500 bài toán cơ bản và nâng cao 5

NGUYEN DLfC TAN - IRAN THI KIM CUdNG N G U Y I N DLfC H A - TO THI YEN - LE THI KIM PHUCJNG - TRAN THI THANH NHAN 500 Bai toan ctf ban va nSng cao ( Tdi ban Idn tlui hai) 1dm = m 3dm = m 9dm = m NHAXUATBAN OAI HOC QUOC GIA HA NOI NGUYEN D C C TAN - TRAN THI KIM CLfCfNG NGUYEN DLfC HOA - TO THI YEN LE Till KIM P H U O N G - TRAN THI THANH NHAN 500 BAI ToA^' CO BAN vA NAN« CAO (Tai ban Ian thuf hai) NllA XUAT BAN OAI HOC QUOC GIA HA NOI LOT NOI DAU Quyen sach "500 bai toan ca ban va nang cao 5" gom cac bai toai di/ac bien scan nhSm giup cac em hoc sinh kha, gioi toan c6 mot tai liei on tap ren luyen toan nang cao ky nSng giai toan, chuan bi cho ca ky thi chon hoc sinh gioi toan cap tri/ang, cap huy^n (quan), cap tin] (thanh pho) Quyen sach di/ac viet bam sat noi dung ciia tC/ng dan vj bai hoc tronj sach giao khoa toan hien hanh MAC du da rat co gAng qua trinh bien soan, song chAc chAi khong tranh khoi thiou sot Chung toi rat mong nhan diigc y kien don] gop tCr ban doc Cdc tdc gii CHirONGI ON TAP VA BO SUNG VE PHAN SO GUI TOAH LIEN QDAN DEN Tl L | - BiNC mni VI DO mtH TICH 5 —+ — 19 11 8 7963 Iha = Ihm ON T A P : KHAI NIEM PHAN SO Viet va doc cac phan so phan gach cheo Hinh ve V// Viet phan so Viet Doc phan so Ta so Mau so //^ f/4i % a) Viot Cc^c thtfang dtrdfi dang phan so 8:5; 25 : 100; 16 : 27 b) Viet c^c so tii nhien sau phan so c6 mau so la 9; 15; Viet cac so Lfng v6i moi diem tren tia so B H C 1 ^ D E F ^ — I — I — I — I — v Viet so thich hcfp vao trong: a) b) = n • 246 18 = 100 570 Co qua cam chia cho ngi/oi Moi ngi/di di/oc bao nhieu phan qui cam a) Viet phan so Ian nhat c6 tong tijf so va mau so la 2006 b) Viet phan so b^ nhSi't c6 tong tiJf so v^ mau so la 2006 Giai Hinh ve 11 p rrr i ^ v// y// — a) b) Doc phan so Viet phan so Viet Hai phan s^u 12 Nam phan miioi hai 12 Bon phan tam w 8:5=- 25 : 100 = ? 15 25 100 16 : 27 = \ 14 a) b) = = B C -h -f- 14 \_ m" 27 r D 10 14 18 246 18 246| E F H \ — \ — \ 14 1 12 13 14 14 lol 1 1 100 1^ • A I—I Mau so ' TLif so 570 So phan qua cam moi ngiTdi diigc chia la: 2 : = - (qua cam) Dcip s6: - qua cam 2005 P*"'"' a) Phan so Idn nhat c6 tong tuf so vk mau so bang 2006 la: — b) Phan so be nhat c6 tong tiJf so va mau so bang 2006 la: 2006 ON TAP: KHAI NIEM PHAN SO Viet va doc c^c phan so phan gach cheo Hinh •^e Viet phan so Viet Doc phan so Tu so Mau so ^ T/7/ yy/ y// 1 i1 a) Viet cac thiiong di/di dang phan so : 5; 25 : 100; 16 : 27 b) Viet cac so tu nhien sau phan so c6 mau so 1^ 9; 15; Viet cac