Đề tuyển sinh lớp 10 môn Toán năm 2023 - 2024 sở GDĐT Hà Nội

CHINH THIIC

GIAO DUC VA EAO rAO HA NOI ri, tnr ruvnN srNH LoP ro rHPT NAwI Hec2o23-2024

M6n thi: TOAN Ngdy thi: 111612023 Thdi gian lim bdi: 120 phft

bi6uthrlc O=#viB= *-1*'-f vbir>o,r*t Jr-l r-L 1) Tinh gi6 tri cta biiSu thrlc A ?,hi r = 9. r- 2) Chung minh B = +3-. {z+1 3) fim tdtch gi|tri ctra r de A.B = 4.

CAu II (2,0 didm) t) Gidi bdi todn sau bdng cdch lQp phtong trinh hodc h€ phwong trinh:

Theo kiS ho4ch, mQt phan xuong phai ldm xong 900 sin phAm ffong mQt sti ngiy quy tlinh. Thuc t6, mdi ngiy ph6n xudng da hm <tuoc n$du hon 15 s6n ph6m so vcri s6 sin phAm phii l1m trong mQt ngiy theo k9 ho4ch. Vi ttr6 3 nghy tru6c khi tri5t ttroi han, phdn xucrng da lim xong 900 san phAm. H6i theo kii hoach, mdi ngny phal xuong phai lim bao nhi6u san ph6m? (Gie dinh rang s5 s6n ph6m mn phdn xucrng ldm tlucy. c trong mdi ngiy li blng nhau.) 2) MOt ttrOi gO dang hinh tru c6 b6n k(nh t16y ld S}crnvi chi6u caold l20cm. Tinh tne tfcn cria khiii gd d6(liiyn=3,14).

CAu IfI (2,5 diiim)

*-3Y=7

*. 2y =B 1) Giei hO phuong fiinh

2) Trong m{t pheng bq dQ Ory, cho parabol (P), A = rz vdduong mang (d) : y = (m + 2)r - m. a) Chrmg mirh (d) ludn clt (P) t4i hai <li6m phAn biet. b) Gqi r, vd, rr li hoinh tl6 c6c giao di6m cria (d) ve (P). Tim t6t ci giltti cua m di) a*a= . 1 frt fr, rr+ rr-2

Cf,u IV (3,0 didm) Cho tam gidc ABC c6 ba g6c nhen (,4,B < AC), nQi titip tlucrng trbn (O)" Tii5p tuyiSn tai ditim A cta tluong trbn (O) cit dulng thtng BC tai di6m ,S. Goi 1 ld chAn dudng vu6ng g6c k6 tr) tfi6m O dlnduong thtng BC. 1) Chung minh tr? gi6c SAOI ldt& gi6c ngi tiiip. 2) Ggi H vd, D lAn luqt ld chdn c6c dulng w6ng g6c k6 tu di6m A d6ncdc dudmg thing SO vd ,9C. ^ Chtmg minh OAH = IAD. 3) Ve dulng cao CE cria tam gi6c ABC. Gsi Q li trung dii5m cria doan thing BE. Dutmgthhng QD cit ducrng thing AH tai di6m K. Chung rrrlnh BQ. BA = BD. BI vi ttudng thing CK song song vcri tlu<mg

thlng SO.

Cdu V (0,5 cti€m)

Cho hai s6 thyc ducrng a vd b th6a mdn a +b <2. Chrmg -irh ,o' , * -!-.1. a'+b b"+a --------rffir Cdn bQ coi thi khdng gidi thtch gi thAm. Hqt6nthisinh:... ........S6b6odanh:, Hq t6n vi chfi kf cria ; il;;i ;i5 i; Hs ten vd cht ki cria c6n b0 coi thi sri 2: