慈溪市二模高三數(shù)學(xué)試卷

慈溪市二模高三數(shù)學(xué)試卷一、選擇題

1.已知函數(shù)\(f(x)=x^3-3x+2\)，則函數(shù)的對(duì)稱中心是（）

A.(0,-1)

B.(1,0)

C.(0,2)

D.(1,2)

2.若復(fù)數(shù)\(z\)滿足\(|z-1|=|z+1|\)，則\(z\)的幾何意義是（）

A.\(z\)在復(fù)平面上的軌跡是實(shí)軸

B.\(z\)在復(fù)平面上的軌跡是虛軸

C.\(z\)在復(fù)平面上的軌跡是單位圓

D.\(z\)在復(fù)平面上的軌跡是兩條直線

3.已知數(shù)列\(zhòng)(\{a_n\}\)的前\(n\)項(xiàng)和為\(S_n=n^2+n\)，則數(shù)列的通項(xiàng)公式為（）

A.\(a_n=2n+1\)

B.\(a_n=n^2+n\)

C.\(a_n=n+1\)

D.\(a_n=2n-1\)

4.已知向量\(\mathbf{a}=(2,3)\)，向量\(\mathbf=(1,2)\)，則\(\mathbf{a}\cdot\mathbf\)的值為（）

A.7

B.5

C.3

D.1

5.若等差數(shù)列\(zhòng)(\{a_n\}\)的前\(n\)項(xiàng)和為\(S_n=3n^2+2n\)，則該數(shù)列的首項(xiàng)\(a_1\)為（）

A.1

B.2

C.3

D.4

6.已知函數(shù)\(f(x)=\ln(x+1)-\ln(x-1)\)，則\(f(x)\)的定義域是（）

A.\((1,+\infty)\)

B.\((-\infty,-1)\cup(1,+\infty)\)

C.\((-1,1)\)

D.\((-\infty,-1)\cup(1,+\infty)\)

7.已知函數(shù)\(f(x)=x^2-4x+4\)，則\(f(x)\)的圖像的對(duì)稱軸為（）

A.\(x=-2\)

B.\(x=2\)

C.\(x=0\)

D.\(x=1\)

8.若等比數(shù)列\(zhòng)(\{a_n\}\)的前\(n\)項(xiàng)和為\(S_n=2^n-1\)，則該數(shù)列的首項(xiàng)\(a_1\)為（）

A.1

B.2

C.4

D.8

9.已知函數(shù)\(f(x)=\sqrt{x^2+1}\)，則\(f(x)\)的反函數(shù)為（）

A.\(y=\sqrt{x^2-1}\)

B.\(y=\frac{1}{\sqrt{x^2+1}}\)

C.\(y=\frac{1}{\sqrt{x^2-1}}\)

D.\(y=\sqrt{\frac{1}{x^2+1}}\)

10.若等差數(shù)列\(zhòng)(\{a_n\}\)的前\(n\)項(xiàng)和為\(S_n=\frac{n}{2}(a_1+a_n)\)，則該數(shù)列的公差\(d\)為（）

A.1

B.2

C.3

D.4

二、判斷題

1.向量\(\mathbf{a}=(2,3)\)和\(\mathbf=(1,2)\)的點(diǎn)積\(\mathbf{a}\cdot\mathbf\)等于7。（）

2.函數(shù)\(f(x)=\frac{1}{x}\)在其定義域內(nèi)是連續(xù)的。（）

3.在等差數(shù)列中，任意兩項(xiàng)之和等于它們中間項(xiàng)的兩倍。（）

4.復(fù)數(shù)\(z=a+bi\)的模\(|z|\)等于\(a^2+b^2\)。（）

5.函數(shù)\(f(x)=x^3\)在其定義域內(nèi)是增函數(shù)。（）

三、填空題

1.若函數(shù)\(f(x)=ax^2+bx+c\)的圖像開(kāi)口向上，且頂點(diǎn)坐標(biāo)為\((h,k)\)，則\(a\)的取值范圍是\(a>\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\

四、簡(jiǎn)答題

1.簡(jiǎn)述數(shù)列\(zhòng)(\{a_n\}\)是等差數(shù)列的充分必要條件，并給出一個(gè)例子說(shuō)明。

2.請(qǐng)解釋函數(shù)\(f(x)=\ln(x)\)的導(dǎo)數(shù)\(f'(x)\)的幾何意義。

3.如何判斷一個(gè)二次函數(shù)\(f(x)=ax^2+bx+c\)的圖像是開(kāi)口向上還是向下？

4.簡(jiǎn)述向量積（叉積）的定義及其幾何意義。

5.請(qǐng)解釋為什么在實(shí)數(shù)范圍內(nèi)，函數(shù)\(f(x)=\frac{1}{x}\)是單調(diào)遞減的。

五、計(jì)算題

1.計(jì)算下列極限：\(\lim_{x\to0}\frac{\sin(x)}{x}\)。

2.解下列微分方程：\(y'+2xy=e^x\)。

3.求函數(shù)\(f(x)=x^3-6x^2+9x\)的導(dǎo)數(shù)\(f'(x)\)。

4.已知向量\(\mathbf{a}=(2,-3)\)和\(\mathbf=(1,4)\)，計(jì)算\(\mathbf{a}\cdot\mathbf\)和\(\mathbf{a}\times\mathbf\)。

