Sổ tay toán học của thầy Nguyễn Tiến Đạt Ôn thi tốt nghiệp THPT cấp tốc. Bao gồm các nội dung cHUONr. 1lAM s() . 000000 ........................ oo 00 .... · oo · ... . .. . .. 00 . ........ 00 00 ... 9 BAll. E>~O HAM 00 0000 00 00 .. . 00 0 .. 00 oo uo oo o .... .. 00000000 00 .. 00 00 .... . 0 00 00 00 00 o oooo oo ooo 00 00 .. 00 00 .. .... 00 00 .. 00 .. 9 BA12. sv BttN THitN 00 00 00 . .... ...... 00 00 .. 00 00 .............. 00 ..... ...... ....... 00 0 ......... . .. ...... .. ... OOoooo 1 1 DQng 1. Tit, cac 1o6ng don d~u (d hal An .. 00 0 0000 00 00 uoooooo 00 uoo 00 00 oooo 00 ooOO 0000000 .. 00 .. 000 A) BAI 8. PHlJONG TRlNH TI~P TU N .. ... oo ... ...... oo .. oo .. .. oo .. ........... , .. oo .oo, .. oo .. oo .. . oo ....... . 42 CHUONG , MU ·A •_OG ~JT .. . .... oo 00000000000000 0000 0000000000 00. 00 oooooooo · · 00 ... .45 BAll . CONG THlJC MO VA LOGARIT ..... oo .. oooooo•ooooooooo .. . oo.oo o oo oooo0000oo oo ... 45 BAI2. PT. BPT MO VA L()GARIT ............................................................................ 46 Dc;mg l. Pruong tri:lh mu ........ .. , .. ............................................ 48 Dong 2. Phuong t·inh logart ....................................................... 50 DO:lQ 3. Bot phi.Jong trinh mu ... . .. .. . .. .. .. . . .. .. .. . .. .. .. .. . ...................... 51 D~:mg 4. Bot phuong Mnh logartt ........................................................ 53 DQng 5. Prllor~ M~ oot prl1ong trlnh mO logarf+ cua m .............. 54 BAI3 BAI TOAN THI,IC Tf: LAI K£p ..................................................................... 56 CHVdNG .J. nu.JH KHQNG GIAN .......... .............................................. 59 BAI 1. KH6t E>A DISN ............................................................................................ 59 BAI2. H~ TfCH KH61 CHOP .... ......................................................................... 61 Dong 1. X6c dlnh di.JQC c hileu coo va dlen tlch day .. . .... .. .. .. . .. .. .. . 61 Dorg 2. n sO Kh61 chOp ....... · .. .... ...... .. ............... .... ...... . ..... .. .. .... .... ..c.. A BAI3. MAr cAu KH61 cAu .. .............. ............................................................... 66 BAI4.HlNHN61l KH61N6N .............................................................. 69 BAI5. HlNH TRV KH61 TRV ............................................................................... . 72 CHVdl~ 3: IGilvEN HAM VA TfCf1 PHAN ............................................. 74 BAll NGUY~N HAM ............................................................................................ 74 Dc:;.rg 1. BOng lguyen ham co b6n ........ ........... ................ 74 Dc;~rg 2 Nguyen ham tl1ng phon ................................................. n DQrg 3. 1\Jguyem ham dc:;.rg huu tl ......................................... ......... . 18 DQrg 4. Nguyen ham dol b1en dc:;.ng 1 . .. . .. . . . . . .. . . .. . .. . .......... 80 Dana 5. Nguyen hOm d61 bien dQng 2 .. ........... ... .... ... ... . .. .. .... .. .. . .. . . B 1 BAI2. TfCH PHAN ............................................................................................. 86 0Qng I Tich phOn d61 b1en dc;mg ... ................................................. 86 Dc;mg 2. Tich phOr d o1 bien dc,mg 2 . .................................................... 