https //digital camscanner onelink me/P3GL/g26ffx3k 1 MUC LUC • • 01 Di 9D s61 • s{J GD&DT HA NOi 2022 02 Di 9D SO 2 • s{J GD&DT HAI PHONG 2022 03 DE 9D SO 3 • s{J GD&DT NGHE AN 2022 04 DE 9D SO 4 • s[.]
MU• C LU• C DE CIAI 01 77 06 88 11 102 16 114 21 06 DE 9D so • s{J GD&DT ale GIANG 2022 - L1 126 26 138 01 DE 9D 32 150 08 DE 9D SO - s{J GD&DT HOA a)NH 2022 36 163 09 DE 9D SO - s{J GD&DT THAI NGUYEN 2022 41 174 10 Df 9D SO 1O - SO GD&DT ViNH PHOe 2022 46 187 i 51 200 12 DE 9D SO 12 - SO GD&DT HA TiNH 2022-n L4:: 55 210 , ; 60 223 65 233 ' 70 244 > 74 01 Di 9D s61 • s{J GD&DT HA NOi 20 22 02 Di 9D SO • s{J GD&DT HAI PHONG 2022 03 DE 9D SO • s{J GD&DT NGHE AN 2022 04 DE 9D SO 4• s{J GD&DT NAM DINH 2022 - L1 05 Df 9D SOS • s{J GD&DT NAM DINH 2022 • L2 - so - sa GD&DT ale GIANG 2022 - L2 - - - - - 11 D( 9D S011 - SO GD&DT HA TiNH 2022 - - - \ 13 DE 9D SO 13 - SO GD&DT LANG SON 2022 • 14 DE 9D SO 14- SO GD&DT GIA LAI 2022 - - - - - _-_-_-_ = - 15 D( 9D SO 15 • SO GD&DT cA MAU 2022 BANGBAPAN I Đăng ký học https://studyinvietnam.net/ PHAN I: BE BAI , � • � ' ,· ,_ • ' i ; Đăng ký học https://studyinvietnam.net/ , Di LuviN Dl'M - s61 SO GD&f>T HA N(>I 2022 I Ciu 1: HQ tat ca cac nguyen ham aia ham so/( x) =- tren (0;+«>)la X I B I A.-,+C x· D lnx C ln x +C X , x +2 y+I z-3 = -=T°? Caul: Vecto naosau dayla mQt• vecto chi phuong cua duong th!ng - - = _2 B.;;; (-2;-3 D ii;3 C (32 ( -2; -; ;-l) A.u4 ; 1) 1;) ( ; ;) Ui Cau3: Trong khong gian Oxyz, cho ba diem A{2;0;0),B(0;3;0) va C(0;0;4) M�t phing {ABC) c6 phuong trinh D !.+l+.:.=I B �+l+.:=-1 A:.=l.=! C �+l+.:=o 234 234 23 23 Cau 4: Cho mJt cau c6di�n tich bing I 6,rcm • Ban kinh aia m�t cau bing A.4cm B 2cm C efii.cm D ✓3cm B x=l4 C x= II D x=l3 Cau S: Phuong trlnh l g1 ( x-5) =2c6 nghi�m la o A.x=7 ,3 ( =) S; ham so f'(x) lien h,lc tren do� (2;3) ) 1/ Cau 6: Cho ham so/(x)c6/(2=- f Khi f'(x)dx bing A.6 B Cau7: Vi a,b la haisoth1,1cduong tuyy, l g1 (a o o A3l g1 o a+lo g3 b b B l g a+f t g3 b o C ) bing C 3(log o D log3 b) D a+ lo g3 a+3l g3 b o Cau 8: Cho ham so /( x) c6 d(lo ham lien t\lc tren R va k la m()tsoth1,1c Khing dfnh naosau day sai? B f kf( x )dx=kff( x )dx A.J[/(x))�x=/(x) C C [Jf(x)dx]' =f( + J x) Cau 9: So giao die'm aia thj hamso = x4 -4x2 I voi lf\lc hoanhla y A.0 B C D Cau 10: Do thj cua ham so y = x3 -3x2 + la duong cong hinh naoduoi day? + , A J D f[J (x) +k)dx = f (x)dx + kdx T B -I C z -I D Trangl Đăng ký học https://studyinvietnam.net/ ioofLuviMoiic-,ot'iM"-™!