Practice gce model questions vol1 computer_studies 2021 Past Questions

Question 1 View Details

Consider a relation R(A,B,C,D) with the functional dependencies (A \rightarrow B), (BC \rightarrow D) and (D \rightarrow A\).\n\n(a) List all candidate keys of R.\n(b) State the highest normal form (1NF, 2NF, 3NF or BCNF) that R satisfies.\n(c) Give a lossless‑join, dependency‑preserving decomposition of R into relations that are in BCNF.

A. Candidate keys: AC, BD, AB. Highest normal form: 1NF. BCNF decomposition: R1(A,C), R2(B,D), R3(C,D).

Correct B. Candidate keys: BC, AC, CD. Highest normal form: 3NF. BCNF decomposition: R1(A,B), R2(B,C,D), R3(D,A).

C. Candidate keys: BC, AD, CD. Highest normal form: BCNF. BCNF decomposition: R1(A,C), R2(B,D), R3(A,B,D).

D. Candidate keys: AB, AD, BD. Highest normal form: 2NF. BCNF decomposition: R1(A,B), R2(C,D), R3(A,D).

Correct Answer: B

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Question 2 View Details

The ENIAC was completed in 1945, while the Manchester Mark I became operational in 1949. Which of these two computers was operational first?

A. IBM 701

B. Manchester Mark I

Correct C. ENIAC

D. UNIVAC I

Correct Answer: C

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Question 3 View Details

A file of 1500 bytes is compressed by a scheme that reduces its size by 30 % and then adds a 128‑byte header. The compressed file is stored on a disk that uses a block size of 512 bytes, each block incurring a 16‑byte overhead for metadata. How many disk blocks are required to store the file?

Correct A. 3

B. 4

C. 5

D. 2

Correct Answer: A

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Question 4 View Details

In a spreadsheet, column A (A2:A10) holds quantities, column B (B2:B10) holds unit prices, and column D (D2:D10) holds a category code (single letters).\n\nWrite a single formula to be entered in cell E2 that returns the total discounted revenue for all rows whose category code is "A". The discount rule is: if the product of quantity and unit price exceeds 2000, apply a 5 % discount to that row's total; otherwise use the full total. The formula should be copy‑able without modification to other rows (i.e., it must refer to the whole ranges).

A. =SUMPRODUCT((D2:D10="A")*IF(A2:A10*B2:B10>=2000, A2:A10*B2:B10*0.95, A2:A10*B2:B10))

Correct B. =SUMPRODUCT((D2:D10="A")*IF(A2:A10*B2:B10>2000, A2:A10*B2:B10*0.95, A2:A10*B2:B10))

C. =SUMPRODUCT((D2:D10="A")*IF(A2:A10*B2:B10>2000, A2:A10*B2:B10*0.90, A2:A10*B2:B10))

D. =SUMPRODUCT((D2:D10="A")*A2:A10*B2:B10*0.95)

Correct Answer: B

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Question 5 View Details

Given the tables below:\n\nEmployees(EmpID, DeptID, Salary)\n\n| EmpID | DeptID | Salary |\n|------|--------|--------|\n| 1 | 10 | 5000 |\n| 2 | 10 | 6000 |\n| 3 | 20 | 5500 |\n| 4 | 20 | 4500 |\n| 5 | 30 | 7000 |\n\nDepartments(DeptID, ManagerID)\n\n| DeptID | ManagerID |\n|--------|-----------|\n| 10 | 1 |\n| 20 | 3 |\n| 30 | 5 |\n\nConsider the SQL query:\n\n```sql\nSELECT d.DeptID\nFROM Departments d\nWHERE d.ManagerID IN (\n SELECT e.EmpID\n FROM Employees e\n WHERE e.Salary > (\n SELECT AVG(Salary)\n FROM Employees\n WHERE DeptID = d.DeptID\n )\n)\nGROUP BY d.DeptID\nHAVING COUNT(*) = 1;\n```\n\nWhich DeptID(s) are returned by this query?

