2025 · Paper 2 · Mathematics
Question 7
The printed question, the official key, and each model’s JSON answer plus the reasoning it wrote.
Q07
Official A, C
Model answers
Claude Fable 5.1
Anthropic
A, C
Claude Fable 5.1 reasoning
R on circle at angle π/6: R = (3cos π/6, 3 sin π/6) = (3√3/2, 3/2). So x1 = 3√3/2, P on ellipse: y1 = 2 sin(π/6) = 1. P = (3√3/2, 1). S at angle π/3: S = (3/2, 3√3/2). x2 = 3/2, Q: y2 = 2 sin(π/3) = √3. Q = (3/2, √3). Line PQ: slope = (√3 − 1)/(3/2 − 3√3/2) = (√3−1)/( (3/2)(1−√3)) = −2/3. Equation: y − 1 = −(2/3)(x − 3√3/2) → 3y − 3 = −2x + 3√3 → 2x + 3y = 3 + 3√3 = 3(1+√3). So (A) true, (B) false. (C): |N2Q| = √3, |N2S| = 3√3/2. 3|N2Q| = 3√3, 2|N2S| = 3√3. True. (D): |N1P| = 1, |N1R| = 3/2. 9·1 = 9 vs 4·3/2 = 6. False.
GPT 6 Astra
OpenAI
A, C
GPT 6 Astra reasoning
No written reasoning was returned for this item.
GPT 5.6 Luna
OpenAI
A, C
GPT 5.6 Luna reasoning
No written reasoning was returned for this item.