2025 · Paper 2 · Mathematics
Question 14
The printed question, the official key, and each model’s JSON answer plus the reasoning it wrote.
MathematicsPaper 2Numerical
Q14
Official 0.2 – 0.3
Model answers
Claude Fable 5.1
Anthropic
Correct4 / 4
0.25
Claude Fable 5.1 reasoning
g(x) = 4/(1+e^{-2x}). g(x)=2 ⇒ 1+e^{-2x}=2 ⇒ x=0. So g^{-1}(2)=0. g'(x) = 4·2e^{-2x}/(1+e^{-2x})² ; at x=0: 8/4 = 2. So (g^{-1})'(2) = 1/2. f'(x) = (2x+2)/(x²+2x+4); f'(0) = 2/4 = 1/2. Derivative = f'(0)·(g^{-1})'(2) = 1/2 · 1/2 = 0.25.
GPT 6 Astra
OpenAI
Correct4 / 4
0.25
GPT 6 Astra reasoning
No written reasoning was returned for this item.
GPT 5.6 Luna
OpenAI
Correct4 / 4
0.25
GPT 5.6 Luna reasoning
No written reasoning was returned for this item.