68 Dc:;.ng l. n,_., phon tung phon . . . .. .. . .. .. . .. . ... .. . .... . .. .. . .. . . .. . .. . . .. .. . 90 BAI 3. UNG Dl,lNG TCH PHAN ............................................................................. 91 BAI2. PT. BPT MO VA L()GARIT ............................................................................ 46 Dc;mg l. Pruong tri:lh mu ........ .. , .. ............................................ 48 Dong 2. Phuong t·inh logart ....................................................... 50 DO:lQ 3. Bot phi.Jong trinh mu ... . .. .. . .. .. .. . . .. .. .. . .. .. .. .. . ...................... 51 D~:mg 4. Bot phuong Mnh logartt ........................................................ 53 DQng 5. Prllor~ M~ oot prl1ong trlnh mO logarf+ cua m .............. 54 BAI3 BAI TOAN THI,IC Tf: LAI K£p ..................................................................... 56 CHVdNG .J. nu.JH KHQNG GIAN .......... .............................................. 59 BAI 1. KH6t E>A DISN ............................................................................................ 59 BAI2. H~ TfCH KH61 CHOP .... ......................................................................... 61 Dong 1. X6c dlnh di.JQC c hileu coo va dlen tlch day .. . .... .. .. .. . .. .. .. . 61 Dorg 2. n sO Kh61 chOp ....... · .. .... ...... .. ............... .... ...... . ..... .. .. .... .... ..c.. A BAI3. MAr cAu KH61 cAu .. .............. ............................................................... 66 BAI4.HlNHN61l KH61N6N .............................................................. 69 BAI5. HlNH TRV KH61 TRV ............................................................................... . 72 CHVdl~ 3: IGilvEN HAM VA TfCf1 PHAN ............................................. 74 BAll NGUY~N HAM ............................................................................................ 74 Dc:;.rg 1. BOng lguyen ham co b6n ........ ........... ................ 74 Dc;~rg 2 Nguyen ham tl1ng phon ................................................. n DQrg 3. 1\Jguyem ham dc:;.rg huu tl ......................................... ......... . 18 DQrg 4. Nguyen ham dol b1en dc:;.ng 1 . .. . .. . . . . . .. . . .. . .. . .......... 80 Dana 5. Nguyen hOm d61 bien dQng 2 .. ........... ... .... ... ... . .. .. .... .. .. . .. . . B 1 BAI2. TfCH PHAN ............................................................................................. 86 0Qng I Tich phOn d61 b1en dc;mg ... ................................................. 86 Dc;mg 2. Tich phOr d o1 bien dc,mg 2 . .................................................... 68 Dc:;.ng l. n,_., phon tung phon . . . .. .. . .. .. . .. . ... .. . .... . .. .. . .. . . .. . .. . . .. .. . 90 BAI 3. UNG Dl,lNG TCH PHAN ............................................................................. 91 DQng 1. Dii;ln tfch hinh chang .............................................................. 91 DQ TRONG KHONG GIAN OXYl ................................. 128 BAll. H~TOAD¢TRONGKH0NGG AN ......................................................... l28 BAt 2. TlCH CO HUONG VA CING DVNG .......................................................... 131 8AI3. PHUONG TRlNH MATCAU ....................................................................... l48 BAI4. PHUONG TRlNH MAT PHANG .................................................................. 