MCQ Blog FRQ 2021
| Number | Name | Topic | Skills |
|---|---|---|---|
| Q56 | Combine data sources | 2.3 | 5.B |
| Q52 | Binary search on list of 128 items | 3.11 | 1.D |
| Q51 | Research proposal best suited for citizen science | 5.4 | 1.C |
| Q46 | Filtering and sorting restaurant data | 2.4 | 2.B |
| Q38 | Situation where simulation is unsuitable | 3.16 | 1.D |
| Q32 | Statement about public key encryption | 5.6 | 5.E |
| Q27 | Avoid bias in app development | 5.3 | 5.E |
| Q14 | Error in isIncreasing procedure | 1.4, 3.10, 3.12 | 4.C |
Q56
Why Option A (Spreadsheets I and II) is Correct: To determine whether students who play sports are more or less likely to have higher GPAs than non-athletes, we need:
- Student GPAs (from Spreadsheet I)
- Information about which students play sports (from Spreadsheet II)
By combining these two spreadsheets using the unique student ID as the common identifier, we can create groups of athletes vs. non-athletes and compare their GPAs.
Why the Other Options Are Incorrect:
- Option B (Spreadsheets I and IV): While Spreadsheet I has GPA data, Spreadsheet IV only tells us about students who play multiple sports, not all athletes. We wouldn’t be able to identify non-athletes.
- Option C (Spreadsheets II and III): This combination lacks complete GPA information. Spreadsheet III only includes students with GPAs above 3.5, which would bias our analysis.
- Option D (Spreadsheets III and IV): Both of these spreadsheets contain partial data sets. We need complete GPA information for all students, not just high-performing ones or multi-sport athletes.
Q52
Why Option B (8) is Correct: In binary search, the maximum number of elements examined is logarithmic to the total number of elements (log₂n). For a list of 128 elements:
- log₂(128) = log₂(2⁷) = 7
The question asks for the closest value to the maximum number of examinations. This would be 7, but the closest option provided is 8.
Why the Other Options Are Incorrect:
- Option A (2): Far too small for a binary search on 128 items.
- Option C (64): This is half the list size, which would be the worst-case for linear search, not binary search.
- Option D (128): This represents examining every element, which would be a linear search, not a binary search.
Q51
Why Option A (Collecting pictures of birds…) is Correct: This proposal is best suited for citizen science because:
- It can be done by untrained volunteers around the world
- It requires simple equipment (cameras/smartphones) that many people already have
- The data collection is straightforward and doesn’t require specialized knowledge
- It can generate a large, diverse dataset from global participants
Why the Other Options Are Incorrect:
- Option B (Monitoring cells in a laboratory): Requires specialized equipment, laboratory access, and scientific training.
- Option C (Using a simulation): Requires technical expertise in simulation software and scientific modeling.
- Option D (Performing 3D scans of proteins): Requires highly specialized, expensive equipment and expert knowledge in biochemistry.
Q46
Why Option D (I, II, and III) is Correct: The goal is to find the restaurant that accepts credit cards and has the highest rating.
All three sequences would work:
- Sequence I: Filter out restaurants with no ratings → Filter out restaurants not accepting credit cards → Sort by rating (highest first)
- Sequence II: Filter out restaurants with no ratings → Sort by rating → Filter out restaurants not accepting credit cards
- Sequence III: Sort by rating → Filter out restaurants with no ratings → Filter out restaurants not accepting credit cards
Since sorting puts the highest-rated restaurant first, and both required filters are applied in all three sequences, any of these would work.
Why the Other Options Are Incorrect:
- Option A (I and II only): Sequence III would also work - the order of operations would still find the correct result.
- Option B (I and III only): Sequence II would also work - sorting before filtering still gives the correct result.
- Option C (II and III only): Sequence I would also work - filtering before sorting still gives the correct result.
Q38
Why Option D (When the solution requires real-world data inputs that are continually measured at regular intervals) is Correct: Simulations are least suitable when you need continuous real-time data inputs. Simulations typically work with predefined or historical data, not live measurements that change regularly. The real-time, continuous nature of such data makes simulation impractical.
Why the Other Options Are Incorrect:
- Option A (Large number of trials conducted quickly): This is actually an ideal use case for simulation, which can run trials much faster than real-world experiments.
- Option B (Simplifying assumptions in modeling): This is a typical characteristic of simulation, not a limitation - simulations often rely on simplifying assumptions.
- Option C (Too costly or dangerous to conduct in the real world): This is one of the primary benefits of simulation - testing dangerous or expensive scenarios safely.
Q32
Why Option A (Public key encryption enables parties to initiate secure communications through an open medium, such as the Internet, in which there might be eavesdroppers) is Correct: This accurately describes the purpose and function of public key encryption - it allows secure communication over insecure channels where third parties might intercept messages.
Why the Other Options Are Incorrect:
- Option B (Public key is not considered secure because it can be intercepted): False - the public key is designed to be shared openly and interception doesn’t compromise security.
- Option C (Only allows encryption of text documents): False - public key encryption can be used for any digital data.
- Option D (Uses a single key that should be kept secure): False - public key encryption uses a key pair (public and private), not a single key.
Q27
Why Option B (Inviting a random sample of all users to try out the new algorithm and provide feedback before it is released to a wider audience) is Correct: This approach is least likely to introduce bias because:
- Random sampling ensures diverse user representation
- It doesn’t favor any particular user group
- It collects feedback from a representative user population
- It tests the algorithm before wide-scale deployment
Why the Other Options Are Incorrect:
- Option A (Enticing users who use the app at least ten hours per week): Creates bias toward power users, missing casual users’ perspectives.
- Option C (Providing the algorithm only to teenage users): Creates age-based bias, ignoring other demographics.
- Option D (Testing with users in the developers’ city): Creates geographic/cultural bias, missing diverse global perspectives.
Q14
Why Option C (Lines 8 and 12 should be interchanged) is Correct: The procedure is supposed to return true if the list is increasing and false otherwise. The current logic:
- If any value is less than its predecessor, it returns true (line 8)
- After checking all elements, it returns false (line 12)
This is backwards. By swapping lines 8 and 12:
- If any value is less than its predecessor, it would return false (finding a decreasing pair)
- After checking all elements (and finding none decreasing), it would return true
Why the Other Options Are Incorrect:
- Option A (In line 3, 2 should be changed to 1): This would create an off-by-one error, as we need to compare from the second element onward.
- Option B (In line 6, < should be changed to >): This would reverse the comparison logic, returning true for decreasing lists.
- Option D (Lines 10 and 11 should be interchanged): This wouldn’t fix the core logical error and would cause additional issues with the count increment.