Õøt£ä 4 Ÿ, |ÛõbYåÑ a1, a2, a3, a4
t° (16%) (i) max{a1, a2, a3, a4

90 ç ×çRŠpç bç

…¿ðÑl„pæ, ~øƬ˙ŸÊ, Ž.™pæU

1. q N = 2¹³¹+ 192 (20%)

(i) úkL<£cb n, „p:2³ⁿ− 1 u 7 íIb

(ii) „p N u 224 íIb

(iii) N uÖýPíb

(iv) N \ 224 Î(F)í¼uÖýPb? w2 log₁₀2 = 0.3010.

2. q m ÑøÝŠ5cb (16%)

(i) t„: úL<AÍb n, Xn

k=1

k(k + 1)(k + 2) · · · (k + m) = 1

m + 2· n(n + 1)(n + 2) · · · (n + m + 1)

(ii) ‚à (i) 5!‹, t„:Pⁿ

k=1

k³=^n2(n+1)₄ ²

3. Õøt£ä 4 Ÿ, |ÛõbYåÑ a1, a2, a3, a4
t° (16%) (i) max{a₁, a₂, a₃, a₄} = 4 5œ0

(ii) a1≤ a2≤ a3≤ a4 5œ0

4. qšÑ r íÆqQ£ÆÕ~£ n i$íÞ }Ñ sn, tn (16%)

(i) ° s8: t8

(ii) J sn: tn= 3 : 4, °n

5. Þ,úõ O, A, B, 7/ OA = OB = 1, ∠AOB = θ, (0 < θ < π)
qõ P ÊJ B Ñÿõ, ¬õ O Dõ A íò( ` ÑÄ(íÓ(,‰, 1pOA= ~a,^−→ OB= ~b,^−→ OP = ~p^−→ (16%)

(i) t„:(~p · ~a)²− 2(~p · ~b) + 1 = 0

(ii) ç(¨ OP z ∠AOB ù}v, / OP = 2, ° θ M

6. *õ P (−1, 1,√

5) }²Þ E : 3x + 4y − 6 = 0 £Þ F : x − 2y + 2√

5z + 3 = 0 T(, w

—}Ñ A, B sõ (16%)

(i) °õ A, B íè™

(ii) ° ∆P AB íÞ

1