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人教A版选修2-2双基限时练1.docx

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马鸣风萧萧

高中数学学习材料

马鸣风萧萧*整理制作

双基限时练(一)

1．已知函数f(x)＝x2－2x上两点A，B的横坐标分别为xA＝0，xB＝1，则直线AB的斜率为( )

A．1 B．－1

C．2 D．－2

解析 斜率k＝f1－f01－0＝－11＝－1.

答案 B

2．物体的运动规律是s＝s(t)，物体在t至t＋Δt这段时间内的平均速度是( )

A.v－＝stt B.v－＝sΔtΔt

C.v－＝ΔsΔt D．Δt→0时，v－＝ΔsΔt

解析 v－＝st＋Δt－stΔt＝ΔsΔt.

答案 C

3．如果质点M按规律s＝3t2运动，那么在t＝3时的瞬时速度为( )

A．6 B．18

C．54 D．81 马鸣风萧萧 解析 ΔsΔt＝st＋Δt－stΔt

＝3t2＋6tΔt＋3Δt2－3t2Δt＝6t＋3Δt.

∴当Δt→0时，v－＝6t＝6×3＝18.

答案 B

4．某质点A沿直线运动的方程为y＝－2x2＋1，则该质点从t＝1到t＝2时的平均速度为( )

A．－4 B．－8

C．－6 D．6

解析 ΔyΔx＝－2×22＋1－－2×12＋12－1＝－6.

答案 C

5．下表为某大型超市一个月的销售收入情况表，则本月销售收入的平均增长率为( )

日期 5 10 15 20 25 30

销售收入(万元) 20 40 90 160 275 437.5

A.一样 B．越来越大

C．越来越小 D．无法确定

解析 计算每5天的平均增长率，然后加以比较知，平均增长率越来越大．

答案 B

6．设C是成本，q是产量，且C(q)＝3q2＋10，若q＝q0，则产量增加量为10时，成本增加量为________．

解析 ΔC＝C(q0＋10)－C(q0) 马鸣风萧萧 ＝3(q0＋10)2＋10－(3q20＋10)

＝3(q20＋20q0＋100)－3q20

＝60q0＋300.

答案 60q0＋300

7．函数y＝x2在x0到x0＋Δx之间的平均变化率为k1，在x0－Δx到x0的平均变化为k2，则k1与k2的大小关系是________．(填k1>k2，k1

解析 k1＝x0＋Δx2－x20Δx＝2x0＋Δx.

k2＝x20－x0－Δx2Δx＝2x0－Δx.

∵k1－k2＝2Δx，而Δx符号不确定，故k1与k2的大小不确定．

答案 不确定

8．已知曲线y＝1x－1上两点A2，－12，

B2＋Δx，－12＋Δy，当Δx＝1时，割线AB的斜率为________．

解析 ∵Δx＝1，∴2＋Δx＝3，Δy＝13－1－12－1＝－16.∴kAB＝ΔyΔx＝－16.

答案 －16

9．求函数y＝－2x2＋5在区间[2,2＋Δx]内的平均变化率．

解 ∵Δy＝－2(2＋Δx)2＋5－(－2×22＋5)＝－8Δx－2(Δx)2，

∴函数在区间[2,2＋Δx]上的平均变化率为ΔyΔx＝－8Δx－2Δx2Δx＝－8－2Δx.

10．比较函数f(x)＝2x与g(x)＝3x，当x∈[1,2]时，平均增长率的马鸣风萧萧 大小．

解 设f(x)＝2x在x∈[1,2]时的平均增长率为k1，则

k1＝f2－f12－1＝2，

设g(x)＝3x在x∈[1,2]时的平均增长率为k2，则

k2＝g2－g12－1＝6.

∵k1

11．在受到制动后的t秒内一个飞轮上一点P旋转过的角度(单位：弧度)由函数φ(t)＝4t－0.3t2(单位：秒)给出．

(1)求t＝2秒时，P点转过的角度；

(2)求在2≤t≤2＋Δt时间段内P点转过的平均角速度，其中①Δt＝1，②Δt＝0.1，③Δt＝0.01.

解 (1)当t＝2时，φ(2)＝4×2－0.3×22

＝8－1.2＝6.8(弧度)．

(2)∵ΔφΔt＝φ2＋Δt－φ2Δt

＝42＋Δt－0.32＋Δt2－6.8Δt

＝4－1.2－0.3Δt＝2.8－0.3Δt，

∴①当Δt＝1时，平均角速度为ΔφΔt＝2.8－0.3×1＝2.5(弧度/秒)；

②当Δt＝0.1时，平均角速度为ΔφΔt＝2.8－0.3×0.1＝2.77(弧度/秒)；

③当Δt＝0.01时，平均角速度为ΔφΔt＝2.8－0.3×0.01＝2.797(弧度马鸣风萧萧 /秒)．

12．已知三个函数f1(x)＝2x，f2(x)＝x2，f3(x)＝2x.

(1)指出三个函数在[0，＋∞)上的单调性；

(2)取x1＝0，x2＝2，x3＝4，x4＝6，Δx＝2.

