Answer: shortened term

Single best cause among the named options

Textbook held constant later
Term length restored

See what remained when the effect vanished

Prompt: Exam scores fell after switching textbooks and after shortening the term. A later cohort used the new book with the original term length and scored like the historical baseline. What better explains the drop?

Solution: The new textbook with the old calendar matched baseline, so the book was not sufficient to cause the drop.


Answer: 10:00,11:00,09:00

No overlapping exclusive resources
Respect windows

Identify constrained tasks
Place unconstrained fillers
Check finish

Prompt: Tasks: taxes 2h unconstrained; passport 1h only 10:00-12:00; groceries 1h anytime. Work starts 09:00, no overlap. List start times as HH:MM for passport, taxes, groceries in that order, finishing as early as possible.

Solution: Groceries 09:00-10:00, passport 10:00-11:00 (inside the window), taxes 11:00-13:00. Finish 13:00.


Answer: 13:00,13:30,12:30

No overlapping exclusive resources
Respect windows

Hood only 13:00-14:00
Analysis depends on hood

Identify constrained tasks
Place unconstrained fillers
Check finish

Prompt: A chemist needs 30 min of fume-hood time, 45 min of analysis that requires the hood product, and 20 min of glassware wash that can run anytime. The hood is free only 13:00-14:00. Start at 12:30. Give start times HH:MM for hood, analysis, wash in that order with no overlap.

Solution: Wash 12:30-12:50 (or any pre-hood slot). Hood must start 13:00. Analysis after hood: 13:30. Wash cannot be after if we want a feasible early plan; 12:30 wash works.


Answer: A,B,A

No overlapping exclusive resources
Respect windows

Identify constrained tasks
Place unconstrained fillers
Check finish

Prompt: Three talks of 20 min must be scheduled in rooms A then B then A again (A cannot host two consecutive talks). Slots are 09:00, 09:30, 10:00. Assign rooms as a comma-separated list in slot order.

Solution: A, A, A would consecutive-A. A,B,A alternates and uses A twice.


Answer: 08:30

No overlapping exclusive resources
Respect windows

Identify constrained tasks
Place unconstrained fillers
Check finish

Prompt: You have a 15-min bus at :00 and :30 past each hour and a 10-min walk to the stop. You leave home at 08:07. What is the earliest bus you can catch as HH:MM?

Solution: Arrive at stop 08:17, missing 08:00. Next is 08:30.


Answer: 17:20

No overlapping exclusive resources
Respect windows

Identify constrained tasks
Place unconstrained fillers
Check finish

Prompt: Bake 25 min, cool 10 min, glaze 5 min, in that order, no overlap. Oven is free from 16:40. When is glazing finished as HH:MM?

Solution: Bake 16:40-17:05, cool 17:05-17:15, glaze 17:15-17:20.


Answer: Ann:lab,Bea:field,Cal:desk

Write the bipartite graph
Find a maximum matching

Prompt: Assign {Ann, Bea, Cal} to {desk, lab, field}. Ann refuses field, Bea refuses desk, Cal refuses lab, and the lab must go to Ann. List person:job alphabetically by person.

Solution: Lab is Ann. Bea cannot desk so Bea field. Cal gets desk.


Answer: 1

Write the bipartite graph
Find a maximum matching

Prompt: Four students want two lab benches. Compatible pairs are (Ada, Ben), (Ada, Cyd), (Ben, Di). Maximize pairs without sharing a person. How many pairs can you seat?

Solution: Any two of those pairs share Ada or Ben. Maximum matching size is 1.


Answer: 2

Write the bipartite graph
Find a maximum matching

Prompt: Tutors {T1,T2} and students {S1,S2,S3}. Each tutor takes at most one student. Allowed: T1-S1, T1-S2, T2-S2, T2-S3. Maximum number of matched students?

Solution: Two tutors, so at most 2. T1-S1 and T2-S3 is a maximum matching.


Answer: 3

Prompt: A triangle graph (3 vertices all adjacent) is to be vertex-colored. What is the chromatic number?

Solution: K3 needs three colors.


Answer: 2

Prompt: A cycle of 4 vertices (square) is to be vertex-colored. Chromatic number?

Solution: Even cycles are bipartite, so 2-colorable.


Answer: 2

Prompt: How many proper 2-colorings does a single edge (2 vertices, 1 edge) have if colors are {red, blue} and the two vertices must differ? Count labeled colorings, not up to swapping colors.

Solution: Red-blue or blue-red. Same-color is forbidden.


Answer: 2

Prompt: A path of 3 vertices needs vertex colors so adjacent vertices differ. Using 2 colors, how many labeled colorings?

Solution: Ends must match each other (both differ from the middle). 2 choices for the middle, then ends are forced. Wait: middle has 2 choices, each end has 1 remaining color. 2 colorings. Yes.


Answer: Tuesday

Apply weekday or month-length arithmetic

Prompt: 2026-08-18 is a Tuesday. What weekday is 2026-08-25 (same calendar)?

Solution: Seven days later is the same weekday.


Answer: 2026-08-28

Apply weekday or month-length arithmetic

Prompt: A project starts Monday 2026-08-17 and lasts 10 working days, skipping Saturday and Sunday, no holidays. What is the finish date YYYY-MM-DD?

Solution: Mon 17 through Fri 21 is 5 days; Mon 24 through Fri 28 is 5 more. Finish Friday 28.


Answer: 59

Apply weekday or month-length arithmetic

Prompt: From 2026-01-01 to 2026-03-01, how many calendar days elapse if we count the end date but not the start date (date difference)?

Solution: 2026 is not a leap year: 31 days in Jan + 28 in Feb = 59 to March 1.


Answer: 2026-08-20 09:00

Apply weekday or month-length arithmetic

Prompt: A 48-hour timer starts 2026-08-18 09:00. When does it end, local civil time with no DST change, as YYYY-MM-DD HH:MM?

Solution: 48 hours is exactly two days later at the same clock time.


Answer: 42

Prompt: A bill is $90. Three people split equally, then one person covers a $12 tip on top of their share. How many dollars does that person pay in total?

Solution: Share 30, plus 12 tip = 42.


Answer: 47.5

Prompt: Items cost 15, 25, and 10. A 10% coupon applies only to the most expensive item. What is the total after the coupon, in dollars?

Solution: 25*0.9=22.5; 15+22.5+10=47.5.


Answer: 10

Prompt: Four people share a $80 bill. One paid $50 already as a deposit. How much does each of the other three still owe if the deposit counts toward the group total and remaining is split equally among the three?

Solution: Remaining 30, three people, 10 each.


Answer: 27.6

Prompt: A taxi is $18 plus $2 per extra rider. Three extra riders and a 15% tip on the pre-tip fare. What is the total, dollars (one decimal if needed)?

Solution: Fare 18+6=24; tip 3.6; total 27.6.


Answer: undetermined

Translate to set inclusion or implication

Prompt: All widgets are gadgets. Some gadgets are branded. Does it follow that some widgets are branded? Answer yes, no, or undetermined.

Solution: The branded gadgets might all lie outside the widget subset.


Answer: no

Translate to set inclusion or implication

Prompt: No squares are circles. All tiles in set T are squares. Are any tiles in T circles? Answer yes, no, or undetermined.

Solution: T ⊆ squares, squares ∩ circles = empty, so T ∩ circles = empty.


Answer: yes

Translate to set inclusion or implication

Prompt: Every intern is a contractor. Maya is an intern. Is Maya a contractor? Answer yes, no, or undetermined.

Solution: Universal instantiation: intern ⇒ contractor.


Answer: undetermined

Translate to set inclusion or implication

Prompt: If the server is down then alerts fire. Alerts fired. Is the server down? Answer yes, no, or undetermined.

Solution: Affirming the consequent. Alerts can fire for other reasons.


Answer: SYN-ACK

Defensive systems behaviour, not exploits

Name the protocol step
Apply the recovery rule

Prompt: A handshake is: SYN, SYN-ACK, ACK. Packet 2 is lost and the client retries SYN. What is the next packet the server should send if it had not seen the first SYN complete?

Solution: A new SYN starts the handshake; server replies SYN-ACK.


Answer: COMMIT

Defensive systems behaviour, not exploits

Name the protocol step
Apply the recovery rule

Prompt: Two-phase commit: coordinator sent PREPARE and got YES from both workers, then crashed before COMMIT. Workers are waiting. After restart, what must the coordinator send to remain consistent if it had logged the decision to commit?

Solution: If the commit decision was logged, replay COMMIT, not ABORT.


Answer: either depending on the scheduler

Defensive systems behaviour, not exploits

Name the protocol step
Apply the recovery rule

Prompt: A mutex is locked by thread A. Thread B waits. A unlocks. Who may run the critical section next: only B, only A, or either depending on the scheduler?

Solution: Unlock does not donate the lock to B unless the API says so.


Answer: yes

Defensive systems behaviour, not exploits

Name the protocol step
Apply the recovery rule

Prompt: HTTP GET is retried after a timeout with no response. The original GET was side-effect free. Is the retry safe with respect to duplicate effects? Answer yes or no.

Solution: GET is specified as safe/idempotent; duplicate GET should not create extra effects.


Answer: 7

Prompt: Cities: Oslo-Bergen 5, Oslo-Trondheim 7, Bergen-Trondheim 4, Bergen-Stavanger 2. Shortest Oslo to Stavanger length?

Solution: Oslo-Bergen-Stavanger = 5+2 = 7. Via Trondheim is longer.


Answer: 2

Prompt: Grid: A connected to B and D; B to C; D to C. All edges cost 1. How many distinct shortest A-C paths (as vertex sequences)?

Solution: A-B-C and A-D-C, both length 2.


Answer: 4

Prompt: Directed edges A→B 3, A→C 9, B→C 4, B→D 1, C→D 1. Shortest A to D?

Solution: A-B-D = 3+1 = 4. A-B-C-D = 8. A-C-D = 10.


Answer: 2

Prompt: An undirected star with center H and leaves A,B,C. Edge weights 1. Distance A to B?

Solution: Must go A-H-B.


Answer: 3

Place each item in the first bin with room

Prompt: Pack items [5, 6, 5, 8] into bins of capacity 10 using first-fit decreasing. How many bins are used?

Solution: Sort descending [8, 6, 5, 5]; first-fit uses 3 bins.


Answer: 2

Place each item in the first bin with room

Prompt: Pack items [5, 4, 6, 4] into bins of capacity 10 using first-fit decreasing. How many bins are used?

Solution: Sort descending [6, 5, 4, 4]; first-fit uses 2 bins.


Answer: 2

Place each item in the first bin with room

Prompt: Pack items [2, 4, 6, 6] into bins of capacity 10 using first-fit decreasing. How many bins are used?

Solution: Sort descending [6, 6, 4, 2]; first-fit uses 2 bins.


Answer: 3

Place each item in the first bin with room

Prompt: Pack items [3, 9, 6, 8] into bins of capacity 12 using first-fit decreasing. How many bins are used?

Solution: Sort descending [9, 8, 6, 3]; first-fit uses 3 bins.


Answer: 4

Place each item in the first bin with room

Prompt: Pack items [10, 10, 9, 9] into bins of capacity 12 using first-fit decreasing. How many bins are used?

Solution: Sort descending [10, 10, 9, 9]; first-fit uses 4 bins.


Answer: 3

Place each item in the first bin with room

Prompt: Pack items [2, 8, 7, 6] into bins of capacity 10 using first-fit decreasing. How many bins are used?

Solution: Sort descending [8, 7, 6, 2]; first-fit uses 3 bins.


Answer: 2

Place each item in the first bin with room

Prompt: Pack items [3, 5, 2, 6] into bins of capacity 10 using first-fit decreasing. How many bins are used?

Solution: Sort descending [6, 5, 3, 2]; first-fit uses 2 bins.


Answer: 3

Place each item in the first bin with room

Prompt: Pack items [2, 14, 14, 4] into bins of capacity 15 using first-fit decreasing. How many bins are used?

Solution: Sort descending [14, 14, 4, 2]; first-fit uses 3 bins.


Answer: 3

Place each item in the first bin with room

Prompt: Pack items [10, 9, 6, 4] into bins of capacity 12 using first-fit decreasing. How many bins are used?

Solution: Sort descending [10, 9, 6, 4]; first-fit uses 3 bins.


Answer: 3

Place each item in the first bin with room

Prompt: Pack items [8, 12, 9, 3] into bins of capacity 15 using first-fit decreasing. How many bins are used?

Solution: Sort descending [12, 9, 8, 3]; first-fit uses 3 bins.


Answer: 4

Place each item in the first bin with room

Prompt: Pack items [7, 8, 7, 7] into bins of capacity 12 using first-fit decreasing. How many bins are used?

Solution: Sort descending [8, 7, 7, 7]; first-fit uses 4 bins.


Answer: 2

Place each item in the first bin with room

Prompt: Pack items [3, 4, 7, 8] into bins of capacity 15 using first-fit decreasing. How many bins are used?

Solution: Sort descending [8, 7, 4, 3]; first-fit uses 2 bins.


Answer: 3

Place each item in the first bin with room

Prompt: Pack items [9, 6, 12, 8] into bins of capacity 15 using first-fit decreasing. How many bins are used?

Solution: Sort descending [12, 9, 8, 6]; first-fit uses 3 bins.


Answer: 2

Place each item in the first bin with room

Prompt: Pack items [2, 9, 3, 7] into bins of capacity 15 using first-fit decreasing. How many bins are used?

Solution: Sort descending [9, 7, 3, 2]; first-fit uses 2 bins.


Answer: 3

Place each item in the first bin with room

Prompt: Pack items [7, 3, 8, 10] into bins of capacity 12 using first-fit decreasing. How many bins are used?

Solution: Sort descending [10, 8, 7, 3]; first-fit uses 3 bins.


Answer: 3

Place each item in the first bin with room

Prompt: Pack items [9, 8, 2, 5] into bins of capacity 10 using first-fit decreasing. How many bins are used?

Solution: Sort descending [9, 8, 5, 2]; first-fit uses 3 bins.


Answer: 4

Place each item in the first bin with room

Prompt: Pack items [7, 11, 14, 9] into bins of capacity 15 using first-fit decreasing. How many bins are used?

Solution: Sort descending [14, 11, 9, 7]; first-fit uses 4 bins.


Answer: 3

Place each item in the first bin with room

Prompt: Pack items [9, 14, 2, 5] into bins of capacity 15 using first-fit decreasing. How many bins are used?

Solution: Sort descending [14, 9, 5, 2]; first-fit uses 3 bins.


Answer: 3

Place each item in the first bin with room

Prompt: Pack items [10, 4, 6, 9] into bins of capacity 12 using first-fit decreasing. How many bins are used?


Answer: 2

Place each item in the first bin with room

Prompt: Pack items [9, 3, 2, 12] into bins of capacity 15 using first-fit decreasing. How many bins are used?

Solution: Sort descending [12, 9, 3, 2]; first-fit uses 2 bins.