A. 40

B. 30

C. 10

Correct D. 20

Correct Answer: D

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Question 6 View Details

In a spreadsheet, cells B2:D5 contain monthly sales (in naira) for products A, B and C. The total sales for each product are calculated in row 6 using the formula $=SUM(B2:B5)$ for product A, $=SUM(C2:C5)$ for product B and $=SUM(D2:D5)$ for product C. Cell B7 (commission for product A) contains $=IF(B6>5000, B6*0.08, B6*0.05)$. Cells C7 and D7 calculate commission using a VLOOKUP: $=C6*VLOOKUP(C6,$G$1:$H$3,2,TRUE)$ and $=D6*VLOOKUP(D6,$G$1:$H$3,2,TRUE)$ respectively, where the lookup table in G1:H3 is: $\begin{array}{c|c} \text{Threshold (\pounds)} & \text{Rate}\\\hline 0 & 0.04\\ 3000 & 0.06\\ 6000 & 0.09\\ \end{array}$ The overall commission is in cell E7 with the formula $=B7+C7+D7$. The sales data are: - January: A 1200, B 2500, C 1800 - February: A 1500, B 3200, C 2100 - March: A 1700, B 2900, C 2400 - April: A 1900, B 3400, C 2600 What is the overall commission (in naira) displayed in E7?

A. 2500

B. 2350

Correct C. 2385

D. 2420

Correct Answer: C

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Question 7 View Details

Given the following tables: Students( StudentID, Name, DeptID ) \begin{array}{c|c|c} \text{StudentID} & \text{Name} & \text{DeptID}\\\hline 1 & Alice & D01\\ 2 & Bob & D02\\ 3 & Carol & D01\\ 4 & Dave & D03\\ 5 & Eve & D02\\ \end{array} Enrolments( StudentID, CourseCode, Grade ) \begin{array}{c|c|c} \text{StudentID} & \text{CourseCode} & \text{Grade}\\\hline 1 & CS101 & 78\\ 1 & MA101 & 85\\ 2 & CS101 & 92\\ 2 & PH101 & 88\\ 3 & MA101 & 73\\ 3 & CS101 & 67\\ 4 & PH101 & 90\\ 5 & CS101 & 55\\ \end{array} Dept( DeptID, DeptName, Budget ) \begin{array}{c|c|c} \text{DeptID} & \text{DeptName} & \text{Budget}\\\hline D01 & Engineering & 500000\\ D02 & Science & 300000\\ D03 & Arts & 200000\\ \end{array} Consider the SQL query: SELECT d.DeptName, AVG(e.Grade) AS AvgGrade FROM Dept d JOIN Students s ON d.DeptID = s.DeptID JOIN Enrolments e ON s.StudentID = e.StudentID WHERE e.Grade >= (SELECT AVG(Grade) FROM Enrolments) GROUP BY d.DeptName HAVING COUNT(DISTINCT s.StudentID) >= 2; What result set does this query return?

A. Science, 84.0

B. Engineering, 81.5

C. Arts, 90.0

Correct D. No rows (empty result set)

Correct Answer: D

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Question 8 View Details

Two software packages are being considered for a five‑year period. - **Software A**: an annual subscription of £120. Each subsequent year the subscription fee increases by 5 % over the previous year. - **Software B**: a one‑time purchase price of £450. It includes a maintenance fee of £30 per year for the first three years; from year 4 onward the maintenance fee increases by 50 % each year. Which software has the lower total cost over the five‑year period? State the total cost for each package (rounded to two decimal places) and indicate the cheaper option.

A. Software A (total cost £652.50, cheaper than Software B)

Correct B. Software B (total cost £652.50, cheaper than Software A)

C. Software A (total cost £700.00, cheaper than Software B)

D. Software B (total cost £660.00, cheaper than Software A)

Correct Answer: B

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Question 9 View Details

A (12, 8) Hamming code uses even parity. The eight data bits are $D_1 D_2 D_3 D_4 D_5 D_6 D_7 D_8 = 1\,0\,1\,1\,0\,0\,1\,0$. Parity bits are placed at positions 1, 2, 4 and 8. After encoding, the transmitted 12‑bit word has a single‑bit error introduced at position 9. (a) Determine the values of the four parity bits. (b) Using the received word, calculate the syndrome, locate the erroneous bit, correct it, and give the corrected 8‑bit data word. Provide the final corrected data bits as an 8‑bit binary string.

Correct A. 10110010

B. 10011010

C. 10110100

D. 11110010

Correct Answer: A

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Question 10 View Details

A company owns the network 192.168.48.0/22. It needs subnets that can each accommodate at least 200 hosts. (a) Determine the subnet mask that satisfies this requirement. (b) How many such subnets can be created from the original /22 network? (c) Do the IP addresses 192.168.49.130 and 192.168.51.250 belong to the same subnet? Answer "Yes" or "No".

A. Maybe

B. Yes

C. Cannot determine

Correct D. No

Correct Answer: D

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Question 11 View Details

An 5 MB file is to be transmitted over a 2 Mbps link using a protocol that adds a 64‑byte header and a 16‑byte trailer to each packet. Each packet carries 1024 bytes of payload. The bit‑error rate of the link is $10^{-6}$; a packet that contains any error must be retransmitted. Assuming errors in different bits are independent, estimate the expected transmission time (in seconds) for the whole file, ignoring propagation delay.

