TSIA2- Chapter 5 – Algebraic Reasoning – Question Set 4

#1. A shipping costs problem requires solving: 3x + 12 = 45. What is the value of x?

12

13

9

11

#2. In a concert ticket pricing scenario: 2x – 8 = 22. Solve for x.

13

14

16

15

#3. A bakery inventory problem: 5x + 15 = 70. What is x?

12

11

13

10

#4. Solving this hourly wage calculation equation: 4x – 20 = 60. Find x.

22

18

19

20

#5. A subscription fees problem: 6x + 9 = 51. What is the value of x?

7

8

9

6

#6. In temperature conversion: 2x – 5 = 13. Solve for x.

9

8

7

10

#7. A package weight problem: 3x + 18 = 42. Find x.

7

8

9

6

#8. Solving for book pricing: 7x – 14 = 35. What is x?

5

7

6

8

#9. A cafe supplies equation: 4x + 8 = 32. Find x.

7

6

5

8

#10. Solving the gym membership problem: 5x – 25 = 50. What is x?

15

13

16

14

#11. Rearrange this rectangular perimeter formula P = 2l + 2w to solve for w.

w = (P – 2l)/2

w = P/2 – l

w = P – 2l

w = (P + 2l)/2

#12. Using the triangle area formula A = bh/2, solve for h.

h = A/(2b)

h = b/(2A)

h = 2A/b

h = 2A – b

#13. From this motion equation v = u + at, rearrange to find a.

a = t/(v – u)

a = v – u – t

a = (v – u)/t

a = (v + u)/t

#14. Solve the force formula F = ma for m.

m = F – a

m = F/a

m = Fa

m = a/F

#15. Rearranging the linear function y = mx + b to solve for m gives:

m = (y – b)/x

m = (y + b)/x

m = y/x – b

m = x/(y – b)

#16. From the circle circumference equation C = 2πr, express r in terms of C.

r = C/(π)

r = C – 2π

r = C/(2π)

r = 2πC

#17. Solve the interest formula I = Prt for t.

t = Pr/I

t = I – P – r

t = I/(Pr)

t = IPr

#18. Rearranging the z-score formula formula z = (x – μ)/σ to solve for x:

x = (z + μ)/σ

x = σ/z + μ

x = z + μ/σ

x = zσ + μ

#19. Solve the weight limit inequality: 3x < 60

x < 20

x < 19

x > 20

x > 19

#20. For this budget constraint problem, solve: 5x + 10 ≥ 35

x ≤ 4

x ≤ 5

x ≥ 4

x ≥ 5

#21. Which inequality solution matches this temperature range: 2x – 8 > 12

x ≤ 10

x = 10

x > 11

x < 11

#22. Solve the enrollment threshold inequality: 4x ≤ 100

x > 25

x < 24

x > 24

x < 25

#23. For this age requirement problem, solve: x + 5 > 21

x ≥ 16

x ≤ 16

x ≤ 17

x ≥ 17

#24. Which inequality solution matches this distance boundary: 6x < 90

x = 15

x ≤ 15

x > 16

x < 16

#25. Solve the quantity limit inequality: 2x + 3 ≤ 25

x > 10

x > 11

x < 10

x < 11

#26. For this payment minimum problem, solve: 7x – 14 ≥ 42

x ≤ 7

x ≥ 8

x ≤ 8

x ≥ 7

#27. Which inequality solution matches this capacity constraint: 3x ≤ 75

x = 25

x < 26

x > 26

x ≤ 25

#28. Solve the speed restriction inequality: x – 10 < 55

x < 63

x > 63

x > 64

x < 64

#29. For this score requirement problem, solve: 8x + 4 > 60

x ≤ 7

x ≥ 7

x ≥ 8

x ≤ 8

#30. Which inequality solution matches this inventory check: 5x – 20 ≤ 80

x < 21

x = 20

x > 21

x ≤ 20

#31. Solve the absolute value equation: |2x – 5| = 11

-8 or 3

8 or 3

8 or -3

6 or -4

#32. Solve the absolute value equation: |x + 3| = 7

-4 or 10

4 or 10

-4 or -10

4 or -10

#33. Solve the absolute value equation: |3x – 6| = 9

-5 or 1

5 or -2

5 or 1

5 or -1

#34. Solve the absolute value equation: |x – 4| = 6

10 or -2

6 or 2

10 or 2

-10 or 2

#35. Solve the absolute value equation: |2x + 1| = 7

-3 or 4

3 or -5

3 or 4

3 or -4

#36. Find all solutions to: |x + 8| = 5

-3 or -13

5 or -13

3 or 13

-3 or 13

#37. Find all solutions to: |4x – 3| = 5

1.25 or -0.5

2 or -0.5

2 or 0.5

-2 or 0.5

#38. Find all solutions to: |2x – 10| = 4

-7 or 3

6 or 4

7 or 3

7 or -3

#39. Find all solutions to: |x – 1| = 8

-9 or 7

9 or -7

9 or 7

8 or -8

#40. Find all solutions to: |3x + 2| = 11

-3 or 13/3

3 or 13/3

3 or -13/3

4 or -4

#41. Use substitution to solve this inventory management system: y = 2x + 1 and 3x + y = 16