Answer: 9

costs={'Ivy': 5, 'Jules': 4, 'Kiran': 6, 'Lane': 2}

Enumerate subsets containing required names

Prompt: Select a team from ['Ivy', 'Jules', 'Kiran', 'Lane'] with costs {'Ivy': 5, 'Jules': 4, 'Kiran': 6, 'Lane': 2}. Must include ['Ivy', 'Jules']. Minimize total cost. What is that cost?

Solution: Cheapest feasible set ['Ivy', 'Jules'] costs 9.


Answer: 11

costs={'Jules': 8, 'Kiran': 3, 'Lane': 5, 'Mira': 3}

Enumerate subsets containing required names

Prompt: Select a team from ['Jules', 'Kiran', 'Lane', 'Mira'] with costs {'Jules': 8, 'Kiran': 3, 'Lane': 5, 'Mira': 3}. Must include ['Jules', 'Kiran']. Minimize total cost. What is that cost?

Solution: Cheapest feasible set ['Jules', 'Kiran'] costs 11.


Answer: 12

costs={'Kiran': 9, 'Lane': 3, 'Mira': 4, 'Nico': 9}

Enumerate subsets containing required names

Prompt: Select a team from ['Kiran', 'Lane', 'Mira', 'Nico'] with costs {'Kiran': 9, 'Lane': 3, 'Mira': 4, 'Nico': 9}. Must include ['Kiran', 'Lane']. Minimize total cost. What is that cost?

Solution: Cheapest feasible set ['Kiran', 'Lane'] costs 12.


Answer: 12

costs={'Ivy': 6, 'Jules': 6, 'Kiran': 8, 'Lane': 9}

Enumerate subsets containing required names

Prompt: Select a team from ['Ivy', 'Jules', 'Kiran', 'Lane'] with costs {'Ivy': 6, 'Jules': 6, 'Kiran': 8, 'Lane': 9}. Must include ['Ivy', 'Jules']. Minimize total cost. What is that cost?

Solution: Cheapest feasible set ['Ivy', 'Jules'] costs 12.


Answer: 14

costs={'Jules': 9, 'Kiran': 5, 'Lane': 9, 'Mira': 4}

Enumerate subsets containing required names

Prompt: Select a team from ['Jules', 'Kiran', 'Lane', 'Mira'] with costs {'Jules': 9, 'Kiran': 5, 'Lane': 9, 'Mira': 4}. Must include ['Jules', 'Kiran']. Minimize total cost. What is that cost?

Solution: Cheapest feasible set ['Jules', 'Kiran'] costs 14.


Answer: 13

costs={'Kiran': 8, 'Lane': 5, 'Mira': 4, 'Nico': 3}

Enumerate subsets containing required names

Prompt: Select a team from ['Kiran', 'Lane', 'Mira', 'Nico'] with costs {'Kiran': 8, 'Lane': 5, 'Mira': 4, 'Nico': 3}. Must include ['Kiran', 'Lane']. Minimize total cost. What is that cost?

Solution: Cheapest feasible set ['Kiran', 'Lane'] costs 13.


Answer: 14

costs={'Ivy': 6, 'Jules': 8, 'Kiran': 7, 'Lane': 6}

Enumerate subsets containing required names

Prompt: Select a team from ['Ivy', 'Jules', 'Kiran', 'Lane'] with costs {'Ivy': 6, 'Jules': 8, 'Kiran': 7, 'Lane': 6}. Must include ['Ivy', 'Jules']. Minimize total cost. What is that cost?

Solution: Cheapest feasible set ['Ivy', 'Jules'] costs 14.


Answer: 8

costs={'Jules': 2, 'Kiran': 6, 'Lane': 6, 'Mira': 9}

Enumerate subsets containing required names

Prompt: Select a team from ['Jules', 'Kiran', 'Lane', 'Mira'] with costs {'Jules': 2, 'Kiran': 6, 'Lane': 6, 'Mira': 9}. Must include ['Jules', 'Kiran']. Minimize total cost. What is that cost?

Solution: Cheapest feasible set ['Jules', 'Kiran'] costs 8.


Answer: 13

costs={'Kiran': 4, 'Lane': 9, 'Mira': 9, 'Nico': 7}

Enumerate subsets containing required names

Prompt: Select a team from ['Kiran', 'Lane', 'Mira', 'Nico'] with costs {'Kiran': 4, 'Lane': 9, 'Mira': 9, 'Nico': 7}. Must include ['Kiran', 'Lane']. Minimize total cost. What is that cost?


Answer: 15

costs={'Ivy': 7, 'Jules': 8, 'Kiran': 9, 'Lane': 7}

Enumerate subsets containing required names

Prompt: Select a team from ['Ivy', 'Jules', 'Kiran', 'Lane'] with costs {'Ivy': 7, 'Jules': 8, 'Kiran': 9, 'Lane': 7}. Must include ['Ivy', 'Jules']. Minimize total cost. What is that cost?

Solution: Cheapest feasible set ['Ivy', 'Jules'] costs 15.


Answer: 10

costs={'Jules': 5, 'Kiran': 5, 'Lane': 8, 'Mira': 5}

Enumerate subsets containing required names

Prompt: Select a team from ['Jules', 'Kiran', 'Lane', 'Mira'] with costs {'Jules': 5, 'Kiran': 5, 'Lane': 8, 'Mira': 5}. Must include ['Jules', 'Kiran']. Minimize total cost. What is that cost?

Solution: Cheapest feasible set ['Jules', 'Kiran'] costs 10.


Answer: 10

costs={'Kiran': 8, 'Lane': 2, 'Mira': 7, 'Nico': 9}

Enumerate subsets containing required names

Prompt: Select a team from ['Kiran', 'Lane', 'Mira', 'Nico'] with costs {'Kiran': 8, 'Lane': 2, 'Mira': 7, 'Nico': 9}. Must include ['Kiran', 'Lane']. Minimize total cost. What is that cost?

Solution: Cheapest feasible set ['Kiran', 'Lane'] costs 10.


Answer: 16

costs={'Ivy': 8, 'Jules': 8, 'Kiran': 4, 'Lane': 9}

Enumerate subsets containing required names

Prompt: Select a team from ['Ivy', 'Jules', 'Kiran', 'Lane'] with costs {'Ivy': 8, 'Jules': 8, 'Kiran': 4, 'Lane': 9}. Must include ['Ivy', 'Jules']. Minimize total cost. What is that cost?

Solution: Cheapest feasible set ['Ivy', 'Jules'] costs 16.


Answer: 6

costs={'Jules': 2, 'Kiran': 4, 'Lane': 7, 'Mira': 3}

Enumerate subsets containing required names

Prompt: Select a team from ['Jules', 'Kiran', 'Lane', 'Mira'] with costs {'Jules': 2, 'Kiran': 4, 'Lane': 7, 'Mira': 3}. Must include ['Jules', 'Kiran']. Minimize total cost. What is that cost?

Solution: Cheapest feasible set ['Jules', 'Kiran'] costs 6.


Answer: 12

costs={'Kiran': 9, 'Lane': 3, 'Mira': 9, 'Nico': 2}

Enumerate subsets containing required names

Prompt: Select a team from ['Kiran', 'Lane', 'Mira', 'Nico'] with costs {'Kiran': 9, 'Lane': 3, 'Mira': 9, 'Nico': 2}. Must include ['Kiran', 'Lane']. Minimize total cost. What is that cost?


Answer: 12

costs={'Ivy': 4, 'Jules': 8, 'Kiran': 4, 'Lane': 3}

Enumerate subsets containing required names

Prompt: Select a team from ['Ivy', 'Jules', 'Kiran', 'Lane'] with costs {'Ivy': 4, 'Jules': 8, 'Kiran': 4, 'Lane': 3}. Must include ['Ivy', 'Jules']. Minimize total cost. What is that cost?


Answer: 15

costs={'Jules': 9, 'Kiran': 6, 'Lane': 7, 'Mira': 8}

Enumerate subsets containing required names

Prompt: Select a team from ['Jules', 'Kiran', 'Lane', 'Mira'] with costs {'Jules': 9, 'Kiran': 6, 'Lane': 7, 'Mira': 8}. Must include ['Jules', 'Kiran']. Minimize total cost. What is that cost?

Solution: Cheapest feasible set ['Jules', 'Kiran'] costs 15.


Answer: 10

costs={'Kiran': 3, 'Lane': 7, 'Mira': 8, 'Nico': 7}

Enumerate subsets containing required names

Prompt: Select a team from ['Kiran', 'Lane', 'Mira', 'Nico'] with costs {'Kiran': 3, 'Lane': 7, 'Mira': 8, 'Nico': 7}. Must include ['Kiran', 'Lane']. Minimize total cost. What is that cost?


Answer: defer

votes=['defer', 'defer', 'reject', 'defer', 'accept', 'defer', 'accept']

Prompt: Seven reviewers vote ['defer', 'defer', 'reject', 'defer', 'accept', 'defer', 'accept']. Majority (ties broken by accept>reject>defer). What is the outcome?

Solution: Counts {'accept': 2, 'reject': 1, 'defer': 4}; winner defer.


Answer: accept

votes=['accept', 'defer', 'defer', 'reject', 'accept', 'defer', 'accept']

Prompt: Seven reviewers vote ['accept', 'defer', 'defer', 'reject', 'accept', 'defer', 'accept']. Majority (ties broken by accept>reject>defer). What is the outcome?

Solution: Counts {'accept': 3, 'reject': 1, 'defer': 3}; winner accept.


Answer: accept

votes=['reject', 'accept', 'defer', 'defer', 'accept', 'reject', 'accept']

Prompt: Seven reviewers vote ['reject', 'accept', 'defer', 'defer', 'accept', 'reject', 'accept']. Majority (ties broken by accept>reject>defer). What is the outcome?

Solution: Counts {'accept': 3, 'reject': 2, 'defer': 2}; winner accept.


Answer: reject

votes=['reject', 'reject', 'reject', 'accept', 'accept', 'defer', 'reject']

Prompt: Seven reviewers vote ['reject', 'reject', 'reject', 'accept', 'accept', 'defer', 'reject']. Majority (ties broken by accept>reject>defer). What is the outcome?

Solution: Counts {'accept': 2, 'reject': 4, 'defer': 1}; winner reject.


Answer: accept

votes=['defer', 'defer', 'accept', 'accept', 'accept', 'accept', 'defer']

Prompt: Seven reviewers vote ['defer', 'defer', 'accept', 'accept', 'accept', 'accept', 'defer']. Majority (ties broken by accept>reject>defer). What is the outcome?

Solution: Counts {'accept': 4, 'reject': 0, 'defer': 3}; winner accept.


Answer: reject

votes=['reject', 'reject', 'defer', 'reject', 'defer', 'reject', 'defer']

Prompt: Seven reviewers vote ['reject', 'reject', 'defer', 'reject', 'defer', 'reject', 'defer']. Majority (ties broken by accept>reject>defer). What is the outcome?

Solution: Counts {'accept': 0, 'reject': 4, 'defer': 3}; winner reject.


Answer: reject

votes=['reject', 'reject', 'reject', 'accept', 'reject', 'reject', 'accept']

Prompt: Seven reviewers vote ['reject', 'reject', 'reject', 'accept', 'reject', 'reject', 'accept']. Majority (ties broken by accept>reject>defer). What is the outcome?

Solution: Counts {'accept': 2, 'reject': 5, 'defer': 0}; winner reject.


Answer: reject

votes=['accept', 'reject', 'defer', 'reject', 'defer', 'reject', 'defer']

Prompt: Seven reviewers vote ['accept', 'reject', 'defer', 'reject', 'defer', 'reject', 'defer']. Majority (ties broken by accept>reject>defer). What is the outcome?

Solution: Counts {'accept': 1, 'reject': 3, 'defer': 3}; winner reject.


Answer: 3

Half-open [a,b) treated as overlapping when a < prev_b

Merge if they touch or overlap
Integer endpoints

Prompt: Merge overlapping half-open intervals [(2, 3), (5, 6), (9, 11)] on the integer line. How many disjoint intervals remain?

Solution: Merged [(2, 3), (5, 6), (9, 11)]; count=3.


Answer: 2

Half-open [a,b) treated as overlapping when a < prev_b

Merge if they touch or overlap
Integer endpoints

Prompt: Merge overlapping half-open intervals [(3, 7), (4, 6), (8, 11)] on the integer line. How many disjoint intervals remain?

Solution: Merged [(3, 7), (8, 11)]; count=2.


Answer: 1

Half-open [a,b) treated as overlapping when a < prev_b

Merge if they touch or overlap
Integer endpoints

Prompt: Merge overlapping half-open intervals [(3, 6), (5, 9), (5, 7)] on the integer line. How many disjoint intervals remain?

Solution: Merged [(3, 9)]; count=1.


Answer: 2

Half-open [a,b) treated as overlapping when a < prev_b

Merge if they touch or overlap
Integer endpoints

Prompt: Merge overlapping half-open intervals [(5, 6), (8, 11), (9, 12)] on the integer line. How many disjoint intervals remain?

Solution: Merged [(5, 6), (8, 12)]; count=2.


Answer: 2

Half-open [a,b) treated as overlapping when a < prev_b

Merge if they touch or overlap
Integer endpoints

Prompt: Merge overlapping half-open intervals [(5, 8), (7, 9), (10, 13)] on the integer line. How many disjoint intervals remain?

Solution: Merged [(5, 9), (10, 13)]; count=2.


Answer: 1

Half-open [a,b) treated as overlapping when a < prev_b

Merge if they touch or overlap
Integer endpoints

Prompt: Merge overlapping half-open intervals [(5, 9), (9, 13), (9, 10)] on the integer line. How many disjoint intervals remain?

Solution: Merged [(5, 13)]; count=1.


Answer: 2

Half-open [a,b) treated as overlapping when a < prev_b

Merge if they touch or overlap
Integer endpoints

Prompt: Merge overlapping half-open intervals [(3, 4), (3, 5), (7, 10)] on the integer line. How many disjoint intervals remain?

Solution: Merged [(3, 5), (7, 10)]; count=2.


Answer: 3

Half-open [a,b) treated as overlapping when a < prev_b

Merge if they touch or overlap
Integer endpoints

Prompt: Merge overlapping half-open intervals [(6, 8), (11, 12), (16, 20)] on the integer line. How many disjoint intervals remain?

Solution: Merged [(6, 8), (11, 12), (16, 20)]; count=3.


Answer: 1

Half-open [a,b) treated as overlapping when a < prev_b

Merge if they touch or overlap
Integer endpoints

Prompt: Merge overlapping half-open intervals [(2, 5), (4, 8), (6, 7)] on the integer line. How many disjoint intervals remain?

Solution: Merged [(2, 8)]; count=1.


Answer: 1

Half-open [a,b) treated as overlapping when a < prev_b

Merge if they touch or overlap
Integer endpoints

Prompt: Merge overlapping half-open intervals [(6, 9), (7, 10), (8, 12)] on the integer line. How many disjoint intervals remain?

Solution: Merged [(6, 12)]; count=1.


Answer: 2

Half-open [a,b) treated as overlapping when a < prev_b

Merge if they touch or overlap
Integer endpoints

Prompt: Merge overlapping half-open intervals [(5, 6), (6, 8), (9, 11)] on the integer line. How many disjoint intervals remain?

