Abstraction, automation and systematic problem solving – A-level Computer Science exam questions with mark scheme

1Core4 marks

A company is writing route-planning software for its delivery drones. The software models the town as a set of points (landing pads) joined by straight-line flight paths, each labelled with its length in metres.

(a) Explain why this model is an example of representational abstraction. [1]

(b) State two details of the real town that have been left out of the model. [2]

(c) The software also stores records for drones, delivery vans and cargo bikes. Each is treated as a kind of delivery vehicle that has a maximum load and a top speed. State the type of abstraction being used here. [1]

(a) Unnecessary details have been removed / only the details needed to plan routes are kept (to give a simpler representation of the real town). Do not accept 'it is simpler' alone without reference to removing detail(1)
(b) Any one from: building heights/appearance; street names; roads/pavements (the routes drones do not use); colours/shape of landmarks; trees; people/traffic; exact curves of real flight paths; weather. Ignore details that ARE in the model (distances, landing pads)(1)
(b) A second, different detail from the list above(1)
(c) Abstraction by generalisation / categorisation; accept 'is a kind of' hierarchy / grouping by common characteristics. Do not accept 'inheritance' alone(1)
Answer: (a) Details not needed for route planning are removed. (b) e.g. building appearance, street names. (c) Generalisation / categorisation.
Examiner tip: In (b) students often list something that is actually still in the model, such as distances, which scores nothing.

2Core4 marks

The structure chart below shows how a programmer has designed a quiz program.

(a) State the name of the problem-solving technique, shown in the chart, of breaking a problem into sub-problems that each have an identifiable task. [1]

(b) The finished Mark answer module calls Compare answer and then Update score. State the term for combining procedures into a compound procedure in this way. [1]

(c) Each question is stored as a record holding the question text, four options and the correct option. All the records are then held in a list. Explain how this is an example of composition of data. [1]

(d) Once the design is complete, the programmer writes the code and runs it. State the term used for putting a model into action in this way. [1]

(a) (Top-down) decomposition; accept stepwise refinement. Do not accept 'abstraction'(1)
(b) Composition / procedural composition(1)
(c) Existing/simpler data types (strings, integers) are combined into a record, and the records are combined into a list, to form a compound data object. Must refer to combining data objects into a larger/compound one(1)
(d) Automation(1)
Answer: (a) Decomposition. (b) Composition. (c) Simple data types are combined into records, then into a list: a compound data object. (d) Automation.
Examiner tip: Decomposition breaks a problem down and composition builds back up; examiners will not accept the two terms used the wrong way round.

3Standard5 marks

The algorithm below is written in pseudo-code.

x ← USERINPUT
total ← 0
WHILE x > 0
  d ← x MOD 10
  IF d MOD 2 = 1 THEN
    total ← total + d
  ELSE
    total ← total - d
  ENDIF
  x ← x DIV 10
ENDWHILE
OUTPUT total

(a) Complete a trace table, with columns x, d and total, for the algorithm when the user enters 7258. State the value that is output. [4]

(b) An algorithm must always terminate. Explain why this algorithm will always terminate for any positive integer input. [1]

(a) x column: 7258, 725, 72, 7, 0 (in this order)(1)
(a) d column: 8, 5, 2, 7 (in this order)(1)
(a) total column: 0, −8, −3, −5, 2 (in this order). Allow follow-through from one error in the d column(1)
(a) Output: 2. Allow follow-through from their final value of total(1)
(b) x is (integer) divided by 10 on every iteration so it gets smaller each time / loses a digit, and so must eventually reach 0, making the condition x > 0 false(1)
Answer: x: 7258, 725, 72, 7, 0; d: 8, 5, 2, 7; total: 0, −8, −3, −5, 2. Output 2.
Examiner tip: Do not forget that 8 and 2 are even and are subtracted: the running total goes negative before it ends at 2.

Stuck on Abstraction, automation and systematic problem solving?

Get it sorted in a free 30-minute session

We work through your weakest questions on this topic on Zoom. I reply the same day.

Free 30-min session on this topic Send me 5 questions a day

4Standard3 marks

Three warehouse robots, X, Y and Z, each send status messages. Every robot is either reliable (all its messages are true) or faulty (all its messages are false).

X reports: “Y is faulty.”
Y reports: “X and Z are both faulty.”
Z reports: “Y is reliable.”

Determine which of the robots are reliable and which are faulty. You must show your reasoning. [3]

Considers the case that Y is reliable: then X and Z are faulty, but Z faulty means “Y is reliable” is false, a contradiction (so Y is faulty). Accept an equivalent contradiction reached from another starting assumption(1)
Y is faulty so X's statement is true, so X is reliable(1)
Z's statement (Y is reliable) is false, so Z is faulty; final answer X reliable, Y and Z faulty. Accept a correct check that Y's statement is then false (X is reliable). Correct answer with no reasoning scores this mark only(1)
Answer: X is reliable; Y and Z are faulty.
Examiner tip: An answer with no reasoning only gets 1 mark: show the contradiction that rules out Y being reliable.

