百校聯(lián)盟高一數(shù)學(xué)試卷

百校聯(lián)盟高一數(shù)學(xué)試卷一、選擇題

1.若函數(shù)\(f(x)=x^3-3x\)的導(dǎo)數(shù)\(f'(x)\)等于0，則\(x\)的值為（）

A.0

B.1

C.-1

D.2

2.下列哪個(gè)選項(xiàng)是等差數(shù)列的通項(xiàng)公式（）

A.\(a_n=3n+2\)

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

C.\(a_n=n^2+1\)

D.\(a_n=\frac{1}{2}n(n+1)\)

3.若\(\sin2\theta=\frac{3}{5}\)，且\(\theta\)在第二象限，則\(\cos2\theta\)的值為（）

A.\(-\frac{4}{5}\)

B.\(-\frac{3}{5}\)

C.\(\frac{4}{5}\)

D.\(\frac{3}{5}\)

4.設(shè)\(a,b,c\)是等差數(shù)列，且\(a+b+c=15\)，則\(a^2+b^2+c^2\)的值為（）

A.75

B.90

C.100

D.120

5.若\(\triangleABC\)中，\(\angleA=60^\circ\)，\(\angleB=45^\circ\)，則\(\angleC\)的度數(shù)為（）

A.75^\circ

B.45^\circ

C.90^\circ

D.30^\circ

6.下列哪個(gè)函數(shù)的圖像是關(guān)于\(y\)軸對(duì)稱(chēng)的（）

A.\(f(x)=x^2+1\)

B.\(f(x)=x^3+1\)

C.\(f(x)=\sqrt{x^2}\)

D.\(f(x)=\frac{1}{x}\)

7.若\(a,b,c\)是等比數(shù)列，且\(a+b+c=12\)，\(ab+bc+ca=30\)，則\(abc\)的值為（）

A.36

B.48

C.60

D.72

8.若\(\sin2\theta=\frac{1}{2}\)，則\(\tan\theta\)的值為（）

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

B.\(-\frac{1}{2}\)

C.2

D.-2

9.設(shè)\(a,b,c\)是等差數(shù)列，且\(a+b+c=18\)，\(ab+bc+ca=36\)，則\(a^2+b^2+c^2\)的值為（）

A.216

B.324

C.432

D.540

10.若\(\triangleABC\)中，\(\angleA=30^\circ\)，\(\angleB=45^\circ\)，則\(\angleC\)的度數(shù)為（）

A.45^\circ

B.30^\circ

C.90^\circ

D.60^\circ

二、判斷題

1.若\(x^2+y^2=1\)是一個(gè)圓的方程，則這個(gè)圓的半徑為1。（）

2.在直角坐標(biāo)系中，直線\(y=mx+b\)的斜率\(m\)恒大于0，則這條直線必經(jīng)過(guò)第一象限。（）

3.若\(a,b,c\)是等差數(shù)列，且\(a+b+c=0\)，則\(a^3+b^3+c^3=3abc\)。（）

4.在平面直角坐標(biāo)系中，點(diǎn)\(P(x,y)\)到原點(diǎn)\(O(0,0)\)的距離可以用公式\(\sqrt{x^2+y^2}\)計(jì)算。（）

5.在等差數(shù)列中，任意兩項(xiàng)的差的絕對(duì)值相等。（）

三、填空題

1.若\(f(x)=ax^2+bx+c\)的圖像開(kāi)口向上，則系數(shù)\(a\)的取值范圍是\(a>\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\

四、簡(jiǎn)答題

1.簡(jiǎn)述等差數(shù)列的定義及其通項(xiàng)公式，并舉例說(shuō)明。

2.給定一個(gè)二次函數(shù)\(f(x)=ax^2+bx+c\)，如何通過(guò)圖像判斷該函數(shù)的開(kāi)口方向以及頂點(diǎn)的位置？

3.簡(jiǎn)述直角坐標(biāo)系中，兩點(diǎn)間距離公式的推導(dǎo)過(guò)程。

4.如何判斷一個(gè)三角形是否為直角三角形？請(qǐng)給出兩種不同的方法。

5.簡(jiǎn)述函數(shù)\(f(x)=\frac{1}{x}\)的圖像特征，并說(shuō)明其在哪些象限內(nèi)存在。

五、計(jì)算題

1.計(jì)算下列函數(shù)的導(dǎo)數(shù)：\(f(x)=x^3-6x^2+9x-1\)。

2.已知等差數(shù)列\(zhòng)(\{a_n\}\)的前三項(xiàng)為\(a_1=2\)，\(a_2=5\)，求第10項(xiàng)\(a_{10}\)的值。

