Answer: spent=60; remaining=9; cart=laptopsx1,cablesx1,docksx1

Do not exceed budget
Per-item cap as stated
Listed order

For each item buy min(cap, remaining//cost)

Prompt: You have a procurement budget of 69. Catalogue (unit cost): laptops=12, cables=40, docks=8, monitors=15. Walk the catalogue in listed order. For each item buy up to 1 units without exceeding the remaining budget. Report spent, remaining, and cart as namexqty comma-separated.

Solution: Greedy catalogue walk yields spent=60; remaining=9; cart=laptopsx1,cablesx1,docksx1.


Answer: spent=64; remaining=6; cart=laptopsx2,cablesx1

Do not exceed budget
Per-item cap as stated
Listed order

For each item buy min(cap, remaining//cost)

Prompt: You have a procurement budget of 70. Catalogue (unit cost): laptops=12, cables=40, docks=8, monitors=15. Walk the catalogue in listed order. For each item buy up to 2 units without exceeding the remaining budget. Report spent, remaining, and cart as namexqty comma-separated.

Solution: Greedy catalogue walk yields spent=64; remaining=6; cart=laptopsx2,cablesx1.


Answer: spent=60; remaining=11; cart=laptopsx3,docksx3

Do not exceed budget
Per-item cap as stated
Listed order

For each item buy min(cap, remaining//cost)

Prompt: You have a procurement budget of 71. Catalogue (unit cost): laptops=12, cables=40, docks=8, monitors=15. Walk the catalogue in listed order. For each item buy up to 3 units without exceeding the remaining budget. Report spent, remaining, and cart as namexqty comma-separated.

Solution: Greedy catalogue walk yields spent=60; remaining=11; cart=laptopsx3,docksx3.


Answer: spent=60; remaining=12; cart=laptopsx1,cablesx1,docksx1

Do not exceed budget
Per-item cap as stated
Listed order

For each item buy min(cap, remaining//cost)

Prompt: You have a procurement budget of 72. Catalogue (unit cost): laptops=12, cables=40, docks=8, monitors=15. Walk the catalogue in listed order. For each item buy up to 1 units without exceeding the remaining budget. Report spent, remaining, and cart as namexqty comma-separated.

Solution: Greedy catalogue walk yields spent=60; remaining=12; cart=laptopsx1,cablesx1,docksx1.


Answer: spent=72; remaining=1; cart=laptopsx2,cablesx1,docksx1

Do not exceed budget
Per-item cap as stated
Listed order

For each item buy min(cap, remaining//cost)

Prompt: You have a procurement budget of 73. Catalogue (unit cost): laptops=12, cables=40, docks=8, monitors=15. Walk the catalogue in listed order. For each item buy up to 2 units without exceeding the remaining budget. Report spent, remaining, and cart as namexqty comma-separated.

Solution: Greedy catalogue walk yields spent=72; remaining=1; cart=laptopsx2,cablesx1,docksx1.


Answer: spent=60; remaining=14; cart=laptopsx3,docksx3

Do not exceed budget
Per-item cap as stated
Listed order

For each item buy min(cap, remaining//cost)

Prompt: You have a procurement budget of 74. Catalogue (unit cost): laptops=12, cables=40, docks=8, monitors=15. Walk the catalogue in listed order. For each item buy up to 3 units without exceeding the remaining budget. Report spent, remaining, and cart as namexqty comma-separated.

Solution: Greedy catalogue walk yields spent=60; remaining=14; cart=laptopsx3,docksx3.


Answer: spent=75; remaining=0; cart=laptopsx1,cablesx1,docksx1,monitorsx1

Do not exceed budget
Per-item cap as stated
Listed order

For each item buy min(cap, remaining//cost)

Prompt: You have a procurement budget of 75. Catalogue (unit cost): laptops=12, cables=40, docks=8, monitors=15. Walk the catalogue in listed order. For each item buy up to 1 units without exceeding the remaining budget. Report spent, remaining, and cart as namexqty comma-separated.

Solution: Greedy catalogue walk yields spent=75; remaining=0; cart=laptopsx1,cablesx1,docksx1,monitorsx1.


Answer: spent=72; remaining=4; cart=laptopsx2,cablesx1,docksx1

Do not exceed budget
Per-item cap as stated
Listed order

For each item buy min(cap, remaining//cost)

Prompt: You have a procurement budget of 76. Catalogue (unit cost): laptops=12, cables=40, docks=8, monitors=15. Walk the catalogue in listed order. For each item buy up to 2 units without exceeding the remaining budget. Report spent, remaining, and cart as namexqty comma-separated.

Solution: Greedy catalogue walk yields spent=72; remaining=4; cart=laptopsx2,cablesx1,docksx1.


Answer: spent=76; remaining=1; cart=laptopsx3,cablesx1

Do not exceed budget
Per-item cap as stated
Listed order

For each item buy min(cap, remaining//cost)

Prompt: You have a procurement budget of 77. Catalogue (unit cost): laptops=12, cables=40, docks=8, monitors=15. Walk the catalogue in listed order. For each item buy up to 3 units without exceeding the remaining budget. Report spent, remaining, and cart as namexqty comma-separated.

Solution: Greedy catalogue walk yields spent=76; remaining=1; cart=laptopsx3,cablesx1.