(3, 7)

(2, 5)

(1, 3)

(4, 9)

#42. Use substitution to solve this cost analysis system: x = y – 3 and 2x + y = 12

(2, 5)

(1, 4)

(4, 7)

(3, 6)

#43. Use substitution to solve this distance calculation system: y = 3x – 2 and x + y = 14

(5, 9)

(2, 12)

(4, 10)

(3, 11)

#44. Use substitution to solve this production planning system: x = 2y + 1 and 3x – y = 13

(4, 1)

(5, 2)

(3, 1)

(2, 0)

#45. Use substitution to solve this pricing strategy system: y = -x + 8 and 2x + y = 11

(1, 7)

(2, 6)

(4, 4)

(3, 5)

#46. Use substitution to solve this time scheduling system: x = y + 4 and 2x – 3y = 1

(5, 1)

(6, 2)

(9, 5)

(7, 3)

#47. Use substitution to solve this capacity planning system: y = 2x – 5 and x + y = 10

(3, 4)

(4, 3)

(6, 7)

(5, 5)

#48. Use substitution to solve this resource allocation system: x = 3y – 2 and 2x + y = 11

(1, 3)

(4, 1)

(3, 2)

(2, 4/3)

#49. Use substitution to solve this revenue modeling system: y = 4x + 1 and 2x + y = 19

(4, 17)

(1, 5)

(3, 13)

(2, 9)

#50. Use substitution to solve this demand forecasting system: x = 2y – 3 and 3x + y = 14

(2, 2.5)

(4, 4.5)

(1, 2)

(3, 3)

#51. Use elimination to solve this resource distribution problem: 2x + 3y = 12 and 4x – 3y = 6

(4, 1)

(3, 2)

(2, 2)

(1, 3)

#52. Use elimination to solve this supply chain problem: 3x + 2y = 13 and 2x – 2y = 4

(2, 3)

(1, 4)

(3, 2)

(4, 1)

#53. Use elimination to solve this logistics problem: x + 2y = 8 and 3x – 2y = 4

(1, 3.5)

(2, 3)

(3, 2.5)

(4, 2)

#54. Use elimination to solve this budgeting problem: 2x + y = 9 and 3x – y = 6

(3, 3)

(4, 1)

(2, 2)

(1, 4)

#55. Use elimination to solve this production problem: 4x + 3y = 23 and 4x – y = 11

(2, 3)

(5, 1)

(3, 2)

(4, 2.33)

#56. Use elimination to solve this inventory problem: 2x + 5y = 14 and 2x – y = 2

(1, 3)

(2, 2)

(4, 0)

(3, 1)

#57. Use elimination to solve this pricing problem: 3x + 4y = 24 and 3x – 2y = 6

(4, 1.5)

(5, 1)

(3, 2)

(2, 3)

#58. Use elimination to solve this analytics problem: 5x + 2y = 16 and 3x – 2y = 8

(2, 1)

(4, 0)

(3, 0.5)

(1, 2)

#59. Use elimination to solve this forecasting problem: 2x + 3y = 11 and 4x + 3y = 17

(1, 3)

(3, 1.67)

(4, 1)

(2, 2)

#60. Use elimination to solve this scheduling problem: 3x + 2y = 10 and x + 2y = 6

(4, 1)

(2, 2)

(3, 1.5)

(1, 2.5)

#61. Two gardens have a combined area of 150 sq ft. One garden is 30 sq ft larger than the other. Find the area of each garden.

90 and 60 sq ft

100 and 50 sq ft

80 and 70 sq ft

75 and 75 sq ft

#62. At a theater, adult tickets cost $12 and child tickets cost $8. If 150 tickets sold for $1560, how many of each were sold?

80 adults, 70 children

100 adults, 50 children

60 adults, 90 children

90 adults, 60 children

#63. A manufacturer produces two types of batteries. Type A takes 2 hours to make, Type B takes 3 hours. If 30 batteries took 80 hours total, how many of each?

15 A and 15 B

12 A and 18 B

20 A and 10 B

10 A and 20 B

#64. Two investments total $5000. One earns 5% annually, the other 8%. If combined annual earnings are $340, find each investment.

