FSA/ALGEBRA BELLRINGERS 1st Semester FSA/EOC Review

1. Evaluate (-3)² · 2³ · (-4)³

1. Solution: -4608 (-3)² = -3 · -3 = 9 2³ = 2 · 2 · 2 = 8 (-4)³ = -4 · -4 · -4 = -64 9 · 8 · -64 = -4608

2. Write an algebraic expression for each word phrase: A. The quotient of x and 8 B. The sum of 20 and x C. The product of r and y D. 8 more than the difference of 15 and x

2. Solution: A. x/8 or x ÷ 8 (Quotient represents division) B. 20 + x (Sum represents addition) C. r x y (Product represents mult.) D. 8 + (15 – x) or (15 – x) + 8 (Difference represents subtraction)

3. Simplify the expression: 10[ 3(5 – 2 · 2) + 6(3 – 1) ]

3. Solution: 150 10 [ 3 (5 - 2 · 2) + 6 (3 – 1)] 10 [ 3 (5 – 4) + 6 (3 – 1)] 10 [ 3 (1) + 6 (2) ] 10 [ 3 + 12 ] 10 [ 15 ] 10 · 15 150

4. Evaluate the expression given values of the variables: m = 6 n = 2 y = 1.5 2m + 3n – 3 2y

4. Solution: 5 m = 6 n = 2 y = 1.5 2m + 3n – 3 SO 2(6) + 3(2) - 3 12 + 6 - 3 3 18 - 3 15 = 5

5. Solve: 3 8 + 16 =

5. Solution: 6 3 8 = 2 because 2 · 2 · 2 = 8 16 = 4 because 4 · 4 = 16

6. Write an algebraic expression: A state park charges an entrance fee of $20 plus $18 for each night of camping. Write an algebraic expression describing the total cost of camping for n nights? How much would it cost for 2 nights?

6. Solution: $18n + $20 or $20 + $18n 2 nights = $56 n = number of nights $20 is a one time fee $18n represents each night $18n + $20 $18(2) + $20 $36 + $20 = $56

7. Solve if c = 3 and d = 5 (3c2 - 3d)2 - 21

7. Solution: 123 (3c2 – 3d)2 – 21 (3 · 32 – 3 · 5)2 – 21 (3 · 9 – 3 · 5)2 – 21 (27 – 15)2 – 21 (12)2 – 21 144 – 21 123

8. Write an algebraic expression: The table shows how the total cost of a field trip depends on the number of students attending the trip. Write an expression that represents the total cost of the tickets. How much would it cost for 50 students to attend? Number of Students Total Cost 20 (12 x 20) + 150 40 (12 x 40) + 150 60 (12 x 60) + 150

8. Solution: N = Number of Students (12 · N) + 150 (12 · 50) + 150 600 + 150 $750 for 50 students to attend

9. Define absolute value and complete the following problems:

9. Solution: Absolute value is the distance a number is from “0”. 4|3 + 8| = 4|11| = 4 · 11 = 44 C. 2|-7| - 6|9| = 2 · 7 – 6 · 9 = 14 – 54 = -40

10. Simplify: A. ( 3 1/2 )² B. ( 6 1/2 )²

10. Solution: A. ( 3 1/2 )² = 3 1 2 ·2 = 3 B. ( 6 1/2 )² = 6 1/2·2/1 = 6 2/2 = 6

11. Solve: A. -29 – (-11) = B. -6 + -8 = C. -1 – 3 = 8 4

11. Solution: A.-29 – (-11) = -29 + (+11) = -18 B. -6 + -8 = -14 C. -1 – 3 = -1 – 6 = -7 8 4 8 8 8 (You need a common denominator to add or subtract fractions)

12. Solve: A. -4 · 3 · -2 = B. -8 + 5 · -1 = C. -7 – (-1) · 3 + 6 =

12. Solution: A. -4 · 3 · -2 = -12 · -2 = 24 B. -8 + 5 · -1 = -8 + -5 = -13 C. -7 – (-1) · 3 + 6 = -7 + (+1) · 3 + 6 = -7 + 3 + 6 -4 + 6 = 2

13. Simplify Each Expression: B. 32 1/5 - 81 1/2 C. 125 2/3

13. Solution: A. 64 1/3 = ∛64 = ∛ 4 3 = 4 B. 32 1/5 - 81 1/2 = 5 32 - 2 81 = 5 2 5 - 2 9 2 = 2 – 9 = -7 C. 125 2/3 = 125 1 3 ·2 = ( 125 1/3 )² = ( 3 125 )² = (∛ 5 3 )² = 5² = 25