so lifng vdi moi diem tren tia so B D E F ^—\—h- H \ \- Viet so thich hop vao trong: a) = b) = n ^ 246 18 n 100 570 Co qua cam chia cho nguai Moi ngi/ai dugc bao nhieu phan qt cam a) Viet phan so Idn nhat c6 tong ttf so va mau so la 2006 b) Viet phan so b^ nhat c6 tong tuf so va mau so la 2006 Giai Hinh ve J ^ a) b) m % 12 Nam phan miidi hai 12 Bon phan tam 25 : 100 = a) b) 16 : 27 = ^—I—\ 14 = = 14 18 246 H' 18 246 lol lol 15 27 B 100 25 100 15 ' ?9 • 14 Mau so 8:5=- A Tijfso % I—h Viet Hai phan sau 1' Doc phan so ^ w^ Viet phan so D -f10 14 E F H 1 12 13 14 14 570 So phan qua cam moi ngUdi diigc chia la: 2 : = - (qua cam) , Bap s6: — qua cam 2005 ^ a) Phan so Idn nhat cd tong tuf so va mau so bang 2006 la: -— b) Phan so be nhat cd tong tiif so va mau so bang 2006 la: 2006 ON TAP: TINH CHAT CO BAN CUA PHAN SO a) c a c phan so toi gian la: 3' 50 30 b) P h a n so rut gon diioc la ' 36 10 50 50 : = Rut gon: — = ' 15 15:5 , 1x5 a) - = = — ; 6x5 30 ^, 10 10x6 60 b) — = = —; 7x6 42 b) 30 36 56 :7 63 : 202 : 101 5 : 101 II 56 63 202 d) 505 25 25 : 25 _ ^ 100 " 0 : ~ ' 216 _ : _ , ^ 270 " 270 : 54 5' 30 : _ 36 : " Giuf nguyen — = 5x7 6x7 col 00 Rut gon cac phan so sau: 25 , 216 ,, 202 a) b) —c) d) • 100 63 270 505 Q nu ' K' -' 50 30 Cho cac phan so: - ; - ; — ; — ^ 15 36 a) P h a n so nao toi gian? b) P h a n so' nao c6n rut gon diioc Hay rut gon phan so d6 Quy dong mau so' cac phan so sau: a) — va — b) — va - 30 10 Trong cac phan so' di/di day, phan so' so' nao bang — 80 20 80 80 50' 2' 100' 160' 4' 11 Tinh nhanh bang each rut gon: , 175xx 94 x2 5x , 346xx98xx25 a) b) 84 12 Tim cac phan so bang va c6 mau so la so tif nhien nho hon 22 112 • Giai 35 42 10 Cac phan so bdng phan so — la: 80 80 • • 2' 4' 160 5x3x6x7x3 11 a) x x =6 7x9x5 7x9x5 4x9x2 1 b) x x 36x8x5 4x9x2x4x5 4x5 20 cd: 12 Ta cd 84 84 :28 112 112:28 Vay cac phan so' can tim la: 6, 9_ 1^ 15 4' 8' 12' 16 20 ON TAP: SO SANK HAI PHAN SO 13 Dien dau (, =) vao d trong: •o^Di d)4n^ 5^—J 14 So sanh hai phan so' sau: 25 b) - va a) — va ; 75 100 15 Dien so' thich hap vao trong: < n 36 ^^^ < — 36 16 Viet cac phan so sau theo thuf tu" til be den Idn: , 19 a) - ; —; b) - ; — ; — 9 12 24 17 Vdi ba so tU nhien 8, 7, Hay viet: a) Phan so be hcfn b) Phan so Idn hcfn c) Phan so bang 18 Tim cac phan so Idn hon — va b^ hon — ma cd mau so la 54 27 BODE 17 ^i)e flu: HQC SINH GIOI BAC TIEU HQC TINH yTC^QlTC TCJOC / K h o a thi: 2003 - 2004 * C a u 1: (3 d i e m ) Tim tat ca cac gia tri cua cac chd sd a va b cho sd 3a57b vda chia het cho