$3000 at 8%, $2000 at 5%

$1000 at 8%, $4000 at 5%

$1500 at 8%, $3500 at 5%

$2000 at 5%, $3000 at 8%

#65. A store sells notebooks at $3 each and pens at $1.50 each. In one day, 200 items sold for $450. How many notebooks?

100 notebooks

150 notebooks

80 notebooks

120 notebooks

#66. The sum of two numbers is 45. Their difference is 13. Find both numbers.

29 and 16

32 and 13

28 and 17

30 and 15

#67. A train travels from City A to City B at 60 mph and returns at 40 mph. Total time is 10 hours. What is the distance?

200 miles

300 miles

240 miles

180 miles

#68. A recipe requires flour and sugar in a ratio where flour is 1.5 times sugar by weight. Total is 10 lbs. Find each amount.

6 lbs flour, 4 lbs sugar

8 lbs flour, 2 lbs sugar

7 lbs flour, 3 lbs sugar

5 lbs flour, 5 lbs sugar

#69. Two pipes fill a tank. One fills it in 6 hours alone, the other in 8 hours. How long together?

3.43 hours

2.5 hours

3 hours

4 hours

#70. A paddler travels 24 miles downstream in 3 hours, upstream in 4 hours. Find boat speed and current.

boat: 6 mph, current: 0.5 mph

boat: 10 mph, current: 3 mph

boat: 7 mph, current: 1 mph

boat: 8 mph, current: 2 mph

#71. An event has 200 attendees. VIP tickets are $50, regular are $20. Revenue is $6500. Find each ticket type.

40 VIP, 160 regular

75 VIP, 125 regular

60 VIP, 140 regular

50 VIP, 150 regular

#72. Two alloys: one is 30% copper, other is 60% copper. Combine to make 100 kg of 45% copper alloy. How much of each?

30 kg and 70 kg

40 kg and 60 kg

45 kg and 55 kg

50 kg of each

#73. A company’s profit increased from $50k to $80k. One division earned $20k, other earned $60k. What were original amounts?

$20k and $80k

$30k and $50k

$15k and $65k

varies by division

#74. In a class of 32 students, there are 4 more girls than boys. How many of each?

20 girls, 12 boys

17 girls, 15 boys

19 girls, 13 boys

18 girls, 14 boys

#75. A rectangle’s length is 3 inches more than width. Perimeter is 50 inches. Find dimensions.

length: 16, width: 9

length: 12, width: 13

length: 14, width: 11

length: 15, width: 10

#76. Two accounts have $8000 total. Account A has $1000 more than Account B. Find each amount.

A: $5500, B: $2500

A: $4000, B: $4000

A: $4500, B: $3500

A: $5000, B: $3000

#77. A total of 1200 feet of fencing encloses two adjacent rectangular fields of equal area. Find dimensions if length is twice width.

80 x 40 feet

varies

120 x 60 feet

100 x 50 feet

#78. Gas costs $0.05 per mile, maintenance costs $0.03 per mile. Annual costs are $960 for 12,000 miles. Verify the model.

needs more info

does not check

incomplete model

checks out

#79. A student scores 85 and 92 on first two tests. What score is needed on the third test to average 90?

91

93

95

90

#80. Store A sells apples at $2 per pound, Store B at $2.50 per pound. You buy 10 pounds for $22. How many from each store?

6 from A, 4 from B

7 from A, 3 from B

5 from A, 5 from B

8 from A, 2 from B

#81. Simplify using laws of exponents: x^3 · x^5

x^8

x^2

x^15

2x^8

#82. Simplify using laws of exponents: (2^3)^2

8^2 = 64

2^5 = 32

2^6 = 64

4^6 = 4096

#83. Simplify using laws of exponents: x^10 / x^4

x^14

1/x^6

x^6

x^4

#84. Simplify using laws of exponents: (3x^2)^3

9x^6

6x^6

27x^6

27x^5

#85. Simplify using laws of exponents: (ab)^4

ab^4

4ab

a^4b

a^4b^4

#86. Simplify using laws of exponents: 2^5 · 2^3

4^8 = 65536

2^3 = 8

2^8 = 256

2^15 = 32768

#87. Simplify using laws of exponents: y^7 / y^2

y^5

1/y^5

y^9

y^2

#88. Simplify using laws of exponents: (5a^3b^2)^2

25a^5b^4

5a^6b^4

25a^6b^4

10a^6b^4

#89. Simplify using laws of exponents: x^-3 · x^7

x^4

x^10

1/x^4

x^-21

#90. Simplify using laws of exponents: (4^2)^-1

16

1/4 = 0.25

1/16 = 0.0625

4

#91. Express in scientific notation or standard form: 4500000

4.5 × 10^5

4.5 × 10^6

45 × 10^5

4.5 × 10^-6

#92. Express in scientific notation or standard form: 0.000082

8.2 × 10^-5

8.2 × 10^-4

82 × 10^-6

8.2 × 10^5

#93. Express in scientific notation or standard form: 2.5 × 10^8

250000000

25000000

2500000

2.5 × 10^-8

#94. Simplify or convert: (3 × 10^4)(2 × 10^3)