14. Simplify Each Expression: B. 2³/2⁶ C. (2 · 3)³ D. (3/4)² E. (2³)²

14. Solution: A. 4² · 4³ = 4²⁺³ = 4⁶ = 4·4·4·4·4·4=4096 B. 2³/2⁶ = 2¯³ = 1/2³ = 1/2·2·2 = 1/8 C. (2 · 3)³ = 6³ = 6·6·6 = 216 D. (3/4)² = 3²/4² = 9/16 E. (2³)² = 2⁶ = 2·2·2·2·2·2 = 64

15. Simplify Each Expression B. 2¯³ · 5¯² C. 2/4¯² D. 6¯⁴ · 6¯¹

15. Solution: A. 3¯² = 1/3² = 1/9 B. 2¯³ · 5¯² = 1/2³ · 1/5² = 1/8 · 1/25 = 1/200 C. 2/4¯² = 2·4² = 2·16 = 32 D. 6¯⁴·6¯¹ = 6¯⁴⁺¯¹ = 6¯⁵ = 1/6⁵ = 1/6·6·6·6·6 = 7776

16. Label the Real Numbers: Rational, Irrational, Integers, Whole (Some may have more than 1 Label) C. 10 D. -8/17 E. 8 F. -12 G. 3 8

16. Solution: Label the Real Numbers: Rational, Irrational, Integers, Whole A. -5 – Rational, Integer B. 0 – Rational, Integer, Whole C. 10 - Irrational D. -8/17 - Rational E. 8 – Rational, Integer, Whole F. -12 – Rational, Integer G. 3 8 - 3 2³ = 2 – Rational, Integer, Whole

17. Name the property A. -y + 0 = -y B. 13(-11) = (-11)13 C. -5 · (m · 8) = (-5 · m) · 8 D. 2.6 · 1 = 2.6

17. Solution: A. -y + 0 = -y Identity Property of Addition B. 13(-11) = -11(13) Commutative Property of Multiplication C. -5 · (m · 8) = (-5 · m) · 8 Associative Property of Multiplication D. 2.6 · 1 = 2.6 Identity Property of Multiplication

18. Use the distributive property: A. 6(4y – 7) = B. -2(-5y – 8) = C. 4(3 + 4y – 2m +9n) =

18. Solution: A. 6(4y – 7) = 24y - 42 B. -2(-5y – 8) = 10y + 16 C. 4(3 + 4y – 2m +9n) = 12 + 16y – 8m + 36n

19. Simplify each expression: A. 6y – 7 + 4 – m B. 5mn – 3mn +7mn -1 C. 2(y + 3) – 4(y – 2)

19. Solution: Combine “like” terms. A. 6y – 7 + 4 – m -m + 6y - 3 B. 5mn – 3mn +7mn -1 9mn - 1 C. 2(y + 3) – 4(y – 2) Distribute 2y + 6 – 4y + 8 -2y + 14

20. Tell whether the given number is a solution of each equation: A. 5x + 1 = 16; -3 B. 2 = 10 – 4y; 2 C. 14 = 1x + 5; 9

20. Solution. Substitute the given number into the equation. A. 5x + 1 = 16; -3 5(-3) + 1 = 16 -15 + 1 = 16 -14 = 16 NO B. 2 = 10 – 4y; 2 2 = 10 – 4(2) 2 = 10 – 8 2 = 2 YES C. 14 = 1x + 5; 9 14 = 1(9) + 5 14 = 9 + 5 14 = 14 YES

21. Is the ordered pair a solution of the equation? (Yes or No) A. y = x – 4; (5, 1) B. y = -x; (-7,7) C. y = -3x + 3; (2, 6)

21. Solution: (x,y) A. y = x – 4; (5, 1) 1 = 5 – 4; 1 = 1 YES B. y = -x; (-7,7) 7 = -(-7) 7 = 7 YES C. y = -3x + 3; (2, 6) 6 = -3(2) + 3 6 = -6 + 3 6 = -3 NO

22. Evaluate the expression: h = -1 and k = -3 (2h)3 – (k3 – h2)

22. Solution: 20 h = -1 and k = -3 (2h)3 – (k3 – h2) (2 · -1)3 – ((-3)3 – (-1)2) (-2)3 – ((-27) – 1) -8 – (-28) -8 + 28 20