��� tlu nhu hlnh v� �n Cau ll: Cho hAm 55 y /(x) ro dll thl 56 diem ' a /(x) IA D, A.I D C cau 12: Trong khOng glan Oxyz, cho dl�m M thoa M tlnic OM • ii+ i TQa d� diem M IA D (0;2;1) C {1;2;0) A.(2;0;1) D, (2;1;0) Cau 13 : Trong khong glan Oxyz, cho mt l cau ( S) co phllOng trlnh x + Jr + Z _ 2x + 4y-4z _ 27 • o TQa d� tam cua mt t cau ( S) la O J B.(2;-4;4) A.(-2;4;-4) C (l;-2;2) Cau 14: Cho ham so y = f(x) va ham so y=g(x)co thi nhu hlnh ve Di�n tfch S aia phan g�ch cheo hlnh ve tren duq c tinh bing cong thuc A.S = f 1/(x)-g(x�dx C S = J[f(x)-g(x)]dx D (-1;2;-2) B S =l![/(x)-g(x)], t D S = Jlg(x)- /(x)]dx • Cau 15: Ti�m c� dung aia thi ham so y = !.:!:.3._ co phuong trlnh D.x= -2x+I B x=.! A.x=-2 C.x=2 Cau 16: Trong cac khing dinh sau, khbg dinh naodung? A Ham so y = log X dong bien tren (O; +«>) B.Ham so y = log X nghtch bien tren (O; +«>) C Ham so y = log X nghtch bien tren R D Ham so y = log X dong bien tren R Cau 17: Cho ham so y = /(x) co bang bien thien nhu hlnh ve Ham soda cho nghtch bien tren khoang nao du6iday? B (-oo;4) A.(-oo;-2) D (0;+«>) C (-2;3) r(x) -� - -2 +>: -.-:-+ :: -:' -=0 + - /(1) Cau 18: The tich khoi tang nv c6 di�n tichday B = va chieu cao h = bfug A.32 B 24 C 14 D 42 Cau 19: Trong khong gian Oxyz, cho diem A(l;2;3) va m�t phing (P):x-2y+3z+2=0 Duong thing di qua A va vuong g6c v6i m�t phing (P) c6 phuong trlnh la: A.{::�:�21 z=3+3t B.i::��21 lz=3-3t C.i::�:+21 lz=3+3t Trang_ Đăng ký học https://studyinvietnam.net/ {x= l+t D y=2-2t z=3+3t !9_o_l_L�� _C�_!::-� !'�/ mlv HG-uvfH ciu& CH( au 20: Trong cac gioi hfl\ sau, gioi h,n NO blng 07 B lim( A.lim2" ¼)" C lim4" Ou 21: Cho n,keN• va n�k COnglhlic naoduoidlydung? A.c•• B c• = "' " A:I C " (n-A)IAI C c• " a "' (,i-A)I D C! =nl au 22: Cho ham s6' /(x) c6doo ham f'(x) = x(x-1) 56diem a.re tri cua hAm 5()dA cho la A �4 Cau 23: So phU"Clien hqp cua � phuc z =5-2/la A z=-S+2i B z==2+Si Cau 24: So c�nh cua hlnh lip phuong bing A B 12 - C.I n3 C z=S+21 D z=-5-2/ C D 10 C D=IR\{3} D D=(3;+«>) Cau 25: Tip xac dµili cua ham so y = (x' -27)' la A D=[3;-+;-5] C.(-5;-1) D.