Integration Track · ~25 min

进阶挑战卷 · 数学 × ML 就绪度

The Challenge Set · Math × ML Readiness

10 道有难度的真题：竞赛档数学 + 进入神经网络所需的数学。做完立刻给出你的进轨建议。不限时,但建议一口气完成。

Ten genuinely hard, real questions: competition-band math plus the exact math a neural network needs. Your track placement appears the moment you finish. Untimed — but take it in one sitting.

  1. Q1If x + 1/x = 4, then x³ + 1/x³ =

    若 x + 1/x = 4,则 x³ + 1/x³ =

  2. Q2The remainder when 3¹⁰⁰ is divided by 8 is

    3¹⁰⁰ 除以 8 的余数是

  3. Q3How many distinct arrangements are there of the letters of LEVEL?

    单词 LEVEL 的字母全排列共有多少种?

  4. Q4The area of the triangle with sides 13, 14, 15 is

    三边为 13、14、15 的三角形面积是

  5. Q5Let f(x) = x² − 2. Then f(f(3)) =

    设 f(x) = x² − 2,则 f(f(3)) =

  6. Q6A training loss starts at 1.0 and halves every epoch. After which epoch does it first drop below 0.01?

    训练误差从 1.0 开始每轮减半,第几轮后首次低于 0.01?

  7. Q7The matrix [[1,2],[3,4]] times the column vector (1,1)ᵀ equals

    矩阵 [[1,2],[3,4]] 乘以列向量 (1,1)ᵀ 等于

  8. Q8Let f(x) = (2x+1)³. Then f′(1) =

    设 f(x) = (2x+1)³,则 f′(1) =

  9. Q9Three fair coins are tossed. Given at least one head, the probability all three are heads is

    抛三枚硬币,已知至少一枚正面,三枚全正面的概率是

  10. Q10For x > 0, the minimum value of x + 4/x is

    对 x > 0,x + 4/x 的最小值是