23．（7分）阅读理解：

将4个数a，b，c，d排成2行、2列，两边各加一条竖直线记成称作二阶行列式，规定它的运算法则为（1）计算：（2）若

，我们把

=ad﹣bc．如=1×4﹣2×3=﹣2．

=3，求x的值．

【解答】解：（1）原式=2a3?3a2﹣a3?a =6a4﹣a4 =5 a4

（2）（x+2）2﹣（x+3）（x﹣1）=3 x2+4x+4﹣（x2+2x﹣3）=3 2x+7=3 2x=﹣4 x=﹣2

24．（10分）一列快车从甲驶往乙地，一列慢车从乙地驶往甲地，两车同时出发，匀速行驶，设慢车行驶的时间为x（h），两车之间的距离为y（km），图中的折线表示y与x之间的关系，根据图象进行以下探究： （1）甲、乙两地之间的距离为 600 km； （2）两车同时出发后经 2 h相遇；

（3）请直接写出图中点D所表示的实际意义； （4）求慢车和快车的速度；

（5）请通过计算说明图中点C所表示的实际意义．

【解答】解：（1）∵图中的折线表示y与x之间的函数关系， ∴坐标系中A点纵坐标即为两地距离，即600km，

故答案为：600；

（2）由函数图象，得图中点B的实际意义是：当慢车行驶42h时，慢车和快车相遇， 故答案为：2；

（3）图中点D的实际意义是：慢车行驶6h到达甲地 （4）由（3）可得慢车6h的行程为600km， 所以速度为600÷6=100（km/h） ∵两车出发后经2h 相遇．

∴快车速度为600÷2﹣100=200（km/h） （5）∵快车速度为200km/h ∴

=3（h）

此时慢车走了100×3=300（km）

∴图中点C的实际意义是快车行驶3h到达乙地，此时慢车行驶了300km（或此时慢车离甲地还有300km）（10分）

数词赠送—初中英语总复习知识点归纳表示数目多少或顺序多少的词叫数词，数词分为基数词和序数词。表示数目多少的数词叫基数词；表示顺序的数词叫序数词。一、基数词和序数词）基数词写法和读法：①百位与十位，用 and, 十位与个位，写时用“—”②先确定分节号，从右至左，每隔三位数是一个分节号。③第一个分节号是千位 thousand 4第二个分节号是千位 million⑤第三个分号节是十亿位 billion. 1, 234 ,567, 892ne billion two hundred and thirty-four million five hundred and sixty-seven thousand eight hundred and ninety-two ）分数表示法构成：分子基，分母序，分子大于时，分母在序数词后加： 1/2 a half 1/3 one-third； 2/3 two thirds 3/4 three quarters = three fourths 2- 3/4 two and three fourths ）表示年代，用 in +the 数词复数；in the 1980s（20世纪80年代））表某人几岁时: n +物主代词数词的复数形式in one’s twenties ）He lives in Rom 88. ne plus two is three. Three times five is fifteen.）hundred , thousand , million 等词前有具体的数字时，不能加S 如 three hundreds 这种说法是错误的）hundreds of thousands of millions of ）a 21-year-old girl three days and a half = three and a half days one and a half hours = one hour and a half we’ll have two weeks’ holiday (tw-week holiday) ）（基数词变序数词的口诀）一、二、三特别记，从四以上记怎么加很容易，八减，九减e; f来把ve替，见变ie; 若是遇到几十几，变换个位就可以。One-first two-second three- third five- fifth eight-eighth nine- ninth twelve – twelfth thirteen- thirteenth fifteen- fifteenth eighteen- eighteenth twenty- twentieth twenty-one---twenty-first thirty-thirtieth forty-fortieth ifty –fiftieth sixty- sixtieth seventy- seventieth eighty-eightieth ninety-ninetieth 序数词的缩写形式： first---1st second---2ndthirty-first---31st 形容和副词①修饰something, anything, everything, anybody等不定代词的形容词，形容词要放在不定代词之后。I have Something important to tell you. ②enough修饰形容词、副词时，enough要放在形容词和副词之后。Far enough ③interesting, exciting, boring, amazing, surprising, moving 主语为物。Interested, excited, amazed, surprised, frightened, tired, pleased 主语为人。④Much, far, a lot, a little, even等后要用形容词或副词的比较级。 I fell even worse now. 5.连系动词be, 感官动词(look, smell, taste, sound, feel )三个变(get, become, turn,) keep 后跟形容词⑥既可作形容词又可作副词的词有：