(-1;-too) Cau 43: Choham so y = f( x) c6 bang bien thien nhuhinh ve C6 bao nhieu gia tri nguyen cu.a tham so m thuQC do� [-10;10] de ham so h(x) =IJ(x)-ml c6 dung diem a.re tri ? A.18 B.21 C.2O D.19 /(x) Cau 44: Cho Iang trv ABC.A' B 'C' c6 di�n tich tam giac A'BC bkg 4, khoang each tir A den BC bkg 3, g6c gifra hai m�t phing (A'BC) va (A'B'C') bkg 30° The tich khoi Iang tn.i ABC.A'B'C' b�g C.3✓3 B.2 A.6 Cau45: Chohamso y=f(x).Dothj y=f'(x) tren [-3;0] nhuhinh ve sau (phan ducmg cong ctia thj Ia mQt phan cua parabol • f(Inx) y = ax2 +bx+ c ) Cho I -' dx = - , g1.a, trt /(0) b�ang e_, X A.2 B.-2 C.1 D.� STUDYINVIETNAM.NET Trang_ Đăng ký học https://studyinvietnam.net/ D.12 )' =-=-■-f lM lu '- THAYN\IUJtN\,ll� 1c) of L H �ttAC l)lt.M '- - - - - - - - - - - - -�":': s�� oi LUYlN 01tM - s6 sa GD&l>T HAI PHONG 2022 36,r Khi d6 thi!' Heh V cua khoi diu c6 rung ban kinh bing Ciu 1: Biel di�n tfch roa m�t clu bing C.36,r C.12,r A 4ir B 324,r Ciu2: Cho khoi chop co di�n tfchday bAng S va the tich bAng V Khi co chreu cao h cua khoi chopda choduvc tinh blog rong thuc nao dtroi day? 3V V V 3S B.h=- D.h=- C.li=- A.h=- S 3S s V , J , , I I J C.iu3: Biet /(x}n =-5 va g(x}n=3 Khido /[g(x)-2/(x)}u bing I B.-11 D.13 C.-7 Cau 4: Voi n la so nguyen duong y 16n hon 1, m� de nao duoiday dung? ( - ) ( - 2) A.A,;=2n B.A;= n n D.A;= n n t _ C.A;=n(n-1) 2 A.8 I I au 5: Neu J /( x}ix =4 va J /( x}ix =3 thi J /( x)ix bing A.-7 B.-1 C.7 C.iu 6: Cho ham so y= f (x) co bang bien thien nhu ;r hinh ve ben Ham soda cho nghjch bien tren khoang nao dum day? B.(3;-t«>) A.(-I;+oo) C.(-2;0) D.l f(:r) /(:r) + -2 - -1 - 0 + D.(-2;-l) thi d x+l y-1 z-3 Oxyz, d•A• A , dum "dAay khAong thUQC , duong , ang :-= - = 1em nao Cau 7: Trong khAong gtan • -2 C.Q(-7;-3;7) B.N(5;5;-t) D.P(-4;-l;l) A.M(2;3;1) 2 C.iu 8: Trong khong gian Oxyz, cho mijt cau (S) :(x+ 2) +(y- 3) +(z+1) =I.Tam cua mijt cau (S co tQa dQ la A.(-2;-3;-l) B.(2;3;1) C.(2;-3;1) D.(-2;3;-1) C.y'=.! D.y'=- - Cau 9: Tren khoang (0;+oo), d�o ham cua ham so y =log3 (3x) la ' ln3_ A.y = B.y'=- - X xJnJ Cau 10: Modun cua so phuc z=I -3i b!ng B 2✓2 A ✓IO X xln3 C.8 D.10 Cau 11: Cho khoi non c6 ban kinh day r = va clueu cao h =12 The tich cua khoi non da cho b�g A.l00tr B.300tr C.180JT D.60n Trang6 Đăng ký học https://studyinvietnam.net/ Cau 12: Tfp xacdinh cua ham sil y=(l- x)i la C.R B.R\{l} D.( «J;I) A.