qwq-32b-preview๊ฐ€ ํ‹€๋ ธ๋˜ ์• ๋“ค์ด๋ผ์„œ ๊ทธ ๋ฌธํ•ญ๋“ค ์œ„์ฃผ๋กœ ์‹œ์ผœ๋ด„

o1 pro ์•„๋‹ˆ๊ณ  ์ผ๋ฐ˜ o1 (full)


๋ฌธ์ œ ๋ฒˆํ˜ธ ์˜†์— %๋Š” ๋ฌธํ•ญ๋ณ„ ์ •๋‹ต๋ฅ 

(๋ฒ”์œ„๋กœ ๋˜์–ด์žˆ๋Š”๊ฑด ํ™•ํ†ต/๊ธฐํ•˜/๋ฏธ์  ์„ ํƒ๋ณ„๋กœ ์ •๋‹ต๋ฅ ์ด ๋‹ฌ๋ผ์„œ ๊ทธ๋Ÿผ)


1. 21๋ฒˆ (8%~30%) ํ†ตํ•ฉ์ˆ˜๋Šฅ ์ดํ›„ 21๋ฒˆ ์—ญ๋Œ€ ์ตœ์ € ์ •๋‹ต๋ฅ 

ํ•จ์ˆ˜ $f(x) = x^3 + ax^2 + bx + 4$๊ฐ€ ๋‹ค์Œ ์กฐ๊ฑด์„ ๋งŒ์กฑ์‹œํ‚ค๋„๋ก ํ•˜๋Š” ๋‘ ์ •์ˆ˜ $a, b$์— ๋Œ€ํ•˜์—ฌ $f(1)$์˜ ์ตœ๋Œ“๊ฐ’์„ ๊ตฌํ•˜์‹œ์˜ค. [4์ ] \begin{center} \setlength{\fboxsep}{1em} \cornersize{.3} \ovalbox{ \parbox{0.9\textwidth}{ ๋ชจ๋“  ์‹ค์ˆ˜ $\alpha$์— ๋Œ€ํ•˜์—ฌ \[ \lim_{x \to \alpha} \frac{f(2x+1)}{f(x)} \] ์˜ ๊ฐ’์ด ์กด์žฌํ•œ๋‹ค. } } \end{center}

๋ฌธ์ œ๋“ค์€ ์œ„์™€ ๊ฐ™์ด QwQ ๋•Œ๋ž‘ ๋™์ผํ•œ LaTeX ํฌ๋งท์œผ๋กœ ์ œ๊ณตํ•จ



7cf3c028e2f206a26d81f6e642847c6d

1ํŠธ ์ •๋‹ต (1๋ถ„ 38์ดˆ ์ƒ๊ฐ)


2. 22๋ฒˆ (4%~13%) ํ†ตํ•ฉ์ˆ˜๋Šฅ ์ดํ›„ 22๋ฒˆ ์—ญ๋Œ€ ์ตœ์ € ์ •๋‹ต๋ฅ 

7ff3c028e2f206a26d81f6e743827d68

1ํŠธ ์˜ค๋‹ต (1๋ถ„ 36์ดˆ ์ƒ๊ฐ)


ํ‹€๋ ธ๋‹ค๊ณ  ๋‹ค์‹œ ํ’€์–ด๋ณด๋ผ๊ณ  ํ•จ

7ef3c028e2f206a26d81f6e744837c6e

2ํŠธ ์ •๋‹ต (1๋ถ„ 37์ดˆ ์ƒ๊ฐ)


(22๋ฒˆ์ด ์ˆ˜์—ด ๋ฌธ์ œ๋ผ์„œ ๋‹ค๋ฅธ ๋ชจ๋ธ๋“ค๋„ ๊ฑฐ์˜ ๋ชป ๋งž์ถ˜๊ฑฐ๋กœ ๋“ค์Œ)


3. 29๋ฒˆ (์ด๊ฑด qwq๋„ ๋งžํ˜”๋˜ย ๋ฌธ์ œ๊ธด ํ•จ) (21%)

78f3c028e2f206a26d81f6e641807164

1ํŠธ ์ •๋‹ต (50์ดˆ ์ƒ๊ฐ)


3. 30๋ฒˆ (18%)

79f3c028e2f206a26d81f6e74386766a

1ํŠธ ์ •๋‹ต (6๋ถ„ 4์ดˆ ์ƒ๊ฐํ•จ;;)

7bf3c028e2f206a26d81f6e6448370

๊ฝค ์ธ์ƒ์ ์ธ๋“ฏ



์ข…ํ•ฉํ•ด์„œ ์˜ˆ์ƒ ์ ์ˆ˜๋กœ ๋ณด์ž๋ฉด

๋‚˜๋จธ์ง€ ๋ฌธ์ œ๋“ค์€ ๊ฑฐ์˜ ๋งžํžย ๊ฒƒ ๊ฐ™์•„์„œ,


2025 ์ˆ˜๋Šฅ ๋ฏธ์  ์›์ ์ˆ˜ 96์  ~ ์ปจ๋””์…˜ ์ข‹์œผ๋ฉด 100์ ๋„ ๋ ๊ฑธ๋กœ ๋ณด์ž„


QwQ 32B Preview๋Š” 88์ 

o1 preivew๋Š” 80์ ์ด์—ˆ์Œ.