vUa chia het cho * C a u 2: (4 d i e m ) ^^ , ' 1997 2001 a) So sanh phan so: va 2005 2001 12 b) Viet tat ca ca phan so cd gia tri bang phan so' — cho moi * * * * phan so dd cd tU so va mau so deu la nhdng so cd hai chd sd C a u 3: (3 d i e m ) Cho bieu Ihdc: A = (x + 44,8) + (X - 43,1) + (x + 11 1) + (v - 39.7» + c^4 ^^4lJ Khoa thi: 2003 - 2004 *Cau 1: (5 diem) Cho bieu thdc: A = 235 x 106 - 24255 : (240 - a), vdi a < 240 1) Tim gia tri cua bieu thdc a a = 2) Tim gia tri sd tU nhien a de bieu thdc A cd gia tri nhd nhat Gia tri nhd nhat dd bang bao nhieu? *Cau2: (4 diem) Tim mpt so td nhien cd hai chd so, biet rang neu them chd sd vao xen gida hai chd so cua so dd thi ta duac sd mdi Idn ban lan so can tim dan vi * Cau 3: (5 diem) Cd giao Lan cd mdt so' quyen vd, cd da lan dem vd thddng cho cac chau hpc gidi Biet rang lan deu neu cd thddng cho cac chau them quyen nda thi se het — so' vd cua cd; lan thd hai neu cd thddng cho cac chau them mpt quyen vd nda thi se het — so' vd cdn lai cua cd; lan thd , ' ba cd dem — sd vd cdn lai sau hai lan thddng trUde vdi hai quyen nda thddng cho cac chau Sau lan thddng cd Lan cdn lai quyen vd Em hay tinh xem Idc dau cd Lan cd bao nhieu quyen vd? Moi lan cd thddng cho cac chau may quyen vd? * Cau 4: (6 diem) Hinh ve ben cho biet: ABCD la hinh chd nhat cd AB = 5cm; AD = 4cm Tia Ax vudng gdc vdi AB; SC cat AB d M 1) Em hay tinh tong difn tich tam giac ADM va BCM Khi S di chuyen tren tia Ax thi tdng dd cd thay ddi khdng? Vi sao? 2) Cho AS = 2,4cm Hay tinh dien tich cac tam giac SDC; SMD va di?n tich hinh thang AMCD 3) Mudn cho dien tich hinh thang AMCD = 16cm^ thi dp dai AS bang bao nhieu? 155 BODE 19 ^e (hi: HOC SINH GIOI BAC TIEU HOC • • TiNH loittiQ • ylm Khoa thi: 2003 - 2004 * Cau 1: (7 diem) a) Tim gia tri cua x bieu thdc sau: (627 - 138) : (x : 2) = 163 b) Em hieu ve hf thap phan nhd the nao? Trong h^ thap phan ngUdi ta dung nhdng chd sd nao de viet so? * Cfiu 2: (5 diem) a) Viet tiep ba so hang day so sau: 1; 3; 7; 15; 31; b) MOt so sau giam di 20% thi phai tang them bao nhieu ph4n tram so mdi de lai ddoc so cu * Cfiu 3: (3 diem) • Anh Long uong - c6c c^ phd den v^ pha them sCfa cho Aky cdc Sau lai uong them — coc c^ phe sCfa d6 roi pha them sCfa cho dAy coc, lai uong tiep — coc ca phe siifa n^y roi pha them sCfa cho ddy coc Cudi cdng udng het cdc ca phe sda Hdi anh Long uong nhi^u ca ph^ han hay nhieu sda han? * Cfiu 4: (5 diem) Cho tam giac ABC Hay ve cac each chia tam giac dd ba hinh tam giac cd di?n tich bang (trinh bay rd ca sd ba