Answer: spent=75; remaining=3; cart=laptopsx1,cablesx1,docksx1,monitorsx1

Do not exceed budget
Per-item cap as stated
Listed order

For each item buy min(cap, remaining//cost)

Prompt: You have a procurement budget of 78. Catalogue (unit cost): laptops=12, cables=40, docks=8, monitors=15. Walk the catalogue in listed order. For each item buy up to 1 units without exceeding the remaining budget. Report spent, remaining, and cart as namexqty comma-separated.

Solution: Greedy catalogue walk yields spent=75; remaining=3; cart=laptopsx1,cablesx1,docksx1,monitorsx1.


Answer: spent=72; remaining=7; cart=laptopsx2,cablesx1,docksx1

Do not exceed budget
Per-item cap as stated
Listed order

For each item buy min(cap, remaining//cost)

Prompt: You have a procurement budget of 79. Catalogue (unit cost): laptops=12, cables=40, docks=8, monitors=15. Walk the catalogue in listed order. For each item buy up to 2 units without exceeding the remaining budget. Report spent, remaining, and cart as namexqty comma-separated.

Solution: Greedy catalogue walk yields spent=72; remaining=7; cart=laptopsx2,cablesx1,docksx1.


Answer: spent=76; remaining=4; cart=laptopsx3,cablesx1

Do not exceed budget
Per-item cap as stated
Listed order

For each item buy min(cap, remaining//cost)

Prompt: You have a procurement budget of 80. Catalogue (unit cost): laptops=12, cables=40, docks=8, monitors=15. Walk the catalogue in listed order. For each item buy up to 3 units without exceeding the remaining budget. Report spent, remaining, and cart as namexqty comma-separated.

Solution: Greedy catalogue walk yields spent=76; remaining=4; cart=laptopsx3,cablesx1.


Answer: spent=75; remaining=6; cart=laptopsx1,cablesx1,docksx1,monitorsx1

Do not exceed budget
Per-item cap as stated
Listed order

For each item buy min(cap, remaining//cost)

Prompt: You have a procurement budget of 81. Catalogue (unit cost): laptops=12, cables=40, docks=8, monitors=15. Walk the catalogue in listed order. For each item buy up to 1 units without exceeding the remaining budget. Report spent, remaining, and cart as namexqty comma-separated.

Solution: Greedy catalogue walk yields spent=75; remaining=6; cart=laptopsx1,cablesx1,docksx1,monitorsx1.


Answer: spent=80; remaining=2; cart=laptopsx2,cablesx1,docksx2

Do not exceed budget
Per-item cap as stated
Listed order

For each item buy min(cap, remaining//cost)

Prompt: You have a procurement budget of 82. Catalogue (unit cost): laptops=12, cables=40, docks=8, monitors=15. Walk the catalogue in listed order. For each item buy up to 2 units without exceeding the remaining budget. Report spent, remaining, and cart as namexqty comma-separated.

Solution: Greedy catalogue walk yields spent=80; remaining=2; cart=laptopsx2,cablesx1,docksx2.


Answer: spent=76; remaining=7; cart=laptopsx3,cablesx1

Do not exceed budget
Per-item cap as stated
Listed order

For each item buy min(cap, remaining//cost)

Prompt: You have a procurement budget of 83. Catalogue (unit cost): laptops=12, cables=40, docks=8, monitors=15. Walk the catalogue in listed order. For each item buy up to 3 units without exceeding the remaining budget. Report spent, remaining, and cart as namexqty comma-separated.

Solution: Greedy catalogue walk yields spent=76; remaining=7; cart=laptopsx3,cablesx1.


Answer: spent=75; remaining=9; cart=laptopsx1,cablesx1,docksx1,monitorsx1

Do not exceed budget
Per-item cap as stated
Listed order

For each item buy min(cap, remaining//cost)

Prompt: You have a procurement budget of 84. Catalogue (unit cost): laptops=12, cables=40, docks=8, monitors=15. Walk the catalogue in listed order. For each item buy up to 1 units without exceeding the remaining budget. Report spent, remaining, and cart as namexqty comma-separated.

Solution: Greedy catalogue walk yields spent=75; remaining=9; cart=laptopsx1,cablesx1,docksx1,monitorsx1.


Answer: spent=80; remaining=5; cart=laptopsx2,cablesx1,docksx2

Do not exceed budget
Per-item cap as stated
Listed order

For each item buy min(cap, remaining//cost)

Prompt: You have a procurement budget of 85. Catalogue (unit cost): laptops=12, cables=40, docks=8, monitors=15. Walk the catalogue in listed order. For each item buy up to 2 units without exceeding the remaining budget. Report spent, remaining, and cart as namexqty comma-separated.

Solution: Greedy catalogue walk yields spent=80; remaining=5; cart=laptopsx2,cablesx1,docksx2.


Answer: spent=84; remaining=2; cart=laptopsx3,cablesx1,docksx1

Do not exceed budget
Per-item cap as stated
Listed order

For each item buy min(cap, remaining//cost)

Prompt: You have a procurement budget of 86. Catalogue (unit cost): laptops=12, cables=40, docks=8, monitors=15. Walk the catalogue in listed order. For each item buy up to 3 units without exceeding the remaining budget. Report spent, remaining, and cart as namexqty comma-separated.