5Standard4 marks

A programmer creates a class Playlist. Internally it stores songs in a private array with a private integer pointer to the next free position. Other parts of the program can only use the public methods AddSong(title), RemoveSong(title) and Length().

(a) Explain how this design uses information hiding. [2]

(b) The programmer later replaces the array with a linked list. Explain why data abstraction means no other part of the program needs to change. [1]

(c) Length() returns the number of songs. A user of the class knows what Length() computes but not how it computes it. State the type of abstraction this is an example of. [1]

(a) The array and pointer (the internal details) are private / cannot be accessed directly from outside the class(1)
(a) Other code can only interact through the public methods / interface, so details that are not essential to using a playlist are hidden (and cannot be changed accidentally)(1)
(b) The way the data is represented/stored is hidden from the rest of the program, which only relies on the (unchanged) interface/methods, so changing the representation does not affect it(1)
(c) Functional abstraction. Do not accept procedural abstraction (that represents a computational method rather than hiding it)(1)
Answer: (a) Array and pointer are private; access only via public methods. (b) Representation hidden behind unchanged interface. (c) Functional abstraction.
Examiner tip: For (a), simply saying the attributes are 'hidden' repeats the question: say they are private and that access is only through the methods.

6Hard5 marks

A sixth-form college must schedule exams so that no student has two exams in the same session. The table shows which pairs of subjects share at least one student.

Subject	Shares students with
Maths	Physics, Chemistry, History
Physics	Maths, Chemistry
Chemistry	Maths, Physics, Biology
Biology	Chemistry, History
History	Biology, Maths

The developer notices that this problem can be solved by reducing it to a graph-colouring problem, where adjacent vertices must have different colours and an algorithm for this already exists.

(a) Explain what is meant by problem abstraction (reduction). [1]

(b) Describe how the exam problem is represented as a graph-colouring problem. [3]

(a) Details are removed from a problem until it is represented in a way that is the same as / can be solved by a problem that has already been solved(1)
(b) Each subject/exam is a vertex/node(1)
(b) An edge joins two subjects that share a student / that clash(1)
(b) Each colour represents a session, so the fewest colours needed (so that no edge joins two same-coloured vertices) is the fewest sessions(1)
(c) 3. Accept with a valid schedule e.g. {Maths, Biology}, {Physics, History}, {Chemistry}; ignore missing schedule(1)
Answer: (a) Remove detail until it matches an already-solved problem. (b) Subjects = vertices, clashes = edges, colours = sessions. (c) 3.
Examiner tip: In (b) say what each colour stands for: without linking colours to sessions the model has no meaning for the original problem.

7Standard5 marks

A cinema booking program asks the user how many tickets they want. The program should accept only whole numbers from 1 to 8 inclusive.

(a) For each test value below, state whether it is normal, boundary or erroneous test data. [3]

5
8
“three”

(b) Explain why the programmer should test the value 9 as well as the value 8. [1]

5: normal / typical(1)
8: boundary(1)
“three”: erroneous (wrong data type, should be rejected)(1)
(b) To check that the limit is applied correctly / that values just outside the valid range are rejected; e.g. a check written with ≤ 9 or < 9 instead of ≤ 8 would be detected. Accept 'to detect off-by-one errors in the comparison'(1)
(c) Testing carried out by / with the intended users (client) to check that the system meets their requirements (before it is accepted). Must refer to users/client AND requirements(1)
Answer: (a) 5 normal, 8 boundary, “three” erroneous. (b) Checks the upper limit is enforced exactly. (c) Testing by the intended users that the system meets the requirements.
Examiner tip: Boundary data is at the edge of the valid range; students often call 8 'normal' because it is valid.

8Hard5 marks

A year is a leap year if it is divisible by 4, except that a year divisible by 100 is only a leap year if it is also divisible by 400.

A student has written the following function.