23. Simplify each expression: A. -8(2x – (4 – 7)) B. -.5(-6 + 12y)

23. Solution: A. -8(2x – (4 – 7)) -8(2x – (-3)) -8(2x + 3) -16x – 24 -.5(-6 + 12y) 3 – 6y

24. Solve the following equations: A. 5x = -15 8 B. -1 = x + 5

24. Solution A. 5x = -15 8 8 ·5x = -15 ·8 5 8 5 x = -24 B. -1 = x + 5 5 8 5 x = -24 B. -1 = x + 5 -5 -5 -6 = x

25. Solve the following equation: A. 15 + x = -21 10

25. Solution: -360 A. 15 + x = -21 -15 10 -15 x = -36 10 -15 10 -15 x = -36 10 10 ·x = -36 ·10 1 1 X = -360

26. Solve the following equation: -15 = 5(3x – 10) – 5x

26. Solution: 3.5 -15 = 5(3x – 10) – 5x Distribute -15 = 15x – 50 – 5x Combine -15 = 10x – 50 Solve for x +50 + 50 35 = 10x Divide 10 10 3.5 = x

27. Define the variable, write an equation and solve: Breanna’s pizza shop charges $9 for a large cheese pizza. Additional toppings cost $1.25 per topping. Brittany paid $15.25 for her large pizza. How many toppings did she order?

27. Solution: 5 toppings t = # of toppings 9 + 1.25t = 15.25 -9 -9 .00 -9 -9 .00 1.25t = 6.25 1.25 1.25 t = 5 toppings

28. Define the variable, write an equation, and solve. Ms. Seli ate at the same restaurant four times. Each time she ordered a salad and left a $5 tip. She spent a total of $54. Find the cost of each salad.

28. Solution: $8.50 C = cost of each salad 4(c + 5) = 54 4c + 20 = 54 -20 -20 4c = 34 4 4 c = 8.50

29. Solve the equation: 14 + 3x = 8x – 3(x – 4)

29. Solution: x = 1 14 +-2x = 12 14 + 3x = 8x – 3(x – 4) Distribute 14 + 3x = 8x – 3x + 12 Combine 14 + 3x = 5x + 12 -5x -5x 14 +-2x = 12 -14 -14 -2x = -2 -2 -2 x = 1

30. Solve the literal equation for c:

30. Solution: P · S = C + I + G + N ·P 1 P 1 PS = C + I + G + N - I – G – N = - I - G - N SO C = PS – I – G - N

31. What is the value of x in the equation? 100 – 3x = x

31. Solution: x = 25 100 – 3x = x -x -x 100 – 4x = 0 -100 -100 -100 -100 -4x = -100 -4 -4 x = 25

32. Define the variable and solve: Mr. Meader is buying lunch for his friends(If he has any). He decides to buy chicken wraps and chips for each person. Chicken wraps cost $3.20 and chips cost $0.75 each. What is the maximum number of people Mr. Meader can feed if he has $20?(He is so cheap)

32. Solution: 5 people X = maximum # of people Mr. Meader can feed 3.20x + .75x = 20 3.95x = 20 3.95 3.95 x ≈ 5.06 so x = 5 people

33. Define the variable and solve: The fare for a taxi is $7.50 plus $0.40 per mile. Coach Woodside paid a total fare of $13.50 to take a taxi from Jackson to his house.(His car broke down & no one would give him a ride). What is the distance, in miles, from Jackson to his house? (Poor Coach)

33. Solution: 15 miles X = # of miles 7.50 + .40x = 13.50 -7.50 - 7.50 -7.50 - 7.50 .40x = 6.00 .40 .40 x = 15 miles

34. Solve: 2x – 3(4x+5) = -6(x – 3) - 1

34. Solution: -8 2x – 3(4x+5) = -6(x – 3) - 1 + 15 +15 -4x = 32 -4 -4 x = -8

35. Solve the literal equation for “x”. x + r + 1 = 0 t

35. Solution: x = -1t - r x + r + 1 = 0 t -1 -1 x + r = -1 t -r -r x = -1t - r

36. Solve the proportion: x + 3 = x – 3 7 6

36. Solution: 39 x + 3 = x – 3 7 6 7(x-3) = 6(x+3) Distribute 7 6 7(x-3) = 6(x+3) Distribute 7x – 21 = 6x + 18 -6x -6x 1x – 21 = 18 +21 +21 x = 39

37. Which property of equality is illustrated in each equation? B. (2 + 3) + 4 = 2 + (3 + 4) C. 3 + 9 = 9 + 3

37. Solution A. Distributive Property B. Associative Property of Addition C. Commutative Property of Addition

A. Solve for r in terms of C: 38. A. Solve for r in terms of C: C = 2πr B. Solve for “x”: 1 2 𝑥 + 2 3 = 2 6

A. Solve for r in terms of C: 38. Solution: A. Solve for r in terms of C: C = 2πr = C = r 2 π 2 π 2 π B. Solve for “x”: 1 2 𝑥 + 2 3 = 2 6 − 2 3 same as ( 4 6 ) 1 2 𝑥 = −2 6 (Multiply ½ by the reciprocal) X = −2 6 · 2 1 = −4 6 = −2 3

39. Choose the correct equation that can be used to find the total earnings (T) for h hours: Raquel works at the zoo and uses the chart to keep track of her hours: A. T = h + 8 B. T = 10h – 8 C. T = 8h Hours (h) Total Earnings (T) 4 32 6 48 10 80 15 120 h ?

