(A) (B) (C) (D) 查看更多

 

題目列表(包括答案和解析)

一、選擇題(每小題5分,共50分)

6ec8aac122bd4f6e

二、填空題(每小題4分,共28分)

6ec8aac122bd4f6e

三、解答題

18.解:(Ⅰ)由已有

6ec8aac122bd4f6e

6ec8aac122bd4f6e6ec8aac122bd4f6e

                                    (4分)

 

6ec8aac122bd4f6e

                                            (6分)

 

(Ⅱ)由(1)6ec8aac122bd4f6e6ec8aac122bd4f6e                                 (8分)

所以6ec8aac122bd4f6e              (10分)

6ec8aac122bd4f6e                                                      (12分)

6ec8aac122bd4f6e

6ec8aac122bd4f6e                                  (14分)

 

19.解:(Ⅰ)同學(xué)甲同學(xué)恰好投4次達(dá)標(biāo)的概率6ec8aac122bd4f6e           (4分)

(Ⅱ)6ec8aac122bd4f6e可取的值是6ec8aac122bd4f6e

6ec8aac122bd4f6e                                              (6分)

6ec8aac122bd4f6e                                            (8分)

6ec8aac122bd4f6e                                              (10分)

6ec8aac122bd4f6e的分布列為

6ec8aac122bd4f6e

3

4

5

6ec8aac122bd4f6e

6ec8aac122bd4f6e

6ec8aac122bd4f6e

                                                                      (12分)

所以6ec8aac122bd4f6e的數(shù)學(xué)期望為6ec8aac122bd4f6e                   (14分)

 

20.解:(Ⅰ)∵PA⊥底面ABCD,BC6ec8aac122bd4f6e平面AC,∴PA⊥BC

∵∠ACB=90°,∴BC⊥AC,又PA∩AC=A,∴BC⊥平面PAC                (4分)

 

(Ⅱ)取CD的中點(diǎn)E,則AE⊥CD,∴AE⊥AB,又PA⊥底面ABCD,∴PA⊥AE

建立如圖所示空間直角坐標(biāo)系,則

A(0,,0,0),P(0,0,6ec8aac122bd4f6e),C(6ec8aac122bd4f6e,0),D(6ec8aac122bd4f6e,0)

6ec8aac122bd4f6e6ec8aac122bd4f6e,6ec8aac122bd4f6e6ec8aac122bd4f6e                  (6分)

易求6ec8aac122bd4f6e為平面PAC的一個法向量.

6ec8aac122bd4f6e為平面PDC的一個法向量                                  (9分)

∴cos6ec8aac122bd4f6e

故二面角D-PC-A的正切值為2.  (11分)

(Ⅲ)設(shè)6ec8aac122bd4f6e,則

   6ec8aac122bd4f6e,

解得點(diǎn)6ec8aac122bd4f6e,即6ec8aac122bd4f6e   (13分)

6ec8aac122bd4f6e6ec8aac122bd4f6e(不合題意舍去)或6ec8aac122bd4f6e

所以當(dāng)6ec8aac122bd4f6e6ec8aac122bd4f6e的中點(diǎn)時,直線6ec8aac122bd4f6e與平面6ec8aac122bd4f6e所成角的正弦值為6ec8aac122bd4f6e   (15分)

 

21.解:(Ⅰ)設(shè)直線6ec8aac122bd4f6e的方程為:6ec8aac122bd4f6e

6ec8aac122bd4f6e6ec8aac122bd4f6e,所以6ec8aac122bd4f6e的方程為6ec8aac122bd4f6e                     (4分)

6ec8aac122bd4f6e6ec8aac122bd4f6e點(diǎn)的坐標(biāo)為6ec8aac122bd4f6e.

可求得拋物線的標(biāo)準(zhǔn)方程為6ec8aac122bd4f6e.                                       (6分)

(Ⅱ)設(shè)直線6ec8aac122bd4f6e的方程為6ec8aac122bd4f6e,代入拋物線方程并整理得6ec8aac122bd4f6e    (8分)     

設(shè)6ec8aac122bd4f6e6ec8aac122bd4f6e

設(shè)6ec8aac122bd4f6e,則6ec8aac122bd4f6e

6ec8aac122bd4f6e

6ec8aac122bd4f6e

6ec8aac122bd4f6e

6ec8aac122bd4f6e                                      (11分)

當(dāng)6ec8aac122bd4f6e時上式是一個與6ec8aac122bd4f6e無關(guān)的常數(shù).

所以存在定點(diǎn)6ec8aac122bd4f6e,相應(yīng)的常數(shù)是6ec8aac122bd4f6e.                                     (14分)

 

22.解:(Ⅰ)當(dāng)6ec8aac122bd4f6e6ec8aac122bd4f6e              (2分)

6ec8aac122bd4f6e6ec8aac122bd4f6e上遞增,在6ec8aac122bd4f6e上遞減

所以6ec8aac122bd4f6e在0和2處分別達(dá)到極大和極小,由已知有

6ec8aac122bd4f6e6ec8aac122bd4f6e,因而6ec8aac122bd4f6e的取值范圍是6ec8aac122bd4f6e.                                   (4分)

(Ⅱ)當(dāng)6ec8aac122bd4f6e時,6ec8aac122bd4f6e6ec8aac122bd4f6e

6ec8aac122bd4f6e可化為6ec8aac122bd4f6e6ec8aac122bd4f6e,記6ec8aac122bd4f6e

6ec8aac122bd4f6e                                        (7分)

6ec8aac122bd4f6e6ec8aac122bd4f6e,

6ec8aac122bd4f6e6ec8aac122bd4f6e上遞減,在6ec8aac122bd4f6e上遞增.

6ec8aac122bd4f6e

從而6ec8aac122bd4f6e上遞增

因此6ec8aac122bd4f6e6ec8aac122bd4f6e                           (10分)

(Ⅲ)假設(shè)6ec8aac122bd4f6e6ec8aac122bd4f6e,即6ec8aac122bd4f6e6ec8aac122bd4f6e=6ec8aac122bd4f6e

6ec8aac122bd4f6e,

6ec8aac122bd4f6e                                     (12分)

6ec8aac122bd4f6e,6ec8aac122bd4f6e6ec8aac122bd4f6e(x)=0的兩根可得,6ec8aac122bd4f6e

從而有6ec8aac122bd4f6e

6ec8aac122bd4f6e

6ec8aac122bd4f6e≥26ec8aac122bd4f6e,這與6ec8aac122bd4f6e<26ec8aac122bd4f6e矛盾.                                

故直線6ec8aac122bd4f6e與直線6ec8aac122bd4f6e不可能垂直.                                               (15分)

 


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