求三个函数分别在区间[xi，xi＋Δx](i＝1,2,3,4)上的平均变化率(列成表格即可)；

(3)分析三个函数在[xi，xi＋Δx](i＝1,2,3,4，…)上随自变量的增加，其平均变化率的变化情况．

解 (1)根据一次函数、二次函数和指数函数性质可知．函数f1(x)＝2x，f2(x)＝x2，f3(x)＝2x在[0，＋∞)上都是增函数．

(2)列表：

函数ΔyΔx区间 [0,2] [2,4] [4,6] [6,8]

f1(x)＝2x 2 2 2 2

f2(x)＝x2 2 6 10 14

f3(x)＝2x 32 6 24 96

(3)由上表可知：函数f1(x)＝2x随着自变量的增大，在自变量增量Δx都是2的条件下，各区间上的函数平均变化率都相等，这说明函数呈匀速增长状态．函数f2(x)＝x2在各区间上的平均变化率不相等，并且越来越大，这说明函数值随自变量增长的速度越来越快．函数f3(x)＝2x在各区间上的平均变化率不相等，并且越来越大，这说明f3(x)的函数值随自变量增长的速度越来越快，并且比f2(x)的增长速度快的多．

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基 础 夯 实

Ⅰ.用所给动词的适当形式填空

1．He was careless. If he ________ (put) the gold watch in a safe

place, he ________ (not lose) it.

答案 had put; wouldn't/shouldn't/couldn't/mightn't have lost

2．He's been away since last Sunday. If he ________ (be) here

yesterday, he ________ (attend) the concert.

答案 had been; would/could/might/should have attended

3．If you had posted the letter, Joan ________ (receive) it last

Monday.

答案 would/could/might/should have received

4．We didn't know her address. If we ________ (know) it, we

________ (send) a note to her.

答案 had known; would/could/might/should have sent

5．The suggestion that he ________ (invite) was rejected.

答案 (should) be invited

6．He gave the order that nothing ________ (touch) until the

police arrived.

答案 (should) be touched

7．It is strange that you ________ (misunderstand) me!

【名师一号】高中英语 Unit 16 Lesson 2 Name Stories双基限时练 北师大版选修6

【名师一号】高中英语 Unit 16 Lesson 2 Name Stories双基限时练 北师大版选修6

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Ⅰ.单词拼写

1．People suffered many (困苦) during that long winter.

答案 hardships

2．He gave a (生动的) account of his life as a fighter pilot.

答案 vivid

3．We should be fully aware of the (重要性) of television in shaping our ideas.

答案 significance

4．The (起源) of the word remains unknown.

答案 origin

5．Don't be dby the first failure — try again!

答案 discouraged

6．We must not be blind to the (痛苦) of others.

答案 suffering

7．An aamount of snow fell here last week.

答案 abnormal

8．He came up with an (极佳的) idea.

答案 admirable

9．Mozart's father found that his son had a mtalent.

答案 musical

10．This is a (特定的) tool for opening doors.

答案 specific

Ⅱ.单项填空

1．Her description about the man is still________in my memory.

A．vividly B. vividness

C. vivid D. expression

答案与解析 C 句意：她对那个男人的描述我还记得清清楚楚。根据语境应选用形容词作表语，故排除A(副词)、B(名词)、D(名词)三项。

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双基限时练(三) Unit 1 Part Ⅲ

Ⅰ.单词拼写

1．By the time the case comes to ________(审判)，he will have

spent a year in prison.

答案 trial

2. The kids watched as the coin ________(下沉) to the bottom of

the pool.

答案 sank

3. Two guards stood at the main ________(入口) to the cinema.

答案 entrance

4. The bomb ________(爆炸) in the centre of the city.

答案 exploded

5. There was much lively ________ (辩论) about whether women

should spend more time in the home.

答案 debate

6. Do you have enough ________ (证据) to prove that you are

right?

答案 evidence

7. The two groups met for ________ (非正式的) talks.

答案 informal

8. They were both experienced ________ (水手)．

答案 sailors

Ⅱ.用适当的介词填空

1．The man entered the room ________ the back door.

答案 by 2．Much ________ Mr. Lin's surprise, Miss Li alone got three

gold medals.

答案 to

3．Apart ________ his being late that morning, he also had bad

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双基限时练(六) Unit 2 Part Ⅲ

基 础 夯 实

Ⅰ.用括号内所给单词的适当形式填空

1．The ________ (warm) of the room made me sleepy.

答案 warmth

2．I could not see the road properly because of the ________

(dark)．

答案 darkness

3．Through his own efforts, Lang Lang's dream of becoming a(n)

________ (piano) came true at last.

答案 pianist

4．The old man is well-known as a(n) ________ (violin) in his

village.

答案 violinist

5．Be careful! A truck ________ (load) with supplies is running

downhill.

答案 loaded

Ⅱ.完成句子

1．这个方法听起来不错，但需要试验一下。

The method seems good but needs to be ________ ________.

答案 tried out

2．当那个女孩看到蛇时，她发出了一声尖叫。

When the girl saw the snake, she ________ ________ ________

________. 答案 let out a scream

3．虽然玛丽学习负担很重，但她并没有放弃她的爱好。

Although Mary has ________ ________ ________ ________，

she doesn't give up her hobbies.

答案 a heavy study load