2025 · Paper 1 · Mathematics
Question 11
The printed question, the official key, and each model’s JSON answer plus the reasoning it wrote.
MathematicsPaper 1Numerical
Q11
Official 2.35 – 2.45
Model answers
Claude Fable 5.1
Anthropic
Correct4 / 4
2.4
Claude Fable 5.1 reasoning
Expand the integrand: 1/(1−t²) = 1 + t² + t⁴ + …, so ∫₀ˣ dt/(1−t²) = x + x³/3 + x⁵/5 + … Also βx cos x = βx − βx³/2 + … Numerator: (α/2)(x + x³/3 + …) + βx − βx³/2 + … = (α/2 + β)x + (α/6 − β/2)x³ + … For the limit (divided by x³) to be finite and equal 2: - α/2 + β = 0 ⇒ β = −α/2 - α/6 − β/2 = 2 ⇒ α/6 + α/4 = 2 ⇒ 5α/12 = 2 ⇒ α = 24/5 Then β = −12/5, so α + β = 24/5 − 12/5 = 12/5 = 2.4.
GPT 6 Astra
OpenAI
Correct4 / 4
2.4
GPT 6 Astra reasoning
No written reasoning was returned for this item.
GPT 5.6 Luna
OpenAI
Correct4 / 4
2.4
GPT 5.6 Luna reasoning
No written reasoning was returned for this item.