15CI BAI 5. PHUONG TRlNH ElUONG THANG ............................................................ 157 BAI6. HlNH CHI(U KHOANG CACH ........... . ...................................... 165 8AJ 7. M¢T s6 D~NG GIAI NHANH CI,IC TRl KlIONG GIAN ............................ 167 BA1 8. PHUONG ?HAP TOA f)O HOA ................................................................ 170 DQng 1. Dii;ln tfch hinh chang .............................................................. 91 DQ TRONG KHONG GIAN OXYl ................................. 128 BAll. H~TOAD¢TRONGKH0NGG AN ......................................................... l28 BAt 2. TlCH CO HUONG VA CING DVNG .......................................................... 131 8AI3. PHUONG TRlNH MATCAU ....................................................................... l48 BAI4. PHUONG TRlNH MAT PHANG .................................................................. 15CI BAI 5. PHUONG TRlNH ElUONG THANG ............................................................ 157 BAI6. HlNH CHI(U KHOANG CACH ........... . ...................................... 165 8AJ 7. M¢T s6 D~NG GIAI NHANH CI,IC TRl KlIONG GIAN ............................ 167 BA1 8. PHUONG ?HAP TOA f)O HOA ................................................................ 170
Sta.r book- Chuyen gia sach luy'n thi C CJn" ~~ "~ ,., DAY DU cAc D~NG BAI HAY THI CUA BQ GIAO DI,JC I TOANHOC • A ,., ,., ON THI DAI HOC CAP TOC X01 T T THAY NGUYEN TIEN OAT LOI NOI DAU Chao cac em hQc sinh THPT, d~c bi~t Ia hQc sinh l&p 12 chuAn hi thi f)~i hQc Chi vai thang d€m nguqc d€n ki thi THPT QG 2021, hi~n t~i dang la giai do~n C\fC ki gdp rut, quy€t dinh trgc ti€p d€n di6m s6 cua cac em V &i nhfmg yeu cdu kh~t khe cua ki thi S~p t&i, cac b~n hQC sinh l&p 12 dang g~p phai "khling hmlng" v&i qua nhiSu mon hQc va ki€n thtrc phai ghi nh& DiSu d6 dfin d€n tinh tr~ng "hQc tru&c quen sau" va di6m thi thu thuemg chi dimg l~i a mtrc 5-6 Hi6u duqc nhfmg kh6 khan do, "Bq SA tay ki~n thii'c Chftt LU'f}'llg Nhftt" da duqc Thdy bien so~n va due k€t kinh nghi~m tU cac anh chi d~t 26-28 di6m thi f)~i hQc, giup cac em h~ th6ng ki€n thtrc ddy du hon, tang t6c giai ds thi va d~t di6m cao f)~c bi~t v&i mon Toan, cu6n sA tay Toan hqc - On thi D~i hqc cftp tfic" se la trq thu d~c lvc nhdt giup em btrt pha di6m 8+ ki thi THPT QG 2021: H~ th6ng ddy du cong thtrc va each giai cac d~ng bai di6n hinh xac sudt 90% xudt hi~n DS thi THPT QG C~p nh~t phuong phap giai nhanh m&i nhdt tang gdp ldn t6c d9 giai tr~c nghi~m, myo b(rt t6c dS thi v&i Casio, Vinacal Trinh bay ro rang, khoa hQc, dS tra ctru va vo cimg nho gQn, ti~n lqi on t~p Cu6n "SB tay Toan hqc - On thi D~i hqc cftp tfic" duqc thi€t k€ phu hqp v&i mQi d6i tuqng hQc sinh, ill hQc sinh gioi d€n mAt g6c dSu co th6 t1;r tra ctru dS dang! Hy VQng cu6n s6 tay se dBng hanh cfing cac Sl tU chinh phl)C canh CUa f)~i hQC cong! Than ai, ij119!1& cHUONr ' 1-lAM s(') BAll BA12 000000 oo 00 · oo · 00 E>~O HAM 00 0000 00 00 00 00 oo uo oo o 00000000 00 00 00 00 00 00 00 o oooo oo ooo 00 00 00 00 sv Btt'N THitN 00 00 00 00 00 DQng2 nm thaMs6d~ hOm s6 don dl$u tr€m mlend oo oo Dr q ip An A ~ o ., •., Cho hinh chop S.ABCD co day ABCD la hinh thoi tam goc o c~nh a, Bii5 = 120° Oic m~t phling ( SAB) va (SAD) cimg vuong goc v&i m~t day GQi M la trung di~m SD, th~ tich khfii chop S.ABCD la a : • Hay tinh khmlng each h tir M t&i m~t phling ( SBC) theo a A.h = aJm