A. 25.47 seconds (approximately)

B. 30.00 seconds (approximately)

C. 20.15 seconds (approximately)

Correct D. 22.83 seconds (approximately)

Correct Answer: D

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Question 12 View Details

A 1024‑bit data block is transmitted with a 16‑bit CRC generated by the polynomial $G(x)=x^{16}+x^{12}+x^{5}+1$. Each bit is flipped independently with probability $10^{-4}$. Approximate the probability that a block containing at least one error passes the CRC check (i.e., the error is undetected).

A. 7.8 \times 10^{-7} (approximately)

B. 1.0 \times 10^{-6} (approximately)

Correct C. 1.5 \times 10^{-6} (approximately)

D. 2.3 \times 10^{-5} (approximately)

Correct Answer: C

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Question 13 View Details

A programmer must store up to 10,000 integer records and support four operations: insert, delete, search by key, and retrieve the $k^{\text{th}}$ smallest element (where $k$ is given at query time). She can choose either (i) a balanced binary search tree (BST) or (ii) a hash table together with a lazily‑updated sorted array. For each operation, give the worst‑case asymptotic time complexity for both structures, and state which structure gives the lower overall worst‑case time for a mixed workload consisting of 40% inserts, 30% deletes, 20% searches and 10% $k^{\text{th}}$ queries. Present the answer as a table and a brief justification.

A. Balanced BST is inferior; see table above for detailed complexities.

B. Both structures have equal performance; see table above for detailed complexities.

Correct C. Balanced BST is superior; see table above for detailed complexities.

D. Hash table is superior; see table above for detailed complexities.

Correct Answer: C

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Question 14 View Details

Relation $R(A,B,C,D,E)$ has the functional dependencies: $A \rightarrow B$, $A \rightarrow C$, $BC \rightarrow D$, and $D \rightarrow E$.\n(a) Find all candidate keys of $R$.\n(b) Produce a lossless‑join, dependency‑preserving decomposition of $R$ into relations that are in Third Normal Form (3NF). List the resulting relations.

A. Candidate key: B. 3NF decomposition: R1(A,B), R2(B,C,D), R3(D,E).

B. Candidate key: A. 3NF decomposition: R1(A,B), R2(A,C,D), R3(D,E).

Correct C. Candidate key: A. 3NF decomposition: R1(A,B,C), R2(B,C,D), R3(D,E).

D. Candidate key: A,B. 3NF decomposition: R1(A,B), R2(A,C,D), R3(D,E).

Correct Answer: C

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Question 15 View Details

Consider the following Python program intended to compute the sum $S = 1! + 2! + \dots + n!$:\n\n```python\ndef fact(k):\n if k == 0:\n return 0\n else:\n return k * fact(k-1)\n\ndef series(n):\n total = 0\n for i in range(1, n+1):\n total += fact(i)\n return total\n\nn = int(input())\nprint(series(n))\n```\nThe program is run with input $n = 5$. Identify the logical error, give the corrected version of the function $fact$, and state the output produced after the correction.

A. 155

Correct B. 153

C. 144

D. 120

Correct Answer: B

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Question 16 View Details

The ENIAC was completed in 1945, the IBM 701 was introduced in 1952, and the Apple I was released in 1976. List these computers in order from earliest to latest.

A. IBM 701, ENIAC, Apple I

Correct B. ENIAC, IBM 701, Apple I

C. Apple I, ENIAC, IBM 701

D. ENIAC, Apple I, IBM 701

Correct Answer: B

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Question 17 View Details

A processor has a two‑level cache hierarchy. Level 1 (L1) cache has a hit rate of 90% and an access time of $1$ ns. Level 2 (L2) cache is accessed only on an L1 miss; its hit rate (relative to L1 misses) is 80% and its access time is $5$ ns. Main memory access time is $100$ ns. Assuming a miss in L2 also requires a main‑memory access, calculate the average memory access time in nanoseconds.

A. 5.0

Correct B. 3.5

C. 4.5

D. 2.5

Correct Answer: B

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Question 18 View Details

A 120 MB file is compressed using an algorithm that reduces its size by 35% of the original. The compressed file is then encrypted, which adds an overhead equal to 5% of the compressed size. What is the final size of the file in megabytes (to one decimal place)?

Correct A. 81.9

B. 84.0

C. 74.1

D. 44.1

Correct Answer: A

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Question 19 View Details

The first computer mouse was invented in 1964, while the first graphical user interface was demonstrated in 1973. Which of these two inventions came first?