5.設(shè)\(a,b,c\)是等比數(shù)列的前三項(xiàng)，且\(a+b+c=6\)，\(abc=8\)，求該等比數(shù)列的公比\(r\)。

六、案例分析題

1.案例背景：某班級(jí)有學(xué)生30人，數(shù)學(xué)考試成績(jī)呈正態(tài)分布，平均分為70分，標(biāo)準(zhǔn)差為10分?，F(xiàn)有一名學(xué)生數(shù)學(xué)考試成績(jī)?yōu)?0分，請(qǐng)問(wèn)該生的成績(jī)?cè)诎嗉?jí)中的位置？

分析要求：

-利用正態(tài)分布的性質(zhì)，計(jì)算該生成績(jī)高于平均分的概率。

-分析該生成績(jī)?cè)诎嗉?jí)中的位置，并給出相應(yīng)的描述。

2.案例背景：某企業(yè)生產(chǎn)一批產(chǎn)品，產(chǎn)品的質(zhì)量指標(biāo)服從正態(tài)分布，平均值為100克，標(biāo)準(zhǔn)差為5克。企業(yè)規(guī)定，產(chǎn)品重量必須在95克到105克之間，否則視為不合格?，F(xiàn)從該批產(chǎn)品中隨機(jī)抽取一個(gè)樣本，其重量為98克，請(qǐng)問(wèn)該樣本是否合格？

分析要求：

-利用正態(tài)分布的性質(zhì)，計(jì)算產(chǎn)品重量在95克到105克之間的概率。

-判斷該樣本是否合格，并解釋原因。

七、應(yīng)用題

1.應(yīng)用題：某工廠生產(chǎn)一種產(chǎn)品，每件產(chǎn)品的成本為20元，售價(jià)為30元。根據(jù)市場(chǎng)調(diào)查，每增加1元售價(jià)，銷售量將減少10件。現(xiàn)計(jì)劃提高售價(jià)以增加利潤(rùn)，問(wèn)售價(jià)提高多少元時(shí)，利潤(rùn)最大？最大利潤(rùn)是多少？

2.應(yīng)用題：一家商店銷售兩種商品，商品A和商品B。商品A的售價(jià)為50元，每增加1元，銷量減少5件；商品B的售價(jià)為100元，每增加1元，銷量減少10件。商店的總成本是商品A和商品B成本之和的固定值。問(wèn)如何定價(jià)這兩種商品，可以使商店的總利潤(rùn)最大？

3.應(yīng)用題：某班級(jí)有男生和女生共40人，男生和女生的人數(shù)之比為3:2。為了提高班級(jí)的數(shù)學(xué)成績(jī)，學(xué)校決定從男生中選拔5名學(xué)生參加數(shù)學(xué)競(jìng)賽。問(wèn)選拔的這5名學(xué)生中，男生和女生的比例大約是多少？

4.應(yīng)用題：一家公司計(jì)劃在一段時(shí)間內(nèi)對(duì)生產(chǎn)線進(jìn)行升級(jí)，以降低生產(chǎn)成本。已知升級(jí)前后的生產(chǎn)成本函數(shù)分別為\(C_1(x)=2000+40x\)和\(C_2(x)=3000+20x\)，其中\(zhòng)(x\)是生產(chǎn)的產(chǎn)品數(shù)量。問(wèn)在生產(chǎn)多少件產(chǎn)品時(shí)，升級(jí)后的生產(chǎn)成本將低于升級(jí)前的生產(chǎn)成本？

本專業(yè)課理論基礎(chǔ)試卷答案及知識(shí)點(diǎn)總結(jié)如下：

一、選擇題

1.B

2.A

3.C

4.A

5.B

6.D

7.B

8.B

9.C

10.A

二、判斷題

1.√

2.×

3.√

4.√

5.√

三、填空題

1.\(a>0\)

2.\(y=\frac{1}{x}\)

3.\(-2\)

4.\(a^2+b^2\)

5.\(\frac{1}{2}\)

四、簡(jiǎn)答題

1.充分必要條件是：若數(shù)列\(zhòng)(\{a_n\}\)是等差數(shù)列，則存在常數(shù)\(d\)，使得\(a_{n+1}-a_n=d\)對(duì)所有\(zhòng)(n\)成立。例如，數(shù)列\(zhòng)(1,4,7,10,\ldots\)是等差數(shù)列