Problem Analysis #common_05

Motif 3 · Run 1

Python ● execution succeeded
Correct
11.57s
1,910 toks

Infron · Motif 3 · 46문항 × 3회 · Python TAR. 131,072 output tokens · 기본 1,800초 · 6+1 turns. ACC는 전체 138회, Pass@1은 각 문항의 첫 유효 시도, Pass@3는 3회 내 정답으로 계산합니다.

Problem Statement

함수 f(x)=(x+2)(2x2−x−2)f(x)=(x+2)(2x^2-x-2)에 대하여 f′(1)f\prime(1)의 값은?

① 66 ② 77 ③ 88 ④ 99 ⑤ 1010

최종 답은 선택지 번호 1~5 중 하나를 \boxed{} 안에 쓰세요.

Ground Truth
3
Recorded model response / solution
Reasoning Process

Recorded Python call:

import sympy as sp
x=sp.symbols('x')
f=(x+2)*(2*x**2-x-2)
fp=sp.diff(f,x)
val=sp.simplify(fp.subs(x,1))
print("f'(x)=",fp)
print("f'(1)=",val)
Tool Output
Execution succeeded f'(x)= 2*x**2 - x + (x + 2)*(4*x - 1) - 2 f'(1)= 8
Reasoning Process
f(x)=(x+2)(2x2−x−2)f(x)=(x+2)(2x^2-x-2)

곱의 미분법을 적용하면

f′(x)=(2x2−x−2)+(x+2)(4x−1)f'(x)=(2x^2-x-2)+(x+2)(4x-1)

따라서

f′(1)=(2−1−2)+(1+2)(4−1)=(−1)+3⋅3=8f'(1)=(2-1-2)+(1+2)(4-1)=(-1)+3\cdot 3=8

정답은 선택지 ③입니다.

3\boxed{3}
Final Model Output
3

Comparative Analysis (Pcommon_05) (Average across runs)

Averages use reported measurements only. Missing usage is not treated as zero.

Avg Time Taken

Union Alpha
29.0
Solar Pro 4
16.4
Motif 3
13.2
MiMo V2.6 Pro
12.5
Grok 4.7
9.9
Muse Spark 1.3
6.6
DeepSeek V4.1 Flash
4.7
Solar Mini 4 Preview
1.9

Avg Token Usage

Grok 4.7
4,754
Solar Pro 4
3,780
Muse Spark 1.3
3,109
DeepSeek V4.1 Flash
2,451
Solar Mini 4 Preview
2,448
Union Alpha
2,274
Motif 3
2,164
MiMo V2.6 Pro
2,022
    CSAT 2026 · Problem common_05 · Motif 3 | EntropyMath