2. figure out算出，了解，明白，估计，推测

I can’t figure out what you want to say.

We must figure out how to solve the problem.

figure n. 轮廓，体形，画像，数字，形状

I could see a tall figure near the door.

What a fine figure of a man!

a great figure in history历史上的大人物

have a head for figures数字概念强的头脑

I’m not good at figures. 我计算不行。_{K^S*5U.C#O%下}

1. settle down安坐，安居，使安静，使镇静

She settled down in the armchair and began to read a book.

He finally settled down to his study. _{K^S*5U.C#O%下}

拓展：

The insect settled on a leaf. 一只昆虫落在一片树叶上

They settled the dispute among themselves. 他们自己把这个争端解决了。

考点例题：_{K^S*5U.C#O%下}

Something is disturbing him, so he can’t _______________________________(安下心来工作).

3. strike vt. /n. (strike-struck-struck/ stricken) _{K^S*5U.C#O%下}

(1)打； 敲；击； 袭击；划火柴

A terrible typhoon struck Shenzhen last year.

I struck a match and held it to his cigarette.

(2)突然想起；某种想法突然出现；给人留下印象

An idea suddenly struck me. = An idea occurred to me.

Her kindness struck everyone present deeply. _{K^S*5U.C#O%下}

拓展：辨析：strike, beat, hit

strike除了“打；击”的意思外，还有“攻击；袭击”之意；另外它可以指时钟的“报时”。

beat着重指用棍、棒等连续地打或击。另外，它还可以指“心跳、水浪拍打岸边”

hit一般指一次性的“打、击”

考点例题：

1)The criminal gang ____________________ the man so severely that he almost died.

2)I left immediately after the clock __________________________ twelve.

3)The girls put on their new dresses and got ready to __________________ the town.

4)What _______________ me was their enthusiasm for work.

5)___________________________ while the iron is hot.

2. worthwhile adj. 值得做的；值得出力的

I think teaching foreign language is worthwhile.

Her interest makes our efforts worthwhile.

This is a worthwhile cause.

拓展：辨析：worth, worthy, worthwhile

(1)worth只能做表语，后接名词或主动形式的动名词

The job is worth our efforts.

This novel is worth reading again.

(2)worthy既可以做表语，还可以做定语。做表语时后接名词或加个of后再接名词或不定式的被动形式；

He is a worthy winner. 他是个名副其实的赢家

She said she was not worthy to be my wife.

This book is worth reading.

=The book is worthy ___________________________.

=The book is worthy _________________________.

(3)worthwhile既可做表语，还可以做定语。做表语时后面接不定式或动名词。

It is worthwhile doing/ to do sth.

考点例题：

1)It’s __________________ much more than I paid for it.

2)Mr. Wang is a ____________________ gentleman.

3)His suggestion is ___________________ considering.

4)His suggestion is _____________________ of consideration.

5)His suggestion is ______________________ consideration.

6)The doctor decided it would not be ______________________ to continue the treatment.

1. wealthy adj. 富有的；丰富的

Around noon they arrived in Toronto, the most wealthy and biggest city in Canada.

拓展：

a wealthy land富饶的土地

a wealthy family富裕的家庭

to live a healthy and wealthy life过健康富裕的生活

wealth n. 财富

a man of wealth富人

考点例题：

His parents got rich by making money on the stock market, so he lived in a w_______ family.

8.(浙江卷文19)设a1，d为实数，首项为a1，公差为d的等差数列{an}的前n项和为Sn，满足+15=0。

(Ⅰ)若=5，求及a1；

(Ⅱ)求d的取值范围。

解析：本题主要考查等差数列概念、求和公式等基础知识，同时考查运算求解能力及分析问题解决问题的能力。

(Ⅰ)解：由题意知S6==-3,

A6=S6-S5=-8

所以

解得a1=7

所以S6= -3,a1=7

(Ⅱ)解：因为S5S6+15=0,

所以(5a1+10d)(6a1+15d)+15=0,

即2a12+9da1+10d2+1=0.

故(4a1+9d)2=d2-8.

所以d2≥8.[

故d的取值范围为d≤-2或d≥2.

7.(四川卷文20)已知等差数列的前3项和为6，前8项和为-4。

(Ⅰ)求数列的通项公式；

(Ⅱ)设，求数列的前n项和

6. (陕西卷理16文16)已知{an}是公差不为零的等差数列，a1＝1，且a1，a3，a9成等比数列.

(Ⅰ)求数列{an}的通项;　　

(Ⅱ)求数列{2an}的前n项和Sn.

解由题设知公差

由成等比数列得

解得(舍去)

故的通项

,

由等比数列前n项和公式得

5.(山东卷文18)已知等差数列满足：，.的前n项和为.

　(Ⅰ)求 及；

(Ⅱ)令(),求数列的前n项和.

[命题意图]本题考查等差数列的通项公式与前n项和公式的应用、裂项法求数列的和，熟练数列的基础知识是解答好本类题目的关键。

[解析](Ⅰ)设等差数列的公差为d，因为，，所以有

，解得，

所以；==。

(Ⅱ)由(Ⅰ)知，所以bn===，

所以==，

即数列的前n项和=。

4.(山东卷理18)已知等差数列满足：，，的前n项和为．

(Ⅰ)求及；

(Ⅱ)令bn=(nN*)，求数列的前n项和．

[解析](Ⅰ)设等差数列的公差为d，因为，，所以有

，解得，

所以；==。

(Ⅱ)由(Ⅰ)知，所以bn===，

所以==，

即数列的前n项和=。

[命题意图]本题考查等差数列的通项公式与前n项和公式的应用、裂项法求数列的和，熟练数列的基础知识是解答好本类题目的关键。