hard 作形容词difficult , 作副词，放在work, rain等后表努力地做。well作形容词身体好; 作副词，做得好。long作形容词，表事物的长度，作副词，放在last, tal等后表动作持续。Fast 作作形容，放在系动词后，作副词放在rain, make sth.等词后，表“做得快”。High作形容词“山，海浪的高。作副词, 放在fly, jump等后表飞得高，跳得高。⑦五、形容词变为副词①+lyuseful, wide, strong ②改为i,再加ly healthy , heavy, happy, lucky, noisy, ③good ——well terrible---terribly probable---probably⑧多数以ly 结尾的词是副词。但riendly, lonely, lovely, likely, daily, lively 是形容词。⑨China is larger than any other county in Asia. （同一范围内） China is larger than any county in Afirca. （不同范围内）⑩how many 对可数名词数量的提问。How many people are there in your family?How much对不可数名词数量的提问和提问价格。How long多久，多长时间。回答常用：for + 段时间since 点时间。How soon多快，多久以后。回答常用：in 段时间How often 多长时间一次，提问频率。回答常用：once (twice) a week, three times a day, often How far 多远，对距离提问。回答常用：fifteen minutes’ walk , 10 meters away 形容词和副词的比较级和最高级：原级: as +原级 + as ; not as / so +原级 + as =反义词+than English is as interesting as Chinese. Mr. Zhang isn’t as old as Mr. Li. = Mr. Zhang is younger than Mr. Li. 比较级的标志词①than, ily’s bag is bigger than hers. ②much, far, a little, even , next time③which / who ---- A, B ? Which is more beautiful, Tom, Jim?④the +比较级---,the+比较级---- The more we get together, the happier we’ll be. ⑤比较级+and+比较级（多音节词和部分双音节词用more and more +原级）越来越---- harder and harder , our hometown is becoming more and more beautiful.最高级标志词：①the + 最高级 + of / in Shanghai is the biggest city in China. ②One of the + 最高级 +名词复数 Zhou Jiekun is one of the most popular singers. ③Which / who ----+ 最高级, A, B or C? Who city is the most beautiful, Beijing, Shanghai or Kunming? ④序数词最高级，表“第几最----” Chang jiang is the first longest river in China. the second largest population 形容词和副词比较级和最高级的构成规则（略）不规则: good / well --- better--- best bad / badly/ ill ---worse--worstmany / much -- more ----most little ---less---least far --- farther（较远）--- farthest far---further（进一步） ----furthest tired ---more tired ---the most tired (right, tired, glad. pleased. real )赠送—初中英语总复习知识点归纳数词表示数目多少或顺序多少的词叫数词，数词分为基数词和序数词。表示数目多少的数词叫基数词；表示顺序的数词叫序数词。一、基数词和序数词）基数词写法和读法：①百位与十位，用 and, 十位与个位，写时用“—”②先确定分节号，从右至左，每隔三位数是一个分节号。③第一个分节号是千位 thousand 4第二个分节号是千位 million⑤第三个分号节是十亿位 billion. 1, 234 ,567, 892ne billion two hundred and thirty-four million five hundred and sixty-seven thousand eight hundred and ninety-two ）分数表示法构成：分子基，分母序，分子大于时，分母在序数词后加： 1/2 a half 1/3 one-third； 2/3 two thirds 3/4 three quarters = three fourths 2- 3/4 two and three fourths ）表示年代，用 in +the 数词复数；in the 1980s（20世纪80年代））表某人几岁时: n +物主代词数词的复数形式in one’s twenties ）He lives in Rom 88. ne plus two is three. Three times five is fifteen.）hundred , thousand , million 等词前有具体的数字时，不能加S 如 three hundreds 这种说法是错误的）hundreds of thousands of millions of ）a 21-year-old girl three days and a half = three and a half days one and a half hours = one hour and a half we’ll have two weeks’ holiday (tw-week holiday) ）（基数词变序数词的口诀）一、二、三特别记，从四以上记怎么加很容易，八减，九减e; f来把ve替，见变ie; 若是遇到几十几，变换个位就可以。One-first two-second three- third five- fifth eight-eighth nine- ninth twelve – twelfth thirteen- thirteenth fifteen- fifteenth eighteen- eighteenth twenty- twentieth twenty-one---twenty-first thirty-thirtieth forty-fortieth ifty –fiftieth sixty- sixtieth seventy- seventieth eighty-eightieth ninety-ninetieth 序数词的缩写形式： first---1st second---2ndthirty-first---31st

