Name: __________________________________ Per: ___ My Exam is: _____________

Semester Exam Review 2017-2018

Topic 1: Writing and Solving Equations and Inequalities

In #1 – 3, solve each equation. Use inverse operations.

1. 8𝑥 − 21 − 5𝑥 = −15 2. 3𝑥 − 10 = 2(4𝑥 − 5) 3. −2(𝑥 + 2) = −2𝑥 + 1

4. The rectangle and square have equivalent perimeters. Which equation would you use to find the perimeter of each figure?

A 5𝑥 − 1 = 3𝑥 + 8

B 8𝑥 = 7

C 2(2𝑥 − 1) + 2(3𝑥) = 3𝑥 + 8

D 2(2𝑥 − 1) + 2(3𝑥) = 4(3𝑥 + 8)

In #5 – 7, solve and graph each inequality. If you multiply or divide by a negative number, flip the symbol!!!

5. 20 + 10𝑥 − 8 < 2 6. −3(2 − 𝑥) ≤ 6(𝑥 − 1) 7. 2(𝑥 − 2) ≤ −2(1 − 𝑥)

3𝑥 + 8 2𝑥 − 1

3𝑥

8. Canoe Rentals Inc. rents canoes for $8 plus $3 per hour or any part of an hour.

Write and solve an inequality to find how many hours you can rent a canoe if you want to spend at most $25?

F 3𝑥 + 8 > 25 5 hours H 8𝑥 + 3 ≤ 25 2 hours

G 3𝑥 + 8 ≤ 25 6 hours J 8 + 3𝑥 ≤ 25 5 hours

In #9 and 10, solve and graph each compound inequality. There are two types!!!

“OR” has a graph that goes in opposite directions, and “AND” has a graph that meets in the middle.

9. 1 < 2𝑥 + 7 ≤ 9 10. 4 − 15𝑥 ≥ 4 or 12𝑥 > 36

In #11 and 12, write the compound inequality represented by each graph. 11. 12.

________________________ _______________________

Topic 2: Functions

13. Circle all the relations that are functions. There could be more than one answer!!!

A { (1,1), (1,2), (1,3) } C { (2,0), (3, 5), (4, 10) }

B { (-3,-3), (-1, -3), (1,-3) } D { (5,1), (-4, 5), (5,2) }

14. For which value of 𝑥 is the relation not a function? {(0, 1), (x, 0), (3, 5), (2, 6)}

F 0 H 5

G 1 J 6

In #15 – 17, determine whether or not the relation is a function. Each x can be paired with only one y.

15. 16. 17.

In #18 and 19, find the value of each function.

18. For 𝑓(𝑥) = −3𝑥 + 2, find 𝑓(4). 19. For 𝑔(𝑥) = −𝑥 − 4, find the value of

𝑔(𝑥) when 𝑥 = −5.

Use the graph of function ℎ for #20 – 24.

20. Find ℎ(−1). 21. Find ℎ(3).

22. Find ℎ(0).

23. What is the domain? 24. What is the range?

A {𝑥|−8, −6.5, −2, 3} F {𝑦|−7 ≤ 𝑦 ≤ 3} B {𝑥|−8 ≤ 𝑥 ≤ 3} G {𝑥|−8 ≤ 𝑥 ≤ 3} C {𝑥|−5 ≤ 𝑥 ≤ 3} H {𝑦|−7, −5, 4, 5} D (𝑦|−7 ≤ 𝑦 ≤ 5) J (𝑦|−7 ≤ 𝑦 ≤ 5)

25. What is the range of the function 𝑓(𝑥) = −1

2𝑥 + 6 when the domain is {−8, 0, 2}?

A {10, 6, 5.5} C {2, 6, 7}

B {10, 6, 5} D {4, 0, −1}

Use the following scenario for #26 – 28. Sketch a picture!!!

A swimming pool has a volume of 8,500 gallons. It is being drained at a rate of 500 gallons

per hour.

26. Which function represents the situation?

F 𝑓(𝑥) = 8,500 + 500𝑥 H 𝑓(𝑥) = 8,500 − 500𝑥

G 8,500 = −500𝑥 J 𝑓(𝑥) = 8,500𝑥 − 500

27. What is the greatest value in the range for this situation?

A 8,500 C 500 B 17 D cannot be determined

28. What is the greatest value in the domain for this situation?

F 8,500 H 500

G 17 J cannot be determined

29. The total cost of renting a pontoon boat is a function of the number of hours the boat is rented. A boat rental store charges a $125 cleaning/restock fee plus $65

per half hour up to a maximum of 6 hours.

Which of the following statements is not correct?

A There are a maximum of 12-half-hour intervals within the 6-hour time period.

B The maximum value in the range is 905.

C The total cost for renting the boat for 5 hours is $650. D The total cost for renting the boat for 4 hours is $645.

Topic 3: Linear Functions 𝑚 =𝑦2−𝑦1

𝑥2−𝑥1

In #30 and 31, use the slope formula to find the slope of the line that passes through

the given points. 30. (-2,9) and (10,1) 31. (1,5) and (1,-3)

32. Which table shows the same rate of change of 𝑦 with respect to 𝑥 as 𝑦 = −2 +3

4𝑥?

In #33 – 35, identify the slope, and write the equation of the graphed line in slope-

intercept form.

33. 34. 35. slope: ____________________ slope: ____________________ slope: ___________________

equation: ________________ equation: ________________ equation: ________________

36. Which of the following is a correct description of the graphed line?

I The line has a positive slope. II The line represents the linear parent function.

III The line represents a direct variation.