39. Solution: C 32/4 = 8 48/6 = 8 80/10 = 8 120/15 = 8 Therefore Raquel makes $8 an hour so her Total earnings would be represented by T = 8h

40. Write an equation and solve: A company that refinishes our gym floor charges $200 for materials plus $35 per hour for labor. What will be the total cost if it takes two 8- hour days to re-do the gym floor?

40. Solution: $760 T = Total Cost Materials: $200 Labor: 16 hours at $35 per hour 35(16) + 200 = T 560 + 200 = $760

41. Solve: 5x + 1 = 3x – 5 8 4

41. Solution: 11 5x + 1 = 3x – 5 8 4 4(5x + 1) = 8(3x – 5) Distribute 8 4 4(5x + 1) = 8(3x – 5) Distribute 20x + 4 = 24x – 40 -24x -24x -4x + 4 = -40 -4 -4 -4x = -44 -4 -4 x = 11

42. Are the numbers given a solution of the inequality? 3x + 1 > -3 A. -3 B. -1

42. Solution: 3x + 1 > -3 A. 3(-3) + 1 > -3 -9 + 1 > -3 -8 > -3 NO B. 3(-1) + 1 > -3 -3 + 1 > -3 -2 > -3 YES

43. Write an inequality for each graph: -1 0 1 2 3 B. -1 0 1 2 3

43. Solution: A. x ≤ 3 (A closed circle includes the number) B. X > -1 (An open circle does not include the number)

44. Solve the following inequalities: A. X – 4 + 2 ≥ 10 B. 5x + 5 – 4x < 8 C. -4x ≤ 20

44. Solution: A. X – 4 + 2 ≥ 10 x – 2 ≥ 10 +2 +2 x ≥ 12 +2 +2 x ≥ 12 B. 5x + 5 – 4x < 8 1x + 5 < 8 -5 -5 x < 3 C. -4x ≤ 20 (Reverse the sign) -4 -4 x ≥ -5

45. Solve and graph the inequality: 3x + 6 ≤ -5(x + 2)

45. Solution: 3x + 6 ≤ -5(x + 2) Distribute 3x + 6 ≤ -5x + -10 +5x +5x -6 -6 8x ≤ -16 8 8 x ≤ -2 -3 -2 -1

46. Solve:

46. Solution: A. 0.40 x + (2x + 0.15) + (x + 0.05) = 1.8 - .2 - .2 4x = 1.6 4 4 x = .4

47. Remember: Distance = Rate · Time Distance = 47. Remember: Distance = Rate · Time Distance = ?, Rate = 30, Time = Solve for “t”

47. Solution: 75 miles 50(t – 1) = 30t Distribute 50t – 50 = 30t Solve for “t” -30t -30t 20t – 50 = 0 +50 +50 20t = 50 20 20 Time = 2.5 hours Remember: distance = rate · time So distance = 30 · 2.5 Distance = 75 miles

48. Solve for “a”:

48. Solution: a ≤ 19.56 1.2(a + 0.065a) ≤ 25 Distribute 1.2a + .078a ≤ 25 Combine “Like” Terms 1.278a ≤ 25 1.278 1.278 a ≤ 19.56

49. Solve and Graph: 15 ≤ 7n – 2(n – 10) < 35

49. Solution: -1 ≤ n < 3 15 ≤ 7n – 2(n – 10) < 35 -20 -20 -20 -5 ≤ 5n < 15 5 5 5 -1 ≤ n < 3

50. Solve and Graph: 84 ≤ 86 + 85 + 80 + x ≤ 86 4

50. Solution: 85 ≤ x ≤93 4 ·84 ≤ 86 + 85 + 80 + x ≤ 86 · 4 4 -251 -251 -251 85 ≤ x ≤ 93 85 93

51. Solve and Graph 3x + 2 < -7 or -4x + 5 < 1

51. Solution: x < -3 or x > 1 -2 -2 -5 -5 3x < -9 or -4x < -4 The sign reverses 3 3 -4 -4 x < -3 or x > 1 -3 0 1

50. Solve

50. Solution: 12 T = 4 breeds of cattle Z = 3 breeds of cattle T x Z = 3 x 4 = 12 elements

51. Solve

51. Solution: 11 K U P = 2,10,11,14,18 (K U P) ∩ D = { 11 } Remember that union “unites” everything together and intersection is what is in common between the sets. The GREATEST age would be 11.