6 × 10^7

6 × 10^-7

6 × 10^6

6 × 10^12

#95. Simplify or convert: 9 × 10^-4 / 3 × 10^-2

3 × 10^1

3 × 10^2

3 × 10^-2

3 × 10^-6

#96. Simplify or convert: 0.0000039

3.9 × 10^-5

39 × 10^-7

3.9 × 10^-6

3.9 × 10^6

#97. Perform the operation: (3x^2 + 2x – 5) + (x^2 – 4x + 3)

4x^2 – 2x + 2

4x^2 – 2x – 2

3x^2 – 2x – 2

4x^2 + 2x – 2

#98. Perform the operation: (5x^3 – 2x + 1) – (2x^3 + x – 4)

3x^3 – 3x + 5

3x^3 + x + 5

3x^3 – x + 5

3x^3 – 3x – 3

#99. Perform the operation: (4x^2 – 6x) + (2x^2 + 8x – 3)

6x^2 – 2x – 3

6x^2 + 14x – 3

6x^2 + 2x + 3

6x^2 + 2x – 3

#100. Perform the operation: (7x – 4) – (3x + 2)

4x + 6

4x – 6

4x – 2

10x – 6

#101. Perform the operation: (2x^3 + x^2) + (3x^3 – 2x^2 + 5x)

-x^3 – x^2 + 5x

5x^3 – x^2 – 5x

5x^3 + x^2 + 5x

5x^3 – x^2 + 5x

#102. Perform the operation: (9x^2 – 5x + 2) – (4x^2 + 3x – 1)

5x^2 + 8x + 3

5x^2 – 8x + 3

5x^2 – 2x + 1

5x^2 – 8x – 3

#103. Perform the operation: (x^3 + 4x^2 – x + 8) + (2x^2 – x – 3)

x^3 + 6x^2 – 2x + 5

x^3 + 6x^2 – 2x – 5

x^3 + 4x^2 – 2x + 5

3x^3 + 6x^2 + 5

#104. Perform the operation: (6x^2 + 9) – (2x^2 – 3x + 5)

4x^2 + 3x – 4

4x^2 – 3x + 4

4x^2 + 3x + 4

8x^2 + 3x + 4

#105. Expand the product: (x + 2)(x + 5)

x^2 + 3x + 10

x^2 + 7x + 10

x^2 – 7x + 10

x^2 + 10x + 7

#106. Expand the product: (2x – 3)(x + 4)

2x^2 + 11x – 12

2x^2 + 5x + 12

2x^2 – 5x – 12

2x^2 + 5x – 12

#107. Expand the product: (x + 3)^2

x^2 + 6x + 9

x^2 + 9

x^2 – 6x + 9

x^2 + 6x – 9

#108. Expand the product: (2x – 1)(3x + 2)

6x^2 + 7x – 2

6x^2 + x + 2

6x^2 + x – 2

6x^2 – x – 2

#109. Expand the product: x(x^2 – 4x + 3)

x^3 – 4x^2 + 3x

x^3 + 4x^2 + 3x

x^2 – 4x + 3

x^3 – 4x^2 – 3x

#110. Expand the product: (x – 4)(x + 4)

x^2 – 16

x^2 + 16

x^2 – 8

x^2 – 8x

#111. Expand the product: (3x + 2)(2x – 5)

6x^2 – 15x – 10

6x^2 – 11x – 10

6x^2 – 11x + 10

6x^2 + 11x – 10

#112. Expand the product: (x – 2)(x^2 + 2x + 4)

x^3 – 2x^2 – 4

x^3 – 8

x^3 – 8x

x^3 + 8

#113. Factor completely: x^2 + 7x + 12

(x + 3)(x + 4)

(x + 1)(x + 12)

(x + 2)(x + 6)

(x – 3)(x – 4)

#114. Factor completely: x^2 – 5x – 6

(x – 6)(x + 1)

(x + 6)(x – 1)

(x – 3)(x – 2)

(x + 3)(x + 2)

#115. Factor completely: 2x^2 + 11x + 5

(2x – 1)(x – 5)

(x + 1)(2x + 5)

(2x + 5)(x + 1)

(2x + 1)(x + 5)

#116. Factor completely: x^2 – 9

(x – 3)^2

(x – 9)(x + 1)