(l;-+«>) Cau 13: Trong khong glan Oxyz, cho m•t phAng (a): 5x-y- 4z + Vecto nAo duoi dlyIA ml)t vecto phap tuy�n cua (a)7 D.n4 a(-4;-1;5) c.;;;-=(5; -1;3) B.,rJ =(5;-l;-4 ) A.n, =(-1;-4;3) Ciu 14: Cho cap sl> �ng (11.) v6i u, = -2 vll u, = COng sal cua ci'p sc:S c◊ng di choblng A.3 B.2 C.-2 D.6 tat cA cac nguycn 4x la Mm cua ham s5 / ( x) = sin xHQ 15: Cau D.-cosx- x2 +C C.cosx-2x2 +C A.-cosx-2x2 +C B.cos.x- 4x2 +C Cau 16: Giao die'm cua tht ham s5 y = x, +3x + v6i tn,tc hoanh c6lQa di) la D.(0; 4) C.(-4;0) A.(1;0) B.(-1;0) Clu17: ChoMm SO y = f(x) li Cnl\lclml R vAc6 , _2 l x \ bang xet dau cua /'{ x) nhu hinh ve Sodiem J' (x) + o - o - o + C\fC ttj cua ham so /(x) la D.3 B.2 A.O C.l _.,, -1 :r Cau18: O,o ham so y = f( x) co bang bien thien nhu hinh ve Gia ttj C\fC d�i aia ham soda chobhlg B.3 A.I C.-1 D.O + - + y Ciu19: Biet di�n tich aia mi;>t m�t aia khoi lipphuong b3ng 16 Khi the tich aia khoi lipphuong d6b3ng B.16 A.256 C 512 D.64 "" "' 2x+l A : A u4 am so y= ' thangcop I'd a uong ' huong trlnh: Cau 20 : u:m � ngang cuad o Jl.�h' x+ l B.y=-2 A.y=- C.y=2 D.y=l r• A • Ciu 21: Trong khong gian Oxyz chocac vecto a=(-1;0;3) va h={2;2;5) Tich VO huong a.(a+b) b3 A.21 B.25 C.27 D.23 Cau 22: Xet tat ca cac so tlwc ducmg a va b thoa man log3 (�) = log 21 a+ I M�nh de nao duoiday d1 B.a3 =27b3 • C.b3 =27a3 • D.a2 =27b3 • A z z-IS ' • h"" ' A vacop an ao am o uncuasoph'uc + i b�ang Cau 23: Chosop "' h'u c z th'oa man z-I= • z-2i z- A.b2 =27a3 • M d A 2! ' "' Js C ✓2 D 2 Cau 24: Cho hinh l�p phucmg ABCD.A' B'C' D' c6 qnh bkg a (hlnh ve ben) Khoang each gifra haiducmg thfulg BB' va A' D la B ✓3 A A a✓3 B a C a✓2 D a✓2 Trang_ Đăng ký học https://studyinvietnam.net/ • C BA t YDA - - -L_��_Otl - - -c-9- o,tM - - -!./' · r mlv NGuvfN au6c cHf I i.m hQP n�n st.r lY d fng tfch phiiun 1c1 th Mn la , cap n Heh phin giii lhit!I cung ng a d\l ng y phuong phap doi bicn C�au 40• • Quan Siit cac • • Xet I= J sin 2.ef (cos2 x)dr = I � - O�t COS2 X =I, doi can: � -Vi phan ve ==> 2cosx(-sinx )dx = dt � -sin2xdx = dt O I I -Thay vao tich phan: / = ff(t)(-dt) = ff(t)d t = I et A= f /(1-x)dx - D�t I - X =I I ta c6 bang doi �: -Vi phan ve ==> -dx = dt O I I O X l I l -Thay vao tich phan: A= f-J(t)dt = ff(x)dx= +4 = • ChQD D• • Khi d6, ta c6: f[2f(1-x)-3x2 +5 }Ix= f2/(1-x)dx+f(-3x +S)dx = I I I O Cau 41 • De· 1$p phucmg trinhduongthclng ta can tim Diem va VTPT • Xet mit phclng (P) , mft phclng cluia � nen -Nh$n U4 =(1;4;-2) lam vecto chi phucmg - Nh$n A« = (1; 0;-1) lam