Solution: Merged [(5, 8), (9, 11)]; count=2.


Answer: 1

Half-open [a,b) treated as overlapping when a < prev_b

Merge if they touch or overlap
Integer endpoints

Prompt: Merge overlapping half-open intervals [(4, 6), (6, 8), (7, 9)] on the integer line. How many disjoint intervals remain?

Solution: Merged [(4, 9)]; count=1.


Answer: 1

Half-open [a,b) treated as overlapping when a < prev_b

Merge if they touch or overlap
Integer endpoints

Prompt: Merge overlapping half-open intervals [(5, 7), (7, 8), (8, 11)] on the integer line. How many disjoint intervals remain?

Solution: Merged [(5, 11)]; count=1.


Answer: 3

Half-open [a,b) treated as overlapping when a < prev_b

Merge if they touch or overlap
Integer endpoints

Prompt: Merge overlapping half-open intervals [(5, 6), (7, 8), (10, 14)] on the integer line. How many disjoint intervals remain?

Solution: Merged [(5, 6), (7, 8), (10, 14)]; count=3.


Answer: 2

Half-open [a,b) treated as overlapping when a < prev_b

Merge if they touch or overlap
Integer endpoints

Prompt: Merge overlapping half-open intervals [(5, 9), (9, 10), (14, 16)] on the integer line. How many disjoint intervals remain?

Solution: Merged [(5, 10), (14, 16)]; count=2.


Answer: 2

Half-open [a,b) treated as overlapping when a < prev_b

Merge if they touch or overlap
Integer endpoints

Prompt: Merge overlapping half-open intervals [(7, 10), (12, 13), (13, 17)] on the integer line. How many disjoint intervals remain?

Solution: Merged [(7, 10), (12, 17)]; count=2.


Answer: 4

Preserve order
No skipping in the middle

Add chunks until the next would exceed budget

Prompt: A context window has 64 tokens. Pack chunks [7, 13, 17, 20, 13] in order, skipping none except by stopping when the next chunk would overflow. How many chunks are kept?

Solution: Greedy prefix uses 57 tokens and keeps 4 chunks.


Answer: 2

Preserve order
No skipping in the middle

Add chunks until the next would exceed budget

Prompt: A context window has 32 tokens. Pack chunks [20, 7, 11, 15, 8] in order, skipping none except by stopping when the next chunk would overflow. How many chunks are kept?

Solution: Greedy prefix uses 27 tokens and keeps 2 chunks.


Answer: 2

Preserve order
No skipping in the middle

Add chunks until the next would exceed budget

Prompt: A context window has 32 tokens. Pack chunks [8, 10, 15, 16, 15] in order, skipping none except by stopping when the next chunk would overflow. How many chunks are kept?

Solution: Greedy prefix uses 18 tokens and keeps 2 chunks.


Answer: 4

Preserve order
No skipping in the middle

Add chunks until the next would exceed budget

Prompt: A context window has 64 tokens. Pack chunks [17, 11, 12, 15, 14] in order, skipping none except by stopping when the next chunk would overflow. How many chunks are kept?

Solution: Greedy prefix uses 55 tokens and keeps 4 chunks.


Answer: 3

Preserve order
No skipping in the middle

Add chunks until the next would exceed budget

Prompt: A context window has 48 tokens. Pack chunks [13, 14, 15, 12, 7] in order, skipping none except by stopping when the next chunk would overflow. How many chunks are kept?

Solution: Greedy prefix uses 42 tokens and keeps 3 chunks.


Answer: 4

Preserve order
No skipping in the middle

Add chunks until the next would exceed budget

Prompt: A context window has 64 tokens. Pack chunks [7, 19, 16, 16, 20] in order, skipping none except by stopping when the next chunk would overflow. How many chunks are kept?

Solution: Greedy prefix uses 58 tokens and keeps 4 chunks.


Answer: 4

Preserve order
No skipping in the middle

Add chunks until the next would exceed budget

Prompt: A context window has 64 tokens. Pack chunks [17, 19, 9, 12, 13] in order, skipping none except by stopping when the next chunk would overflow. How many chunks are kept?


Answer: 2

Preserve order
No skipping in the middle

Add chunks until the next would exceed budget

Prompt: A context window has 32 tokens. Pack chunks [12, 11, 19, 13, 12] in order, skipping none except by stopping when the next chunk would overflow. How many chunks are kept?

Solution: Greedy prefix uses 23 tokens and keeps 2 chunks.


Answer: 4

Preserve order
No skipping in the middle

Add chunks until the next would exceed budget

Prompt: A context window has 48 tokens. Pack chunks [17, 7, 11, 12, 11] in order, skipping none except by stopping when the next chunk would overflow. How many chunks are kept?

Solution: Greedy prefix uses 47 tokens and keeps 4 chunks.


Answer: 4

Preserve order
No skipping in the middle

Add chunks until the next would exceed budget

Prompt: A context window has 64 tokens. Pack chunks [10, 11, 8, 16, 20] in order, skipping none except by stopping when the next chunk would overflow. How many chunks are kept?

Solution: Greedy prefix uses 45 tokens and keeps 4 chunks.


Answer: 5

Preserve order
No skipping in the middle

Add chunks until the next would exceed budget

Prompt: A context window has 48 tokens. Pack chunks [7, 7, 19, 7, 7] in order, skipping none except by stopping when the next chunk would overflow. How many chunks are kept?

Solution: Greedy prefix uses 47 tokens and keeps 5 chunks.


Answer: 3

Preserve order
No skipping in the middle

Add chunks until the next would exceed budget

Prompt: A context window has 48 tokens. Pack chunks [7, 17, 17, 11, 18] in order, skipping none except by stopping when the next chunk would overflow. How many chunks are kept?

Solution: Greedy prefix uses 41 tokens and keeps 3 chunks.


Answer: 2

Preserve order
No skipping in the middle

Add chunks until the next would exceed budget

Prompt: A context window has 32 tokens. Pack chunks [14, 6, 15, 14, 14] in order, skipping none except by stopping when the next chunk would overflow. How many chunks are kept?

Solution: Greedy prefix uses 20 tokens and keeps 2 chunks.


Answer: 4

Preserve order
No skipping in the middle

Add chunks until the next would exceed budget

Prompt: A context window has 48 tokens. Pack chunks [16, 7, 12, 11, 19] in order, skipping none except by stopping when the next chunk would overflow. How many chunks are kept?

Solution: Greedy prefix uses 46 tokens and keeps 4 chunks.


Answer: 3

Preserve order
No skipping in the middle

Add chunks until the next would exceed budget

Prompt: A context window has 64 tokens. Pack chunks [18, 12, 19, 20, 17] in order, skipping none except by stopping when the next chunk would overflow. How many chunks are kept?

Solution: Greedy prefix uses 49 tokens and keeps 3 chunks.


Answer: 2

Preserve order
No skipping in the middle

Add chunks until the next would exceed budget

Prompt: A context window has 32 tokens. Pack chunks [10, 15, 10, 11, 7] in order, skipping none except by stopping when the next chunk would overflow. How many chunks are kept?

Solution: Greedy prefix uses 25 tokens and keeps 2 chunks.


Answer: 5

Preserve order
No skipping in the middle

Add chunks until the next would exceed budget

Prompt: A context window has 64 tokens. Pack chunks [14, 9, 8, 16, 13] in order, skipping none except by stopping when the next chunk would overflow. How many chunks are kept?

Solution: Greedy prefix uses 60 tokens and keeps 5 chunks.


Answer: 2

Preserve order
No skipping in the middle

Add chunks until the next would exceed budget

Prompt: A context window has 32 tokens. Pack chunks [19, 7, 11, 19, 14] in order, skipping none except by stopping when the next chunk would overflow. How many chunks are kept?

Solution: Greedy prefix uses 26 tokens and keeps 2 chunks.


Answer: no

Prompt: Jobs 0,1,2,3 run in order [2, 0, 1, 3]. Constraints: 0 before 2, and 1 before 3. Is the order valid? Answer yes or no.

Solution: Positions: 0@1, 2@0, 1@2, 3@3 → no.


Answer: no

Prompt: Jobs 0,1,2,3 run in order [3, 2, 0, 1]. Constraints: 0 before 2, and 1 before 3. Is the order valid? Answer yes or no.

Solution: Positions: 0@2, 2@1, 1@3, 3@0 → no.


Answer: no

Prompt: Jobs 0,1,2,3 run in order [0, 3, 1, 2]. Constraints: 0 before 2, and 1 before 3. Is the order valid? Answer yes or no.

Solution: Positions: 0@0, 2@3, 1@2, 3@1 → no.


Answer: no

Prompt: Jobs 0,1,2,3 run in order [2, 1, 0, 3]. Constraints: 0 before 2, and 1 before 3. Is the order valid? Answer yes or no.

Solution: Positions: 0@2, 2@0, 1@1, 3@3 → no.


Answer: no

Prompt: Jobs 0,1,2,3 run in order [1, 2, 3, 0]. Constraints: 0 before 2, and 1 before 3. Is the order valid? Answer yes or no.

Solution: Positions: 0@3, 2@1, 1@0, 3@2 → no.


Answer: no

Prompt: Jobs 0,1,2,3 run in order [1, 2, 0, 3]. Constraints: 0 before 2, and 1 before 3. Is the order valid? Answer yes or no.

Solution: Positions: 0@2, 2@1, 1@0, 3@3 → no.


Answer: no

Prompt: Jobs 0,1,2,3 run in order [1, 3, 2, 0]. Constraints: 0 before 2, and 1 before 3. Is the order valid? Answer yes or no.

Solution: Positions: 0@3, 2@2, 1@0, 3@1 → no.


Answer: no

Prompt: Jobs 0,1,2,3 run in order [2, 3, 0, 1]. Constraints: 0 before 2, and 1 before 3. Is the order valid? Answer yes or no.

Solution: Positions: 0@2, 2@0, 1@3, 3@1 → no.


Answer: yes

Prompt: Jobs 0,1,2,3 run in order [1, 0, 2, 3]. Constraints: 0 before 2, and 1 before 3. Is the order valid? Answer yes or no.

Solution: Positions: 0@1, 2@2, 1@0, 3@3 → yes.


Answer: no

Prompt: Jobs 0,1,2,3 run in order [2, 1, 3, 0]. Constraints: 0 before 2, and 1 before 3. Is the order valid? Answer yes or no.

Solution: Positions: 0@3, 2@0, 1@1, 3@2 → no.


Answer: no

Prompt: Jobs 0,1,2,3 run in order [3, 1, 2, 0]. Constraints: 0 before 2, and 1 before 3. Is the order valid? Answer yes or no.

Solution: Positions: 0@3, 2@2, 1@1, 3@0 → no.


Answer: yes

Prompt: Jobs 0,1,2,3 run in order [0, 1, 2, 3]. Constraints: 0 before 2, and 1 before 3. Is the order valid? Answer yes or no.

Solution: Positions: 0@0, 2@2, 1@1, 3@3 → yes.


Answer: no

Prompt: Jobs 0,1,2,3 run in order [2, 3, 1, 0]. Constraints: 0 before 2, and 1 before 3. Is the order valid? Answer yes or no.

Solution: Positions: 0@3, 2@0, 1@2, 3@1 → no.


Answer: 6

Prompt: SKUs have demand [2, 3, 3] and on-hand [2, 0, 0]. Total units short (unmet demand)?

Solution: shortfall = sum(max(0, demand-stock)) = 6.


Answer: 4

Prompt: SKUs have demand [4, 4, 2] and on-hand [1, 3, 4]. Total units short (unmet demand)?

Solution: shortfall = sum(max(0, demand-stock)) = 4.


Answer: 0

Prompt: SKUs have demand [2, 5, 5] and on-hand [6, 5, 6]. Total units short (unmet demand)?

Solution: shortfall = sum(max(0, demand-stock)) = 0.


Answer: 4

Prompt: SKUs have demand [3, 1, 4] and on-hand [6, 5, 0]. Total units short (unmet demand)?


Answer: 6

Prompt: SKUs have demand [4, 1, 4] and on-hand [0, 6, 2]. Total units short (unmet demand)?


Answer: 2

Prompt: SKUs have demand [5, 4, 5] and on-hand [3, 5, 5]. Total units short (unmet demand)?

Solution: shortfall = sum(max(0, demand-stock)) = 2.


Answer: 4

Prompt: SKUs have demand [4, 3, 1] and on-hand [3, 0, 2]. Total units short (unmet demand)?


Answer: 2

Prompt: SKUs have demand [2, 5, 4] and on-hand [6, 5, 2]. Total units short (unmet demand)?


Answer: 1

Prompt: SKUs have demand [1, 4, 1] and on-hand [1, 3, 4]. Total units short (unmet demand)?

Solution: shortfall = sum(max(0, demand-stock)) = 1.


Answer: 1

Prompt: SKUs have demand [4, 5, 1] and on-hand [3, 6, 2]. Total units short (unmet demand)?


Answer: 4

Prompt: SKUs have demand [3, 2, 3] and on-hand [6, 1, 0]. Total units short (unmet demand)?


Answer: 1

Prompt: SKUs have demand [5, 1, 5] and on-hand [4, 1, 6]. Total units short (unmet demand)?


Answer: 6

Prompt: SKUs have demand [3, 3, 2] and on-hand [1, 0, 1]. Total units short (unmet demand)?


Answer: 1

Prompt: SKUs have demand [3, 2, 2] and on-hand [4, 1, 6]. Total units short (unmet demand)?


Answer: 0

Prompt: SKUs have demand [1, 2, 4] and on-hand [3, 6, 4]. Total units short (unmet demand)?


Answer: 1

Prompt: SKUs have demand [5, 4, 5] and on-hand [5, 5, 4]. Total units short (unmet demand)?


Answer: 0

Even parity over the eight data bits plus the appended bit

Prompt: Eight bits [1, 1, 0, 1, 0, 1, 1, 1] are sent with even parity. What parity bit should be appended (0 or 1) so the nine-bit string has even parity?

Solution: Sum=6; even parity bit=0.


Answer: 1

Even parity over the eight data bits plus the appended bit

Prompt: Eight bits [1, 0, 1, 0, 1, 1, 1, 0] are sent with even parity. What parity bit should be appended (0 or 1) so the nine-bit string has even parity?

Solution: Sum=5; even parity bit=1.


Answer: 0

Even parity over the eight data bits plus the appended bit

Prompt: Eight bits [0, 1, 1, 0, 0, 1, 1, 0] are sent with even parity. What parity bit should be appended (0 or 1) so the nine-bit string has even parity?

Solution: Sum=4; even parity bit=0.


Answer: 0

Even parity over the eight data bits plus the appended bit

Prompt: Eight bits [1, 0, 1, 1, 0, 0, 1, 0] are sent with even parity. What parity bit should be appended (0 or 1) so the nine-bit string has even parity?

Solution: Sum=4; even parity bit=0.