Solution: Greedy catalogue walk yields spent=84; remaining=2; cart=laptopsx3,cablesx1,docksx1.


Answer: spent=75; remaining=12; cart=laptopsx1,cablesx1,docksx1,monitorsx1

Do not exceed budget
Per-item cap as stated
Listed order

For each item buy min(cap, remaining//cost)

Prompt: You have a procurement budget of 87. Catalogue (unit cost): laptops=12, cables=40, docks=8, monitors=15. Walk the catalogue in listed order. For each item buy up to 1 units without exceeding the remaining budget. Report spent, remaining, and cart as namexqty comma-separated.

Solution: Greedy catalogue walk yields spent=75; remaining=12; cart=laptopsx1,cablesx1,docksx1,monitorsx1.


Answer: spent=80; remaining=8; cart=laptopsx2,cablesx1,docksx2

Do not exceed budget
Per-item cap as stated
Listed order

For each item buy min(cap, remaining//cost)

Prompt: You have a procurement budget of 88. Catalogue (unit cost): laptops=12, cables=40, docks=8, monitors=15. Walk the catalogue in listed order. For each item buy up to 2 units without exceeding the remaining budget. Report spent, remaining, and cart as namexqty comma-separated.

Solution: Greedy catalogue walk yields spent=80; remaining=8; cart=laptopsx2,cablesx1,docksx2.


Answer: spent=84; remaining=5; cart=laptopsx3,cablesx1,docksx1

Do not exceed budget
Per-item cap as stated
Listed order

For each item buy min(cap, remaining//cost)

Prompt: You have a procurement budget of 89. Catalogue (unit cost): laptops=12, cables=40, docks=8, monitors=15. Walk the catalogue in listed order. For each item buy up to 3 units without exceeding the remaining budget. Report spent, remaining, and cart as namexqty comma-separated.

Solution: Greedy catalogue walk yields spent=84; remaining=5; cart=laptopsx3,cablesx1,docksx1.


Answer: spent=75; remaining=15; cart=laptopsx1,cablesx1,docksx1,monitorsx1

Do not exceed budget
Per-item cap as stated
Listed order

For each item buy min(cap, remaining//cost)

Prompt: You have a procurement budget of 90. Catalogue (unit cost): laptops=12, cables=40, docks=8, monitors=15. Walk the catalogue in listed order. For each item buy up to 1 units without exceeding the remaining budget. Report spent, remaining, and cart as namexqty comma-separated.

Solution: Greedy catalogue walk yields spent=75; remaining=15; cart=laptopsx1,cablesx1,docksx1,monitorsx1.


Answer: spent=80; remaining=11; cart=laptopsx2,cablesx1,docksx2

Do not exceed budget
Per-item cap as stated
Listed order

For each item buy min(cap, remaining//cost)

Prompt: You have a procurement budget of 91. Catalogue (unit cost): laptops=12, cables=40, docks=8, monitors=15. Walk the catalogue in listed order. For each item buy up to 2 units without exceeding the remaining budget. Report spent, remaining, and cart as namexqty comma-separated.

Solution: Greedy catalogue walk yields spent=80; remaining=11; cart=laptopsx2,cablesx1,docksx2.


Answer: spent=92; remaining=0; cart=laptopsx3,cablesx1,docksx2

Do not exceed budget
Per-item cap as stated
Listed order

For each item buy min(cap, remaining//cost)

Prompt: You have a procurement budget of 92. Catalogue (unit cost): laptops=12, cables=40, docks=8, monitors=15. Walk the catalogue in listed order. For each item buy up to 3 units without exceeding the remaining budget. Report spent, remaining, and cart as namexqty comma-separated.

Solution: Greedy catalogue walk yields spent=92; remaining=0; cart=laptopsx3,cablesx1,docksx2.


Answer: spent=75; remaining=18; cart=laptopsx1,cablesx1,docksx1,monitorsx1

Do not exceed budget
Per-item cap as stated
Listed order

For each item buy min(cap, remaining//cost)

Prompt: You have a procurement budget of 93. Catalogue (unit cost): laptops=12, cables=40, docks=8, monitors=15. Walk the catalogue in listed order. For each item buy up to 1 units without exceeding the remaining budget. Report spent, remaining, and cart as namexqty comma-separated.

Solution: Greedy catalogue walk yields spent=75; remaining=18; cart=laptopsx1,cablesx1,docksx1,monitorsx1.


Answer: spent=80; remaining=14; cart=laptopsx2,cablesx1,docksx2

Do not exceed budget
Per-item cap as stated
Listed order

For each item buy min(cap, remaining//cost)

Prompt: You have a procurement budget of 94. Catalogue (unit cost): laptops=12, cables=40, docks=8, monitors=15. Walk the catalogue in listed order. For each item buy up to 2 units without exceeding the remaining budget. Report spent, remaining, and cart as namexqty comma-separated.

Solution: Greedy catalogue walk yields spent=80; remaining=14; cart=laptopsx2,cablesx1,docksx2.