(x^2 – 9)

(x – 3)(x + 3)

#117. Factor completely: 3x^2 – 12

3(x – 2)(x + 2)

3(x^2 – 4)

3(x – 4)(x + 3)

(3x – 2)(x + 2)

#118. Factor completely: x^2 + 8x + 16

(x + 2)(x + 8)

(x – 4)^2

(x + 8)^2

(x + 4)^2

#119. Factor completely: 4x^2 – 4x – 3

(2x + 3)(2x – 1)

(4x – 3)(x + 1)

(2x – 3)(2x + 1)

(2x – 1)(2x – 3)

#120. Factor completely: x^3 – 8

(x – 2)(x^2 + 2x + 4)

(x – 2)(x + 2)^2

(x + 2)(x^2 – 2x + 4)

(x – 2)^3

#121. Solve by factoring: x^2 – 3x – 10 = 0

-2, 5

2, -5

-2, -5

2, 5

#122. Solve by factoring: x^2 + 8x + 15 = 0

-3, 5

3, 5

3, -5

-3, -5

#123. Solve by factoring: 2x^2 – 7x + 3 = 0

2, 3

-1/2, 3

1/2, 3

1/2, -3

#124. Solve by factoring: x^2 – 9 = 0

3, 3

-3, -3

-3, 3

0, 9

#125. Solve by factoring: 3x^2 + 10x – 8 = 0

2/3, 4

2/3, -4

-2/3, -4

-2/3, 4

#126. Solve by factoring: x^2 – 4x = 0

4, 4

0, -4

0, 4

-4, 0

#127. Solve by factoring: 4x^2 – 1 = 0

-2, 2

-1/2, 1/2

-1/2, -1/2

-1, 1

#128. Solve by factoring: x^2 + 6x + 9 = 0

-3, 3

-3 (double)

3 (double)

3, -3

#129. Solve by factoring: 2x^2 – 8x + 6 = 0

-1, 3

1, 3

-1, -3

1, -3

#130. Solve by factoring: x^2 – 5x + 6 = 0

2, -3

2, 3

-2, 3

-2, -3

#131. Use the quadratic formula to solve this school planning equation: x^2 – 5x + 6 = 0

3, 2

1, 6

2, 3

-2, -3

#132. Use the quadratic formula to solve this project management equation: x^2 + 3x – 4 = 0

1, 4

-1, 4

1, -4

-1, -4

#133. Use the quadratic formula to solve this resource allocation equation: 2x^2 – 8x + 6 = 0

-1, 3

-1, -3

1, -3

1, 3

#134. Use the quadratic formula to solve this capacity planning equation: x^2 – 2x – 8 = 0

-4, -2

-4, 2

4, -2

4, 2

#135. Use the quadratic formula to solve this inventory equation: 3x^2 + 6x – 9 = 0

-1, -3

-1, 3

1, -3

1, 3

#136. Use the quadratic formula to solve this metrics equation: x^2 + 4x + 4 = 0

1, 4

-2, 2

-2 (double root)

2 (double root)

#137. Use the quadratic formula to solve this analysis equation: 2x^2 – 3x – 2 = 0

2, -1/2

2, 1/2

-2, -1/2

-2, 1/2

#138. Use the quadratic formula to solve this forecasting equation: x^2 – 7x + 10 = 0

2, -5

-2, -5

-2, 5

2, 5

#139. Use the quadratic formula to solve this production equation: 3x^2 – x – 2 = 0

1, 2/3

1, -2/3

-1, 2/3

-1, -2/3

#140. Use the quadratic formula to solve this demand equation: x^2 + 5x + 6 = 0

2, -3

-2, -3

2, 3

-2, 3

#141. Find the discriminant of x^2 – 4x + 4 to determine number of real solutions in this perfect square scenario.

-4, no real solutions

16, two solutions

0, one solution

4, two solutions

#142. Find the discriminant of x^2 + 2x + 5 to determine number of real solutions in this imaginary scenario.

0, one solution

-16, complex

16, two solutions

-16, no real solutions

#143. Find the discriminant of 2x^2 – 5x – 3 to determine number of real solutions in this two real roots scenario.

25, two solutions

49, two solutions

-49, no solutions

0, one solution

#144. Find the discriminant of x^2 – 6x + 9 to determine number of real solutions in this repeated root scenario.

0, one solution

36, two solutions

12, two solutions

-36, no real

#145. Find the discriminant of 3x^2 + x + 1 to determine number of real solutions in this complex solutions scenario.

-11, no real solutions

11, two solutions

13, two solutions

1, two solutions

#146. Find the discriminant of x^2 + 6x + 8 to determine number of real solutions in this two distinct real scenario.