tam gi^c dd cd di^n tich bang nhau) 156 BO DE 20 (J)e this HQC SINH GI61 BAG TIEU HQC THANH PHO lfM,4 rn0J Khoa thi: 2003 - 2004 * Bai 1: (6 diem) a) Tinh nhanh) 25 X 20,04 + X 20,04 - 2004 x 20,33 + 2004 x 20,04 b) So sanh: 1 1 32 ^ r, 2003 A = — + — + — + — + — vdi B = 16 2004 * Bai 2: (4 diem) Tim so' cd hai chuf so, biet rang neu lay so' dd chia cho chd so' hang ddn vi thi duac thUdng la va du • Bai 3: (5 diem) Ban Yen cd mpt bd hoa hong dem tang cac ban cung ldp Lan Yen tang mpt nda bong hong va them mot bong Lan thd hai tang mpt nUa so bong hong cdn lai va them bong Lan thd ba tang mpt nda so' bong hong cdn lai va them bong Cudi cung cdn lai mpt bong hong danh cho minh Hdi Yen tang cac ban nhieu bdng hong? dau Yen Yen Yen bao * Bai 4: (5 diem) Cho tam giac ABC nhU hinh ve ben Biet H la diem chinh gida diem BC; BI gap ddi lA; CK gap ddi KA Hay so sanh dien tich tam giac IBH, dien tich tam giac KHC va di^n tich td giac AKHI vdi 157 BODE 21 ^£>e thi: HQC SINH GIOI BAG TIEU HQC TINH C^//r 4Q(0 'H^HIC Khoa thi: 2003 - 2004 A Trinh bdy vd chU viet: di^m B Kien thitc vd hi nang: 18 dl^m * Bai 1: (1,5 diem) Mpt sd tu nhien M chia het cho va la so cd 2004 chd sd Cho biet: A, B, C la ba sd' td nhien khac ma tdng cac chd sd cua M la A, tong cac chd so cua A la B va tdng cac chd sd cua B la C Tim C? * Bai 2: (4 diem) 16 1) I lay tim tat ca cac phan so' bang phan sd — ma moi phan sd d6 18 cd td sd va mau sd cd hai chd sd 2) Rut gon roi so sanh phan sd: va 3127 4473 * Bai 3: (5 diem) DTinh: r 12 no -1,75 10^ x 261 ^-^ 7 J 11 60 , X 11 2) Tim tat ca cac cap sd td nhien a va b cho J b a (Vdi < a < b) * Bai 4: (4,5 diem) 1) Mpt ngUdi di xe dap td A de den B dung gid da qui dinh Sau di 10km dau 40 phut, ngudi ay tinh rang neu tiep tuc di vdi van tdc nhu vay thi se sdm ban da dinh 24 phut Cdn neu giam van tdc di km/gid thi cdng van tdi B sdm 10 phut so vdri gid da dinh Tinh khoang each AB 158 2) Mdt cau b6 vao cda hang dinh mua loai but chi mau den, but chi mau xanh Biet rang sd tien mua ba but chi mau den nhieu han sd tien mua mpt but chi mau xanh va sd tien mua hai but chi mau xanh nhieu han sd tien mua nam but chi mau den Hdi gia tien mua mdt but chi moi loai la bao nhieu dong? (Biet gia tien mua mpt but chi khdng qua 1000 dong va la sd trdn tram dong) * Bai 5: (3 d i e m ) Cho hinh vudng ABCD, cac doan thang EI, FK, GL, HM song song vdi hai canh AB va BC cua hinh vudng ABCD tao cac hinh chd nhat ABIE, EIKF, FKLG, GLMH, HMCD Doan thang AC cat doan thang EI, FK, GL, HM lan lUdt tai