Answer: 1

Even parity over the eight data bits plus the appended bit

Prompt: Eight bits [1, 0, 0, 0, 0, 1, 1, 0] are sent with even parity. What parity bit should be appended (0 or 1) so the nine-bit string has even parity?

Solution: Sum=3; even parity bit=1.


Answer: 1

Even parity over the eight data bits plus the appended bit

Prompt: Eight bits [1, 1, 1, 1, 1, 1, 0, 1] are sent with even parity. What parity bit should be appended (0 or 1) so the nine-bit string has even parity?

Solution: Sum=7; even parity bit=1.


Answer: 1

Even parity over the eight data bits plus the appended bit

Prompt: Eight bits [0, 1, 0, 1, 1, 1, 0, 1] are sent with even parity. What parity bit should be appended (0 or 1) so the nine-bit string has even parity?

Solution: Sum=5; even parity bit=1.


Answer: 0

Even parity over the eight data bits plus the appended bit

Prompt: Eight bits [0, 0, 1, 1, 1, 0, 0, 1] are sent with even parity. What parity bit should be appended (0 or 1) so the nine-bit string has even parity?

Solution: Sum=4; even parity bit=0.


Answer: 1

Even parity over the eight data bits plus the appended bit

Prompt: Eight bits [1, 1, 0, 0, 1, 1, 0, 1] are sent with even parity. What parity bit should be appended (0 or 1) so the nine-bit string has even parity?

Solution: Sum=5; even parity bit=1.


Answer: 1

Even parity over the eight data bits plus the appended bit

Prompt: Eight bits [1, 0, 0, 1, 1, 0, 0, 0] are sent with even parity. What parity bit should be appended (0 or 1) so the nine-bit string has even parity?

Solution: Sum=3; even parity bit=1.


Answer: 1

Even parity over the eight data bits plus the appended bit

Prompt: Eight bits [0, 0, 1, 0, 0, 1, 0, 1] are sent with even parity. What parity bit should be appended (0 or 1) so the nine-bit string has even parity?

Solution: Sum=3; even parity bit=1.


Answer: 1

Even parity over the eight data bits plus the appended bit

Prompt: Eight bits [0, 0, 0, 0, 1, 0, 1, 1] are sent with even parity. What parity bit should be appended (0 or 1) so the nine-bit string has even parity?

Solution: Sum=3; even parity bit=1.


Answer: 1

Even parity over the eight data bits plus the appended bit

Prompt: Eight bits [0, 1, 1, 1, 0, 0, 1, 1] are sent with even parity. What parity bit should be appended (0 or 1) so the nine-bit string has even parity?

Solution: Sum=5; even parity bit=1.


Answer: 0

Even parity over the eight data bits plus the appended bit

Prompt: Eight bits [0, 1, 1, 1, 1, 1, 1, 0] are sent with even parity. What parity bit should be appended (0 or 1) so the nine-bit string has even parity?

Solution: Sum=6; even parity bit=0.


Answer: 1

Even parity over the eight data bits plus the appended bit

Prompt: Eight bits [0, 0, 1, 0, 1, 1, 0, 0] are sent with even parity. What parity bit should be appended (0 or 1) so the nine-bit string has even parity?

Solution: Sum=3; even parity bit=1.


Answer: 0

Even parity over the eight data bits plus the appended bit

Prompt: Eight bits [1, 0, 0, 1, 1, 0, 1, 0] are sent with even parity. What parity bit should be appended (0 or 1) so the nine-bit string has even parity?

Solution: Sum=4; even parity bit=0.


Answer: 5

CPython / common SQL / git unless stated

Identify the common pitfall
Answer the yes/no or count

Prompt: You need inclusive integers from 3 through 7. In Python, what is list(range(3, 8)) length?

Solution: range(start, stop) excludes stop; 3,4,5,6,7 → 5 values.


Answer: no

CPython / common SQL / git unless stated

Identify the common pitfall
Answer the yes/no or count

Prompt: Two naive datetime values differ by 3600 seconds locally. Does that prove they are one UTC hour apart? Answer yes or no.

Solution: Naive datetimes have no zone; DST and offset make local deltas unreliable as UTC.


Answer: no

CPython / common SQL / git unless stated

inspired_by=stackoverflow topic=json vs eval

Identify the common pitfall
Answer the yes/no or count

Prompt: Should untrusted text be turned into a Python object with eval? yes or no.

Solution: eval executes code. Use json.loads for JSON payloads.


Answer: no

CPython / common SQL / git unless stated

Identify the common pitfall
Answer the yes/no or count

Prompt: Is binary float a safe ledger type for USD cents? yes or no.

Solution: Use integer cents or decimal. Decimal/float rounding is not cash-safe.


Answer: no

CPython / common SQL / git unless stated

Identify the common pitfall
Answer the yes/no or count

Prompt: A dict key is a list. After insertion you mutate the list. Is lookup by the new list guaranteed? yes or no.

Solution: Mutable keys are invalid; lists are unhashable. If a custom mutable key were used, mutation would break the table.


Answer: no

CPython / common SQL / git unless stated

Identify the common pitfall
Answer the yes/no or count

Prompt: Two Python threads each run a tight CPU loop of bytecode. Will they typically use two cores at full speed under CPython's GIL? yes or no.

Solution: CPython's GIL usually serializes bytecode execution on one core.


Answer: no

CPython / common SQL / git unless stated

Identify the common pitfall
Answer the yes/no or count

Prompt: In SQL, does `NULL = NULL` evaluate to TRUE? yes or no.

Solution: NULL comparisons yield UNKNOWN; use IS NULL.


Answer: no

CPython / common SQL / git unless stated

Identify the common pitfall
Answer the yes/no or count

Prompt: You checkout a raw commit SHA. Are new commits still on a named branch? yes or no.

Solution: Detached HEAD: commits are not on a branch until you create/move one.


Answer: 46

Constant acceleration
One-dimensional motion

Prompt: An object starts at 22 m/s and accelerates at 1 m/s2 for 2 s. How far does it travel (metres)?

Solution: s = ut + 1⁄2at2 = 22·2 + 0.5·1·22 = 46.0.


Answer: 88.5

Constant acceleration
One-dimensional motion

Prompt: An object starts at 25 m/s and accelerates at 3 m/s2 for 3 s. How far does it travel (metres)?

Solution: s = ut + 1⁄2at2 = 25·3 + 0.5·3·32 = 88.5.


Answer: 112

Constant acceleration
One-dimensional motion

Prompt: An object starts at 9 m/s and accelerates at 2 m/s2 for 7 s. How far does it travel (metres)?

Solution: s = ut + 1⁄2at2 = 9·7 + 0.5·2·72 = 112.0.


Answer: -14

Constant acceleration
One-dimensional motion

Prompt: An object starts at 5 m/s and accelerates at -2 m/s2 for 7 s. How far does it travel (metres)?

Solution: s = ut + 1⁄2at2 = 5·7 + 0.5·-2·72 = -14.0.


Answer: 132

Constant acceleration
One-dimensional motion

Prompt: An object starts at 19 m/s and accelerates at 1 m/s2 for 6 s. How far does it travel (metres)?

Solution: s = ut + 1⁄2at2 = 19·6 + 0.5·1·62 = 132.0.


Answer: 32

Constant acceleration
One-dimensional motion

Prompt: An object starts at 15 m/s and accelerates at 1 m/s2 for 2 s. How far does it travel (metres)?

Solution: s = ut + 1⁄2at2 = 15·2 + 0.5·1·22 = 32.0.


Answer: 21

Constant acceleration
One-dimensional motion

Prompt: An object starts at 4 m/s and accelerates at 2 m/s2 for 3 s. How far does it travel (metres)?

Solution: s = ut + 1⁄2at2 = 4·3 + 0.5·2·32 = 21.0.


Answer: 34

Constant acceleration
One-dimensional motion

Prompt: An object starts at 18 m/s and accelerates at -1 m/s2 for 2 s. How far does it travel (metres)?

Solution: s = ut + 1⁄2at2 = 18·2 + 0.5·-1·22 = 34.0.


Answer: 182

Constant acceleration
One-dimensional motion

Prompt: An object starts at 19 m/s and accelerates at 2 m/s2 for 7 s. How far does it travel (metres)?

Solution: s = ut + 1⁄2at2 = 19·7 + 0.5·2·72 = 182.0.


Answer: 96

Constant acceleration
One-dimensional motion

Prompt: An object starts at 22 m/s and accelerates at -2 m/s2 for 6 s. How far does it travel (metres)?

Solution: s = ut + 1⁄2at2 = 22·6 + 0.5·-2·62 = 96.0.


Answer: 100

Constant acceleration
One-dimensional motion

Prompt: An object starts at 15 m/s and accelerates at 2 m/s2 for 5 s. How far does it travel (metres)?

Solution: s = ut + 1⁄2at2 = 15·5 + 0.5·2·52 = 100.0.


Answer: 256

Constant acceleration
One-dimensional motion

Prompt: An object starts at 20 m/s and accelerates at 3 m/s2 for 8 s. How far does it travel (metres)?

Solution: s = ut + 1⁄2at2 = 20·8 + 0.5·3·82 = 256.0.


Answer: 63

Constant acceleration
One-dimensional motion

Prompt: An object starts at 2 m/s and accelerates at 2 m/s2 for 7 s. How far does it travel (metres)?

Solution: s = ut + 1⁄2at2 = 2·7 + 0.5·2·72 = 63.0.


Answer: 84

Constant acceleration
One-dimensional motion

Prompt: An object starts at 15 m/s and accelerates at 3 m/s2 for 4 s. How far does it travel (metres)?

Solution: s = ut + 1⁄2at2 = 15·4 + 0.5·3·42 = 84.0.


Answer: 112

Constant acceleration
One-dimensional motion

Prompt: An object starts at 6 m/s and accelerates at 2 m/s2 for 8 s. How far does it travel (metres)?

Solution: s = ut + 1⁄2at2 = 6·8 + 0.5·2·82 = 112.0.


Answer: 26

Constant acceleration
One-dimensional motion

Prompt: An object starts at 12 m/s and accelerates at 1 m/s2 for 2 s. How far does it travel (metres)?

Solution: s = ut + 1⁄2at2 = 12·2 + 0.5·1·22 = 26.0.


Answer: 64

Constant acceleration
One-dimensional motion

Prompt: An object starts at 14 m/s and accelerates at 1 m/s2 for 4 s. How far does it travel (metres)?

Solution: s = ut + 1⁄2at2 = 14·4 + 0.5·1·42 = 64.0.


Answer: 44

Constant acceleration
One-dimensional motion

Prompt: An object starts at 13 m/s and accelerates at -1 m/s2 for 4 s. How far does it travel (metres)?

Solution: s = ut + 1⁄2at2 = 13·4 + 0.5·-1·42 = 44.0.


Answer: -10

Constant acceleration
One-dimensional motion

Prompt: An object starts at 3 m/s and accelerates at -2 m/s2 for 5 s. How far does it travel (metres)?

Solution: s = ut + 1⁄2at2 = 3·5 + 0.5·-2·52 = -10.0.


Answer: 107.5

Constant acceleration
One-dimensional motion

Prompt: An object starts at 19 m/s and accelerates at 1 m/s2 for 5 s. How far does it travel (metres)?

Solution: s = ut + 1⁄2at2 = 19·5 + 0.5·1·52 = 107.5.


Answer: 8

Constant acceleration
One-dimensional motion

Prompt: An object starts at 4 m/s and accelerates at -1 m/s2 for 4 s. How far does it travel (metres)?

Solution: s = ut + 1⁄2at2 = 4·4 + 0.5·-1·42 = 8.0.


Answer: 144

Constant acceleration
One-dimensional motion

Prompt: An object starts at 22 m/s and accelerates at -1 m/s2 for 8 s. How far does it travel (metres)?

Solution: s = ut + 1⁄2at2 = 22·8 + 0.5·-1·82 = 144.0.


Answer: 34.5

Constant acceleration
One-dimensional motion

Prompt: An object starts at 13 m/s and accelerates at -1 m/s2 for 3 s. How far does it travel (metres)?

Solution: s = ut + 1⁄2at2 = 13·3 + 0.5·-1·32 = 34.5.


Answer: 50

Constant acceleration
One-dimensional motion

Prompt: An object starts at 24 m/s and accelerates at 1 m/s2 for 2 s. How far does it travel (metres)?

Solution: s = ut + 1⁄2at2 = 24·2 + 0.5·1·22 = 50.0.


Answer: 2704

Prompt: Compute the kinetic energy in joules of a 8 kg mass moving at 26 m/s.

Solution: KE = 1⁄2mv2 = 0.5·8·262 = 2704.0.


Answer: 80

Prompt: Compute the kinetic energy in joules of a 10 kg mass moving at 4 m/s.

Solution: KE = 1⁄2mv2 = 0.5·10·42 = 80.0.


Answer: 3364

Prompt: Compute the kinetic energy in joules of a 8 kg mass moving at 29 m/s.

Solution: KE = 1⁄2mv2 = 0.5·8·292 = 3364.0.


Answer: 392

Prompt: Compute the kinetic energy in joules of a 4 kg mass moving at 14 m/s.

Solution: KE = 1⁄2mv2 = 0.5·4·142 = 392.0.


Answer: 1152

Prompt: Compute the kinetic energy in joules of a 9 kg mass moving at 16 m/s.

Solution: KE = 1⁄2mv2 = 0.5·9·162 = 1152.0.


Answer: 294

Prompt: Compute the kinetic energy in joules of a 12 kg mass moving at 7 m/s.

Solution: KE = 1⁄2mv2 = 0.5·12·72 = 294.0.


Answer: 1014

Prompt: Compute the kinetic energy in joules of a 12 kg mass moving at 13 m/s.

Solution: KE = 1⁄2mv2 = 0.5·12·132 = 1014.0.


Answer: 1851.5

Prompt: Compute the kinetic energy in joules of a 7 kg mass moving at 23 m/s.

Solution: KE = 1⁄2mv2 = 0.5·7·232 = 1851.5.


Answer: 2592

Prompt: Compute the kinetic energy in joules of a 9 kg mass moving at 24 m/s.

Solution: KE = 1⁄2mv2 = 0.5·9·242 = 2592.0.


Answer: 661.5

Prompt: Compute the kinetic energy in joules of a 3 kg mass moving at 21 m/s.

Solution: KE = 1⁄2mv2 = 0.5·3·212 = 661.5.


Answer: 1083

Prompt: Compute the kinetic energy in joules of a 6 kg mass moving at 19 m/s.

Solution: KE = 1⁄2mv2 = 0.5·6·192 = 1083.0.


Answer: 196

Prompt: Compute the kinetic energy in joules of a 8 kg mass moving at 7 m/s.

Solution: KE = 1⁄2mv2 = 0.5·8·72 = 196.0.


Answer: 1470

Prompt: Compute the kinetic energy in joules of a 15 kg mass moving at 14 m/s.

Solution: KE = 1⁄2mv2 = 0.5·15·142 = 1470.0.


Answer: 2178

Prompt: Compute the kinetic energy in joules of a 9 kg mass moving at 22 m/s.