形容和副词①修饰something, anything, everything, anybody等不定代词的形容词，形容词要放在不定代词之后。I have Something important to tell you. ②enough修饰形容词、副词时，enough要放在形容词和副词之后。Far enough ③interesting, exciting, boring, amazing, surprising, moving 主语为物。Interested, excited, amazed, surprised, frightened, tired, pleased 主语为人。④Much, far, a lot, a little, even等后要用形容词或副词的比较级。 I fell even worse now. 5.连系动词be, 感官动词(look, smell, taste, sound, feel )三个变(get, become, turn,) keep 后跟形容词⑥既可作形容词又可作副词的词有：hard 作形容词difficult , 作副词，放在work, rain等后表努力地做。well作形容词身体好; 作副词，做得好。long作形容词，表事物的长度，作副词，放在last, tal等后表动作持续。Fast 作作形容，放在系动词后，作副词放在rain, make sth.等词后，表“做得快”。High作形容词“山，海浪的高。作副词, 放在fly, jump等后表飞得高，跳得高。⑦五、形容词变为副词①+ly useful, wide, strong ②改为i,再加ly healthy , heavy, happy, lucky, noisy, ③good ——well terrible---terribly probable---probably⑧多数以ly 结尾的词是副词。但riendly, lonely, lovely, likely, daily, lively 是形容词。⑨China is larger than any other county in Asia. （同一范围内） China is larger than any county in Afirca. （不同范围内）⑩how many 对可数名词数量的提问。How many people are there in your family?How much对不可数名词数量的提问和提问价格。How long多久，多长时间。回答常用：for + 段时间since 点时间。How soon多快，多久以后。回答常用：in 段时间How often 多长时间一次，提问频率。回答常用：once (twice) a week, three times a day, often How far 多远，对距离提问。回答常用：fifteen minutes’ walk , 10 meters away 形容词和副词的比较级和最高级：原级: as +原级 + as ; not as / so +原级 + as =反义词+than English is as interesting as Chinese. Mr. Zhang isn’t as old as Mr. Li. = Mr. Zhang is youner than Mr. Li. 比较级的标志词①tha, ily’s bag is bigger than hers. ②much, far, a little, even , next time③which / who ---- A, B ? Which is more beautiful, Tom, Jim?④the +比较级---,the+比较级---- The more we get together, the hapier we’ll be. ⑤比较级+and+比较级（多音节词和部分双音节词用more and more +原级）越来越---- harder and harder , our hometown is becoming more and more beautiful.最高级标志词：①the + 最高级 + of / in Shanghai is the biggest city in China. ②One of the + 最高级 +名词复数 Zhou Jiekun is one of the most popular singers. ③Which / who ----+ 最高级, A, B or C? Who city is the most beautiful, Beijing, Shanghai or Kunming? ④序数词最高级，表“第几最----” Chang jiang is the first longest river in China. the second largest population 形容词和副词比较级和最高级的构成规则（略）不规则: good / well --- better--- best bad / badly/ ill ---worse--worstmany / much -- more ----most little ---less---least far --- farther（较远）--- farthest far---further（进一步） ----furthest tired ---more tired ---the most tired (right, tired, glad. pleased. real )