Answer: spent=92; remaining=3; cart=laptopsx3,cablesx1,docksx2

Do not exceed budget
Per-item cap as stated
Listed order

For each item buy min(cap, remaining//cost)

Prompt: You have a procurement budget of 95. Catalogue (unit cost): laptops=12, cables=40, docks=8, monitors=15. Walk the catalogue in listed order. For each item buy up to 3 units without exceeding the remaining budget. Report spent, remaining, and cart as namexqty comma-separated.

Solution: Greedy catalogue walk yields spent=92; remaining=3; cart=laptopsx3,cablesx1,docksx2.


Answer: spent=75; remaining=21; cart=laptopsx1,cablesx1,docksx1,monitorsx1

Do not exceed budget
Per-item cap as stated
Listed order

For each item buy min(cap, remaining//cost)

Prompt: You have a procurement budget of 96. Catalogue (unit cost): laptops=12, cables=40, docks=8, monitors=15. Walk the catalogue in listed order. For each item buy up to 1 units without exceeding the remaining budget. Report spent, remaining, and cart as namexqty comma-separated.

Solution: Greedy catalogue walk yields spent=75; remaining=21; cart=laptopsx1,cablesx1,docksx1,monitorsx1.


Answer: spent=95; remaining=2; cart=laptopsx2,cablesx1,docksx2,monitorsx1

Do not exceed budget
Per-item cap as stated
Listed order

For each item buy min(cap, remaining//cost)

Prompt: You have a procurement budget of 97. Catalogue (unit cost): laptops=12, cables=40, docks=8, monitors=15. Walk the catalogue in listed order. For each item buy up to 2 units without exceeding the remaining budget. Report spent, remaining, and cart as namexqty comma-separated.

Solution: Greedy catalogue walk yields spent=95; remaining=2; cart=laptopsx2,cablesx1,docksx2,monitorsx1.


Answer: spent=92; remaining=6; cart=laptopsx3,cablesx1,docksx2

Do not exceed budget
Per-item cap as stated
Listed order

For each item buy min(cap, remaining//cost)

Prompt: You have a procurement budget of 98. Catalogue (unit cost): laptops=12, cables=40, docks=8, monitors=15. Walk the catalogue in listed order. For each item buy up to 3 units without exceeding the remaining budget. Report spent, remaining, and cart as namexqty comma-separated.

Solution: Greedy catalogue walk yields spent=92; remaining=6; cart=laptopsx3,cablesx1,docksx2.


Answer: spent=75; remaining=24; cart=laptopsx1,cablesx1,docksx1,monitorsx1

Do not exceed budget
Per-item cap as stated
Listed order

For each item buy min(cap, remaining//cost)

Prompt: You have a procurement budget of 99. Catalogue (unit cost): laptops=12, cables=40, docks=8, monitors=15. Walk the catalogue in listed order. For each item buy up to 1 units without exceeding the remaining budget. Report spent, remaining, and cart as namexqty comma-separated.

Solution: Greedy catalogue walk yields spent=75; remaining=24; cart=laptopsx1,cablesx1,docksx1,monitorsx1.


Answer: spent=95; remaining=5; cart=laptopsx2,cablesx1,docksx2,monitorsx1

Do not exceed budget
Per-item cap as stated
Listed order

For each item buy min(cap, remaining//cost)

Prompt: You have a procurement budget of 100. Catalogue (unit cost): laptops=12, cables=40, docks=8, monitors=15. Walk the catalogue in listed order. For each item buy up to 2 units without exceeding the remaining budget. Report spent, remaining, and cart as namexqty comma-separated.

Solution: Greedy catalogue walk yields spent=95; remaining=5; cart=laptopsx2,cablesx1,docksx2,monitorsx1.


Answer: spent=100; remaining=1; cart=laptopsx3,cablesx1,docksx3

Do not exceed budget
Per-item cap as stated
Listed order

For each item buy min(cap, remaining//cost)

Prompt: You have a procurement budget of 101. Catalogue (unit cost): laptops=12, cables=40, docks=8, monitors=15. Walk the catalogue in listed order. For each item buy up to 3 units without exceeding the remaining budget. Report spent, remaining, and cart as namexqty comma-separated.

Solution: Greedy catalogue walk yields spent=100; remaining=1; cart=laptopsx3,cablesx1,docksx3.


Answer: spent=75; remaining=27; cart=laptopsx1,cablesx1,docksx1,monitorsx1

Do not exceed budget
Per-item cap as stated
Listed order

For each item buy min(cap, remaining//cost)

Prompt: You have a procurement budget of 102. Catalogue (unit cost): laptops=12, cables=40, docks=8, monitors=15. Walk the catalogue in listed order. For each item buy up to 1 units without exceeding the remaining budget. Report spent, remaining, and cart as namexqty comma-separated.

Solution: Greedy catalogue walk yields spent=75; remaining=27; cart=laptopsx1,cablesx1,docksx1,monitorsx1.


Answer: spent=95; remaining=8; cart=laptopsx2,cablesx1,docksx2,monitorsx1

Do not exceed budget
Per-item cap as stated
Listed order

For each item buy min(cap, remaining//cost)

Prompt: You have a procurement budget of 103. Catalogue (unit cost): laptops=12, cables=40, docks=8, monitors=15. Walk the catalogue in listed order. For each item buy up to 2 units without exceeding the remaining budget. Report spent, remaining, and cart as namexqty comma-separated.