0, one solution

-4, no solutions

4, two solutions

36, two solutions

#147. Find the discriminant of 4x^2 – 4x + 1 to determine number of real solutions in this perfect trinomial scenario.

-16, no real

0, one solution

16, two solutions

4, two solutions

#148. Find the discriminant of x^2 – 10x + 25 to determine number of real solutions in this repeated root scenario.

-100, no real

0, one solution

400, two solutions

100, two solutions

#149. Find the discriminant of 2x^2 + 3x – 5 to determine number of real solutions in this distinct roots scenario.

49, two solutions

-49, no real

0, one solution

25, two solutions

#150. Find the discriminant of x^2 + x + 1 to determine number of real solutions in this complex scenario.

3, two solutions

-3, no real solutions

1, two solutions

-1, no real

#151. A ball is thrown upward with initial velocity 64 ft/s. Height h = -16t^2 + 64t. When does it hit ground?

1 second

2 seconds

8 seconds

4 seconds

#152. A rectangular garden has perimeter 40 ft. Area is 96 sq ft. Find dimensions.

15 by 6 ft

12 by 10 ft

12 by 8 ft

10 by 8 ft

#153. Revenue from selling x items: R = -2x^2 + 100x. Maximum revenue?

$1200

$1300

$1000

$1250

#154. An object falls from 400 ft. h = -16t^2 + 400. When hits ground?

3 seconds

6 seconds

5 seconds

4 seconds

#155. A product’s profit: P = -3x^2 + 120x – 300. Find break-even points.

x = 5, 10

x = 2.95, 33.71

x = 0, 40

x = 1, 2

#156. A bridge cable forms parabola y = 0.01x^2. Height at x = 50?

25 feet

50 feet

12.5 feet

100 feet

#157. An arch spans 20 ft, height 8 ft. Find equation.

y = -x^2 + 8

y = -0.08x^2 + 8

y = -0.08x + 8

y = 0.08x^2 – 8

#158. Interest compounded annually. P(1 + r)^2 = 1100 with P = 1000. Find rate.

3%

10%

5%

4%

#159. Two consecutive integers: sum of squares = 145. Find integers.

6 and 7

8 and 9

9 and 10

7 and 8

#160. Picture frame: outer is 10×12, inner border 2 in. Inner area 60 sq in. Check frame width.

3 inches

1.5 inches

1 inch

2 inches

#161. Given f(x) = 3x – 2, find f(5).

15

11

13

17

#162. Given g(x) = x^2 + 4x, find g(3).

27

19

25

21

#163. Given h(x) = 2/x, find h(4).

1

2

0.5

0.25

#164. Given f(x) = |x – 3|, find f(1).

4

1

3

2

#165. Given p(x) = x^3 – 2x, find p(2).

8

6

4

2

#166. Given q(x) = √(x + 5), find q(4).

2.5

1.5

3

4

#167. Given r(x) = (2x + 1)/(x – 1), find r(2).

7

4

3

5

#168. Given s(x) = e^x, find s(0) approximately.

e

2.718

1

0

#169. Find the domain of f(x) = 3x + 2

All real numbers

x ≥ 0

x ≠ 0

x > 0

#170. Find the domain of g(x) = 1/x

All real numbers except 0

x ≥ 0

All real numbers

x > 0

#171. Find the domain of h(x) = √x

x ≥ 0

x ≤ 0

All real numbers

x > 0

#172. Find the range of f(x) = x^2

y ≥ 0

y ≤ 0

y > 0

All real numbers

#173. Find the domain of g(x) = 1/(x-3)

All real numbers except 3

x ≥ 3

All real numbers

x > 3

#174. Find the domain of h(x) = √(x – 4)

x ≥ 0

All real numbers

x ≥ 4

x > 4

#175. Find the range of f(x) = |x|

All real numbers

y ≤ 0

y ≥ 0

y > 0

#176. Find the range of g(x) = 2x + 5

y ≥ 5

All real numbers

y > 5

y ≠ 0

#177. Find the domain of f(x) = x^2 – 4

x > -2

x ≥ 0

x > 0

All real numbers

#178. Find the domain of h(x) = ln(x)

x ≥ 0

x > 0

x ≠ 0

All real numbers

#179. Find the slope of the line through Points: (2, 5) and (4, 11).

2

4

5

3

#180. Find the slope of the line through Points: (1, 8) and (5, 0).

-1

1

-2

2

#181. Find the slope of the line through Points: (3, 2) and (3, 7).

Undefined

0

-1

1

#182. Find the slope of the line through Points: (6, 4) and (2, 4).

1

Undefined

-1

0

#183. Find the slope of the line f(x) = 2x – 7.