vecto chi phucmg 2(2;1;0) �� A(3;1;-1)/ � •Dodo vecto phap tuyen rua mit phclng (P) la: n, =[U,1 ,U4]=(-4;-l;-4) =-1{ 4;1;4) • M�t khac mit phclng (P) di qua diem M ( 2; I; O) nen ta c6 phucmg trinh: 4(x -2)+(y-1)+4(z-0) = c>4x+y+4z-9 =0 • Ti.rd6, ta dtrQc a=4;b=4;c=-9 suy ra: a+b+c =4+4-9 =-1 ChQn C Cau 42 • Xet bat phmmgtrinh: I-log.! (x + 1) � log7 (mx2+4x+m) •D.KXD: mx +4x+m>0dung VxelR -1H1: Neu m=0⇒4x>0⇒x>O ⇒ sai vi XE R -1H2:Neu m.t:0,De'batphmmgtrlnhb�c2: mx2 +4x+m>O dung 'v'xelR m 2 ,1 < [16- 4m < c> m >4 [ > c> mO m>O Suyra m>2 (1) • Do bat phucmg trinh c6 nhieu log, ta dua cac log ve chung co so 2 BP T ¢=> log7 - Jog11 (x + 1) � log7 (mx2 + 4x + m) ¢=> log7 + log7 (x +I) � log7 (mx + 4x+ m) � lo g1[7(x +1)]� log7 (mx2 +4x+m) 7x +7 � mx2 +4x+m � (m-7)x +4x+m-7 � O luondung 'v'xe JR Trang_ 241 Đăng ký học https://studyinvietnam.net/ • Ta xet tnrong hqp -TIU: m-1 = m = ⇒4x SO x s O ⇒ Sai vi can \fx e R _ TIU: m -7 � O , De bat phuung trlnh b$c dung \fx e R A so 16-4(m-7} SO m -14m+45 � O mSS ⇒{ m-1 y'(O) (./l · Trang244 Đăng ký học https://studyinvietnam.net/ - GIAI CHI Tltt Df LUYtN DlfM - s6 15 SCI GD&DT CA MAU 2022 uANGoAPAN 2.B 10.B 3.B 9.D 4.A 8.A S.A 7.D 6.D 13.C 20.A 19.C 14.B 18.B 15.B 16.D 17.A tt.A 23.D 30.A 29.C 24.A 28.A 25.A 27.B 21.c 26.C 33.B 40.A 39.B 34.C 38.B 35.A 37.C 31.B 36.C 43.D 44.B 45.C 41.A ,., � l d· x-l y z+2 c6 mQt vector chi phuong voi tQa dQ chinh la mau so au t: • Du Tam 1(1;3;-2) Chqn A Cau 6: • T a c6 : Jf'(x)dt = J(x}I; = /(4)-/(1) ⇒ 17 = /(4)+12 /(4) = 17-12 /( 4) = Ch9n D Cau 7: • Quan sat BIT z 1-00 f(x) -2 + I II + + +oo -Ta thay: + O�o ham doi dau di qua ba die'm x= -2; x = va x=2 + Ham so lien h,lc tren R nen ham so ciing lien h,IC t�i ba diein x = -2;x = l va x = => Ham so c6ba diein a.re ttj Chqn D Trang245 Đăng ký học https://studyinvietnam.net/ • nl Ciu 8: • Nhic 1,i rong thuc chinh hop: A! = nl ➔ A' Chon A (n-k)! � ( n- 3) ! Cau 9: •Cong thuc tfnh dien tkh xung quanh hinh n6n: Sut =,rrl Chon D Cau 10: Debiet:diem nao thu(k m�t phing, ta thay toad x> log) Do ro so a=3 > I nen gift nguyen clueu bat phuong trlnh Chqn A =2-3i 1c1 thi"' et cung cap: C"au 29: • G·.1 , , z2 =2+1 {z• a Cach 1: Giai l\f luin • Co Zz = 2+; ⇒ Zz = 2-;, do: W =Z1Z2 +Z2 =(2-3i}(2-i)+2+i =4-6i-2i+3i +2+i =4-6i-2i-3+2+ i =3-7i a Cach 2: Barn may tinh • Bl: Nhan IModel+�:CMPLX