B.h = aJm C.h = 2J5a D.h = 2J5a 38 19 19 @( Ufl gild ) ChQn h~ tf\lc tQa d9 nhu hinh ve, Oz/ISA Khi do: J (a2 ) (2-a ) ( ) (-a4 ;4 J -;o J (-a - (a2 ; - J - (a O(O;O;O),A aJ3 D 0;( ~SB= ~ ;0;0 ,B 0-aJ3 ; ;0 ,C ~s ;o;2a ,M ;0;0 aJ3 ;a -aJ3 aJ3 -;-2a ,SC=(a;0;-2a),SM= ;-;-a 4 v~y d(M,(SBC))= J[:W,scJ.8MJ ams J[_JJ = SB SC 38 q Dap an A ' 179 J Cho hinh chop S.ABCD c6 day ABCD Ia hinh vuong c~nh a, SAB la tam giac d~u va n~m m~t ph~ng vuong g6c v&i m~t ph~ng day Tinh khoang each h ru di~m A d~n m~t ph~ng m~t ben (SCD) A h= affi ~ IJ)I D h= B h=a a.f3 1a1 ) a X ChQn h~ tf\lc tQa d9 c6 g6c t~i H , tf\lc hoanh la HA , tf\lc tung la HE , tf\lc cao Ia HS nhu hinh H(O;O;O) , A(-~ ;0;0), s( 0;0; a~J c(~ ;a;O} n(- a·a·o) 2' ' - ] =( 0;-a J3 -;-a [ -SC,SD 2J a3J3 ~ i[sc,Si5J.:4CI am V~yd(A,(SCD))= SC,SD =~= 3a 1[ JI ¢ Dap an B 180 -+a 1i) TOANTHfiY ~T Cho hinh lang ttv dtrng ABC.A'B'C' co m~t day ABC Ia tam giac vuong t~i B co AB = a,AC = aJ3,A'B = 2a GQi M Ia trung di€m cua AC Khofmg each tir M d~n (A'BC) Ia A aJ3 B aJ3 C 3a 2 D 3a Chn h~ tf\lc toa d9 nhu hinh ve Khi do: y X J r;:; (aJ2 a ;0 B(O;O;O);A(O;a;O);C(a'I/L;O;O);A'(O;a;2a);M - -;2 Taco: BA' = (O;a;a.fi);BC BA'.BC = (O;a J6;-a = (aJ2;0;0) Ji) = a fi (O;.J3;1) Khidophuongtrinh (A'BC) :J3y-z=0 aJ3 aJ3 Suyra d(M,(A'BC))= =- :> Dap an A 181 ABC.A'B' C' co m~t day la tam giac d~u c~nh AB = 2a Hinh chi~u vuong goc cua A' len m~t ph~ng (ABC) trimg v&i trung di~m H cua c~nh AB Bi~t goc gifra c~nh ben va Cho hinh lang tfl,l m~t day bing 60° Tinh khoang each tir di~m B d~n m~t ph~ng ( ACC'A') theo a la A J39 a 13 C 2J21 a B .Jij a Ch9n h~ t11,1c t9a d9 O.xyz cho: z X H(O;O;O) ,B( a;O;O),A( -a;O;O) ,c( O;a.J3;o ),A'( O;O;a.J3) Taco: AC = (a;a.J3;o) ; AA' = (a;O;av'3"); AB = ( a;a;O) V~y d(B,(ACC'A'))= ~ Dap anD 182 r;-;I( AC 1\AA')ABI =~a lAc AAA'I ho hinh chop tam giac d~u S.ABC c6 qmh day b~ng a GQi G Ia trQng tam tam giac ABC G6c giua dm'mg thing SA v&i m~t phing (ABC) b~ng 60° Khoang each gifta hai dm'mg thing GC vaSA b~ng A aJ5 B.~ C aJ5 10 D a.fi ~lillglill) ChQn h~ ttVC tQa d() Oxyz, v6i G 0, Ox= GA, Oy I INC, Oz = =GS (Hinh ve) z s B J- ( - = ( -aJ3 suy -GS = (O;O;a),GC ; a ;0 , AS= -aJ3 ;0;a l[ac,:4SJ.asl suyra d(SA,GC)= l>ap I[_JI oc,As J aJ5 =- an A 183 Cho hinh chop ru giac d~u S.ABCD c6 qnh day b~ng a, SA = a.fi Mla trung di~m cua c~nh BC G6c gifra hai m~t ph~ng (SDM) v6i (SBC) b~ng 2Jli M A arctan-110 B arctan-11 2M 2M C arctan-33 D arctan 11 , _ I :Y • Ch9n Mt111c t9a d{) Oxyz, v6i Ox = OC,Oy = OB,Oz =OS Khi d6 , D[o·-, aJ2 ·oJ , , M[aJ2 , aJ2 ,·oJ·s[o·o· , , , aMJ s(o·!!.-· , 2, o) ·, c(!!.-· ' o·, o) -BC (a-· ·0 a(2 1·-1·0 ) u ,· 2, 2, , , == 184 a ) =- a _ ii) TO~N Tli~Y D~T SC=[ ~;0;- a~)=~(l;O;-JiO)=~.v, n=[x,y]=(-6.J5;2.J5;-2) va k =[u,v]=(M;M;-1) ln.fl lnl-lfl cos rp =- - = di~n Cho tU J*tst ~ Suyra tan rp = 2M 11 >Dap an D OABC co OA, OB, OC doi map an D Cho hinh l~p phuang ABCD.A B'C'D' c6 dl) dai C!;inh b~ng I Gi M, N , P, Q l~n lugt la trung di~m cua cac C!;lnh AB , BC , C'D' va DD' Tinh th~ tich khfli tlr di~n MNPQ 1 B.- A.- 12 (& 1.0 24 C.8 I D.- glcit) D'=O Chn M tf\lc ta d9 Oxyz cho: Ox=D'A' Oy=D'C' Oz=D'D 189 A' _ B' X Khid6: A(1;0;1), B(1;1;1), C(0;1;1), D(0;0;1), A'(1;0;0), B'(1·1·0) C'(0·1·0) '' ' '' ) -MP= ( -1·-·1 -1J -MIQ= ( -1· · 1) Taco: -MN= (-1 -·-·o 2'2' ' '2'2' '2'2 1[- -J-1 = 4+8-8 =4 MN,MP MQ ~ VMNPQ 11 11 -J-1 ~ Dap an B =6.1 1[MN,MP MQ =24 .I 190