Solution: Greedy catalogue walk yields spent=95; remaining=8; cart=laptopsx2,cablesx1,docksx2,monitorsx1.


Answer: spent=100; remaining=4; cart=laptopsx3,cablesx1,docksx3

Do not exceed budget
Per-item cap as stated
Listed order

For each item buy min(cap, remaining//cost)

Prompt: You have a procurement budget of 104. Catalogue (unit cost): laptops=12, cables=40, docks=8, monitors=15. Walk the catalogue in listed order. For each item buy up to 3 units without exceeding the remaining budget. Report spent, remaining, and cart as namexqty comma-separated.

Solution: Greedy catalogue walk yields spent=100; remaining=4; cart=laptopsx3,cablesx1,docksx3.


Answer: spent=75; remaining=30; cart=laptopsx1,cablesx1,docksx1,monitorsx1

Do not exceed budget
Per-item cap as stated
Listed order

For each item buy min(cap, remaining//cost)

Prompt: You have a procurement budget of 105. Catalogue (unit cost): laptops=12, cables=40, docks=8, monitors=15. Walk the catalogue in listed order. For each item buy up to 1 units without exceeding the remaining budget. Report spent, remaining, and cart as namexqty comma-separated.

Solution: Greedy catalogue walk yields spent=75; remaining=30; cart=laptopsx1,cablesx1,docksx1,monitorsx1.


Answer: spent=104; remaining=2; cart=laptopsx2,cablesx2

Do not exceed budget
Per-item cap as stated
Listed order

For each item buy min(cap, remaining//cost)

Prompt: You have a procurement budget of 106. Catalogue (unit cost): laptops=12, cables=40, docks=8, monitors=15. Walk the catalogue in listed order. For each item buy up to 2 units without exceeding the remaining budget. Report spent, remaining, and cart as namexqty comma-separated.

Solution: Greedy catalogue walk yields spent=104; remaining=2; cart=laptopsx2,cablesx2.


Answer: spent=100; remaining=7; cart=laptopsx3,cablesx1,docksx3

Do not exceed budget
Per-item cap as stated
Listed order

For each item buy min(cap, remaining//cost)

Prompt: You have a procurement budget of 107. Catalogue (unit cost): laptops=12, cables=40, docks=8, monitors=15. Walk the catalogue in listed order. For each item buy up to 3 units without exceeding the remaining budget. Report spent, remaining, and cart as namexqty comma-separated.

Solution: Greedy catalogue walk yields spent=100; remaining=7; cart=laptopsx3,cablesx1,docksx3.


Answer: spent=75; remaining=33; cart=laptopsx1,cablesx1,docksx1,monitorsx1

Do not exceed budget
Per-item cap as stated
Listed order

For each item buy min(cap, remaining//cost)

Prompt: You have a procurement budget of 108. Catalogue (unit cost): laptops=12, cables=40, docks=8, monitors=15. Walk the catalogue in listed order. For each item buy up to 1 units without exceeding the remaining budget. Report spent, remaining, and cart as namexqty comma-separated.

Solution: Greedy catalogue walk yields spent=75; remaining=33; cart=laptopsx1,cablesx1,docksx1,monitorsx1.


Answer: spent=104; remaining=5; cart=laptopsx2,cablesx2

Do not exceed budget
Per-item cap as stated
Listed order

For each item buy min(cap, remaining//cost)

Prompt: You have a procurement budget of 109. Catalogue (unit cost): laptops=12, cables=40, docks=8, monitors=15. Walk the catalogue in listed order. For each item buy up to 2 units without exceeding the remaining budget. Report spent, remaining, and cart as namexqty comma-separated.

Solution: Greedy catalogue walk yields spent=104; remaining=5; cart=laptopsx2,cablesx2.


Answer: 14

Do not insert extra parentheses that change meaning.

Apply precedence
Compute the product
Add

Prompt: Evaluate 2 + 3 * 4 using standard arithmetic precedence.

Solution: Multiplication binds first: 3 * 4 = 12, then 2 + 12 = 14.


Answer: -3

Isolate x
Simplify
Check by substitution

Prompt: Solve for x: x + 5 = 2.

Solution: Subtract 5 from both sides: x = 2 - 5 = -3.


Answer: 1

f(0) is undefined.
Nearby values approach 1.

Recognize the indeterminate form
Recall or compute the standard limit
State 1

Prompt: Compute lim_{x -> 0} (sin x)/x. Direct substitution is undefined; still give the limit.

Solution: The two-sided limit is 1. A 0/0 form at a point does not by itself imply the limit is missing.


Answer: 4

Assume a particle model and constant mass.

Net force and mass are given in SI units.

Prompt: A net force of 12 N acts on a 3 kg mass. What is the acceleration magnitude in m/s^2?

Solution: Newton's second law: a = F/m = 12/3 = 4 m/s^2.


Answer: 8

Apply the definition
Compute
Record the number

Prompt: What is 17 - 9?


Answer: 42

Apply the definition
Compute
Record the number

Prompt: What is 6 × 7?


Answer: 5

Apply the definition
Compute
Record the number

Prompt: Solve 3x - 6 = 9. What is x?

Solution: 3x=15, x=5.


