新高考數(shù)學(xué)二輪復(fù)習(xí)對(duì)點(diǎn)題型第13講二項(xiàng)式定理（學(xué)生版）

第13講二項(xiàng)式定理真題展示2022新高考一卷第13題知識(shí)要點(diǎn)整理知識(shí)點(diǎn)一二項(xiàng)式定理(a＋b)n＝(n∈N*)．(1)這個(gè)公式叫做二項(xiàng)式定理．(2)展開(kāi)式：等號(hào)右邊的多項(xiàng)式叫做(a＋b)n的二項(xiàng)展開(kāi)式，展開(kāi)式中一共有項(xiàng)．(3)二項(xiàng)式系數(shù)：各項(xiàng)的系數(shù)Ceq\o\al(k,n)(k∈{0,1,2，…，n})叫做二項(xiàng)式系數(shù)．知識(shí)點(diǎn)二二項(xiàng)展開(kāi)式的通項(xiàng)(a＋b)n展開(kāi)式的第項(xiàng)叫做二項(xiàng)展開(kāi)式的通項(xiàng)，記作Tk＋1＝.知識(shí)點(diǎn)三二項(xiàng)式系數(shù)的性質(zhì)對(duì)稱(chēng)性在(a＋b)n的展開(kāi)式中，與首末兩端“等距離”的兩個(gè)二項(xiàng)式系數(shù)相等，即Ceq\o\al(m,n)＝Ceq\o\al(n－m,n)增減性與最大值增減性：當(dāng)k<eq\f(n＋1,2)時(shí)，二項(xiàng)式系數(shù)是逐漸增大的；當(dāng)k>eq\f(n＋1,2)時(shí)，二項(xiàng)式系數(shù)是逐漸．最大值：當(dāng)n為偶數(shù)時(shí)，中間一項(xiàng)的二項(xiàng)式系數(shù)SKIPIF1<0最大；當(dāng)n為奇數(shù)時(shí)，中間兩項(xiàng)的二項(xiàng)式系數(shù)SKIPIF1<0，SKIPIF1<0相等，且同時(shí)取得最大值各二項(xiàng)式系數(shù)的和(1)Ceq\o\al(0,n)＋Ceq\o\al(1,n)＋Ceq\o\al(2,n)＋…＋Ceq\o\al(n,n)＝；(2)Ceq\o\al(0,n)＋Ceq\o\al(2,n)＋Ceq\o\al(4,n)＋…＝Ceq\o\al(1,n)＋Ceq\o\al(3,n)＋Ceq\o\al(5,n)＋…＝2n－1三年真題一、單選題1．若SKIPIF1<0，則SKIPIF1<0（

）A．40 B．41 C．SKIPIF1<0 D．SKIPIF1<02．在SKIPIF1<0的二項(xiàng)展開(kāi)式中，第SKIPIF1<0項(xiàng)的二項(xiàng)式系數(shù)是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．在SKIPIF1<0的展開(kāi)式中，SKIPIF1<0的系數(shù)為（

）．A．SKIPIF1<0 B．5 C．SKIPIF1<0 D．104．SKIPIF1<0的展開(kāi)式中x3y3的系數(shù)為（

）A．5 B．10C．15 D．205．（1+2x2）（1+x）4的展開(kāi)式中x3的系數(shù)為A．12 B．16 C．20 D．24二、填空題6．在SKIPIF1<0的展開(kāi)式中，SKIPIF1<0的系數(shù)是__________．7．在SKIPIF1<0的展開(kāi)式中，常數(shù)項(xiàng)為_(kāi)_________．8．SKIPIF1<0的展開(kāi)式中SKIPIF1<0的系數(shù)為_(kāi)_______________（用數(shù)字作答）．9．已知多項(xiàng)式SKIPIF1<0，則SKIPIF1<0__________，SKIPIF1<0___________．10．SKIPIF1<0的展開(kāi)式中的常數(shù)項(xiàng)為_(kāi)_____.11．在SKIPIF1<0的展開(kāi)式中，SKIPIF1<0的系數(shù)是_________．12．SKIPIF1<0的展開(kāi)式中常數(shù)項(xiàng)是__________（用數(shù)字作答）．13．SKIPIF1<0展開(kāi)式中的常數(shù)項(xiàng)為_(kāi)_______.三、雙空題14．已知多項(xiàng)式SKIPIF1<0，則SKIPIF1<0___________，SKIPIF1<0___________.【答案】

SKIPIF1<0;