Solution: KE = 1⁄2mv2 = 0.5·9·222 = 2178.0.


Answer: 729

Prompt: Compute the kinetic energy in joules of a 18 kg mass moving at 9 m/s.

Solution: KE = 1⁄2mv2 = 0.5·18·92 = 729.0.


Answer: 4312

Prompt: Compute the kinetic energy in joules of a 11 kg mass moving at 28 m/s.

Solution: KE = 1⁄2mv2 = 0.5·11·282 = 4312.0.


Answer: 81

Prompt: Compute the kinetic energy in joules of a 2 kg mass moving at 9 m/s.

Solution: KE = 1⁄2mv2 = 0.5·2·92 = 81.0.


Answer: 729

Prompt: Compute the kinetic energy in joules of a 2 kg mass moving at 27 m/s.

Solution: KE = 1⁄2mv2 = 0.5·2·272 = 729.0.


Answer: 1078

Prompt: Compute the kinetic energy in joules of a 11 kg mass moving at 14 m/s.

Solution: KE = 1⁄2mv2 = 0.5·11·142 = 1078.0.


Answer: 72

Prompt: Compute the kinetic energy in joules of a 9 kg mass moving at 4 m/s.

Solution: KE = 1⁄2mv2 = 0.5·9·42 = 72.0.


Answer: 20

Prompt: A current of 1 A flows through 20 Ω. What is the voltage drop in volts?

Solution: V = IR = 1·20 = 20.


Answer: 16

Prompt: A current of 2 A flows through 8 Ω. What is the voltage drop in volts?

Solution: V = IR = 2·8 = 16.


Answer: 102

Prompt: A current of 6 A flows through 17 Ω. What is the voltage drop in volts?

Solution: V = IR = 6·17 = 102.


Answer: 55

Prompt: A current of 2.5 A flows through 22 Ω. What is the voltage drop in volts?

Solution: V = IR = 2.5·22 = 55.0.


Answer: 18

Prompt: A current of 3 A flows through 6 Ω. What is the voltage drop in volts?

Solution: V = IR = 3·6 = 18.


Answer: 9

Prompt: A current of 1.5 A flows through 6 Ω. What is the voltage drop in volts?

Solution: V = IR = 1.5·6 = 9.0.


Answer: 25

Prompt: A current of 1 A flows through 25 Ω. What is the voltage drop in volts?

Solution: V = IR = 1·25 = 25.


Answer: 76

Prompt: A current of 4 A flows through 19 Ω. What is the voltage drop in volts?

Solution: V = IR = 4·19 = 76.


Answer: 37.5

Prompt: A current of 1.5 A flows through 25 Ω. What is the voltage drop in volts?

Solution: V = IR = 1.5·25 = 37.5.


Answer: 75

Prompt: A current of 5 A flows through 15 Ω. What is the voltage drop in volts?

Solution: V = IR = 5·15 = 75.


Answer: 70

Prompt: A current of 5 A flows through 14 Ω. What is the voltage drop in volts?

Solution: V = IR = 5·14 = 70.


Answer: 18

Prompt: A current of 2 A flows through 9 Ω. What is the voltage drop in volts?

Solution: V = IR = 2·9 = 18.


Answer: 13.5

Prompt: A current of 0.75 A flows through 18 Ω. What is the voltage drop in volts?

Solution: V = IR = 0.75·18 = 13.5.


Answer: 12

Prompt: A current of 3 A flows through 4 Ω. What is the voltage drop in volts?

Solution: V = IR = 3·4 = 12.


Answer: 1.25

Prompt: A current of 0.25 A flows through 5 Ω. What is the voltage drop in volts?

Solution: V = IR = 0.25·5 = 1.25.


Answer: 16.5

Prompt: A current of 0.75 A flows through 22 Ω. What is the voltage drop in volts?

Solution: V = IR = 0.75·22 = 16.5.


Answer: 17.25

Prompt: A current of 0.75 A flows through 23 Ω. What is the voltage drop in volts?

Solution: V = IR = 0.75·23 = 17.25.


Answer: 52.5

Prompt: A current of 2.5 A flows through 21 Ω. What is the voltage drop in volts?

Solution: V = IR = 2.5·21 = 52.5.


Answer: 270

Prompt: A sample has density 2700 kg/m3 and volume 0.1 m3. What is its mass in kg?

Solution: m = ρV = 2700·0.1 = 270.0.


Answer: 1930

Prompt: A sample has density 19300 kg/m3 and volume 0.1 m3. What is its mass in kg?

Solution: m = ρV = 19300·0.1 = 1930.0.


Answer: 10

Prompt: A sample has density 1000 kg/m3 and volume 0.01 m3. What is its mass in kg?

Solution: m = ρV = 1000·0.01 = 10.0.


Answer: 135

Prompt: A sample has density 2700 kg/m3 and volume 0.05 m3. What is its mass in kg?

Solution: m = ρV = 2700·0.05 = 135.0.


Answer: 100

Prompt: A sample has density 1000 kg/m3 and volume 0.1 m3. What is its mass in kg?

Solution: m = ρV = 1000·0.1 = 100.0.


Answer: 780

Prompt: A sample has density 7800 kg/m3 and volume 0.1 m3. What is its mass in kg?

Solution: m = ρV = 7800·0.1 = 780.0.


Answer: 78

Prompt: A sample has density 7800 kg/m3 and volume 0.01 m3. What is its mass in kg?

Solution: m = ρV = 7800·0.01 = 78.0.


Answer: 20

Prompt: A sample has density 1000 kg/m3 and volume 0.02 m3. What is its mass in kg?

Solution: m = ρV = 1000·0.02 = 20.0.


Answer: 390

Prompt: A sample has density 7800 kg/m3 and volume 0.05 m3. What is its mass in kg?

Solution: m = ρV = 7800·0.05 = 390.0.


Answer: 27

Prompt: A sample has density 2700 kg/m3 and volume 0.01 m3. What is its mass in kg?

Solution: m = ρV = 2700·0.01 = 27.0.


Answer: 515468

Prompt: An ideal gas has n=2 mol, T=310 K, V=0.01 m3. Using R=8.314 J/(mol·K), compute P in pascals.

Solution: P = nRT/V = 2.0·8.314·310/0.01 = 515468.0.


Answer: 49551.44

Prompt: An ideal gas has n=1 mol, T=298 K, V=0.05 m3. Using R=8.314 J/(mol·K), compute P in pascals.

Solution: P = nRT/V = 1.0·8.314·298/0.05 = 49551.44.


Answer: 45394.44

Prompt: An ideal gas has n=1 mol, T=273 K, V=0.05 m3. Using R=8.314 J/(mol·K), compute P in pascals.

Solution: P = nRT/V = 1.0·8.314·273/0.05 = 45394.44.


Answer: 90788.88

Prompt: An ideal gas has n=2 mol, T=273 K, V=0.05 m3. Using R=8.314 J/(mol·K), compute P in pascals.

Solution: P = nRT/V = 2.0·8.314·273/0.05 = 90788.88.


Answer: 247757.2

Prompt: An ideal gas has n=2 mol, T=298 K, V=0.02 m3. Using R=8.314 J/(mol·K), compute P in pascals.

Solution: P = nRT/V = 2.0·8.314·298/0.02 = 247757.2.


Answer: 145495

Prompt: An ideal gas has n=0.5 mol, T=350 K, V=0.01 m3. Using R=8.314 J/(mol·K), compute P in pascals.

Solution: P = nRT/V = 0.5·8.314·350/0.01 = 145495.0.


Answer: 24775.72

Prompt: An ideal gas has n=0.5 mol, T=298 K, V=0.05 m3. Using R=8.314 J/(mol·K), compute P in pascals.

Solution: P = nRT/V = 0.5·8.314·298/0.05 = 24775.72.


Answer: 116396

Prompt: An ideal gas has n=2 mol, T=350 K, V=0.05 m3. Using R=8.314 J/(mol·K), compute P in pascals.

Solution: P = nRT/V = 2.0·8.314·350/0.05 = 116396.0.


Answer: 64433.5

Prompt: An ideal gas has n=0.5 mol, T=310 K, V=0.02 m3. Using R=8.314 J/(mol·K), compute P in pascals.

Solution: P = nRT/V = 0.5·8.314·310/0.02 = 64433.5.


Answer: 247757.2

Prompt: An ideal gas has n=1 mol, T=298 K, V=0.01 m3. Using R=8.314 J/(mol·K), compute P in pascals.

Solution: P = nRT/V = 1.0·8.314·298/0.01 = 247757.2.


Answer: 226972.2

Prompt: An ideal gas has n=1 mol, T=273 K, V=0.01 m3. Using R=8.314 J/(mol·K), compute P in pascals.

Solution: P = nRT/V = 1.0·8.314·273/0.01 = 226972.2.


Answer: 113486.1

Prompt: An ideal gas has n=0.5 mol, T=273 K, V=0.01 m3. Using R=8.314 J/(mol·K), compute P in pascals.

Solution: P = nRT/V = 0.5·8.314·273/0.01 = 113486.1.


Answer: 17.87202381

m(H2)=2.0 g
stoichiometry 2:2 for H2:H2O

Convert to moles
Apply mole ratio
Convert to grams

Prompt: For 2 H2 + O2 → 2 H2O, how many grams of water form from 2 g of H2 if oxygen is in excess? Use M(H2)=2.016 g/mol and M(H2O)=18.015 g/mol.

Solution: mol H2 = 2.0/2.016 = 0.9920634920634921. mol H2O = mol H2 = 0.9920634920634921. mass = 0.9920634920634921·18.015 = 17.87202380952381.


Answer: 53.61607143

m(H2)=6.0 g
stoichiometry 2:2 for H2:H2O

Convert to moles
Apply mole ratio
Convert to grams

Prompt: For 2 H2 + O2 → 2 H2O, how many grams of water form from 6 g of H2 if oxygen is in excess? Use M(H2)=2.016 g/mol and M(H2O)=18.015 g/mol.

Solution: mol H2 = 6.0/2.016 = 2.9761904761904763. mol H2O = mol H2 = 2.9761904761904763. mass = 2.9761904761904763·18.015 = 53.61607142857143.


Answer: 35.74404762

m(H2)=4.0 g
stoichiometry 2:2 for H2:H2O

Convert to moles
Apply mole ratio
Convert to grams

Prompt: For 2 H2 + O2 → 2 H2O, how many grams of water form from 4 g of H2 if oxygen is in excess? Use M(H2)=2.016 g/mol and M(H2O)=18.015 g/mol.

Solution: mol H2 = 4.0/2.016 = 1.9841269841269842. mol H2O = mol H2 = 1.9841269841269842. mass = 1.9841269841269842·18.015 = 35.74404761904762.


Answer: 71.48809524

m(H2)=8.0 g
stoichiometry 2:2 for H2:H2O

Convert to moles
Apply mole ratio
Convert to grams

Prompt: For 2 H2 + O2 → 2 H2O, how many grams of water form from 8 g of H2 if oxygen is in excess? Use M(H2)=2.016 g/mol and M(H2O)=18.015 g/mol.

Solution: mol H2 = 8.0/2.016 = 3.9682539682539684. mol H2O = mol H2 = 3.9682539682539684. mass = 3.9682539682539684·18.015 = 71.48809523809524.


Answer: 4

25 °C
ideal dilute solution
complete dissociation

Prompt: A strong acid is fully dissociated at [0.0001 ] mol/L H+. What is the pH?

Solution: pH = -log10[H+] = -log10(0.0001) = 4.0.


Answer: 2

25 °C
ideal dilute solution
complete dissociation

Prompt: A strong acid is fully dissociated at [0.01 ] mol/L H+. What is the pH?

Solution: pH = -log10[H+] = -log10(0.01) = 2.0.


Answer: 1

25 °C
ideal dilute solution
complete dissociation

Prompt: A strong acid is fully dissociated at [0.1 ] mol/L H+. What is the pH?

Solution: pH = -log10[H+] = -log10(0.1) = 1.0.


Answer: 3

25 °C
ideal dilute solution
complete dissociation

Prompt: A strong acid is fully dissociated at [0.001 ] mol/L H+. What is the pH?

Solution: pH = -log10[H+] = -log10(0.001) = 3.0.


Answer: 3870

Prompt: Heat 2 kg of a material with c=387 J/(kg·K) through ΔT=5 K. What energy in joules is required?

Solution: Q = mcΔT = 2.0·387·5 = 3870.0.


Answer: 16736

Prompt: Heat 0.2 kg of a material with c=4184 J/(kg·K) through ΔT=20 K. What energy in joules is required?

Solution: Q = mcΔT = 0.2·4184·20 = 16736.0.


Answer: 41840

Prompt: Heat 1 kg of a material with c=4184 J/(kg·K) through ΔT=10 K. What energy in joules is required?

Solution: Q = mcΔT = 1.0·4184·10 = 41840.0.


Answer: 52300

Prompt: Heat 0.5 kg of a material with c=4184 J/(kg·K) through ΔT=25 K. What energy in joules is required?

Solution: Q = mcΔT = 0.5·4184·25 = 52300.0.


Answer: 167360

Prompt: Heat 2 kg of a material with c=4184 J/(kg·K) through ΔT=20 K. What energy in joules is required?

Solution: Q = mcΔT = 2.0·4184·20 = 167360.0.


Answer: 9000

Prompt: Heat 0.5 kg of a material with c=900 J/(kg·K) through ΔT=20 K. What energy in joules is required?

Solution: Q = mcΔT = 0.5·900·20 = 9000.0.


Answer: 41840

Prompt: Heat 0.5 kg of a material with c=4184 J/(kg·K) through ΔT=20 K. What energy in joules is required?

Solution: Q = mcΔT = 0.5·4184·20 = 41840.0.


Answer: 20920

Prompt: Heat 0.2 kg of a material with c=4184 J/(kg·K) through ΔT=25 K. What energy in joules is required?

Solution: Q = mcΔT = 0.2·4184·25 = 20920.0.


Answer: 8368

Prompt: Heat 0.2 kg of a material with c=4184 J/(kg·K) through ΔT=10 K. What energy in joules is required?

Solution: Q = mcΔT = 0.2·4184·10 = 8368.0.


Answer: 2700

Prompt: Heat 0.2 kg of a material with c=900 J/(kg·K) through ΔT=15 K. What energy in joules is required?

Solution: Q = mcΔT = 0.2·900·15 = 2700.0.


Answer: 36000

Prompt: Heat 2 kg of a material with c=900 J/(kg·K) through ΔT=20 K. What energy in joules is required?

Solution: Q = mcΔT = 2.0·900·20 = 36000.0.


Answer: 83680

Prompt: Heat 2 kg of a material with c=4184 J/(kg·K) through ΔT=10 K. What energy in joules is required?

Solution: Q = mcΔT = 2.0·4184·10 = 83680.0.


Answer: 20920

Prompt: Heat 1 kg of a material with c=4184 J/(kg·K) through ΔT=5 K. What energy in joules is required?

Solution: Q = mcΔT = 1.0·4184·5 = 20920.0.


Answer: 0.125

Prompt: A wave travels at 3e+08 m/s with frequency 2.4e+09 Hz. What is its wavelength in metres?