cac diem P, Q, R, S (hinh ve) Cho biet dp dai doan thang AE = GH = HD = 1cm; EF = 1,5cm; FG = 0,5cm Hay so sanh tdng dien tich cac hinh APE, FQRG, va HSCD vdi tdng dien tich cac hinh PIKQ va RLMS 159 BO DE 22 ^e thi: HOC SINH G161 BAC TIEU HOC • a TINH • TCCAJ ^ixftcm^ Khoa thi: 2003 - 2004 * Cfiu 1: (5 diem) a) Tim hai sd tU nhien x va y lien tiep cho: x < 20,04 < y b) Cd mdt sd chd cai ghep lai vdi thanh: GIAP THAN, gid nguyen thd tu cac chd cai, sau dd thay cac chd cai zkz chd sd (chd cai khac thi chd sd khac nhau) cho thay xong ta ddoc mpt sd td nhien Idn nhat cd chd sd chia het cho ca 2; 3; Ghi lai each doc sd tu nhien em vda lap duoc * Cfiu 2: (5 diem) a) Tinh ket qua: i + 0,25+ ^ n 25.^ r ^ „ -rt«, ^ „ 45) + +- + 0,75 + + 50% + - -ãã 0,55 + -ô-v8 lOOy lOOj 1x2x3 b) DOi tuyen bdng da mi-ni cua huy^n M tham gia Hdi Khoe Phu Ddng cap tinh gom cac ban hpc sinh ldp va ldp Du dinh s6 ban tham gia dpi tuyen bdng da dang hpc ldp chiem 20% sd vien ca d^i nhdng cd mOt ban dang hpc ldp khdng tham gia ddae ma thay bdi mdt ban dang hpc ldp Khi dd sd ban hpc ldp tham gia dpi bdng chi bang 10% sd vien cua ca d^i Tinh tdng sd vien dOi M tham gia dd thi • Cfiu 3: (6 diem) a) Cd 24 hinh Ifip phuang dan vi, dp dai canh moi hinh lap phdong 14 1cm Ddng 24 hinh lap phuang dd xep (ghep) lai de duoc m^t hinh hpp chd nhat cd chieu dai 3cm, chilu rpng 2cm va chilu cao la 4cm - Em hay v§ minh hoa hinh hop chd nhat em vda xep ddoc - Tinh di^n tich xung quanh hinh hOp chd nhat dd 160 b) Mpt m^nh vudn hinh chd nhat, ngUdi ta md rpng chieu dai 40%, md rpng chieu rpng 30% Hdi dipn tich manh vudn tang bao nhieu phan tram? • Cfiu 4: (2 diem) Cho hinh ve Em hay chpn bdn sd tu nhien 1; 2; 3; di4n moi sd vao mdt d trdng cho hang ngang, hang dpe va dddng cheo deu cd du bdn sd tu nhien da cho Trinh bay va chd viet: diem BO DE 23 • e tltl: HQC SINH G l l BAC TIEU HQC TINH ^T3( 7a)c^ Khoa thi: 2004 - 2005 • Bai 1: (4 diem) Cho day sd: i2 ' 6i ' 1J_2 ' 2^0 ' — 30"" 1) Hay tinh tdng cua 10 sd hang dau tien cua day sd tren 2) So ^ cd phai 1^ mdt sd hang cua day sd tren khdng? Vi sao? 10200 • Bai 2: (6 diem) Cho bieu thdc A =- 13,8 : (5,6 - x) 1) Tinh gia tri cua bieu thdc A x = 4,91 2) Tim gia tri cua x A == 3) Hay tim hai gia tri cda x de thay vao bieu thdc, ta dUdc A < • Bai 3: (6 diem) Cung mpt luc, mpt d td di td A va mpt xe m^y di td B nguoc chieu ve den dia didm C d gida A va B C each A 160 km va each B 161 136 km Van toe cua to la 52 km/gid, cua xe may la 38 km/gicr 1) Hoi xe n^o d^n C trudc? 