52. Solve

52. Solution: 35 15 Soccer Players + 11 Basketball Players + 9 Soccer and Basketball Players = 35 students

53. Find the range of the function for the given domain. f(x) = 3x² - 1 {2, 4, -3}

53. Solution: Range {11, 47, 26} f(x) = 3x² - 1 f(2) = 3 · 2² - 1 f(-3) = 3 · (-3)² - 1 f(2) = 3 · 4 – 1 f(-3) = 3 · 9 - 1 f(2) = 12 – 1 f(-3) = 27 - 1 f(2) = 11 f(-3) = 26 f(4) = 3 · 4² - 1 f(4) = 3 · 16 – 1 f(4) = 48 – 1 f(4) = 47

54. Solve and Graph: 1 ≤ -2x + 7 < 9

54. Solution: 1 ≤ -2x + 7 < 9 -7 -7 -7 -7 -7 -7 -6 ≤ -2x < 2 Switch the inequality symbols -2 -2 -2 3 ≥ x > -1 Rewrite: -1 < x ≤ 3 -1 3

55. Solve and Graph: 3x – 1 < -7 or 4x + 9 ≥ 13

55. Solution: 3x – 1 < -7 or 4x + 9 ≥ 13 +1 +1 -9 -9 +1 +1 -9 -9 0 -6 0 4 3x < -6 or 4x ≥ 4 3 3 4 4 X < -2 or x ≥ 1 -2 1

56. Solve

56. Solution: 9 Domain (x-values): { 0, 1, 2, 3, 4, 5, 6 } Range (y-values): { 0, 5, 8, 9, 8, 5, 0 } So the greatest element in the range is 9.

57. Solve if C = 3 and d = 5 (3c2 - 3d)2 - 21

57. Solution: 123 (3c2 – 3d)2 – 21 (3 x 32 – 3 x 5)2 – 21 (27 – 15)2 – 21 (12)2 – 21 144 – 21 123

58. Choose the correct answer:

58. Solution: C Domain would represent the days on the x-axis. Range would represent the Dollars on the y-axis. The range in dollars is from $10 - $60 inclusive. Therefore: 10 ≤ y ≤ 60

59. Simplify the expression: 10[ 3(5 – 2 · 2) + 6(3 – 1) ]

59. Solution: 150 10 [ 3 (5 - 2 · 2) + 6 (3 – 1)] 10 [ 3 (5 – 4) + 6 (3 – 1)] 10 [ 3 (1) + 6 (2) ] 10 [ 3 + 12 ] 10 [ 15 ] 10 · 15 150

60. Define absolute value and complete the following problems:

60. Solution: Absolute value is the distance a number is from “0”. B. 4|3 + 2 x 4| = 4|3 + 8| = 4|11| = 4 x 11 = 44 C. 2|-7| - 6|9| = 2 x 7 – 6 x 9 = 14 – 54 = -40

61. Choose the correct answer:

61. Solution: B 4.3/10 = 0.43 8.6/20 = 0.43 12.9/30 = 0.43 17.2/40 = 0.43 21.5/50 = 0.43 So the equation would be p = 0.43d OR you could substitute each number into the equation to see which one works. P = 0.43d so 4.3 = 0.43 x 10 (Yes), 8.6 = 0.43 x 20 (yes) etc.

62. Solve: 14 + 3x = 8x – 3(x – 4)

62. Solution: x = 1 14 +-2x = 12 14 + 3x = 8x – 3(x – 4) Distribute 14 + 3x = 8x – 3x + 12 Combine 14 + 3x = 5x + 12 -5x -5x 14 +-2x = 12 -14 -14 -2x = -2 -2 -2 x = 1

63. Solve the proportion: x + 3 = x – 3 7 6

63. Solution: 39 x + 3 = x – 3 7 6 7(x-3) = 6(x+3) Distribute 7 6 7(x-3) = 6(x+3) Distribute 7x – 21 = 6x + 18 -6x -6x 1x – 21 = 18 +21 +21 x = 39

64. Solve:

64. Solution: 96.5 $637.75 = 300 + 3.5h -300.00 -300 337.75 = 3.5h 3.5 3.5 96.5 = h Total number of hours = 96.5

65. Solve for “a”:

65. Solution: a ≤ 19.56 1.2(a + 0.065a) ≤ 25 Distribute 1.2a + .078a ≤ 25 Combine “Like” Terms 1.278a ≤ 25 1.278 1.278 a ≤ 19.56

66. Solve for “x” x + 12 = 5 9x 9

66. Solution: x = 3 (x + 12) = 5 (9x) 9 9(x + 12) = 45x 9x + 108 = 45x -108 -108 -36x = -108 -36 -36 X = 3

67. Solve for “C” S = C + I + G +N P

67. Solution: C = PS – I – G - N P · S = C + I + G +N ·P 1 P 1 I – G – N - I - G – N PS – I – G – N = C So C = PS – I – G - N