Solution: λ = v/f = 300000000.0/2400000000.0 = 0.125.


Answer: 1.416666667e-07

Prompt: A wave travels at 340 m/s with frequency 2.4e+09 Hz. What is its wavelength in metres?

Solution: λ = v/f = 340/2400000000.0 = 1.4166666666666668e-07.


Answer: 0.6640625

Prompt: A wave travels at 340 m/s with frequency 512 Hz. What is its wavelength in metres?

Solution: λ = v/f = 340/512 = 0.6640625.


Answer: 1171875

Prompt: A wave travels at 3e+08 m/s with frequency 256 Hz. What is its wavelength in metres?

Solution: λ = v/f = 300000000.0/256 = 1171875.0.


Answer: 300000

Prompt: A wave travels at 3e+08 m/s with frequency 1000 Hz. What is its wavelength in metres?

Solution: λ = v/f = 300000000.0/1000 = 300000.0.


Answer: 1.328125

Prompt: A wave travels at 340 m/s with frequency 256 Hz. What is its wavelength in metres?

Solution: λ = v/f = 340/256 = 1.328125.


Answer: 3.409090909

Prompt: A wave travels at 1500 m/s with frequency 440 Hz. What is its wavelength in metres?

Solution: λ = v/f = 1500/440 = 3.409090909090909.


Answer: 681818.1818

Prompt: A wave travels at 3e+08 m/s with frequency 440 Hz. What is its wavelength in metres?

Solution: λ = v/f = 300000000.0/440 = 681818.1818181818.


Answer: 0.75

Mendelian independent segregation
Complete dominance

Write the Punnett square
Count the requested class

Prompt: In a monohybrid Aa × Aa cross with complete dominance, what fraction of offspring are expected to show the dominant phenotype?

Solution: Genotypes: 1 AA : 2 Aa : 1 aa. Dominant phenotype = 3/4.


Answer: 0.5

Mendelian independent segregation
Complete dominance

Write the Punnett square
Count the requested class

Prompt: In a monohybrid Aa × Aa cross, what fraction of offspring are heterozygous?

Solution: Punnett square: AA, Aa, aA, aa. Heterozygotes = 2/4 = 1/2.


Answer: 200

Compute the number of half-lives
Multiply by 1/2 each time

Prompt: A sample of 1600 nuclei has half-life 5 years. How many remain after 15 years?

Solution: N = N0 · (1/2)^(t/T) = 1600 · 0.5^(15/5) = 200.0.


Answer: 500

Compute the number of half-lives
Multiply by 1/2 each time

Prompt: A sample of 1000 nuclei has half-life 4 years. How many remain after 4 years?

Solution: N = N0 · (1/2)^(t/T) = 1000 · 0.5^(4/4) = 500.0.


Answer: 400

Compute the number of half-lives
Multiply by 1/2 each time

Prompt: A sample of 1600 nuclei has half-life 5 years. How many remain after 10 years?

Solution: N = N0 · (1/2)^(t/T) = 1600 · 0.5^(10/5) = 400.0.


Answer: 200

Compute the number of half-lives
Multiply by 1/2 each time

Prompt: A sample of 800 nuclei has half-life 4 years. How many remain after 8 years?

Solution: N = N0 · (1/2)^(t/T) = 800 · 0.5^(8/4) = 200.0.


Answer: 100

Compute the number of half-lives
Multiply by 1/2 each time

Prompt: A sample of 800 nuclei has half-life 5 years. How many remain after 15 years?

Solution: N = N0 · (1/2)^(t/T) = 800 · 0.5^(15/5) = 100.0.


Answer: 250

Compute the number of half-lives
Multiply by 1/2 each time

Prompt: A sample of 1000 nuclei has half-life 4 years. How many remain after 8 years?

Solution: N = N0 · (1/2)^(t/T) = 1000 · 0.5^(8/4) = 250.0.


Answer: 200

Compute the number of half-lives
Multiply by 1/2 each time

Prompt: A sample of 800 nuclei has half-life 2 years. How many remain after 4 years?

Solution: N = N0 · (1/2)^(t/T) = 800 · 0.5^(4/2) = 200.0.


Answer: 800

Compute the number of half-lives
Multiply by 1/2 each time

Prompt: A sample of 1600 nuclei has half-life 5 years. How many remain after 5 years?

Solution: N = N0 · (1/2)^(t/T) = 1600 · 0.5^(5/5) = 800.0.


Answer: 400

Compute the number of half-lives
Multiply by 1/2 each time

Prompt: A sample of 800 nuclei has half-life 5 years. How many remain after 5 years?

Solution: N = N0 · (1/2)^(t/T) = 800 · 0.5^(5/5) = 400.0.


Answer: 800

Compute the number of half-lives
Multiply by 1/2 each time

Prompt: A sample of 1600 nuclei has half-life 4 years. How many remain after 4 years?

Solution: N = N0 · (1/2)^(t/T) = 1600 · 0.5^(4/4) = 800.0.


Answer: 500

Compute the number of half-lives
Multiply by 1/2 each time

Prompt: A sample of 1000 nuclei has half-life 2 years. How many remain after 2 years?

Solution: N = N0 · (1/2)^(t/T) = 1000 · 0.5^(2/2) = 500.0.


Answer: 125

Compute the number of half-lives
Multiply by 1/2 each time

Prompt: A sample of 1000 nuclei has half-life 5 years. How many remain after 15 years?

Solution: N = N0 · (1/2)^(t/T) = 1000 · 0.5^(15/5) = 125.0.


Answer: 0.2407500841

Sun-dominated two-body problem
T in years, a in AU

Prompt: Using Kepler's third law in AU and years (T2 = a3), estimate the orbital period of a planet with semi-major axis 0.387 AU.

Solution: T = a^(3/2) = 0.387^1.5 = 0.24075008411213486 years.


Answer: 1.881384018

Sun-dominated two-body problem
T in years, a in AU

Prompt: Using Kepler's third law in AU and years (T2 = a3), estimate the orbital period of a planet with semi-major axis 1.524 AU.

Solution: T = a^(3/2) = 1.524^1.5 = 1.8813840182163768 years.


Answer: 0.6147626103

Sun-dominated two-body problem
T in years, a in AU

Prompt: Using Kepler's third law in AU and years (T2 = a3), estimate the orbital period of a planet with semi-major axis 0.723 AU.

Solution: T = a^(3/2) = 0.723^1.5 = 0.6147626102813996 years.


Answer: 0.4

Conservative solute
Volumes additive as stated

Prompt: Dilute 0.05 L of a 2 M stock to 0.25 L. What is the final molarity?

Solution: M1V1 = M2V2 ⇒ M2 = 2.0·0.05/0.25 = 0.4.


Answer: 0.2

Conservative solute
Volumes additive as stated

Prompt: Dilute 0.05 L of a 2 M stock to 0.5 L. What is the final molarity?

Solution: M1V1 = M2V2 ⇒ M2 = 2.0·0.05/0.5 = 0.2.


Answer: 1.2

Conservative solute
Volumes additive as stated

Prompt: Dilute 0.05 L of a 6 M stock to 0.25 L. What is the final molarity?

Solution: M1V1 = M2V2 ⇒ M2 = 6.0·0.05/0.25 = 1.2000000000000002.


Answer: 0.6

Conservative solute
Volumes additive as stated

Prompt: Dilute 0.01 L of a 6 M stock to 0.1 L. What is the final molarity?

Solution: M1V1 = M2V2 ⇒ M2 = 6.0·0.01/0.1 = 0.6.


Answer: 3

Conservative solute
Volumes additive as stated

Prompt: Dilute 0.025 L of a 12 M stock to 0.1 L. What is the final molarity?

Solution: M1V1 = M2V2 ⇒ M2 = 12.0·0.025/0.1 = 3.0000000000000004.


Answer: 0.25

Conservative solute
Volumes additive as stated

Prompt: Dilute 0.025 L of a 1 M stock to 0.1 L. What is the final molarity?

Solution: M1V1 = M2V2 ⇒ M2 = 1.0·0.025/0.1 = 0.25.


Answer: 0.12

Conservative solute
Volumes additive as stated

Prompt: Dilute 0.01 L of a 6 M stock to 0.5 L. What is the final molarity?

Solution: M1V1 = M2V2 ⇒ M2 = 6.0·0.01/0.5 = 0.12.


Answer: 1.2

Conservative solute
Volumes additive as stated

Prompt: Dilute 0.05 L of a 12 M stock to 0.5 L. What is the final molarity?

Solution: M1V1 = M2V2 ⇒ M2 = 12.0·0.05/0.5 = 1.2000000000000002.


Answer: 6

Conservative solute
Volumes additive as stated

Prompt: Dilute 0.05 L of a 12 M stock to 0.1 L. What is the final molarity?

Solution: M1V1 = M2V2 ⇒ M2 = 12.0·0.05/0.1 = 6.000000000000001.


Answer: 0.02

Conservative solute
Volumes additive as stated

Prompt: Dilute 0.01 L of a 1 M stock to 0.5 L. What is the final molarity?

Solution: M1V1 = M2V2 ⇒ M2 = 1.0·0.01/0.5 = 0.02.


Answer: 1

Conservative solute
Volumes additive as stated

Prompt: Dilute 0.05 L of a 2 M stock to 0.1 L. What is the final molarity?

Solution: M1V1 = M2V2 ⇒ M2 = 2.0·0.05/0.1 = 1.0.


Answer: 0.6

Conservative solute
Volumes additive as stated

Prompt: Dilute 0.05 L of a 6 M stock to 0.5 L. What is the final molarity?

Solution: M1V1 = M2V2 ⇒ M2 = 6.0·0.05/0.5 = 0.6000000000000001.


Answer: 0.5

Conservative solute
Volumes additive as stated

Prompt: Dilute 0.025 L of a 2 M stock to 0.1 L. What is the final molarity?

Solution: M1V1 = M2V2 ⇒ M2 = 2.0·0.025/0.1 = 0.5.


Answer: 0.1

Conservative solute
Volumes additive as stated

Prompt: Dilute 0.025 L of a 1 M stock to 0.25 L. What is the final molarity?

Solution: M1V1 = M2V2 ⇒ M2 = 1.0·0.025/0.25 = 0.1.


Answer: 64

Exact integer or binary logarithm as specified

Apply the stated formula or place-value conversion

Prompt: An algorithm performs n log2(n) comparisons. For n=16, how many comparisons?

Solution: n log2 n = 16·4.0 = 64.0.


Answer: 2080

Exact integer or binary logarithm as specified

Apply the stated formula or place-value conversion

Prompt: A nested loop runs i=1..n, j=1..i. How many (i,j) pairs for n=64?

Solution: Sum_{i=1..n} i = n(n+1)/2 = 2080.0.


Answer: 5

Exact integer or binary logarithm as specified

Apply the stated formula or place-value conversion

Prompt: How many bits are required to represent the integer 32 in binary (floor(log2 n))?

Solution: floor(log2(32)) = 5.


Answer: 13

Exact integer or binary logarithm as specified

Apply the stated formula or place-value conversion

Prompt: Convert the binary integer 1101 to decimal.

Solution: 11012 = 1310.


Answer: 2048

Exact integer or binary logarithm as specified

Apply the stated formula or place-value conversion

Prompt: An algorithm performs n log2(n) comparisons. For n=256, how many comparisons?

Solution: n log2 n = 256·8.0 = 2048.0.


Answer: 8256

Exact integer or binary logarithm as specified

Apply the stated formula or place-value conversion

Prompt: A nested loop runs i=1..n, j=1..i. How many (i,j) pairs for n=128?

Solution: Sum_{i=1..n} i = n(n+1)/2 = 8256.0.


Answer: 8

Exact integer or binary logarithm as specified

Apply the stated formula or place-value conversion

Prompt: How many bits are required to represent the integer 256 in binary (floor(log2 n))?

Solution: floor(log2(256)) = 8.


Answer: 160

Exact integer or binary logarithm as specified

Apply the stated formula or place-value conversion

Prompt: An algorithm performs n log2(n) comparisons. For n=32, how many comparisons?

Solution: n log2 n = 32·5.0 = 160.0.


Answer: 4

Exact integer or binary logarithm as specified

Apply the stated formula or place-value conversion

Prompt: How many bits are required to represent the integer 16 in binary (floor(log2 n))?

Solution: floor(log2(16)) = 4.


Answer: 58

Exact integer or binary logarithm as specified

Apply the stated formula or place-value conversion

Prompt: Convert the binary integer 111010 to decimal.

Solution: 1110102 = 5810.


Answer: 896

Exact integer or binary logarithm as specified

Apply the stated formula or place-value conversion

Prompt: An algorithm performs n log2(n) comparisons. For n=128, how many comparisons?

Solution: n log2 n = 128·7.0 = 896.0.


Answer: 528

Exact integer or binary logarithm as specified

Apply the stated formula or place-value conversion

Prompt: A nested loop runs i=1..n, j=1..i. How many (i,j) pairs for n=32?

Solution: Sum_{i=1..n} i = n(n+1)/2 = 528.0.


Answer: 6

Exact integer or binary logarithm as specified

Apply the stated formula or place-value conversion

Prompt: How many bits are required to represent the integer 64 in binary (floor(log2 n))?

Solution: floor(log2(64)) = 6.


Answer: 14

Exact integer or binary logarithm as specified

Apply the stated formula or place-value conversion

Prompt: Convert the binary integer 1110 to decimal.

Solution: 11102 = 1410.


Answer: 52

Exact integer or binary logarithm as specified

Apply the stated formula or place-value conversion

Prompt: Convert the binary integer 110100 to decimal.

Solution: 1101002 = 5210.


Answer: 5000000

Prompt: A tensile force of 5000 N acts on a cross-section of 0.001 m2. What is the axial stress in pascals?

Solution: σ = F/A = 5000/0.001 = 5000000.0.


Answer: 2500000

Prompt: A tensile force of 2500 N acts on a cross-section of 0.001 m2. What is the axial stress in pascals?

Solution: σ = F/A = 2500/0.001 = 2500000.0.


Answer: 1250000

Prompt: A tensile force of 2500 N acts on a cross-section of 0.002 m2. What is the axial stress in pascals?

Solution: σ = F/A = 2500/0.002 = 1250000.0.


Answer: 2500000

Prompt: A tensile force of 5000 N acts on a cross-section of 0.002 m2. What is the axial stress in pascals?

Solution: σ = F/A = 5000/0.002 = 2500000.0.


Answer: 500000

Prompt: A tensile force of 1000 N acts on a cross-section of 0.002 m2. What is the axial stress in pascals?

Solution: σ = F/A = 1000/0.002 = 500000.0.


Answer: 1000000

Prompt: A tensile force of 5000 N acts on a cross-section of 0.005 m2. What is the axial stress in pascals?

Solution: σ = F/A = 5000/0.005 = 1000000.0.


Answer: 2000000

Prompt: A tensile force of 10000 N acts on a cross-section of 0.005 m2. What is the axial stress in pascals?

Solution: σ = F/A = 10000/0.005 = 2000000.0.