2) Hoi sau may gia khoang each giCfa hai xe dugc nit ngSn 71 km'' * Bai 4: (4 diem) Cho hinh thang vuong ABCD (nha hinh ve) AB = 6cm; AD = 12cm; BC = ? AD 1) Tinh dien tich hinh thang ABCD 2) keo dai cac canh ben AB va DC, chdng gap tai K Tinh dd dai doan KB BO DE 24 ^Z)/: flu: HOC SINH G l l BAC TIEU HQC TINH thdi gian 95 • IrU so thdi gian 166 • Chia s6' thcfi gian cho mpt so II VAN T C , QUANG DUdNG, TU6] GIAN • Van toe • Quang dUcTng • Thcfi gian CHl/dNG V: ON TAP I N T A P V E SO Tl/ NHIEN, PHAN s , S THAP PHAN, S6 DO DAI LLfONG • On tap ve so' tU nhien • d n tap v^ phan so • d n tap vd so thap phan • On tap ve dp dai va khoi Idpng • d n tap vk dien tich • On tap vk thd' tich • On tap ve thdi gian II d N TAP V6 CAC PHEP TINH Vdl CAC s TU" NHIEN, PI IAN S6, SO THAP PHAN • Phep cpng • Phep tn:^ • Phep nhan • Phep chia • Ndi dung hay sai? • d n tap ve cac phep tinh vdi so thdi gian III d N TAP Vfe HINH HOC • d n tap vk tinh chu vi, dien tich mot so hinh • d n tap vd didn tich, the tich mpt so hinh IV d N TAP VE GIAI TOAN MdT S DANG TOAN D A C B I £ T D A H d C • d n tap v^ bieu 25 B O D T O A N d N LUYgN MgC LyC 99 101 101 103 106 111 110 111 112 113 115 116 117 118 119 119 120 122 124 127 128 130 130 132 134 139 141 165 167 NHA XUAT BAN OAI HOC QUOC GIA HA NOI 16 Hang Chud'i - Hai Ba Tri/ng - Ha Noi Dien thoai:(04) 39714896:(04) 397 24770; Fax: (04) 39714899 Chiu trdch nhiern xuat bdn: Gidni doc : PHUNG QUOC BAO Tong bien tap :PHAM THI Bien tap Che bdn TRAM : TRAN THANH TIEN : CdNG TV SACH-TBGD DLfC TRI Trinh bdy bia : QUOC VlfiT Doi tdc lien ket xiid't bdn : rdN«; TY SACli-TBGD l)Cr TRi SACH LIEN KKT 500 bdi toan cd b a n va nant{ cao Ma so: 1L-138DH2009 In 4.000 cuon kho 16 X 24cm Tai Cong ty TNHH ln& bao bi Hi/ng Phu S5 xu§t ban: 309-2009/CXB/01-48/DHOGHN.ngay 15/4/2009 Qiryet dinh xuat ban s6': 138LK-TN/XB In xong va nop ILAJ chieu Quy 111/2009 ... 50 0 (m) Dien tich dam dat la 50 0 X 50 0 = 250 00 0 (m') = 25 (ha) Dap so: 250 00 0m' = 25 71 = 50 00 0m' Canh cua dam dat hinh thoi; 50 00 : = 1 250 (m) Chieu cao cua dam dat hinh thoi la: 50 00 0 : 1 250 ... chU nhat 1 45 So sanh: 37,37 x 59 59 .59 vA 59 .59 x 3737,37 Giai 138 a) 27 ,5 b) 25, 18 0 ,5 12 .59 0 d) 0, 25 X 19 25 2 75 46. 75 7, 25 ""10,3 21 75 7 25 74,6 75 0,100 43 139 a) 5, 4-2 .5+ 18,26 *> 13 ,5 = 31,76... 1, 85 Giai 146.a) 75, 65 25 15, 13 b) 11.16 21 3.72 06 06 15 147 a) 8.4 : + 56 , 75 = 2,1 = 58 . 85 148 + 56 , 75 b) 177.1 : - 16 .5 = 25, 3 - 16 ,5 = 8,8 Mpt gdi banh can nAng la: 2.04 : = 0,34 (kg) 15 gdi