AQA A-Level Computer Science AS Paper 2, June 2025: Question 1

✅ Correct Answer

The two lozenges to shade are:

• A: 0 [1 mark]
• E: 998 [1 mark]

💡 Key Knowledge

Set ℤ (Integers) represents all positive and negative whole numbers, including zero:

{..., -3, -2, -1, 0, 1, 2, 3, ...}

• 0 is an integer.
• 998 is a positive integer.
• √2 and π are irrational numbers (part of ℝ , not ℤ ).
• 3/4 is a fractional/rational number (part of ℚ , not ℤ ).

🧠 Exam Technique

The question explicitly instructs: "Shade two lozenges." Always scan every option and classify them systematically into their mathematical sets before filling in your answer.

❌ Common Errors & Mark Scheme Traps

• Shading > 2 lozenges: The mark scheme strictly enforces R. more than two lozenges shaded . Shading 3 or more cancels out marks.
• Zero confusion: Forgetting that 0 is indeed an element of ℤ (and ℕ under AQA conventions).

✅ Acceptable Answers

• A number used to represent or describe the position or index of an object/entity placed in an order or sequence. [1 mark]
• OR Awarded by example: explicitly stating at least three ordinal terms, e.g. 1ˢᵗ, 2ⁿᵈ, 3ʳᵈ . [1 mark]

💡 Key Knowledge

• Cardinal numbers: Indicate quantity or "how many" (e.g. 1, 2, 3 items).
• Ordinal numbers: Indicate rank, order, or position in a collection (e.g. 1ˢᵗ, 2ⁿᵈ, 3ʳᵈ, or array indices like 0, 1, 2).

🧠 Exam Technique

Always pair your answer with a concrete keyword: "position", "rank", or "order in a list". If your definition feels vague, back it up with an example sequence ( 1ˢᵗ, 2ⁿᵈ, 3ʳᵈ ) to guarantee the mark.

❌ Common Errors

• Confusing ordinal with cardinal (e.g. answering "a number used for counting items").
• Providing fewer than three examples (e.g. just writing "1ˢᵗ and 2ⁿᵈ" does not meet the mark scheme minimum).

✅ Acceptable Explanations

Any one of the following clear points [1 mark]:

• Real-world quantities/measurements are continuous / not necessarily whole numbers.
• Natural numbers cannot represent fractional or decimal parts required for precision.
• Measurements can take negative values (e.g., temperature), which natural numbers cannot represent.

💡 Key Knowledge

• Natural Numbers (ℕ): Discrete whole counting numbers ( {0, 1, 2, 3, ...} ). Gaps exist between every value; you cannot have 2.45 .
• Real Numbers (ℝ): Continuous numbers including all rational and irrational values. Crucial for physical quantities like length, weight, time, or voltage where values can vary by infinitesimal fractions.

🧠 Exam Technique: Comparison Questions

This is a contrast question ("why X is better suited than Y"). The strongest responses explicitly highlight a limitation of ℕ that ℝ overcomes: "Natural numbers only represent whole numbers, whereas measurements often require fractional/decimal parts."

❌ Common Errors

• Vague answers such as "real numbers are bigger" or "real numbers are more accurate" without explaining why (fractional/continuous nature).
• Failing to mention the nature of measurements (continuous) versus counting (discrete).