Answer: 500000

Prompt: A tensile force of 2500 N acts on a cross-section of 0.005 m2. What is the axial stress in pascals?

Solution: σ = F/A = 2500/0.005 = 500000.0.


Answer: 200000

Prompt: A tensile force of 1000 N acts on a cross-section of 0.005 m2. What is the axial stress in pascals?

Solution: σ = F/A = 1000/0.005 = 200000.0.


Answer: 5000000

Prompt: A tensile force of 10000 N acts on a cross-section of 0.002 m2. What is the axial stress in pascals?

Solution: σ = F/A = 10000/0.002 = 5000000.0.


Answer: 30

One unit per replicate
No blocking factor in this count

Prompt: You will test 6 fertilizer treatments with 5 independent replicates each, fully randomized. How many experimental units do you need?

Solution: units = treatments × replicates = 6×5 = 30.


Answer: 16

One unit per replicate
No blocking factor in this count

Prompt: You will test 4 fertilizer treatments with 4 independent replicates each, fully randomized. How many experimental units do you need?

Solution: units = treatments × replicates = 4×4 = 16.


Answer: 18

One unit per replicate
No blocking factor in this count

Prompt: You will test 6 fertilizer treatments with 3 independent replicates each, fully randomized. How many experimental units do you need?

Solution: units = treatments × replicates = 6×3 = 18.


Answer: 15

One unit per replicate
No blocking factor in this count

Prompt: You will test 5 fertilizer treatments with 3 independent replicates each, fully randomized. How many experimental units do you need?

Solution: units = treatments × replicates = 5×3 = 15.


Answer: 24

One unit per replicate
No blocking factor in this count

Prompt: You will test 6 fertilizer treatments with 4 independent replicates each, fully randomized. How many experimental units do you need?

Solution: units = treatments × replicates = 6×4 = 24.


Answer: 20

One unit per replicate
No blocking factor in this count

Prompt: You will test 4 fertilizer treatments with 5 independent replicates each, fully randomized. How many experimental units do you need?

Solution: units = treatments × replicates = 4×5 = 20.


Answer: 1870.65

Prompt: An ideal gas has n=3 mol, T=300 K, V=4 m^3. Using R=8.314 J/(mol·K), what is P in pascals from PV=nRT?

Solution: P = nRT/V = 3*8.314*300/4 = 1870.65.


Answer: 453.9444

Prompt: An ideal gas has n=2 mol, T=273 K, V=10 m^3. Using R=8.314 J/(mol·K), what is P in pascals from PV=nRT?

Solution: P = nRT/V = 2*8.314*273/10 = 453.94440000000003.


Answer: 415.7

Prompt: An ideal gas has n=1 mol, T=250 K, V=5 m^3. Using R=8.314 J/(mol·K), what is P in pascals from PV=nRT?

Solution: P = nRT/V = 1*8.314*250/5 = 415.7.


Answer: 3741.3

Prompt: An ideal gas has n=3 mol, T=300 K, V=2 m^3. Using R=8.314 J/(mol·K), what is P in pascals from PV=nRT?

Solution: P = nRT/V = 3*8.314*300/2 = 3741.3.


Answer: 2182.425

Prompt: An ideal gas has n=3 mol, T=350 K, V=4 m^3. Using R=8.314 J/(mol·K), what is P in pascals from PV=nRT?

Solution: P = nRT/V = 3*8.314*350/4 = 2182.425.


Answer: 5819.8

Prompt: An ideal gas has n=2 mol, T=350 K, V=1 m^3. Using R=8.314 J/(mol·K), what is P in pascals from PV=nRT?

Solution: P = nRT/V = 2*8.314*350/1 = 5819.8.


Answer: 2269.722

Prompt: An ideal gas has n=2 mol, T=273 K, V=2 m^3. Using R=8.314 J/(mol·K), what is P in pascals from PV=nRT?

Solution: P = nRT/V = 2*8.314*273/2 = 2269.722.


Answer: 581.98

Prompt: An ideal gas has n=2 mol, T=350 K, V=10 m^3. Using R=8.314 J/(mol·K), what is P in pascals from PV=nRT?

Solution: P = nRT/V = 2*8.314*350/10 = 581.98.


Answer: 1361.8332

Prompt: An ideal gas has n=3 mol, T=273 K, V=5 m^3. Using R=8.314 J/(mol·K), what is P in pascals from PV=nRT?

Solution: P = nRT/V = 3*8.314*273/5 = 1361.8332.


Answer: 2494.2

Prompt: An ideal gas has n=2 mol, T=300 K, V=2 m^3. Using R=8.314 J/(mol·K), what is P in pascals from PV=nRT?

Solution: P = nRT/V = 2*8.314*300/2 = 2494.2.


Answer: 4.5

Prompt: A sample has mass 18 kg and volume 4 m^3. What is its density in kg/m^3?

Solution: ρ = m/V = 18/4 = 4.5.


Answer: 14

Prompt: A sample has mass 7 kg and volume 0.5 m^3. What is its density in kg/m^3?

Solution: ρ = m/V = 7/0.5 = 14.0.


Answer: 2.2

Prompt: A sample has mass 11 kg and volume 5 m^3. What is its density in kg/m^3?

Solution: ρ = m/V = 11/5 = 2.2.


Answer: 24

Prompt: A sample has mass 12 kg and volume 0.5 m^3. What is its density in kg/m^3?

Solution: ρ = m/V = 12/0.5 = 24.0.


Answer: 4.5

Prompt: A sample has mass 9 kg and volume 2 m^3. What is its density in kg/m^3?

Solution: ρ = m/V = 9/2 = 4.5.


Answer: 9

Prompt: A sample has mass 9 kg and volume 1 m^3. What is its density in kg/m^3?

Solution: ρ = m/V = 9/1 = 9.0.


Answer: 12

Prompt: A sample has mass 6 kg and volume 0.5 m^3. What is its density in kg/m^3?

Solution: ρ = m/V = 6/0.5 = 12.0.


Answer: 3

Prompt: A sample has mass 3 kg and volume 1 m^3. What is its density in kg/m^3?

Solution: ρ = m/V = 3/1 = 3.0.


Answer: 3.4

Prompt: A sample has mass 17 kg and volume 5 m^3. What is its density in kg/m^3?

Solution: ρ = m/V = 17/5 = 3.4.


Answer: 1

Prompt: A sample has mass 4 kg and volume 4 m^3. What is its density in kg/m^3?

Solution: ρ = m/V = 4/4 = 1.0.


Answer: 17.14285714

Thin-lens equation
Positive real-object distances

Prompt: A thin converging lens has f=12 cm. A real object is u=40 cm away. Using 1/f = 1/v + 1/u with positive distances, what is v in cm?

Solution: 1/v = 1/f - 1/u = 1/12 - 1/40 so v = 17.142857142857146.


Answer: 10.90909091

Thin-lens equation
Positive real-object distances

Prompt: A thin converging lens has f=8 cm. A real object is u=30 cm away. Using 1/f = 1/v + 1/u with positive distances, what is v in cm?

Solution: 1/v = 1/f - 1/u = 1/8 - 1/30 so v = 10.909090909090908.


Answer: 20

Thin-lens equation
Positive real-object distances

Prompt: A thin converging lens has f=12 cm. A real object is u=30 cm away. Using 1/f = 1/v + 1/u with positive distances, what is v in cm?

Solution: 1/v = 1/f - 1/u = 1/12 - 1/30 so v = 20.0.


Answer: 13.33333333

Thin-lens equation
Positive real-object distances

Prompt: A thin converging lens has f=8 cm. A real object is u=20 cm away. Using 1/f = 1/v + 1/u with positive distances, what is v in cm?

Solution: 1/v = 1/f - 1/u = 1/8 - 1/20 so v = 13.333333333333334.


Answer: 7.5

Thin-lens equation
Positive real-object distances

Prompt: A thin converging lens has f=5 cm. A real object is u=15 cm away. Using 1/f = 1/v + 1/u with positive distances, what is v in cm?

Solution: 1/v = 1/f - 1/u = 1/5 - 1/15 so v = 7.499999999999998.


Answer: 30

Thin-lens equation
Positive real-object distances

Prompt: A thin converging lens has f=12 cm. A real object is u=20 cm away. Using 1/f = 1/v + 1/u with positive distances, what is v in cm?

Solution: 1/v = 1/f - 1/u = 1/12 - 1/20 so v = 30.000000000000007.


Answer: 10

Thin-lens equation
Positive real-object distances

Prompt: A thin converging lens has f=8 cm. A real object is u=40 cm away. Using 1/f = 1/v + 1/u with positive distances, what is v in cm?

Solution: 1/v = 1/f - 1/u = 1/8 - 1/40 so v = 10.0.


Answer: 60

Thin-lens equation
Positive real-object distances

Prompt: A thin converging lens has f=12 cm. A real object is u=15 cm away. Using 1/f = 1/v + 1/u with positive distances, what is v in cm?

Solution: 1/v = 1/f - 1/u = 1/12 - 1/15 so v = 60.000000000000014.


Answer: 3.973835306

Prompt: A simple pendulum has length 4 m. Take g=10 m/s2 and T=2π√(L/g). What is the period in seconds?

Solution: T=2π√(4/10) = 3.9738353063184406.


Answer: 1.884955592

Prompt: A simple pendulum has length 0.9 m. Take g=10 m/s2 and T=2π√(L/g). What is the period in seconds?

Solution: T=2π√(0.9/10) = 1.8849555921538759.


Answer: 1.256637061

Prompt: A simple pendulum has length 0.4 m. Take g=10 m/s2 and T=2π√(L/g). What is the period in seconds?

Solution: T=2π√(0.4/10) = 1.2566370614359172.


Answer: 3.141592654

Prompt: A simple pendulum has length 2.5 m. Take g=10 m/s2 and T=2π√(L/g). What is the period in seconds?

Solution: T=2π√(2.5/10) = 3.141592653589793.


Answer: 4.002e-05

Prompt: Two point masses 500000 kg and 300000 kg are 500 m apart. Using G=6.67e-11, what is the Newtonian force magnitude in newtons?

Solution: F=G m1 m2 / r^2 = 4.001999999999999e-05.


Answer: 0.0002001

Prompt: Two point masses 800000 kg and 600000 kg are 400 m apart. Using G=6.67e-11, what is the Newtonian force magnitude in newtons?

Solution: F=G m1 m2 / r^2 = 0.00020009999999999998.


Answer: 0.00010005

Prompt: Two point masses 400000 kg and 600000 kg are 400 m apart. Using G=6.67e-11, what is the Newtonian force magnitude in newtons?

Solution: F=G m1 m2 / r^2 = 0.00010004999999999999.


Answer: 0.0004002

Prompt: Two point masses 800000 kg and 300000 kg are 200 m apart. Using G=6.67e-11, what is the Newtonian force magnitude in newtons?

Solution: F=G m1 m2 / r^2 = 0.00040019999999999997.


Answer: 0.0001250625

Prompt: Two point masses 500000 kg and 600000 kg are 400 m apart. Using G=6.67e-11, what is the Newtonian force magnitude in newtons?

Solution: F=G m1 m2 / r^2 = 0.00012506249999999998.


Answer: 5.0025e-05

Prompt: Two point masses 400000 kg and 300000 kg are 400 m apart. Using G=6.67e-11, what is the Newtonian force magnitude in newtons?

Solution: F=G m1 m2 / r^2 = 5.0024999999999996e-05.


Answer: 5.0025e-05

Prompt: Two point masses 200000 kg and 600000 kg are 400 m apart. Using G=6.67e-11, what is the Newtonian force magnitude in newtons?


Answer: 4

Prompt: 1 mol of solute is dissolved to 0.25 L of solution. What is the molarity in mol/L?

Solution: M = n/V = 1/0.25 = 4.0.


Answer: 1

Prompt: 0.5 mol of solute is dissolved to 0.5 L of solution. What is the molarity in mol/L?

Solution: M = n/V = 0.5/0.5 = 1.0.


Answer: 0.25

Prompt: 0.5 mol of solute is dissolved to 2 L of solution. What is the molarity in mol/L?

Solution: M = n/V = 0.5/2 = 0.25.


Answer: 0.125

Prompt: 0.25 mol of solute is dissolved to 2 L of solution. What is the molarity in mol/L?

Solution: M = n/V = 0.25/2 = 0.125.


Answer: 2

Prompt: 2 mol of solute is dissolved to 1 L of solution. What is the molarity in mol/L?

Solution: M = n/V = 2/1 = 2.0.


Answer: 1

Prompt: 2 mol of solute is dissolved to 2 L of solution. What is the molarity in mol/L?

Solution: M = n/V = 2/2 = 1.0.


Answer: 0.5

Prompt: 0.25 mol of solute is dissolved to 0.5 L of solution. What is the molarity in mol/L?

Solution: M = n/V = 0.25/0.5 = 0.5.


Answer: 0.415625

Prompt: Snell's law: n1 sin θ1 = n2 sin θ2. n1=1.33, n2=1.6, sin θ1=0.5. What is sin θ2?

Solution: sin θ2 = n1 sin θ1 / n2 = 0.415625.


Answer: 0.25

Prompt: Snell's law: n1 sin θ1 = n2 sin θ2. n1=1, n2=1.6, sin θ1=0.4. What is sin θ2?

Solution: sin θ2 = n1 sin θ1 / n2 = 0.25.


Answer: 0.1875

Prompt: Snell's law: n1 sin θ1 = n2 sin θ2. n1=1, n2=1.6, sin θ1=0.3. What is sin θ2?

Solution: sin θ2 = n1 sin θ1 / n2 = 0.18749999999999997.


Answer: 0.3325

Prompt: Snell's law: n1 sin θ1 = n2 sin θ2. n1=1.33, n2=1.6, sin θ1=0.4. What is sin θ2?

Solution: sin θ2 = n1 sin θ1 / n2 = 0.3325.


Answer: 5

Prompt: A sample starts at 80 units. After 4 half-lives, how many units remain (exponential decay, integer-power of two)?

Solution: N = N0 / 2^h = 80/2^4 = 5.0.


Answer: 10

Prompt: A sample starts at 160 units. After 4 half-lives, how many units remain (exponential decay, integer-power of two)?

Solution: N = N0 / 2^h = 160/2^4 = 10.0.


Answer: 80

Prompt: A sample starts at 320 units. After 2 half-lives, how many units remain (exponential decay, integer-power of two)?

Solution: N = N0 / 2^h = 320/2^2 = 80.0.


Answer: 40

Prompt: A sample starts at 160 units. After 2 half-lives, how many units remain (exponential decay, integer-power of two)?

Solution: N = N0 / 2^h = 160/2^2 = 40.0.


Answer: 160

Prompt: A sample starts at 320 units. After 1 half-lives, how many units remain (exponential decay, integer-power of two)?

Solution: N = N0 / 2^h = 320/2^1 = 160.0.


Answer: 80

Prompt: A sample starts at 160 units. After 1 half-lives, how many units remain (exponential decay, integer-power of two)?

Solution: N = N0 / 2^h = 160/2^1 = 80.0.


