Title 01-De-thi-tham-khao-mon-TOAN-Ky-thi-SPT-2025.pdf ✅

llc ttot TR DAI HO SU PHAM O DUC VA DAO TAO oc su'nn.lu tt,t Ngl KHAO 4 trang) + kzn, k ev, +f,,* ez. xi rsr oAxu clA rllc r-tlc xtr ruytx DAr rrec rrE cuiNu euv xlvr zozs udn, roAn Thoi gian tdn bdi: 90 phit (khOng kd thdi gian phdt ili.) Me dd thi: 075 A. TO TRTN PHIfU TRA LOI TRAC NGHIEM Phin I (4 di6m). Thi sinh td toi ti cdu I cldn cdu t 6. txii va n6i cau, thi sinh chi chon m6r phrong dn Ciu l. Tdt ci c6c nghiem cta phuong trinh cos 2x = 0 lA A.x:! 2 C.x =L4 s.r=i+kr,kez. o., =i+ kn,k e v,. a Ciu 2. X6t m6t diy c6c si5 16 c6 si5 hang tliu li 5, s5 hpg ",r6i li 2n I 3 (rL e N, n > 1), st5 lidn sau hon sti liAn tnrdc 2 don v!. T5ng c6c s5 hang crla diy sii AO Uing A. n(n + 4). B. (n - 1)(n + a). C. (n + 1)(n + 4). D. (n + 2)(n + +). Ciu 3. BAt phuong trinh c6 ctng tdp nghigm vdi b6t phuong trinh ndo sau dAy? A.xz -4x + 1> o. B.x2 -4x - 1> o. C.x2 -4x - 1< o. D.xz -4x + 1< o. Cfl u 4. Cho him st: y - f (x) c6 dqo him trOn m.. Bi6t hnm s6 y = f' (x) c6 dd thi nhu hinl b€n. Phrit bi6u ndo sau dAy ln ilfng? A. Him sti y = f(x) ttat cuc d4i tai x, = -2 vi dat cuc tiiiu tai x, = 1. B. Hdm sii y = /(x) dat cuc ti6u Qi hai tliiim z1 = -2 vd x, = 1. C. Him s5 y = /(x) ttat cuc dai tai hai di6m x, = -2 vit x, = 1. D. Him s6 y = f (x) dat cuc ti6u tai xr = -2 vi tlat cyc dai tai x, = 1. v = f'(x) Ciu 5. Ti6m c&r xi6n cta tld thi him sii y ="::;2 h A.y = x-7. B.y--x+1. C.y=x-2. D.y-x+2. CAu6.Chohims6y= f(x)li6ntyctr€nltth6amanlo/(x)dx:2"A,[l 161ax = 5.Gi6tricta tich phdn Il f @)arui"g A.7. B. -3. C.3. D. -7. Ciu 7. Cho hdm sity ='# Tdm tltii xtng cta dti thi him si5 ta ai6m nio du6i tl6y? A. M(-1; 3). B. N(3; -1). C. P(-1; 5). D. 0(-s;1). o o G),,-N,,7 x Trang 1/4 - Ma de thi 075
Cffu 8. Ngudi ta mu5n lim m6t chi ti6t m6y c6 dang khiii trdn xoay tao thenh khi quay hinh phing D quanh tn:c A, voi D li hinh gioi han boi parabol (P) vi tluong thing a, A li truc di5i ximg cta (P) (xem hinh ve minh hoa b€n). Bi6t a cit 1Pl tai hai tlir-im crich nhau 8 cm vd khodng c6ch tir tlinh ctia (P) d6n a bing 4 cm. Thi! tich chi ti6t m6y bang bao nhi6u? A. 4a cml. B, 8z cm3. C. 16z cml. D. 32r cm3 . Ciu 9. Trong kh6ng gian v6i hQ tga dQ Oxyz, cho m{t ph6ng (P):2x - 6y + 3 = 0. MQt vecto phip tuyiin cta (P) li A. d1 = (2; -6;3). B. i2 = (2;6;3). C. i, = (1; -3;0). O.in - (2;6;0). Ciu 10. Trong kh6ng gian v6i h€ toa tlQ Oxyz, cho di6m e(1;2;3) vd mdt cAu (S) c6 phuong trinh x2 + y2 + (z - 1)2 = 25. MOt tliiim M thay d6i trCn mat cAu (S). DQ dii tlogn