AQA A-Level Computer Science Paper 2, June 2025: Question 2

📐 Step-by-Step Calculation

1. Identify the core formula:
   File size (bits) = Sample Rate × Duration × Sample Resolution
2. Convert file size to bits:
   AQA uses standard decimal prefixes ( 1 MB = 1 000 000 bytes ).
   Total bits = 1.5 × 1 000 × 1 000 × 8 = 12 000 000 bits
3. Calculate total samples taken:
   Total samples = 20 000 Hz × 50 s = 1 000 000 samples
4. Solve for sample resolution:
   Sample resolution = 12 000 000 bits / 1 000 000 samples = 12 bits

✅ Correct Answer & Marking

Answer: 12 bits (or simply 12 )

❌ Common Errors

• Forgetting to multiply by 8: Calculating bytes per sample instead of bits per sample yields 1.5 bytes, which loses the final mark if not converted to 12 bits.
• Binary vs Decimal prefixes: Using 1024 × 1024 instead of 1000 × 1000. In AQA questions, unless "mebibytes (MiB)" is specified, use SI decimal multipliers (10⁶).

🧠 Exam Technique

Always show each line of rearrangement clearly. If you make an arithmetic error at the very end, examiners will credit intermediate multiplications (e.g. converting megabytes to bits) to salvage 1 mark.

💡 The 3 Essential Stages of ADC

An ADC converts a continuous analogue physical wave into a sequence of binary digits via three successive actions:

1. Sampling: The analogue signal/wave is sampled at regular, fixed time intervals.
2. Measurement: The amplitude (or voltage) of the wave is measured at each sample point.
3. Quantisation & Encoding: The measured amplitude is quantised (rounded to the nearest representable discrete level) and coded into a fixed number of binary bits.

✅ Mark Scheme Requirements

Marks are awarded based on how many of the three stages are described:

• 2 marks: All 3 key points fully covered.
• 1 mark: 1 or 2 key points covered.

❌ Common Errors & Misconceptions

• Vague descriptions: Writing "it turns sound into 1s and 0s" gets 0 marks. You must mention regular time intervals and measuring amplitude.
• Mentioning graphs: The mark scheme explicitly states: "Reject references to graphs" (e.g. "plotting the wave on a graph"). ADCs are hardware circuits, not graphing tools!

✅ Three Valid Approaches (Choose ONE only)

You must stick to one cause and give a complete explanation (1 mark for cause, 1 mark for consequence):

Route A: Sample Resolution is too low

• Not enough bits are allocated per sample point (1 mark).
• This causes quantisation error: amplitudes must be rounded to the nearest discrete binary level, leading to a discrepancy between actual and recorded values (1 mark).

Route B: Sampling Rate is too low (Nyquist Theorem)

• Samples are not taken frequently enough / does not satisfy Nyquist's theorem (1 mark).
• The sampling rate is less than twice the highest frequency present, meaning high-frequency details are lost or aliased; values between samples must be approximated (1 mark).

Route C: Lossy Compression

• Lossy compression has been applied (1 mark).
• Frequencies outside normal hearing ranges or quieter sounds are permanently removed (1 mark).

🧠 Exam Technique & Examiner Notes

• If you mention Nyquist's theorem directly: stating "the sampling rate is not at least twice the frequency of the highest frequency component" secures both marks immediately.
• Not Enough: Saying "the sound is digital and not analogue" or "it is converted to binary" is too vague to gain credit.

💡 MIDI vs Sampled Audio Principles

• Sampled Audio (e.g. WAV/MP3): Stores thousands of amplitude snapshots per second (e.g. 44 100 measurements every single second), irrespective of whether a note changes or is silent.
• MIDI (.mid): Does not store audio waves. It is an event-based control protocol. It only records instructions (pitch, note on, note off, velocity, duration, instrument channel).

✅ Model Answer [2 Marks]

Award 1 mark for each distinct concept:

1. Event Instructions (1 mark): MIDI does not record audio waves; it stores event messages / instructions explaining how to recreate the sound (e.g. note pitch, duration, velocity).
2. Frequency of Data Points (1 mark): A piece of music contains far fewer musical events (notes) than the thousands of samples per second required to record continuous audio. Individual notes can sustain for seconds with only two messages (Note On and Note Off).

❌ Common Examiner Traps

• "Repeated sounds are stored only once": Marked as Not Enough (NE). MIDI synthesizers reference instruments in separate patch banks, but simply writing that duplicate notes are stored once does not explain why MIDI is smaller overall.
• Confusing MIDI with MP3: MIDI does not use psychoacoustic compression or remove inaudible frequencies. It is not an audio recording at all.

🧠 Top Tip for Full Marks

Contrast events with samples. Writing: "MIDI stores event instructions (like pitch and note duration) rather than raw sound, and musical pieces consist of far fewer note events than the tens of thousands of samples taken every second in sampled audio" is an examiner-favourite response that guarantees 2/2.