Answer: 40

Apply the definition
Compute
Record the number

Prompt: A rectangle is 5 by 8. What is the area?


Answer: 1/6

Apply the definition
Compute
Record the number

Prompt: A fair six-sided die. P(rolling a 5) as a reduced fraction a/b. Report a/b.

Solution: One favorable face of six.


Answer: 5

Apply the definition
Compute
Record the number

Prompt: Mean of 2, 4, 6, 8?


Answer: 5

Apply the definition
Compute
Record the number

Prompt: Two 10 ohm resistors in parallel. Equivalent resistance in ohms?

Solution: 1/R=1/10+1/10; R=5.


Answer: 4

Apply the definition
Compute
Record the number

Prompt: A wave travels 12 m in 3 s. Speed in m/s?


Answer: 24

Apply the definition
Compute
Record the number

Prompt: How many grams in 2 mol of a 12 g/mol element?

Solution: m=nM=24 g.


Answer: 60

Apply the definition
Compute
Record the number

Prompt: mgh with m=2 kg, g=10 m/s2, h=3 m. Potential energy in J?

Solution: E=60 J.


Answer: 15

Apply the definition
Compute
Record the number

Prompt: A loop runs n=5 times, each time doing 3 constant steps. How many steps?


Answer: 6

Apply the definition
Compute
Record the number

Prompt: How many 2-element subsets of {a,b,c,d}?


Answer: 11

Apply the definition
Compute
Record the number

Prompt: Dot product of (1,2) and (3,4)?


Answer: 1

Apply the definition
Compute
Record the number

Prompt: What is 29 mod 7?


Answer: 0.25

Apply the definition
Compute
Record the number

Prompt: Aa × Aa, P(aa) as a decimal 0.25 or fraction 1/4. Report 0.25.

Solution: One of four Punnett cells.


Answer: 16

Apply the definition
Compute
Record the number

Prompt: Arithmetic sequence 4, 7, 10. What is the 5th term?

Solution: a_n=4+3(n-1); n=5 gives 16.


Answer: -2

Apply the definition
Compute
Record the number

Prompt: Magnification m=-v/u with v=10, u=5 (same units). What is m?


Answer: 10

Apply the definition
Compute
Record the number

Prompt: Convert 10 °C of temperature change to kelvin difference.

Solution: ΔT in K equals ΔT in °C.


Answer: Multiplication binds more tightly than addition, matching ordinary arithmetic.

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Prompt: Why does `3 + 2 * 4` evaluate to 11 in Python rather than 20?

Solution: * and / are tighter than + and -. Parentheses override. 2*4=8, then 3+8=11.


Answer: 512; exponentiation associates to the right, so 2**(3**2).

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Prompt: What is the value of `2 ** 3 ** 2` in Python, and which way does `**` associate?

Solution: 3**2 is 9, then 2**9 is 512. Left-associative would have been (2**3)**2 = 64.


Answer: 5

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Prompt: A right triangle has legs 3 and 4. What is the hypotenuse?

Solution: Pythagoras: sqrt(9+16)=sqrt(25)=5.


Answer: 100*pi

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Prompt: A circle has radius 10. What is its area in terms of pi?

Solution: A=pi r^2 = pi*100.


Answer: 1

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Prompt: What is sin(pi/2) in radians?

Solution: pi/2 radians is 90 degrees; sine of a right angle is 1.


Answer: 10

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Prompt: How many 3-element subsets does a 5-element set have?


Answer: 1/2

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Prompt: A fair coin is flipped twice. What is P(exactly one head)?

Solution: Outcomes HH,HT,TH,TT equally likely. Exactly one head: HT, TH. 2/4=1/2.


Answer: 6

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Prompt: What is the determinant of the 2x2 matrix [[2, 0], [0, 3]]?

Solution: ad-bc = 2*3-0*0=6.


Answer: 2

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Prompt: What is 17 mod 5?


Answer: 9

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Prompt: A 2 kg mass moves at 3 m/s. What is its kinetic energy in joules?

Solution: KE=1/2 m v^2 = 0.5*2*9=9 J.


Answer: 4

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Prompt: A 12 V battery drives 3 A through a resistor. What is the resistance in ohms?

Solution: V=IR so R=V/I=12/3=4 ohm.


Answer: 4

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Prompt: Water is H2O. How many moles of hydrogen atoms are in 2 moles of water?

Solution: Each water molecule has 2 H atoms, so 2 mol water contains 4 mol H atoms.


Answer: 2

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Prompt: A wave has speed 10 m/s and frequency 5 Hz. What is the wavelength in meters?

Solution: v=f lambda so lambda=v/f=10/5=2 m.


Answer: 19

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Prompt: f(x)=2x+1 and g(x)=x^2. What is (f ∘ g)(3)?

Solution: g(3)=9, then f(9)=19.


Answer: y is 4. Integers are immutable; x was rebound, y was not.

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Prompt: After `x = 4; y = x; x = 5`, what is y, and did y change because x changed?

Solution: Rebinding x does not follow other names. y still refers to 4.


Answer: 3*x**2

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Prompt: What is the derivative of x^3 with respect to x?

Solution: Power rule: n x^{n-1}. Here n=3.


Answer: 4

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Prompt: An undirected graph has 4 vertices and is a square (cycle of 4). How many edges does it have?