1/2

7

2

-2

#184. Find the slope of the line 3x – y = 5.

1/3

-1/3

-3

3

#185. Find the slope of the line 2x + 3y = 12.

-2/3

2/3

-3/2

3/2

#186. Find the slope of the line y = 5.

0

5

1

Undefined

#187. If f(x) = x^2, what function results from a shift up 3?

g(x) = x^2 – 3

g(x) = 3x^2

g(x) = (x + 3)^2

g(x) = x^2 + 3

#188. If f(x) = x^2, what function results from a shift left 2?

g(x) = (x + 2)^2

g(x) = x^2 + 2

g(x) = x^2 – 2

g(x) = (x – 2)^2

#189. If f(x) = √x, what function results from a reflect over x-axis?

g(x) = -√(x)

g(x) = √(-x)

g(x) = -√x

g(x) = √x – 1

#190. If f(x) = |x|, what function results from a vertical stretch by 2?

g(x) = |2x|

g(x) = 2|x|

g(x) = 0.5|x|

g(x) = |x| + 2

#191. If f(x) = x^3, what function results from a shift right 4?

g(x) = x^3 – 4

g(x) = (x – 4)^3

g(x) = (x + 4)^3

g(x) = x^3 + 4

#192. If f(x) = 1/x, what function results from a shift down 1?

g(x) = 1/(x + 1)

g(x) = 1/x – 1

g(x) = 1/x + 1

g(x) = 1/(x – 1)

#193. Given f(x) = 2x + 3, g(x) = x – 1, find f(g(x)).

2x + 1

2x – 1

2x + 2

2x

#194. Given f(x) = x^2, g(x) = x + 2, find f(g(x)).

x^2 + 4

(x + 2)^2

x^2 + 4x + 4

x^2 + 2

#195. Given f(x) = 1/x, g(x) = 2x, find f(g(x)).

1/(x + 2)

1/(2x)

2/x

1/2x

#196. Given f(x) = 3x – 2, find f^-1(x).

3x – 2

(x – 2)/3

3x + 2

(x + 2)/3

#197. Given f(x) = x^2 + 1, x ≥ 0, find f^-1(x).

√x + 1

√(x + 1)

√(x – 1)

√x – 1

#198. Given f(x) = (2x – 3)/4, find the inverse.

(4x – 3)/2

(2x – 3)/4

(2x + 3)/4

(4x + 3)/2

#199. Given f(x) = 5x + 1, find f^-1(x).

(x – 1)/5

5x + 1

5x – 1

(x + 1)/5

#200. Given f(x) = x^3, find f^-1(x).

3/x

x^(1/3)

1/x^3

x^3

Algebraic Reasoning – Set 4

Results

#1. A shipping costs problem requires solving: 3x + 12 = 45. What is the value of x?

#2. In a concert ticket pricing scenario: 2x – 8 = 22. Solve for x.

#3. A bakery inventory problem: 5x + 15 = 70. What is x?

#4. Solving this hourly wage calculation equation: 4x – 20 = 60. Find x.

#5. A subscription fees problem: 6x + 9 = 51. What is the value of x?

#6. In temperature conversion: 2x – 5 = 13. Solve for x.

#7. A package weight problem: 3x + 18 = 42. Find x.

#8. Solving for book pricing: 7x – 14 = 35. What is x?

#9. A cafe supplies equation: 4x + 8 = 32. Find x.

#10. Solving the gym membership problem: 5x – 25 = 50. What is x?

#11. Rearrange this rectangular perimeter formula P = 2l + 2w to solve for w.

#12. Using the triangle area formula A = bh/2, solve for h.

#13. From this motion equation v = u + at, rearrange to find a.

#14. Solve the force formula F = ma for m.

#15. Rearranging the linear function y = mx + b to solve for m gives:

#16. From the circle circumference equation C = 2πr, express r in terms of C.

#17. Solve the interest formula I = Prt for t.

#18. Rearranging the z-score formula formula z = (x – μ)/σ to solve for x:

