Tiêu đề 2b-Dap-an-De-thi-Toan-chung-CSP-2024.pdf ✅

BO GIAo DUC VA DAo TAo TRIIONG DAI HQC SI.I PHAM HA NQI KV THI TUYEN SINH LOP 10 TRI,ONG THPT CHUYT,N DAI HOC SI' PHAM NAM 2024 ot cnixnrnuc oAp AN-HrJdNc oAN crAr urON rnr: roAN lcuulrcy CAu Dip 6n Ei6m Bni I 3,0 a l'5 Ta c6: A tt-6Ji + lt+6J1= (:-€)'* (r.Jr) =(:-"E).(: +Ji)=e. VAy A':6':216. b 1r5 Gqi hai nghiQm cria phuong trinh x' +bx+c = 0 (1) la p, q. Theo dlnh li Vi-dt, tac6: p+q:-bvdp.q=c, Oeth6y:b:-(p+q). Do24b a c: - 523 n€n-24(p + q) + pq -- 523. Hay pq - 24p - 24q= - 523 e (pq - 2ap) - (24q-242):242 - 523 <+ p(q - 2a) - 24(q - 241 = 242 - tx <+@-2a)(q -24):53:1. s3 =(- 1).(-s3y*;. Kh6ng m6t t6ng qu6t, ta c6 th6 gi6 sri p < q. Suy ra q- 24 > p - 24 (**). Tt (*) vd (+*) suy ra p-24-l,q-24=53 p-24=-53, q-24=-l +) Xdt p - 24 : I vd q- 24: 53: Suy ra p:25 vd q:77. +) Xdtp -24 : -53 vdq -24 : - l: Suy rap : -29 <0 (Loai). Vqy phuong trinh (1) c6 hai nghiQm ld25 vit77. Bni 2 A D 1,5 B E
Hinh trdn c6 b6n kfnh bing 2 n6n diQn tich cria hinh trdn d6 ld Sr,inr, t.an: a.22. Vi ta l6y gid tr! cria r lit 3,14 r€rr Srinr,t.on: 3,14.4 =12,56. Do luc gi6c ABCDEG ld d u n€n tam gi6c OAB ld tam giric d u c6 canh bdnc) Suyra ,S,,, :)r*:*. vita 6ygi6tr!cria..6 ta Lz: n€n s,,, =1,73. Suy ra Srr.ruo =65*, -6.1,73 =10,38. Dod6p hinh trdn (mdu trlng) ndm ngodi lpc gi6c dOu ABCDEG c6 diQn tich le 12,56-10,38=2,18. Suy ra ph hinh tron (mdru trdng) ndm ngodi ng6i sao 6 ciinh c6 di6n tich ld 2,18.2= 4,36. Vay ng6i sao 6 c6nh c6 dign tichlit 12,56-q36 -8,2 (cm2). Bni 3 F B c D 3r0 a I 0 Do t'0 giitc AEMF nQi ti6p n€nAME - AFE. Do EF ll BC nAnAFE = ACB. Md tam gi6c ABC cdn t1i A n€nACB = ABC. Suy ra AME - ABC. V6y tri giric BDME littri giric n6i tiiip. Bdng c6ch chring minh tuong tu, ta c6 tri giitc CDMF lit tri gi6c nQi ti€p. b II0 Do tri giric BDME n6i ti€p n€nBME: BDE. Do DE ll AC n€nBDE: BCA. Do EF /l BC nAnBCA- EFA. Theo chr?ng minh d cAu a), ta c6 AME - AFE. Sr:y ra BME - AME. Do d6 MEld dudng phdn gi6c cta tam gi6c AMB. Sry ru Y MB = 4. EB E H
Ap dqng ttinh li Ta-ldt cho tam giitc ABC v6i DE I I AC, tu "0, Z = -DJ 'EBDB2 = ! suy ,u !! = + =1 ,a, MB : .MBDB2'' zMA. c I 0 Tri gi6c BDME nQi ti6p n€,n BMD - BED. Tri gi6c CDMF ndititip n6n CMD - CFD. Ggi 11 ld trung di mclc'aBD,suy raBH: HD: DC. Do tam gi6c EBD cdn tai E n6n EIl ld dudng ph6n giric cta BED, suy ra BED=2HED. X6t hai tam gi6c EDH vit FCD, ta co DE = CF (do CDEF li! hinh binh hdnh);EDH = FCD;DH: CD Suy ra A,EDH - LFCD (c.g.c). Do d6 HED = DFC. Bni 4 1,5 Dat a-*+JM va b=E -Jzou x Thay x : o - JM vdo b, ta .5, 6 : --J!L,- - J2oA a - t12024 hay (a - fiJ2o2a = 2209 - ab. )1rlo _ ^A N6u a I b $l J2024 = "u',-..uu . Ei6u ndy ld v6 li (vi Jzou as6 v6 ti, a-b 2209 --ab la sr5 rrrru ri do a, b ld cric sti nguy€n). Suy ra a = b vit a. b :2209 (l). a-D Tir (1) suy ra a : 47 hoSc a = - 47. Do db x-47 -Jzou uol" x-a7 -J2024 . Bii 5 l'0 Gid su trong 4t . Khid6 m+n+p-a5 0) Suy ra (o, -2)' +(a,-2)'z +...+(a4s -2)'z -(O-z)'z.m+(2-2)2,n+ (3 -2)'z. p - !7na p, do d6 4m+ p=65 hay p -65 -4m. Y Qy BMD = BED - 2HED - 2DFC = 2CMD.
ThaY P=65-4m vdo (1), ta c6: 45 = m + n + p = m + n + 65 - 4m - -3m + n + 65 = 3m - n - 20. (2) Tuong tu ta c6: (a, -3)' + (a, -3)' +...+(a45- 3)3 - (0- 3)'. m+ (2-3)3.n+ (3 -3)1 . p:)71n- n n€n -27m-n 180 hay 27m+n 280. (3) Tt (2) vd (3) ta c6 hC phuong trinh 3m- n =20 27m+ n=280=30m=300+z=10. V4y trong +S sO da cho c6 10 s6 bang 0.