68. Solve for “x” x + r + 1 = 0 t

68. Solution: x = -1t - r x + r + 1 = 0 t -1 -1 t · x+r = -1 · t 1 t 1 - r - r x = -1t - r

69. Solve: 3 8 + 16 =

69. Solution: 6 3 8 = 2 because 2 · 2 · 2 = 8

70. Simplify Each Expression: B. 32 1/5 - 81 1/2 C. 125 2/3

70. Solution: A. 64 1/3 = ∛64 = ∛ 4 3 = 4 B. 32 1/5 - 81 1/2 = 5 32 - 2 81 = 5 2 5 - 2 9 2 = 2 – 9 = -7 C. 125 2/3 = 125 1 3 ·2 = ( 125 1/3 )² = ( 3 125 )² = (∛ 5 3 )² = 5² = 25

71. Simplify Each Expression: B. 2³/2⁶ C. (2 · 3)³ D. (3/4)² E. (2³)²

71. Solution: A. 4² · 4³ = 4²⁺³ = 4⁶ = 4·4·4·4·4·4=4096 B. 2³/2⁶ = 2¯³ = 1/2³ = 1/2·2·2 = 1/8 C. (2 · 3)³ = 6³ = 6·6·6 = 216 D. (3/4)² = 3²/4² = 9/16 E. (2³)² = 2⁶ = 2·2·2·2·2·2 = 64

72. Simplify Each Expression: B. 2¯³ · 5¯² C. 2/4¯² D. 6¯⁴ · 6¯¹

72. Solution: A. 3¯² = 1/3² = 1/9 B. 2¯³ · 5¯² = 1/2³ · 1/5² = 1/8 · 1/25 = 1/200 C. 2/4¯² = 2·4² = 2·16 = 32 D. 6¯⁴·6¯¹ = 6¯⁴⁺¯¹ = 6¯⁵ = 1/6⁵ = 1/6·6·6·6·6 = 7776

73. Label the Real Numbers: Rational, Irrational, Integers, Whole (Some may have more than 1 Label) C. 10 D. -8/17 E. 8 F. -12 G. 3 8

73. Label the Real Numbers: Rational, Irrational, Integers, Whole (Some may have more than 1 Label) A. -5 – Rational, Integer B. 0 – Rational, Integer, Whole C. 10 - Irrational D. -8/17 - Rational E. 8 – Rational, Integer, Whole F. -12 – Rational, Integer G. 3 8 - 3 2³ = 2 – Rational, Integer, Whole

2nd Semester Bellwork FSA/EOC Review Algebra Dr. Sorensen

1. Solve for “x” x + (2x + 0.15) + (x + 0.05) = 1.8

1. Solution: x = 0.4 x + (2x + 0.15) + (x + 0.05) = 1.8 Distribute x + 2x + 0.15 + x + 0.05 = 1.8 Combine 4x + .20 = 1.8 Solve -.20 -.20 4x = 1.6 Divide 4 4 x = 0.4

2. Solve Breanna has a total of $25 to spend on dinner, which includes a 6.5% sales tax and a 20% tip. Taylor used the inequality shown below to calculate the amount in dollars, a , she can spend before tax and tip. How much would that be? 1.2(a + 0.065a) ≤ 25

2. Solution: a ≤ 19.56 1.2(a + 0.065a) ≤ 25 Distribute 1.2a + .078a ≤ 25 Combine “Like” Terms 1.278a ≤ 25 Divide 1.278 1.278 a ≤ $19.56 approximately

3. Solve for “x” 2x – 3(4x+5) = -6(x – 3) - 1

3. Solution: x = -8 2x – 3(4x+5) = -6(x – 3) - 1 + 15 +15 -4x = 32 -4 -4 x = -8

4. Solve for “x” 3x + 6 ≤ -5(x + 2)

4. Solution: x ≤ -2 3x + 6 ≤ -5(x + 2) Distribute 3x + 6 ≤ -5x + -10 -6 -6 8x ≤ -16 8 8 x ≤ -2

5. Solve: 3x + 2 < -7 or -4x + 5 < 1

5. Solution: x < -3 or x > 1 -2 -2 -5 -5 3x < -9 or -4x < -4 The sign reverses 3 3 -4 -4 x < -3 or x > 1

6. Solve 84 ≤ 86 + 85 + 80 + x ≤ 86 4

6. Solution: 85 ≤ x ≤ 93 4 ·84 ≤ 86 + 85 + 80 + x ≤ 86 · 4 1 4 1 1 4 1 336 ≤ 251 + x ≤ 344 -251 -251 -251 85 ≤ x ≤ 93

7. List the domain and range of the following table. Is this a function? X y 2 3 5 4 6 7

7. Domain are the “x” values – {2,3,4,5} Range are the “y” values – {3,5,6,7} To be a function, every “x” value must be different. (The “y” values can repeat) THIS IS A FUNCTION