3.已知直角坐標(biāo)系中，點(diǎn)\(A(-3,4)\)，點(diǎn)\(B(2,-1)\)，計(jì)算線段\(AB\)的長(zhǎng)度。

4.解下列方程：\(2x^2-5x+3=0\)。

5.若\(\sin^2\theta+\cos^2\theta=1\)，且\(\tan\theta=2\)，求\(\cos\theta\)的值。

六、案例分析題

1.案例背景：

小明在學(xué)習(xí)平面幾何時(shí)，遇到了一個(gè)關(guān)于圓的問(wèn)題。已知圓的半徑為5，圓心坐標(biāo)為\((3,4)\)，現(xiàn)有一直線\(y=mx+n\)與該圓相交。

問(wèn)題：

（1）請(qǐng)寫(xiě)出直線與圓相交的條件。

（2）如果直線\(y=2x-1\)與該圓相交，求交點(diǎn)坐標(biāo)。

（3）若直線與圓相切，求直線斜率\(m\)的取值范圍。

2.案例背景：

小紅在學(xué)習(xí)函數(shù)時(shí)，遇到了一個(gè)關(guān)于指數(shù)函數(shù)的問(wèn)題。已知函數(shù)\(f(x)=a^x\)（\(a>0\)且\(a\neq1\)），且\(f(1)=2\)，\(f(3)=8\)。

問(wèn)題：

（1）求出函數(shù)\(f(x)\)的表達(dá)式。

（2）若函數(shù)\(f(x)\)的圖像經(jīng)過(guò)點(diǎn)\((4,32)\)，求\(a\)的值。

（3）討論當(dāng)\(x\)增大時(shí)，函數(shù)\(f(x)\)的增減性。

七、應(yīng)用題

1.應(yīng)用題：

小華在超市購(gòu)物，買(mǎi)了\(x\)千克蘋(píng)果和\(y\)千克香蕉，蘋(píng)果的價(jià)格為每千克10元，香蕉的價(jià)格為每千克15元。如果小華總共花費(fèi)了150元，請(qǐng)建立方程組并求解\(x\)和\(y\)的值。

2.應(yīng)用題：

小明在游泳時(shí)，從岸邊出發(fā)，以每小時(shí)2公里的速度向正東方向游泳。1小時(shí)后，他發(fā)現(xiàn)偏離了預(yù)定路線，此時(shí)他距離預(yù)定路線的北邊40米。假設(shè)小明的速度保持不變，求他需要向正北方向游多遠(yuǎn)才能回到預(yù)定路線。

3.應(yīng)用題：

一個(gè)工廠生產(chǎn)的產(chǎn)品數(shù)量\(P\)隨時(shí)間\(t\)變化的函數(shù)為\(P(t)=100e^{0.05t}\)。如果現(xiàn)在工廠想要在接下來(lái)的6個(gè)月內(nèi)生產(chǎn)的產(chǎn)品數(shù)量是現(xiàn)在的2倍，請(qǐng)計(jì)算需要多少時(shí)間（以月為單位）。

4.應(yīng)用題：

一輛汽車(chē)從靜止開(kāi)始以勻加速直線運(yùn)動(dòng)，加速度為\(a=2\)米/秒2，求：

（1）汽車(chē)行駛10秒后，它的速度是多少？

（2）汽車(chē)行駛10秒后，它行駛的距離是多少？

（3）如果汽車(chē)在行駛過(guò)程中始終保持這個(gè)加速度，那么它將在多少秒內(nèi)達(dá)到100公里/小時(shí)的速度？

本專(zhuān)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.D

3.A

4.B

5.A

6.D

7.B

8.C

9.C

10.A

二、判斷題

1.√

2.×

3.×

4.√

5.√

三、填空題

1.0

2.5

3.5

4.3

5.3

四、簡(jiǎn)答題

1.等差數(shù)列的定義：一個(gè)數(shù)列，如果從第二項(xiàng)起，每一項(xiàng)與它前一項(xiàng)的差是一個(gè)常數(shù)，這個(gè)數(shù)列就叫做等差數(shù)列。通項(xiàng)公式：\(a_n=a_1+(n-1)d\)，其中\(zhòng)(a_1\)是首項(xiàng)，\(d\)是公差，\(n\)是項(xiàng)數(shù)。

2.通過(guò)二次函數(shù)的圖像判斷開(kāi)口方向：如果\(a>0\)，則圖像開(kāi)口向上；如果\(a<0\)，則圖像開(kāi)口向下。頂點(diǎn)位置：頂點(diǎn)的橫坐標(biāo)為\(-\frac{2a}\)，縱坐標(biāo)為\(\frac{4ac-b^2}{4a}