2025 · Paper 2 · Mathematics
Question 1
The printed question, the official key, and each model’s JSON answer plus the reasoning it wrote.
MathematicsPaper 2Single correct
Q01
Official C
Model answers
Claude Fable 5.1
Anthropic
Correct3 / 3
C
Claude Fable 5.1 reasoning
**Setup:** g(x) = x − α(eˣ + x)/(3(eˣ+1)). At x₀, eˣ⁰ + x₀ = 0, so g(x₀) = x₀ = −eˣ⁰, i.e., g(x₀) + eˣ⁰ = 0. Hence the limit equals |g′(x₀)|. g′(x) = 1 − (α/3)·[(eˣ+1)² − (eˣ+x)eˣ]/(eˣ+1)². At x₀, the bracket equals (eˣ⁰+1)², so g′(x₀) = 1 − α/3. - α = 2: limit = 1/3 - α = 3: limit = 0 So option (C) is true.
GPT 6 Astra
OpenAI
Correct3 / 3
C
GPT 6 Astra reasoning
No written reasoning was returned for this item.
GPT 5.6 Luna
OpenAI
Correct3 / 3
C
GPT 5.6 Luna reasoning
No written reasoning was returned for this item.