#19. Solve the weight limit inequality: 3x < 60

#20. For this budget constraint problem, solve: 5x + 10 ≥ 35

#21. Which inequality solution matches this temperature range: 2x – 8 > 12

#22. Solve the enrollment threshold inequality: 4x ≤ 100

#23. For this age requirement problem, solve: x + 5 > 21

#24. Which inequality solution matches this distance boundary: 6x < 90

#25. Solve the quantity limit inequality: 2x + 3 ≤ 25

#26. For this payment minimum problem, solve: 7x – 14 ≥ 42

#27. Which inequality solution matches this capacity constraint: 3x ≤ 75

#28. Solve the speed restriction inequality: x – 10 < 55

#29. For this score requirement problem, solve: 8x + 4 > 60

#30. Which inequality solution matches this inventory check: 5x – 20 ≤ 80

#31. Solve the absolute value equation: |2x – 5| = 11

#32. Solve the absolute value equation: |x + 3| = 7

#33. Solve the absolute value equation: |3x – 6| = 9

#34. Solve the absolute value equation: |x – 4| = 6

#35. Solve the absolute value equation: |2x + 1| = 7

#36. Find all solutions to: |x + 8| = 5

#37. Find all solutions to: |4x – 3| = 5

#38. Find all solutions to: |2x – 10| = 4

#39. Find all solutions to: |x – 1| = 8

#40. Find all solutions to: |3x + 2| = 11

#41. Use substitution to solve this inventory management system: y = 2x + 1 and 3x + y = 16

#42. Use substitution to solve this cost analysis system: x = y – 3 and 2x + y = 12

#43. Use substitution to solve this distance calculation system: y = 3x – 2 and x + y = 14

#44. Use substitution to solve this production planning system: x = 2y + 1 and 3x – y = 13

#45. Use substitution to solve this pricing strategy system: y = -x + 8 and 2x + y = 11

#46. Use substitution to solve this time scheduling system: x = y + 4 and 2x – 3y = 1

#47. Use substitution to solve this capacity planning system: y = 2x – 5 and x + y = 10

#48. Use substitution to solve this resource allocation system: x = 3y – 2 and 2x + y = 11

#49. Use substitution to solve this revenue modeling system: y = 4x + 1 and 2x + y = 19

#50. Use substitution to solve this demand forecasting system: x = 2y – 3 and 3x + y = 14

#51. Use elimination to solve this resource distribution problem: 2x + 3y = 12 and 4x – 3y = 6

#52. Use elimination to solve this supply chain problem: 3x + 2y = 13 and 2x – 2y = 4

#53. Use elimination to solve this logistics problem: x + 2y = 8 and 3x – 2y = 4

#54. Use elimination to solve this budgeting problem: 2x + y = 9 and 3x – y = 6

#55. Use elimination to solve this production problem: 4x + 3y = 23 and 4x – y = 11

#56. Use elimination to solve this inventory problem: 2x + 5y = 14 and 2x – y = 2

#57. Use elimination to solve this pricing problem: 3x + 4y = 24 and 3x – 2y = 6

#58. Use elimination to solve this analytics problem: 5x + 2y = 16 and 3x – 2y = 8

#59. Use elimination to solve this forecasting problem: 2x + 3y = 11 and 4x + 3y = 17

#60. Use elimination to solve this scheduling problem: 3x + 2y = 10 and x + 2y = 6

#61. Two gardens have a combined area of 150 sq ft. One garden is 30 sq ft larger than the other. Find the area of each garden.

#62. At a theater, adult tickets cost $12 and child tickets cost $8. If 150 tickets sold for $1560, how many of each were sold?

#63. A manufacturer produces two types of batteries. Type A takes 2 hours to make, Type B takes 3 hours. If 30 batteries took 80 hours total, how many of each?

#64. Two investments total $5000. One earns 5% annually, the other 8%. If combined annual earnings are $340, find each investment.

#65. A store sells notebooks at $3 each and pens at $1.50 each. In one day, 200 items sold for $450. How many notebooks?

#66. The sum of two numbers is 45. Their difference is 13. Find both numbers.

#67. A train travels from City A to City B at 60 mph and returns at 40 mph. Total time is 10 hours. What is the distance?

#68. A recipe requires flour and sugar in a ratio where flour is 1.5 times sugar by weight. Total is 10 lbs. Find each amount.

#69. Two pipes fill a tank. One fills it in 6 hours alone, the other in 8 hours. How long together?

#70. A paddler travels 24 miles downstream in 3 hours, upstream in 4 hours. Find boat speed and current.

#71. An event has 200 attendees. VIP tickets are $50, regular are $20. Revenue is $6500. Find each ticket type.

#72. Two alloys: one is 30% copper, other is 60% copper. Combine to make 100 kg of 45% copper alloy. How much of each?

#73. A company’s profit increased from $50k to $80k. One division earned $20k, other earned $60k. What were original amounts?

#74. In a class of 32 students, there are 4 more girls than boys. How many of each?

#75. A rectangle’s length is 3 inches more than width. Perimeter is 50 inches. Find dimensions.

#76. Two accounts have $8000 total. Account A has $1000 more than Account B. Find each amount.

#77. A total of 1200 feet of fencing encloses two adjacent rectangular fields of equal area. Find dimensions if length is twice width.

#78. Gas costs $0.05 per mile, maintenance costs $0.03 per mile. Annual costs are $960 for 12,000 miles. Verify the model.