IV The equation of the line is 𝑦 = 𝑥 + 1.

x

y

x

y

x

y

x

y

37. Use the graph to identify each. 38. Find the 𝑥- and 𝑦-intercepts of the

line −6𝑥 + 4𝑦 = 12. Then graph

using only the intercepts.

a) x-intercept: b) y-intercept:

a) slope: __________

b) 𝑦-intercept: __________

c) 𝑥-intercept: __________

d) equation: ____________

39. Find the 𝑦-intercept of the line 40. Find the 𝑥-intercept of the line

whose equation is 3𝑥 − 5𝑦 = −15. whose equation is 4𝑥 + 𝑦 = 4.

Write the answer as an ordered pair. Write the answer as an ordered pair.

41. Suppose 𝑦 is directly proportional to 𝑥, and 𝑦 = −8 when 𝑥 = 20. What is the direct

variation equation that relates 𝑥 and 𝑦?

F 𝑦 = 20𝑥 H −8 = 20𝑥

G 𝑦 = −2

5𝑥 J 𝑦 = −

5

2𝑥

42. The number of miles driven 𝑚 varies directly with the number of gallons of gas used

𝑔. If Eric drove 297 miles on 9 gallons of gas, how far will he be able to drive on

14 gallons of gas?

43. Which statement is not correct? T-Shirt Shipment

x

y

x

y

Answer Choices

A I only C III and IV B I and II D I, II, and III

44. Which statement correctly describes the rate of change of

the following graph? F The distance traveled is increasing at a constant

rate of 50 miles per hour. G The distance traveled is not a constant rate of

change. H The distance traveled is decreasing at a constant

rate of 40 miles per hour. J The distance traveled is increasing at a constant rate of 40 miles per hour.

45. The table represents some points on the graph of linear function 𝑔. Which situation

can be modeled by this function?

A The cost in dollars of buying 𝑥 used cars for $11,950 each.

B The total cost of paying $325 in rent each month.

C The amount owed on a $24,550 loan after paying $325 per month for 𝑥

months.

D The distance traveled each day on a 24,550-mile trip.

46. Your on-campus apartment costs $750 per month after you pay the yearly deposit of $1500. The total amount spent on rent for the school year can be found by using

the function 𝑦 = 750𝑥 + 1500. Based on this information, which statement about the

graph of this situation is true? F The y-intercept of the graph represents the cost per month

G The y-intercept represents the amount of the deposit

H The variable x represents the total amount spent on rent for the school year

J The slope of the graph represents the number of months the apartment was rented

47. A baby pool that held 120 gallons of water is draining at a rate of 6 gal/min. The function 𝑓(𝑥) = 120 − 6𝑥 gives the amount of water in the pool after 𝑥

minutes. What does the x-intercept represent?

A The pool is draining at a rate of 6 gallons per hour.

C The number of minutes required to drain the entire pool

D The maximum number of gallons the pool can hold

In #48 – 53, use the following progression to help you write equations. You must write the equation in the form that is specifically stated!

Point-Slope Form Slope-Intercept Form Standard Form

𝒚 − 𝒚𝟏 = 𝒎(𝒙 − 𝒙𝟏) 𝒚 = 𝒎𝒙 + 𝒃 𝑨𝒙 + 𝑩𝒚 = 𝑪 48. Write the equation of the line that 49. Write the equation of the line that

passes through (3, -4) with a slope contains the point (-6, 2) and has a

of 2 in point-slope form. slope of 5

3 in slope-intercept form.

50. Write the equation of the line that 51. Convert −6𝑥 + 3𝑦 = −18 to

passes through (-6, -1) with a slope slope-intercept form. of -4 in standard form.

B The number of minutes required to drain one gallon of water

52. Write the slope-intercept form 53. Write the slope-intercept form equation of the line that is parallel equation of the line that is

to 𝑦 =2

3𝑥 − 4 and passes through perpendicular to 𝑦 = 2𝑥 − 4 and

the point (-3, 0). passes through the point (-2, 6).

Use the graph to answer #54 and 55. 54. What would be the slope of a line that

is parallel to the graphed line?

55. What would be the slope of a line that is perpendicular to the graphed line?

56. What is the equation of a line 57. What is the slope of a line parallel to the 𝑥-axis that passes perpendicular to the 𝑥-axis?

through (-4, 5)?

58. Which of the following statements about 𝑦 + 2 = −3(𝑥 − 1) is not true?

F The slope of the line is -3.

G The line represented by the equation passes through point (1, -2).

x

y

x

y

x

y

H When converted to slope-intercept form, the equation is 𝑦 = −3𝑥 + 1.

J The graph of the equation is as follows.

59. Some ice cream sales and the number of lifeguard rescues at a beach for various

days are shown in the table. Determine which statement is not true.

A The data has a strong positive correlation. B The correlation coefficient is approximately 0.95.

C The graph of the data would trend upward.

D This relationship represents a causation.

60. Look at the graphed line. What would be its new equation if the slope is multiplied

by -1, and the y-intercept decreases by 4. F 𝑦 = 3𝑥 + 1

G 𝑦 = −1

3𝑥 − 3

H 𝑦 = −𝑥 − 4

J 𝑦 = −3𝑥 − 3

61. A caterer charges an initial fee of $250 in addition to $12 per plate. If he decides

to increase the cost per plate by $3 but keep the initial fee the same, what would he charge to cater an event for 500 people?

Topic 4: Systems

62. You have 27 coins that are all dimes and quarters. The value of the coins is $4.35. Write and solve a system of equations to find the number of quarters you have.

x

y

x

y

63. Solve the following system by graphing.

{𝑦 = −

1

4𝑥 − 3

20𝑥 + 80𝑦 = 0

x

y