Problem Analysis #3

Kimi K3 · Run 1

Correct

8.23s

471 toks

API · no tools. This is the prompt and response recorded for this attempt; a full solution may not have been returned.

Problem Statement

This is a Korean CSAT mathematics multiple-choice problem. Solve it and put only the correct choice symbol, one of ①, ②, ③, ④, ⑤, inside \boxed{}.

Problem 4 Consider the function f(x) = ( 3x−2 (x <1), x2 −3x+a(x≥1), which is continuous on the entire real line. Determine the value of the constanta. [3 points] ①1 ②2 ③3 ④4 ⑤5

Ground Truth

③

Recorded model response / solution

Reasoning Process

For $f$ to be continuous at $x=1$ :

Left-hand limit: $\lim_{x\to1^-}(3x-2)=3(1)-2=1$ .

Right-hand value: $f(1)=1^2-3(1)+a=a-2$ .

Set equal: $a-2=1$ , so $a=3$ .

\boxed{③}

Final Model Output

③

Comparative Analysis (P3) (Average across runs)

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

Avg Time Taken

Motif 3

10.7

Solar Pro 4

7.8

Kimi K3

7.4

K-EXAONE-2

0.7

Avg Token Usage

Solar Pro 4

672.7

Kimi K3

407.0

K-EXAONE-2

359.7