thing lM lon nh6t h A.2. B. 13. C.8. D.28. Cf,u 11. Ban Long Phin II (2 di6m) , Thi sinh trd ldi cdu I , cdu 2. Trong m6i j, a1,b), c), d) o mii cdu, thi sinh chon tl ng hodc sai. Ciu L Cho him s6y - f(x) - x + L .. a)f'(x)=7-!,-,.,, b) Phuong trinh f'(x) = 0 c6 hai nghi€m phin biQt x --0vitx=2. c) Hdm s6 d6 cho c6 bnng biiin thiOn nhu sau: v' x -aD v -o 0 1 0+ +co +o ) 3 -1 +m d) Him s6 da cho c6 d6 thi nhu sau: -m v \ a4 ;(.: )c ..1a1 ,{0t .-./' y o x 1 Ciu 2. Trong kh6ng gian vdi hQ toa d6 Oxyz, cho duong thing d,:=+ = ii? vi mat phing (P): 2x - 4y - 4z * I = 0. X6t cic vecto i = (Z; Z; t) vl i = (7; -2; -2). a) d li mQt vecto chi phuong cria d. b) i kh6ng ld vecto ph6p tuyiin cria (P). c)i.i=+. d) G6c giiia dudng thing d vi mit phang @) le 630 (lem tr6n kilt quA dtln hing tton vi cta tl6). B. vlTT TRTN TOGTAY THI PhAn trI (1 rfi6m). Thi sinh rrd loi tir cdu I ddn cdu 4. Ddi voi mfii cdu, thi sinh chi viit kit Em, kh6ng trinh bdy suy luQn. CAu l. Thiing k6 si5 ngudi nhiSm virus trong vdng 21 ngiy d mQt c6ng d6ng, ngudi ta nhfln thAy s6 ngudi nhi6m virus vio ngiy thri t lA/(t) = 27t2 - t3.Taxemy = f(t) lnmQthnm s5 xdc tlinh tr€n [ ; 2l ] vn f'(t) le ttic dQ nhi6m virus t4i thdi di6m t. T6c d6 nhi6m virus l6n nhAt vdo ngdy thft bao nhi6u? \ Trang3l4 - Ma dC thi 075 t_ --/ CT
Ciu 2. Trong kh6ng gian v6i h6 toa d6 Oxyz, cho mtrt phing (P) tli qua tliim M(1; -1; 2) vi nhdn haivectod = (0; 1; -1),r) = (2;3; -2) lim c{p vecto chiphuong. Khoing cich ttr tli6m N(2; 1; 3) iltin m[t phing (P) li bao nhi6u? Ciu 3. MQt nghitn ctiu cho th6y c6 5o/o c6c tin nhin tr€n mQt mqng viSn th6ng X li tin nhin quing c6o. Trong cic tin nhin quing crio, 80% tin nhin c6 chria ch[ "sale". Trong cric tin nhin kh6ng quing c6o,2Yo tin nhin c6 chria ch[ "sale". Chon ngiu nhi6n I tin nhin tr6n mang viSn th6ng X. ni6t rang tin nhin d6 c6 chria chf "sale", xic su6t d6 n6 ti tin quing crio bing bao nhi6u (lim trdn k6t qud d6n hing phin trAm)? CAu 4. MdJ dodn tau gtim 3 toa d6 tr€n sdn ga. C6 t hdnh kh6ch lin luot t6n riu, m6i ngudi chon ng6u nhi6n I trong 3 toa. M6i toa tau il€u c6 tht chria d6n t hdnh khrich. Biiit ring toa tau nio cfing c6 it nh6t 2 henh kh6ch, x6c su6t d,5 m5i toa c6 dring 3 hdnh khrich ld bao nhi6u (ldm tron kiit qui d6n hdng phAn tram)? PhAn IV (3 ili6m). Thi sinh trd lai t* cdu 5 diin cdu 7. Ddi vai mii cdu, thi sinh vid qud rrinh vd kel qua suy luan. Ciu 5. Gini phuong trinh: logrx2 + log3x = 7. Ciu 6. Cho hinh lang tru d&ng tam giitc ABC.A'B'C'. Biilt ring ^48 = AC = 3,ETe = 120' vi sti