FUNCTION IsLeap(y)
  IF y MOD 4 = 0 THEN
    RETURN True
  ELSE IF y MOD 100 = 0 THEN
    RETURN False
  ELSE IF y MOD 400 = 0 THEN
    RETURN True
  ELSE
    RETURN False
  ENDIF
ENDFUNCTION

(a) State the value returned by IsLeap(1900) and explain why this shows the function is incorrect. [2]

(b) Rewrite the function in pseudo-code so that it is correct for all years. [3]

(a) Returns True(1)
(a) 1900 is divisible by 100 but not by 400 so it is not a leap year / should return False; the MOD 4 test is done first so the other tests are never reached for 1900(1)
(b) Tests MOD 400 = 0 first (or before the MOD 100 test) and returns True(1)
(b) Then tests MOD 100 = 0 and returns False(1)
(b) Then tests MOD 4 = 0 returning True, otherwise returns False. Accept any correct equivalent, e.g. RETURN (y MOD 4 = 0 AND y MOD 100 ≠ 0) OR y MOD 400 = 0 (award all 3 marks). Ignore minor syntax errors(1)
Answer: (a) True; 1900 is not a leap year because it divides by 100 but not 400. (b) Test 400 first (True), then 100 (False), then 4 (True), else False.
Examiner tip: The order of selection statements matters: the most specific condition must be tested before the general one.

9Hard6 marks

A software house is building an appointment system for a group of veterinary clinics. The project manager plans to use an iterative (agile) approach with prototyping rather than completing each stage fully before starting the next.

Discuss how the analysis and design stages should be carried out for this project, and the benefits and drawbacks of using an iterative approach with prototypes. [6]

Analysis: define the problem, e.g. booking clashes, missed appointments, multiple clinics(1)
Analysis: establish requirements by interviewing/observing/surveying intended users (receptionists, vets, pet owners)(1)
Analysis: produce a data model (e.g. entities Owner, Pet, Vet, Appointment, Clinic and their relationships) – abstraction of the real world(1)
Analysis: agree measurable objectives that can later be used in evaluation(1)
Design: design data structures / database tables, algorithms (e.g. finding a free slot), modular structure (decomposition) and the user interface (HCI) before coding(1)
Iterative: a prototype (e.g. booking screen) is shown to users and refined from feedback; requirements can change between iterations(1)
Benefit: misunderstandings found early; users more satisfied; working parts delivered sooner(1)
Drawbacks: harder to estimate time/cost; scope creep; needs regular user availability; early prototypes may be poorly structured / documentation may be weaker(1)

Level	Marks	What it looks like
Level 3	5–6	Clear, well-organised discussion covering both analysis and design applied to the clinic system, with at least one benefit and one drawback of the iterative approach. Uses correct technical terms throughout.
Level 2	3–4	Describes several relevant activities in analysis and/or design with some application to the context, and makes some comment on the iterative approach; may lack balance or detail.
Level 1	1–2	A few relevant points, mostly generic or list-like, with little application to the context or discussion of the approach.
Level 0	0	Nothing worthy of credit.

Answer: A top answer covers how requirements are gathered from the users and modelled, what is designed before coding, and weighs prototyping benefits against drawbacks.
Examiner tip: Answers that only describe agile in general without applying it to the vet clinics' analysis and design are capped in the middle level.

10Stretch6 marks

The function below is intended to return True if the positive integer n is prime.

FUNCTION IsPrime(n)
  isPrime ← True
  i ← 2
  WHILE i < n
    IF n MOD i = 0 THEN
      isPrime ← False
    ENDIF
    i ← i + 1
  ENDWHILE
  RETURN isPrime
ENDFUNCTION

(a) State how many times the body of the WHILE loop is executed when n is 91. [1]

(b) Identify a positive integer input for which the function returns an incorrect result. [1]

(c) Describe two changes that would make the function more time-efficient. One of your changes must reduce the range of values of i that are tested; explain why this change does not affect the result returned. [3]

(d) With both of your changes made, state how many times the loop body is executed when n is 97. [1]

(a) 89(1)
(b) 1 (returns True but 1 is not prime)(1)
(c) Stop the loop as soon as a factor is found, e.g. add AND isPrime = True to the loop condition / return False immediately(1)
(c) Only test values of i up to the square root of n, e.g. loop WHILE i * i ≤ n (accept: only test 2 then odd values of i, but then the argument mark must match this change)(1)
(c) Explanation for the change that reduces the range of i: if n = a × b with a ≤ b then a ≤ √n, so any composite n has a factor no bigger than √n and no factor is missed. (For the odd-values change: any even n has 2 as a factor, which is still tested, so no odd n is wrongly reported.) The explanation must match the change given(1)
(d) 8 (i = 2 to 9). Allow follow-through for a correctly applied different pair of changes(1)
Answer: (a) 89 (b) 1 (c) Stop at the first factor; loop only while i×i ≤ n, since any composite n has a factor ≤ √n. (d) 8
Examiner tip: In (a) the loop runs for i = 2 to n − 1, which is n − 2 times, not n − 1.

Stuck on this topic?

Book a free 30-minute session on WhatsApp and we'll find exactly which step is costing you the marks. Or build a timed paper on it.

Free 30-minute session