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王亮同學(xué)善于改進(jìn)學(xué)習(xí)方法.他發(fā)現(xiàn)對(duì)解題過(guò)程進(jìn)行回顧反思.效果會(huì)更好.某一天他利用30分鐘時(shí)間進(jìn)行自主學(xué)習(xí).假設(shè)他用于解題的時(shí)間與學(xué)習(xí)收益量的關(guān)系如圖甲所示.用于回顧反思的時(shí)間與學(xué)習(xí)收益量的關(guān)系如圖乙所示(其中是拋物線的一部分.為拋物線的頂點(diǎn)).且用于回顧反思的時(shí)間不超過(guò)用于解題的時(shí)間. (1)求王亮解題的學(xué)習(xí)收益量與用于解題的時(shí)間之間的函數(shù)關(guān)系式.并寫(xiě)出自變量的取值范圍, (2)求王亮回顧反思的學(xué)習(xí)收益量與用于回顧反思的時(shí)間之間的函數(shù)關(guān)系式, (3)王亮如何分配解題和回顧反思的時(shí)間.才能使這30分鐘的學(xué)習(xí)收益總量最大? (學(xué)習(xí)收益總量解題的學(xué)習(xí)收益量回顧反思的學(xué)習(xí)收益量) 解:(1)設(shè). 把代入.得. .······································································································ 自變量的取值范圍是:.···························································· (2)當(dāng)時(shí). 設(shè).···················································································· 把代入.得.. .································································· 當(dāng)時(shí). ············································································································· 即. (3)設(shè)王亮用于回顧反思的時(shí)間為分鐘.學(xué)習(xí)效益總量為. 則他用于解題的時(shí)間為分鐘. 當(dāng)時(shí). .························· 當(dāng)時(shí)..············································································ 當(dāng)時(shí). .····································································· 隨的增大而減小. 當(dāng)時(shí).. 綜合所述.當(dāng)時(shí)..此時(shí).································ 即王亮用于解題的時(shí)間為26分鐘.用于回顧反思的時(shí)間為4分鐘時(shí).學(xué)習(xí)收益總量最大. ······················································································································· 查看更多

 

題目列表(包括答案和解析)

已知n是正整數(shù),pn(xn,yn)是反比例函數(shù)y=的圖象上的一列點(diǎn),其中x1=1,x2=2,…,xn=n,記

T1= x1y2,T2= x2y3,…,T8= x8y9;若T1=1,則T1 •T2 • … •T8的值是__________.(08衢州卷第16題改編)

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李明在一次測(cè)驗(yàn)中做了2道習(xí)題,請(qǐng)你判斷他是否都正確,若有不正確,請(qǐng)?jiān)诖痤}卷相應(yīng)題號(hào)后寫(xiě)上不正確,并寫(xiě)出正確的解答;若正確,則只在答題卷的相應(yīng)題號(hào)后寫(xiě)上“正確”即可
(1)解不等式組
1-
x+1
3
≥0(1)
3-4(x-1)<1(2)

由(1)得x≤2;
由(2)得x>
3
2

3
2
<x≤2

(2)計(jì)算
4
+(
1
2
)-1-2cos60°+(2-π)0

=2+2-1+1=4.

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20、為了了解初三年級(jí)某次數(shù)學(xué)考試成績(jī)情況,教導(dǎo)處對(duì)該年級(jí)若干名學(xué)生的成績(jī)進(jìn)行了抽查(滿分100分,分?jǐn)?shù)取整數(shù)).將所得數(shù)據(jù)整理后,畫(huà)出了頻率分布直方圖的一部分(如圖).所有數(shù)據(jù)共分六組.已知第一、二、四、五、六這五個(gè)分?jǐn)?shù)段的頻率分別是0.04,0.08,0.28,0.24,0.12,第二小組的頻數(shù)是4.
(1)補(bǔ)全頻率分布直方圖;
(2)這次被抽查的學(xué)生人數(shù)是多少?
(3)被抽查的學(xué)生中,及格率是多少?(大于、等于60分為及格)

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李明在一次測(cè)驗(yàn)中做了3道習(xí)題,請(qǐng)你判斷他是否都正確,若有不正確,請(qǐng)?jiān)诖痤}卷相應(yīng)題號(hào)后寫(xiě)上不正確,并寫(xiě)出正確的解答;若正確,則只在答題卷的相應(yīng)題號(hào)后寫(xiě)上“正確”即可.
①化簡(jiǎn)(
1
1-x
-
1
1+x
)÷(
x
x2-1
+x)

=
1+x-1+x
1-x2
×
x2-1
x
+
1+x-1+x
1-x2
×
1
x
=-2+
2
1-x2
=
2x2
1-x2

②解不等式組
1-
x+1
3
≥0(1)
3-4(x-1)<1(2)
由(1)得x≤2;  由(2)得x>
3
2

3
2
<x≤2

③計(jì)算
4
+(
1
2
)-1-2cos60°+(2-π)0
=2+2-1+1=4.

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(2012•泰州一模)王老師對(duì)本校九年級(jí)學(xué)生期中數(shù)學(xué)測(cè)試的成績(jī),進(jìn)行統(tǒng)計(jì)分析:
(1)王老師通過(guò)計(jì)算得出九(1)班,選擇題的平均得分是23.2分,填空題的平均得分是26.2分,解答題的得分是82.6分.則九(1)班數(shù)學(xué)平均得分是多少?(試題共三種題型)
(2)王老師對(duì)解答題第28題的得分進(jìn)行了抽樣調(diào)查,將所得分?jǐn)?shù)x分為三級(jí):A級(jí):x≥8,B級(jí):4≤x<8;C級(jí):0≤x<4,并將調(diào)查結(jié)果繪制成圖①和圖②的統(tǒng)計(jì)圖(不完整).
請(qǐng)根據(jù)圖中提供的信息,解答下列問(wèn)題:
①此次抽樣調(diào)查中,共調(diào)查了
200
200
名學(xué)生,將圖①補(bǔ)充完整;
②求出圖②中C級(jí)所占的圓心角的度數(shù);
③根據(jù)抽樣調(diào)查結(jié)果,請(qǐng)你估計(jì)我校1200名九年級(jí)學(xué)生中大約共有多少名學(xué)生對(duì)28題的解答達(dá)到A級(jí)和B級(jí)?

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