Solution: A C4 has four vertices and four edges.


Answer: 2

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Prompt: Naive recursive Fibonacci without memoization computes F(5). How many times is F(3) evaluated in the standard tree F(n)=F(n-1)+F(n-2) with F(0),F(1) bases?

Solution: F(5) calls F(4) and F(3). F(4) calls F(3) and F(2). F(3) appears twice.


Answer: 5

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Prompt: What is the mean of 2, 4, 6, 8?

Solution: (2+4+6+8)/4 = 20/4 = 5.


Answer: 18

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Prompt: An arithmetic sequence has first term 3 and common difference 5. What is the 4th term?

Solution: a_n = a_1 + (n-1)d = 3 + 3*5 = 18.


Answer: 4

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Prompt: A geometric series has first term 2 and ratio 1/2. What is the infinite sum, if it exists?

Solution: For |r|<1, S=a/(1-r)=2/(1-1/2)=4.


Answer: 25104

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Prompt: How much heat in joules raises 2 kg of water by 3 K if c=4184 J/(kg·K)?

Solution: Q=mcΔT=2*4184*3=25104 J.


Answer: 20

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Prompt: A converging lens has focal length 10 cm. A real object is 20 cm from the lens. Using 1/f = 1/v + 1/u with positive object and image distances, what is the image distance v in cm?

Solution: 1/10 = 1/v + 1/20, so 1/v = 1/10 - 1/20 = 1/20, hence v = 20.


Answer: 1/4

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Prompt: Both parents are heterozygous Aa for a dominant trait. What fraction of offspring are expected aa?

Solution: Punnett: AA, Aa, Aa, aa. One of four is aa.


Answer: 5

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Prompt: A rectangle's length is 3 more than its width. Perimeter is 26. What is the width?

Solution: 2(w+3)+2w=26 => 4w+6=26 => 4w=20 => w=5.


Answer: 3

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Prompt: A singly linked list has 4 nodes. How many next-pointer follows, starting at the head, reach the last node?

Solution: From the first node you take 3 hops to the fourth.


Answer: 3

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Prompt: After `x = 3; y = x; x = 4`, what is y?

Solution: y still refers to the int 3. Rebinding x does not rebind y.


Answer: 2; bool is a subclass of int, True==1.

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Prompt: What is `True + True` in Python, and why is that legal?

Solution: Boolean values participate in integer arithmetic. Prefer explicit int() if the intent is numeric.


Answer: 3 times: 2, 5, 8

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Prompt: How many times does `for i in range(2, 10, 3):` run, and what values of i?

Solution: Start 2, step 3, stop before 10.


Answer: 9

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Prompt: A recipe for 4 people uses 6 eggs. How many eggs for 6 people, scaling linearly?


Answer: Subtraction is left-associative; 16-8-2 = (16-8)-2 = 6.

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Prompt: A student computes 16-8-2 as 16-(8-2)=10. What went wrong?

Solution: Parentheses changed the meaning. Write (16-8)-2 or 16-8-2 consistently.


Answer: 8

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Prompt: Solve 2(x-3)=10. What is x?

Solution: x-3=5, x=8.


Answer: 19

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Prompt: If f(x)=2x+1 and g(x)=x^2, what is f(g(3))?

Solution: g(3)=9, f(9)=19.


Answer: 12

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Prompt: d/dx of x^3 at x=2?

Solution: 3x^2 at 2 is 12.


Answer: The derivative of a constant is 0.

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Prompt: A student says the derivative of a constant 7 is 7. Correction?

Solution: Slope of a horizontal line is zero. 7 is the function value, not the slope.


Answer: They computed circumference; area is 16*pi.

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Prompt: Someone uses area=2πr for a circle of radius 4. What quantity did they compute instead, and what is the area in terms of pi?

Solution: C=2πr, A=πr^2=16π.


Answer: 5/13

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Prompt: A right triangle has opposite 5 and hypotenuse 13. What is sin of that angle as a reduced fraction?


Answer: 10^2 = 100; order matters and repetition is allowed.

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Prompt: Counting passwords of length 2 from 10 symbols with repetition, a student uses C(10,2). What should they use?

Solution: C(10,2) is unordered distinct pairs.


Answer: 10

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Prompt: How many edges in K_5, the complete graph on 5 vertices?


Answer: 1/4

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Prompt: Two fair coins. A student says P(two heads)=1/3 because HH,HT,TH 'wait they listed TT too' — they listed HH, HT, TT and dropped TH. What is the real probability?

Solution: Four equally likely outcomes; only HH.


Answer: 0.8

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Prompt: P(A)=0.3, P(B)=0.5, disjoint. What is P(A or B)?

Solution: Add when disjoint: 0.3+0.5.


Answer: 6

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Prompt: gcd(24, 18) is?

Solution: Euclid: 24=1*18+6, 18=3*6+0.


Answer: The mean is pulled by 100; the median 2.5 (or 2/3 depending on convention) is robust.

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Prompt: Data 1, 2, 3, 100. A student reports the mean as a typical value. Why is the median often better here?

Solution: For even n, median is average of the two central values: (2+3)/2=2.5.


Answer: 45

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Prompt: Geometric: first term 3, ratio 2, 4 terms. Sum?


