2025 · Paper 1 · Mathematics
Question 7
The printed question, the official key, and each model’s JSON answer plus the reasoning it wrote.
MathematicsPaper 1Multi correct
Q07
Official A, D
Model answers
Claude Fable 5.1
Anthropic
Correct4 / 4
A, D
Claude Fable 5.1 reasoning
Let z = x + iy. The condition is |z − (1+2i)| = 2|z − 3i|. Squaring: (x − 1)² + (y − 2)² = 4[x² + (y − 3)²] x² − 2x + 1 + y² − 4y + 4 = 4x² + 4y² − 24y + 36 0 = 3x² + 3y² + 2x − 20y + 31 x² + y² + (2/3)x − (20/3)y + 31/3 = 0 Centre: (−1/3, 10/3). Radius² = (1/3)² + (10/3)² − 31/3 = 1/9 + 100/9 − 93/9 = 8/9, so radius = 2√2/3. Thus S is a circle with centre (−1/3, 10/3) and radius 2√2/3. Options A and D are true.
GPT 6 Astra
OpenAI
Correct4 / 4
A, D
GPT 6 Astra reasoning
No written reasoning was returned for this item.
GPT 5.6 Luna
OpenAI
Correct4 / 4
A, D
GPT 5.6 Luna reasoning
No written reasoning was returned for this item.