QR.II • B2: Nh�p bie'u thuc z1 z2 +z2 =(2-3i}(2-i)+2+i vao may c· Luu y: De nh�p ; ta barn nut IEngI ) [-fi co D=R va y'=3x2 +1>_0 'vxe!R ⇒ �oaman -DapanB: y=x -x +2 c6 D=R va y'=4x -2x2!:0 O In e = log, e = I • Khi do: In (�) = In a-In e = In a-I ChqnB Trang248 Đăng ký học https://studyinvietnam.net/ r- - - · _, tn1H CH1c, Dlht IC)�-t:- - - - - - - - - - - - - � THAY NClMN QU6c CHI 1u32: •GQi d laduongth3ngdiqua M(t:2;-3 vav on u gg6cvoi (P):2x+4y-z+l2 = ) -Do d l(P) ⇒""I ln1r) ⇒ Duong thing d cot VfCP la 11,, =(2;4;-1) • Viy phuong trlnh duong thing d: x-t = y-2 = z+J ChQn B -I c •Ta o / (x) = 3x + co 33: sx U Ci ⇒ J{3x +cosx)dx = 3x 0 Cau 40: • Dfeu ki�n: { log2 x-2�0 e:> { X>0 log 4x�2 e:> { X>0 e:> { ⇒ x � I x�l · 4x�4 X>0 x • Ta xet phucmg trlnh: / (x) = (3 -27 h/tog2 (4x)-2 = l [ x [X =O l J x =3 3x X2 = Jx [ e:> e:> [ e:> X =3 log2 (4x)-2=0 log2 (4x)=2 4x = l x= l J _ -27x =0 X=I • M'a A!"' uieu kiA�n x�1, suy ra: [ x=3 Trang_ 250 Đăng ký học https://studyinvietnam.net/ • !9-�'-L_U)1�_(_!4_1_c_�!' � miv Neuvi;.-ou& , i • �p bang xet dau nhu sau: r 11 f(x) - OJ +oo + • D1,1a vao bang xet dau ta thay: f x) � o (:) X = I [ ( x�3 Do x e [-2022;2022)⇒ [3 s x s 2022 x=I • Viy bat phuong trlnh c6 tat ca 2021 nghi�m nguyen ChQnA Cau 41: • Xet bie·u thuc (i-z1 )(i-zi ) = ;2 -i.z, -i.z2+z,.z2 =-1-i(z, +z2 )+ z1 z2 (1) • Ta c6: z,' Z2 la nghi�m phuc cua phucmg trinh z2 - z + = z1+ z2 = -b = , Ap d\lllg c1jnh Ii Viet ta duc;,c: { _ c �2 z1 z2 - • Thay vao (1) ta duc;,c: (i-z1 )(i-z2 ) =-1-i l + 2= 1-i • Khi d6: [{i-z1 )(i-z2 )J = (-2) 1009 1·1 009 2°19 = (l-i) ° =(1-i) 19 2°18 (1-i) = [(l-i} J 009 (1-i) = (-2i) ) =-2• 009 - 2'009 1· ·2) =-2•009(1+ (1-1·) =-2•009J·(1-1·) =-2•009 (1-1 1009 (1-i) J019 la -21009 • V�y phan th1,1c cua so phuc [(; -z.)(i - Z2) ChQnA Cau 42: • GQi SO la ducmg cao cua hlnh non, thiet di� SAB la tam giac aeu c6 c.àm bg (hlnh ve) ã Dl,mg OH L AB (Do llOAB can t� nen H la tnmg diem AB ) Do SO.LAB ⇒ AB L ( SOH) ⇒ AB L SH ⇒ ((SAB),(Day)) = (OH,SH) = SHO = 60 ' ✓3 � • MAB deuc6c�bang4 ⇒ SH=4.-=2v3 • Xet MOH vuong t�i O: ° s S ✓3 2✓3 =3 sin60° = O ⇒ SO= SH • L� c6: MOB vuong t�i ⇒ OB=✓SB -Sa2 = ✓42 -32 = ✓7 (SB =; 4) ⇒ R = ✓7 (v&i R la ban kinh mijt day aia hinh non) • V�y the tich hinh non la: V =ẵ71'( ) = 771' ã Chqn C Tra1111 251 Đăng ký học https://studyinvietnam.net/ B A � Dti.uviN Cid