the next page if desired to graph separately.

A. 𝑓(𝑥) = 𝑥$ + 3

B. 𝑓(𝑥) = (𝑥 − 2)$

C. 𝑓(𝑥) = −(𝑥 + 2)$

D. 𝑓(𝑥) = (𝑥 + 4)$ − 1

E. 𝑓(𝑥) = H=(𝑥 − 4)$

F. 𝑓(𝑥) = −2𝑥$ − 3


A) 𝑓(𝑥) = 𝑥$ + 3

B) 𝑓(𝑥) = (𝑥 − 2)$

C) 𝑓(𝑥) = (𝑥 + 2)$

D) 𝑓(𝑥) = (𝑥 + 4)$ − 1

E) 𝑓(𝑥) = H=(𝑥 − 4)$

F) 𝑓(𝑥) = −2𝑥$ − 3

Semester 1 Reviewsickles.mysdhc.org/Resources/CourseReviews/LiberalArts...While driving, a nail...

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