Answer: 3/4

Mendelian, independent, complete dominance

Prompt: Aa × Aa, complete dominance. What is P(dominant phenotype) as a reduced fraction a/b? Report a/b.

Solution: 3/4 of the Punnett cells match.


Answer: 1/2

Mendelian, independent, complete dominance

Prompt: Aa × aa testcross, complete dominance. What is P(recessive phenotype) as a reduced fraction a/b? Report a/b.

Solution: 1/2 of the Punnett cells match.


Answer: 9000

Prompt: Q=mcΔT. Mass 1 kg, c=900 J/(kg·K), ΔT=10 K. What is Q in joules?


Answer: 4500

Prompt: Q=mcΔT. Mass 1 kg, c=900 J/(kg·K), ΔT=5 K. What is Q in joules?


Answer: 83600

Prompt: Q=mcΔT. Mass 1 kg, c=4180 J/(kg·K), ΔT=20 K. What is Q in joules?


Answer: 83600

Prompt: Q=mcΔT. Mass 2 kg, c=4180 J/(kg·K), ΔT=10 K. What is Q in joules?


Answer: 967.5

Prompt: Q=mcΔT. Mass 0.5 kg, c=387 J/(kg·K), ΔT=5 K. What is Q in joules?


Answer: 41800

Prompt: Q=mcΔT. Mass 2 kg, c=4180 J/(kg·K), ΔT=5 K. What is Q in joules?


Answer: 10450

Prompt: Q=mcΔT. Mass 0.5 kg, c=4180 J/(kg·K), ΔT=5 K. What is Q in joules?


Answer: 20

Prompt: Archimedes: a fully submerged volume 0.002 m3 in freshwater (ρ=1000 kg/m3), g=10 m/s2. What is the buoyant force in newtons?


Answer: 50

Prompt: Archimedes: a fully submerged volume 0.005 m3 in freshwater (ρ=1000 kg/m3), g=10 m/s2. What is the buoyant force in newtons?


Answer: 100

Prompt: Archimedes: a fully submerged volume 0.01 m3 in freshwater (ρ=1000 kg/m3), g=10 m/s2. What is the buoyant force in newtons?


Answer: 3.9756e-19

Prompt: A photon has frequency 6e+14 Hz. Using E=hf and h=6.626e-34 J·s, what is E in joules?


Answer: 6.626e-19

Prompt: A photon has frequency 1e+15 Hz. Using E=hf and h=6.626e-34 J·s, what is E in joules?

Solution: E=hf=6.626e-34·1e+15=6.625999999999999e-19.


Answer: 3.313e-19

Prompt: A photon has frequency 5e+14 Hz. Using E=hf and h=6.626e-34 J·s, what is E in joules?


Answer: 0.2

Conservative solute
Volumes additive as given

Prompt: Dilute 0.1 L of 2 mol/L solution to 1 L. What is the new concentration in mol/L (C1V1=C2V2)?


Answer: 1

Conservative solute
Volumes additive as given

Prompt: Dilute 0.25 L of 2 mol/L solution to 0.5 L. What is the new concentration in mol/L (C1V1=C2V2)?


Answer: 0.75

Conservative solute
Volumes additive as given

Prompt: Dilute 0.25 L of 6 mol/L solution to 2 L. What is the new concentration in mol/L (C1V1=C2V2)?


Answer: 1

Conservative solute
Volumes additive as given

Prompt: Dilute 0.2 L of 10 mol/L solution to 2 L. What is the new concentration in mol/L (C1V1=C2V2)?


Answer: 0.2

Conservative solute
Volumes additive as given

Prompt: Dilute 0.1 L of 4 mol/L solution to 2 L. What is the new concentration in mol/L (C1V1=C2V2)?


Answer: 53

Linear calibration
No noise term in this item

Prompt: A calibrated sensor is modeled as y=7x+4. If the reading x=7, what is the modeled y?


Answer: 39

Linear calibration
No noise term in this item

Prompt: A calibrated sensor is modeled as y=7x+-3. If the reading x=6, what is the modeled y?


Answer: 18

Linear calibration
No noise term in this item

Prompt: A calibrated sensor is modeled as y=2x+2. If the reading x=8, what is the modeled y?


Answer: 20

Linear calibration
No noise term in this item

Prompt: A calibrated sensor is modeled as y=3x+2. If the reading x=6, what is the modeled y?


Answer: 61

Linear calibration
No noise term in this item

Prompt: A calibrated sensor is modeled as y=9x+-2. If the reading x=7, what is the modeled y?


Answer: 24

Linear calibration
No noise term in this item

Prompt: A calibrated sensor is modeled as y=4x+4. If the reading x=5, what is the modeled y?


Answer: 2.4

Prompt: On a distance-time graph, distance rises 12 m over 5 s of straight-line motion. What is the constant speed in m/s?

Solution: speed = Δs/Δt = 12/5 = 2.4.


Answer: 3

Prompt: On a distance-time graph, distance rises 12 m over 4 s of straight-line motion. What is the constant speed in m/s?

Solution: speed = Δs/Δt = 12/4 = 3.0.


Answer: 2

Prompt: On a distance-time graph, distance rises 10 m over 5 s of straight-line motion. What is the constant speed in m/s?

Solution: speed = Δs/Δt = 10/5 = 2.0.


Answer: 2

Prompt: On a distance-time graph, distance rises 8 m over 4 s of straight-line motion. What is the constant speed in m/s?

Solution: speed = Δs/Δt = 8/4 = 2.0.


Answer: 5

Prompt: On a distance-time graph, distance rises 10 m over 2 s of straight-line motion. What is the constant speed in m/s?

Solution: speed = Δs/Δt = 10/2 = 5.0.


Answer: 193.6

Prompt: A mass of 8 kg moves in a horizontal circle of radius 5 m at 11 m/s. What is the centripetal force in newtons?

Solution: F = mv2/r = 8·112/5 = 193.6.


Answer: 343

Prompt: A mass of 7 kg moves in a horizontal circle of radius 1 m at 7 m/s. What is the centripetal force in newtons?

Solution: F = mv2/r = 7·72/1 = 343.0.


Answer: 196

Prompt: A mass of 8 kg moves in a horizontal circle of radius 2 m at 7 m/s. What is the centripetal force in newtons?

Solution: F = mv2/r = 8·72/2 = 196.0.


Answer: 66.66666667

Prompt: A mass of 8 kg moves in a horizontal circle of radius 3 m at 5 m/s. What is the centripetal force in newtons?

Solution: F = mv2/r = 8·52/3 = 66.66666666666667.


Answer: 81.66666667

Prompt: A mass of 5 kg moves in a horizontal circle of radius 3 m at 7 m/s. What is the centripetal force in newtons?

Solution: F = mv2/r = 5·72/3 = 81.66666666666667.


Answer: 500

Prompt: A mass of 5 kg moves in a horizontal circle of radius 1 m at 10 m/s. What is the centripetal force in newtons?

Solution: F = mv2/r = 5·102/1 = 500.0.


Answer: 18

Prompt: A mass of 4 kg moves in a horizontal circle of radius 2 m at 3 m/s. What is the centripetal force in newtons?

Solution: F = mv2/r = 4·32/2 = 18.0.


Answer: 113.4

Prompt: A mass of 7 kg moves in a horizontal circle of radius 5 m at 9 m/s. What is the centripetal force in newtons?

Solution: F = mv2/r = 7·92/5 = 113.4.


Answer: 54

Prompt: A mass of 4 kg moves in a horizontal circle of radius 6 m at 9 m/s. What is the centripetal force in newtons?

Solution: F = mv2/r = 4·92/6 = 54.0.


Answer: 648

Prompt: A mass of 8 kg moves in a horizontal circle of radius 1 m at 9 m/s. What is the centripetal force in newtons?

Solution: F = mv2/r = 8·92/1 = 648.0.


Answer: 36

Prompt: A mass of 2 kg moves in a horizontal circle of radius 2 m at 6 m/s. What is the centripetal force in newtons?

Solution: F = mv2/r = 2·62/2 = 36.0.


Answer: 58.33333333

Prompt: A mass of 7 kg moves in a horizontal circle of radius 3 m at 5 m/s. What is the centripetal force in newtons?

Solution: F = mv2/r = 7·52/3 = 58.333333333333336.


Answer: 97.2

Prompt: A mass of 6 kg moves in a horizontal circle of radius 5 m at 9 m/s. What is the centripetal force in newtons?

Solution: F = mv2/r = 6·92/5 = 97.2.


Answer: 64

Prompt: A mass of 6 kg moves in a horizontal circle of radius 6 m at 8 m/s. What is the centripetal force in newtons?

Solution: F = mv2/r = 6·82/6 = 64.0.


Answer: 49

Prompt: A mass of 6 kg moves in a horizontal circle of radius 6 m at 7 m/s. What is the centripetal force in newtons?

Solution: F = mv2/r = 6·72/6 = 49.0.


Answer: 96

Prompt: A mass of 8 kg moves in a horizontal circle of radius 3 m at 6 m/s. What is the centripetal force in newtons?

Solution: F = mv2/r = 8·62/3 = 96.0.


Answer: 125

Prompt: A mass of 5 kg moves in a horizontal circle of radius 1 m at 5 m/s. What is the centripetal force in newtons?

Solution: F = mv2/r = 5·52/1 = 125.0.


Answer: 196

Prompt: A mass of 4 kg moves in a horizontal circle of radius 1 m at 7 m/s. What is the centripetal force in newtons?

Solution: F = mv2/r = 4·72/1 = 196.0.


Answer: 2.7

Prompt: Two point charges 3e-06 C and 4e-06 C are 0.2 m apart in vacuum. Magnitude of the Coulomb force in newtons? Use k=9.0e9.

Solution: F=k|q1 q2|/r2 = 9e9·1.2e-11/0.04000000000000001 = 2.6999999999999993.


Answer: 0.009

Prompt: Two point charges 1e-06 C and 1e-06 C are 1.0 m apart in vacuum. Magnitude of the Coulomb force in newtons? Use k=9.0e9.

Solution: F=k|q1 q2|/r2 = 9e9·1e-12/1.0 = 0.009.


Answer: 0.288

Prompt: Two point charges 2e-06 C and 4e-06 C are 0.5 m apart in vacuum. Magnitude of the Coulomb force in newtons? Use k=9.0e9.

Solution: F=k|q1 q2|/r2 = 9e9·8e-12/0.25 = 0.288.


Answer: 0.036

Prompt: Two point charges 1e-06 C and 1e-06 C are 0.5 m apart in vacuum. Magnitude of the Coulomb force in newtons? Use k=9.0e9.

Solution: F=k|q1 q2|/r2 = 9e9·1e-12/0.25 = 0.036.


Answer: 0.45

Prompt: Two point charges 1e-06 C and 2e-06 C are 0.2 m apart in vacuum. Magnitude of the Coulomb force in newtons? Use k=9.0e9.

Solution: F=k|q1 q2|/r2 = 9e9·2e-12/0.04000000000000001 = 0.4499999999999999.


Answer: 0.45

Prompt: Two point charges 2e-06 C and 1e-06 C are 0.2 m apart in vacuum. Magnitude of the Coulomb force in newtons? Use k=9.0e9.


Answer: 1.8

Prompt: Two point charges 2e-06 C and 1e-06 C are 0.1 m apart in vacuum. Magnitude of the Coulomb force in newtons? Use k=9.0e9.

Solution: F=k|q1 q2|/r2 = 9e9·2e-12/0.010000000000000002 = 1.7999999999999996.


Answer: 1.35

Prompt: Two point charges 3e-06 C and 2e-06 C are 0.2 m apart in vacuum. Magnitude of the Coulomb force in newtons? Use k=9.0e9.

Solution: F=k|q1 q2|/r2 = 9e9·6e-12/0.04000000000000001 = 1.3499999999999996.


Answer: 5.4

Prompt: Two point charges 3e-06 C and 2e-06 C are 0.1 m apart in vacuum. Magnitude of the Coulomb force in newtons? Use k=9.0e9.

Solution: F=k|q1 q2|/r2 = 9e9·6e-12/0.010000000000000002 = 5.399999999999999.


Answer: 0.144

Prompt: Two point charges 1e-06 C and 4e-06 C are 0.5 m apart in vacuum. Magnitude of the Coulomb force in newtons? Use k=9.0e9.

Solution: F=k|q1 q2|/r2 = 9e9·4e-12/0.25 = 0.144.


Answer: 0.036

Prompt: Two point charges 2e-06 C and 2e-06 C are 1.0 m apart in vacuum. Magnitude of the Coulomb force in newtons? Use k=9.0e9.

Solution: F=k|q1 q2|/r2 = 9e9·4e-12/1.0 = 0.036.


Answer: 3.6

Prompt: Two point charges 2e-06 C and 2e-06 C are 0.1 m apart in vacuum. Magnitude of the Coulomb force in newtons? Use k=9.0e9.

Solution: F=k|q1 q2|/r2 = 9e9·4e-12/0.010000000000000002 = 3.599999999999999.


Answer: 0.018

Prompt: Two point charges 1e-06 C and 2e-06 C are 1.0 m apart in vacuum. Magnitude of the Coulomb force in newtons? Use k=9.0e9.

Solution: F=k|q1 q2|/r2 = 9e9·2e-12/1.0 = 0.018.


Answer: 3.313035075e-19

Prompt: A photon has frequency 5e+14 Hz. What is its energy in joules? Use h=6.62607015e-34 J·s.

Solution: E=hf=6.62607015e-34·500000000000000.0=3.313035075e-19.


Answer: 3.97564209e-19

Prompt: A photon has frequency 6e+14 Hz. What is its energy in joules? Use h=6.62607015e-34 J·s.


Answer: 4.638249105e-19

Prompt: A photon has frequency 7e+14 Hz. What is its energy in joules? Use h=6.62607015e-34 J·s.

Solution: E=hf=6.62607015e-34·700000000000000.0=4.638249105e-19.


Answer: 6.62607015e-19

Prompt: A photon has frequency 1e+15 Hz. What is its energy in joules? Use h=6.62607015e-34 J·s.

Solution: E=hf=6.62607015e-34·1000000000000000.0=6.62607015e-19.


Answer: 21400.81935

Prompt: Escape speed from a sphere of mass 5.970e+24 kg and radius 1.740e+06 m? Use G=6.6743e-11. Answer in m/s.


Answer: 1692.933236

Prompt: Escape speed from a sphere of mass 7.300e+22 kg and radius 3.400e+06 m? Use G=6.6743e-11. Answer in m/s.


Answer: 11184.9825

Prompt: Escape speed from a sphere of mass 5.970e+24 kg and radius 6.370e+06 m? Use G=6.6743e-11. Answer in m/s.


Answer: 15309.66073

Prompt: Escape speed from a sphere of mass 5.970e+24 kg and radius 3.400e+06 m? Use G=6.6743e-11. Answer in m/s.


Answer: 11213.05026

Prompt: Escape speed from a sphere of mass 6.000e+24 kg and radius 6.370e+06 m? Use G=6.6743e-11. Answer in m/s.