Correct A. The computer mouse

B. Both were invented in the same year

C. Neither was invented in the 20th century

D. The graphical user interface

Correct Answer: A

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Question 20 View Details

A motherboard has four RAM slots. Each slot can hold a DIMM of up to 8 GB. If a user installs DIMMs of 2 GB, 4 GB, 8 GB and leaves one slot empty, what is the total amount of RAM installed in gigabytes?

Correct A. 14

B. 8

C. 12

D. 16

Correct Answer: A

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Question 21 View Details

An organisation evaluates the risk of a security incident using the formula $R = T \times V \times I$, where $T$ is the threat likelihood (a probability between 0 and 1), $V$ is the vulnerability factor (also between 0 and 1), and $I$ is the monetary impact in naira. When the impact is ₦600,000 and the threat likelihood is 0.2, the calculated risk is ₦96,000. (a) Determine the current vulnerability factor $V$. (b) The organisation can reduce the vulnerability by 30 % (i.e., the new vulnerability factor is $0.7V$). If the maximum acceptable risk is ₦100,000, what is the greatest impact $I_{\max}$ (in naira) that can be tolerated after the reduction? Give your answer rounded to the nearest naira.

A. 950000

B. 850000

C. 1000000

Correct D. 892857

Correct Answer: D

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Question 22 View Details

A school needs to transfer a 500 MB file to a remote server. Two internet connections are available: - Connection A: latency $L_{A}=50$ ms, bandwidth $B_{A}=20$ Mbps. - Connection B: latency $L_{B}=120$ ms, bandwidth $B_{B}=50$ Mbps. The file may be split into two parts; part of size $x$ MB is sent over connection A and the remaining $500-x$ MB over connection B, with both transfers occurring simultaneously. The transfer time for a part sent over a connection is $T = L + \dfrac{\text{size (in megabits)}}{B}$. Determine the value of $x$ (in megabytes) that minimises the total transfer time, and compute that minimum time (in seconds). Give $x$ to the nearest megabyte and the time to one decimal place.

A. x = 100 MB, time = 62.1 s

B. x = 160 MB, time = 58.0 s

Correct C. x = 143 MB, time = 57.3 s

D. x = 120 MB, time = 60.5 s

Correct Answer: C

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Question 23 View Details

Consider the relational schema $R(A, B, C, D, E)$ with the set of functional dependencies: $A \rightarrow B$ $B \rightarrow C$ $AD \rightarrow E$ $C \rightarrow D$ (a) List all candidate keys of $R$. (b) Is the schema in Third Normal Form (3NF)? If not, decompose $R$ into a set of relations that are in 3NF, showing the attributes of each resulting relation.

A. Candidate keys: AD, AC, AE. In 3NF. 3NF decomposition: R1(A,B), R2(B,C), R3(C,D), R4(A,D,E).

B. Candidate keys: AD, AC, AE. Not in 3NF. 3NF decomposition: R1(A,B), R2(B,C), R3(C,D), R4(A,E).

C. Candidate keys: AD, AB, AE. Not in 3NF. 3NF decomposition: R1(A,B), R2(B,C), R3(C,D), R4(A,D,E).

Correct D. Candidate keys: AD, AC, AE. Not in 3NF. 3NF decomposition: R1(A,B), R2(B,C), R3(C,D), R4(A,D,E).

Correct Answer: D

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Question 24 View Details

A 12‑bit data word $101100110011$ is to be transmitted using a CRC with generator polynomial $G(x)=x^{4}+x+1$ (binary representation $10011$). 1. Compute the 4‑bit CRC remainder that must be appended to the data word. 2. Suppose the transmitted frame suffers a single‑bit error at the 7th bit (counting from the left). Will the CRC detect this error? Justify your answer.

Correct A. Remainder = 1010; the CRC will detect the error.

B. Remainder = 0111; the CRC will not detect the error.

C. Remainder = 1100; the CRC will detect the error.

D. Remainder = 1010; the CRC will not detect the error.

Correct Answer: A

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Question 25 View Details

In a spreadsheet, cell A1 contains an unknown value $x$. The following formulas are defined: - B1: $=A1^2 - 4*A1 + 3$ - C1: $=\sqrt{B1}$ - D1: $=\text{IF}(C1 > 2,\; C1*5,\; C1*3)$ The displayed value in D1 is 15. Determine all possible values of $x$ that satisfy the spreadsheet calculations. Give your answers in exact form.

A. x = 1 \pm \sqrt{10}

B. x = 2 \pm \sqrt{8}

Correct C. x = 2 \pm \sqrt{10}

D. x = 2 \pm \sqrt{12}

Correct Answer: C

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