8. Solve f(x)=x² + 4; Domain or x = {0,1,2,3}

8. f(x) = {4,5,8,13} f(x) = x² + 4 or y = x² + 4 X (Domain) x² + 4 F(x) or y (Range) 0² + 4 4 1 1² + 4 5 2 2² + 4 8 3 3² + 4 13

9. Which of the following relations is NOT a function 9. Which of the following relations is NOT a function? Why is it not a function? A. {(0,1),(1,2)(2,3),(3,4)} B. {(1,1),(2,4)(3,3),(4,4)} C. {(1,6),(2,2)(1,3),(3,4)} D. {(1,1),(2,5)(3,6),(4,7)}

9. Solution: C C. {(1,6),(2,2)(1,3),(3,4)} A. {(0,1),(1,2)(2,3),(3,4)} B. {(1,1),(2,4)(3,3),(4,4)} C. {(1,6),(2,2)(1,3),(3,4)} D. {(1,1),(2,5)(3,6),(4,7)} The Domain (x) must be different to be a function and the letter “C” has repeating Domains. The Range (y) can repeat and still be a function.

10. Solve Which equation represents the line that passes through the points (5,-4) and (-2,6)? A. 10x + y = 22 B. 10x + 7y = 22 C. 10x – 7y = -22

10. Solution: B Which equation represents the line that passes through the points (5,-4) and (-2,6)? A. 10x + y = 22 NO B. 10x + 7y = 22 YES C. 10x – 7y = -22 NO ***Try each ordered pair until you find an equation that works for both ordered pairs. 10(5) + -4 = 22 NO 10(5) + 7(-4) = 22 YES 10(-2) + 7(6) = 22 YES

11. Solve The slope of a line is ¾. Write an equation of a line that is PARALLEL to the given line and passes through the point (-2,4).

11. Solution: y = 3/4x + 5.5 Remember that y = mx + b The original line is y = 3/4x + 0 The slope of a parallel line would be the same slope so “m” = ¾ Substitute the ordered pair of the new line in for x and y. (-2,4) y = mx + b 4 = ¾ (-2) + b Solve for “b” 4 = -6/4 + b (Add 6/4 to cancel) +6/4 + 6/4 5.5 = b So the new line is y = 3/4x + 5.5

12. Solve The formula for finding the circumference of a circle is C = 2Πr. Which of the following is the same equation solved for r in terms of C? A. r = C Π 2 B. r = C 2 Π

12. Solution: B C = 2Πr To solve for “r”, we need to divide each side by 2Π . C = 2Πr 2Π 2Π r = C 2Π

13. Write an equation that is perpendicular to y = x - 2 and goes through the point (-4,-1).

y = -1/2x - 3 13. Solution: y = -1/2x - 3 y = 2x – 2 : m = 2 b = -2 A perpendicular slope would by the reciprocal slope with the opposite sign, which would be -1/2. Now we need to find the new “b” using (-4,-1) as the point the line goes through. y = mx + b so -1 = (-1/2)-4 + b -1 = 2 + b Solve for “b” -2 -2 -3 = b so the new line would be y = -1/2x - 3

14. Choose the correct equation. Breanna tutors students in math. She uses the chart below to keep track of her total earnings. Which equation can Breanna use to find her total earnings, T, for h hours? A. T = h + 8 B. T = 8h C. T = 6h + 8 Hours (h) Total Earnings (T) 4 32 6 48 10 80 15 120 h ?

14. Solution: B Total Earnings would be $8 times the total hours. T = 8h 32 = 8(4) 48 = 8(6) 80 = 8(10) 120 = 8(15)

15. Name the property. Which property of equality is illustrated by the following equation? (84 x 25) + (84 x 75) = 84(25 + 75) A. Commutative B. Associative C. Distributive D. Property of 0

15. Solution: C - Distributive Review: A. Commutative: (3 + 4) = (4 + 3) B. Associative: (3 + 4) + 5 = 3 + (4 + 5) C. Distributive: 84(25 + 75) = (84 x 25) + (84 x 75) D. Property of 0: 5 x 0 = 0