Answer: 4

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Prompt: Net force 20 N on 5 kg. Acceleration magnitude?

Solution: a=F/m=4 m/s^2.


Answer: 10

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Prompt: A student sets mgh = 1/2 mv^2 and cancels m, then uses g=10, h=5, and reports v=10 forgetting the 2. Compute the actual v from v=sqrt(2gh).

Solution: v=sqrt(2*10*5)=sqrt(100)=10. If they dropped the 2 they would get sqrt(50).


Answer: 24

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Prompt: Work = force times displacement along the force. 8 N through 3 m, parallel. Work in J?

Solution: W=Fd=24 J.


Answer: Series adds; equivalent is 8 ohm.

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Prompt: Two 4 ohm resistors in series are treated as 4 ohm total. Correction and series equivalent?

Solution: Parallel would be 2 ohm. Series 4+4=8.


Answer: 18

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Prompt: Power P=IV. 3 A through 6 V. Power in W?

Solution: P=18 W.


Answer: 2

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Prompt: 2H2 + O2 -> 2H2O. How many moles of O2 are needed for 4 mol H2?

Solution: Ratio H2:O2 is 2:1, so 4 mol H2 need 2 mol O2.


Answer: 5

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Prompt: Period 0.2 s. Frequency in Hz?

Solution: f=1/T=5 Hz.


Answer: 49/9

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Prompt: A student adds two amplitudes 3 and 4 and reports intensity scaled by 7. For coherent in-phase waves, intensity scales with amplitude squared. If amplitude becomes 7, intensity scales by what factor vs amplitude 3?

Solution: I ~ A^2 so (7/3)^2=49/9.


Answer: 6

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Prompt: Heat and temperature are used interchangeably. Give one sentence distinguishing them, then compute Q=mcΔT for m=2, c=1, ΔT=3 (arbitrary units).

Solution: Temperature is a state; heat is energy transferred. Q=2*1*3=6.


Answer: 20

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Prompt: Thin lens: f=10 cm, object at 20 cm. Image distance v from 1/f=1/v+1/u with u=20. What is v in cm?

Solution: 1/10=1/v+1/20 => 1/v=1/20 => v=20.


Answer: 1/4

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Prompt: AaBb x aabb independent assortment. What fraction of offspring are aabb?

Solution: Each locus is a testcross 1/2 recessive; 1/2 * 1/2 = 1/4.


Answer: 5

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Prompt: How many times does `for i in range(5):` run the body?

Solution: range(5) yields 0,1,2,3,4 — five values.


Answer: 4

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Prompt: How many numbers does `list(range(1, 8, 2))` contain?


Answer: 6

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Prompt: A tracing exercise: def add(a,b): return a+b. What is add(add(1,2), 3)?

Solution: Inner add is 3, then 3+3=6.


Answer: 4

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Prompt: Mergesort split of n=8: how many elements in each half after one even split?

Solution: Even n splits into n/2 and n/2.


Answer: 5

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Prompt: Solve 3x - 6 = 9.

Solution: 3x = 15, so x = 5.


Answer: 28

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Prompt: A linear cost is C(n)=4n+12. What is the cost of 7 extra items relative to 0 items?

Solution: C(7)-C(0)=40-12=28. The intercept cancels; only the slope times 7 remains.


Answer: 15

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Prompt: The first three triangular numbers are 1, 3, 6. What is the 5th?

Solution: T_n = n(n+1)/2. T_5=15.


Answer: 4

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Prompt: Solve 5x = 20. x=?

Solution: Divide both sides by 5.


Answer: 81

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Prompt: A square has perimeter 36. What is the area?

Solution: Side 9, area 81.


Answer: 0

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Prompt: dict.fromkeys(['a','b'], 0) maps both keys to what value?

Solution: fromkeys uses a shared default value.


Answer: 3

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Prompt: In SQLite, what does COUNT(*) return on a table with 3 rows including one all-NULL row?

Solution: COUNT(*) counts rows, not non-NULL values. COUNT(column) would skip NULLs in that column.


Answer: 2

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Prompt: A spacecraft of mass 800 kg feels 1600 N of net thrust. What is the acceleration in m/s^2?

Solution: a = F/m = 1600/800 = 2.


Answer: 50

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Prompt: A 4 kg probe moves at 5 m/s. What is its kinetic energy in joules?

Solution: KE=1/2 m v^2 = 0.5*4*25=50.


Answer: 11314

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Prompt: Using v=sqrt(2gR) with g=10 m/s2 and R=6.4e6 m, what is v rounded to the nearest integer m/s?

Solution: 2gR=1.28e8; sqrt(1.28e8)≈11313.71, which rounds to 11314.


Answer: 2

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Prompt: A water wave has period 4 s and wavelength 8 m. What is the speed in m/s?


Answer: 0.3

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Prompt: A tide gauge reads 1.2 m, then 1.5 m. What is the delta in metres?


Answer: 100

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Prompt: A 2 kg rock falls 5 m. Taking g=10 m/s^2 and PE=mgh, what is the loss of gravitational PE in joules?

Solution: mgh=2*10*5=100 J.


Answer: 48000

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Prompt: A map scale is 1:24000. 2 inches on the map is how many inches on the ground?

Solution: 2*24000=48000 inches.