SKIPIF1<0.15．設(shè)SKIPIF1<0，則SKIPIF1<0________；SKIPIF1<0________．16．在二項(xiàng)式SKIPIF1<0的展開(kāi)式中，常數(shù)項(xiàng)是________；系數(shù)為有理數(shù)的項(xiàng)的個(gè)數(shù)是_______.四、解答題17．設(shè)SKIPIF1<0.已知SKIPIF1<0.（1）求n的值；（2）設(shè)SKIPIF1<0，其中SKIPIF1<0，求SKIPIF1<0的值.三年模擬一、單選題1．SKIPIF1<0的展開(kāi)式中的常數(shù)項(xiàng)是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．202．“SKIPIF1<0”是“SKIPIF1<0的二項(xiàng)展開(kāi)式中存在常數(shù)項(xiàng)”的（

）A．充分非必要條件 B．必要非充分條件C．充要條件 D．既非充分也非必要條件3．SKIPIF1<0的展開(kāi)式中x項(xiàng)的系數(shù)為（

）A．568 B．－160 C．400 D．1204．已知SKIPIF1<0的展開(kāi)式中SKIPIF1<0的系數(shù)為10，則實(shí)數(shù)a的值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．25．二項(xiàng)式SKIPIF1<0展開(kāi)式中SKIPIF1<0的系數(shù)為（

）A．120 B．135 C．140 D．1006．若二項(xiàng)式SKIPIF1<0SKIPIF1<0的展開(kāi)式中只有第7項(xiàng)的二項(xiàng)式系數(shù)最大，若展開(kāi)式的有理項(xiàng)中第SKIPIF1<0項(xiàng)的系數(shù)最大，則SKIPIF1<0（

）A．5 B．6 C．7 D．87．SKIPIF1<0展開(kāi)式中SKIPIF1<0的系數(shù)為（

）A．SKIPIF1<0 B．21 C．SKIPIF1<0 D．35二、填空題8．在SKIPIF1<0的展開(kāi)式中，SKIPIF1<0的系數(shù)為_(kāi)_________.9．在二項(xiàng)式SKIPIF1<0的展開(kāi)式中，系數(shù)最大的項(xiàng)的系數(shù)為_(kāi)_________（結(jié)果用數(shù)值表示）.10．已知SKIPIF1<0的展開(kāi)式中SKIPIF1<0的系數(shù)是20，則實(shí)數(shù)SKIPIF1<0__________.11．SKIPIF1<0的二項(xiàng)展開(kāi)式中SKIPIF1<0的系數(shù)為_(kāi)_____.12．若SKIPIF1<0的展開(kāi)式中SKIPIF1<0的系數(shù)為10，則SKIPIF1<0______．13．在SKIPIF1<0的二項(xiàng)展開(kāi)式中，SKIPIF1<0項(xiàng)的系數(shù)是___________.14．已知SKIPIF1<0（n是正整數(shù)），SKIPIF1<0，則SKIPIF1<0________．15．在SKIPIF1<0展開(kāi)式中，含有SKIPIF1<0項(xiàng)的系數(shù)為_(kāi)_____．16．已知常數(shù)SKIPIF1<0，在SKIPIF1<0的二項(xiàng)展開(kāi)式中，SKIPIF1<0項(xiàng)的系數(shù)等于SKIPIF1<0，則SKIPIF1<0_______.17．在SKIPIF1<0的二項(xiàng)展開(kāi)式中SKIPIF1<0項(xiàng)的系數(shù)為_(kāi)_____．18．在SKIPIF1<0的展開(kāi)式中SKIPIF1<0的系數(shù)為_(kāi)_________.19．若SKIPIF1<0的展開(kāi)式的二項(xiàng)式系數(shù)和為32，則展開(kāi)式中x的系數(shù)為_(kāi)_____.20．已知SKIPIF1<0的展開(kāi)式中，僅有第5項(xiàng)的二項(xiàng)式系數(shù)最大，則展開(kāi)式中有理項(xiàng)的個(gè)數(shù)為_(kāi)__________．21．已知SKIPIF1<0且滿(mǎn)足SKIPIF1<0能被8整除，則符合條件的一個(gè)SKIPIF1<0的值為_(kāi)__________.22．SKIPIF1<0的展開(kāi)式中SKIPIF1<0的系數(shù)為_(kāi)_____（用數(shù)字作答）．23．己知SKIPIF1<0，則SKIPIF1<0________.（用數(shù)字作案）24．SKIPIF1<0的展開(kāi)式中的常數(shù)項(xiàng)為_(kāi)__________.25．SKIPIF1<0的展開(kāi)式中常數(shù)項(xiàng)