16. Solve Which of the following is an equation of a horizontal line? A. 3x + 6y = 0 B. -3y = 21 C. -3x = 21

16. Solution: B: -3y = 21 y = -7 C.-3x = 21 -3 -3 x = -7 A. 3x + 6y = 0 -3x -3x 6y = -3x + 0 so y = -1/2x + 0 6 6 B. -3y = 21 -3 -3 y = -7 C.-3x = 21 -3 -3 x = -7

17. Which of the following is an equation of a vertical line? A. 3x + 6y = 0 B. -3y = 21 C. -3x = 21

17. Solution: C -3x = 21 A. 3x + 6y = 0 -3x -3x 6y = -3x so y = -1/2x + 0 (Direct 6 6 Variation) B. -3y = 21 -3 -3 y = -7 (Horizontal line across the y- axis at -7) C. .-3x = 21 -3 -3 x = -7 (Vertical line across the x axis at -7)

18.

19.

19. Solution: D (2,-2) According to the graph, the ordered pairs include the following points: (‐4, ‐3), (‐2, 1), (0, 0), (2, 3), (2, ‐2), (3, 1), (4, 3) The x‐coordinate 2 is repeated in two different points, so this does not represent a function. If (2,2) is removed, then this would be considered a function.

20. An architect designed an outdoor staircase for a house. The relationship between the height of the steps and the length of the tread is modeled by the equation 57x – 95y = 0. Which of the following represents the slope of the equation? A. 5/3 B. 3/2 C. 2/3 D. 3/5

20. Solution: m=57/95 = 3/5 y = mx + b 57x – 95y = 0 Solve for Y -57x -57x -95y =-57x -95 -95 y = 57x 95 So the slope = 57 ÷ 19 = 3 95 19 5

21. Brianna plotted the two points (20, 75) and (45, 150) on a graph. What is the x- coordinate of the x-intercept of the line that contains these two points? Hint: Use y=mx + b and find the slope and y-intercept. Then find the x-intercept ( ,0). ***This is a bonus buck problem!

21. Solution: The x-coordinate of the x-intercept is -5. y=mx + b m = 150-75 = 75 = 3 SO y=3x + b 45-20 25 Find b by substituting one of the ordered pairs in for x and y. I will use (20,75). 75 = 3(20) + b 75 = 60 + b 15 = b SO y = 3x + 15 To find the x- intercept we need to place a “0” in for y and solve for x. It’s easier if the equation is in standard form: -3x + y = 15

21. Continued: ( ,0) -3x + y = 15 -3x + 0 = 15 -3x = 15 -3 -3 x = -5 So the x-intercept is (-5,0)

22.

22. Solution: 25 degrees

23.

23. Solution: 96.5

24.

24. Solution: B p=0.43d Substitute the numbers from the table into the equations to see which one works. A. 4.3 = (4.3)(10) NO B. 8.6 = (.43)(20) YES

25.

25. Solution: C

26.

26. Solution: 504

27.

27. Solution: A

28.

28. Solution: C 5x + 2y ≤ 50 -5x -5x 2y ≤ -5x + 50 2 2 2 2 2 2 y ≤ -5 + 25 m = -5 b = 25 2 2

29.

29. Solution: A

30. Solution

30. Solution: 12.6 y = mx + b 70x + 50y = 630 -70x -70x 50 50 50 y = -7x + 12.6 m = -7 b = 12.6 5 5

31.

31. Solution: C Since line PQ goes down, we know the slope must be negative, so it has to be A or C. (6,12)(11,10) 10 – 12 = -2 11 – 6 5 y = mx + b 12 = -2 ·6 + b 5 12 = -2.4 + b +2.4 +2.4 14.4 = b so y = -2x + 14.4

32.

32. Solution: 2

33.

33. Solution: 6 Slope of the original line: (-6,1)(4,-4) -4 – 1 = -5 = -1 Reciprocal and opp. m = 2 4-(-6) 10 2 y = mx + b (4,-4) is the intersection point -4=2(4) + b -4 = 8 + b -8 -8 -12 = b so y = 2x + -12 ( ,0) Standard Form -2x + y = -12 -2x + 0 = -12 -2 -2 x = 6 (6,0)

34.

34. Solution: -8.4 or -42/5

35. **Bonus Buck Problem – you must show your work!

35. Solution: C X = Medium Sandwich: $5.39 Y = Large Sandwich: $6.89 Choice “C”: Russ: 3x + 2y = 29.95 3(5.39) + 2(6.89) = 29.95 16.17 + 13.78 = 29.95 YES Stacy: 4x + 1y = 28.45 4(5.39) + 1(6.89) = 28.45 21.56 + 6.89 = 28.45 YES

36. Bonus Buck Problem – You must show your work.

36. Solution: 9 Songs

37.

37. Solution: A

38.

38. Solution: B 16x 2x

39.

39.

40.

40. Solution: 35

41.

41. Solution: