BÀI TÂP CẢ NĂM 6 ĐẾN 9

.·~- \ l - ' BAI T.AP TlJA.N ? \d CANAM ! ~· T , s" G xao VIen: ·····~oo:.•···~·•o•••••oe•••••• - = - => ~ - = - => = -=-=DC AC DC 4 7 30 40 (em );DC= (em) => BD = 7 · · { AC.lAB b Tam giac ABC vuong tai A nen => DH II AC DH.lAB " DH: ;: BD D·-H = -24 ' ABC co' DH /l AC nen-·==-.·-·=> T amg1ac AC BC Tam giac AliD vuong t?iH c6 _A; = 45° =>.1 AHD can t?i H => AH = DH 24 r;:; =>AD =AH +DH =-.v2(cm) Bai6 a AM =9 em; CM = 6cm · b BN Ia phan giac g6c ngoai g6c B cua tam giac ABC => NC = BC => NC = 10 =>NC= 0(cm) NA AB AC+NC 15 TUAN24 Bai x: tu6i each day nam (x E N*) => tu6i my d6: 5x c:> Tu6i illy va nam sau lfui luqt la 5x + va X + Phuong trinh: 5x + = 3(x + 6) ~ x = (tm} V?y hi~n 10 tu6i va my 34 tu6i Bai x: (km) la d9 dai quang duCm.g AB (x > O) c:> Vd\fdinh: ~ (km/h); Vthvct~: ~(km/h) X X c:> PT: -+10=-¢> x==420 (tm) V?y quang duCm.g AB dai 420 km Bai x (m): CR cua HCN =>CD cua HCN: 320 68 2 x = 160 -x (m) Phuong trinh: (x + 2)(17_0- x)- x(260- x) = 2700 ¢>X= V~y Bai x: 70 (tm) CR cua HCN la 70m va CD la 90m , S6 tfun tham len rna xi nghi~p d?t theo hqp d6ng (~EN*) Phuang trinh: 21 x -x=24¢) x=480 20 K~t lu~n: 480 tfun B~i 5· MBC (/) l\HIK theo ti ~6 k ~ 30 25 =i IK = 25cm·' HI= 15cm·' HK = 20cm · Bai PnEF = 22cm; PinK= 11 Ocm ¢ Bai HI= 18cm; HK = 24cm; IK = 36cm ! • Bai x: s6 tern thu (x TUAN25 EN*); s6 hi thu: 36- x Phuo-ng trinh: 500x + 100(36- x) = 11600 x = 20 V~y Bai c6 20 tern thu; 16 hi thu v to thu nh§t X (Ian/h) (x > 0) => v to thu hai =X+ (km/h) PT: ~ x = 3(x+8) ¢) x = 48 ~ K~t lu~ Bai X (h) la thai gian hai d9i cling lam d~n s6 diy l?i cua d9i I g~p d6i d9i II (x > 0) ¢ : PT: I 000- 120x = 2(950- 160x) ¢> x = 4,5 (tim)=> K~t lu~ Bai a 6ABC (/) l\DEF theo ti s6 b L\DEF (/) MBC theo ti s6 _!_ Bai a AB = 12cm; AC = 18cm; BC = 24cm 69 DE=!._ DF AB 4' AC -8.15.-= A -~ =.!_ EF =_!_=> LillEF (/) MBC 4' BC 10~~; · E= fJ ~ 4S ; fL= t - ~- 30° Bru a BC = lOcm; HK = 20cm b MBC (/) MllK theo ti s6 ~ TUANJ6 Biti Quang du 0) ¢ Thai gian luc diva luc v~ l§n luot Ia: ~ (gia) va ~ (gia) - ¢ PT: ~-~= Bai 40 36 60 50 ~ 50 40 x=l20 (tm) => K€t luau v th\IC cua ca no: X (kmlh) (x > 5) V xuoi: X+ (kmfh), V nguqc: X- (kmfh) c:> PT: 3(x + 5) = 4(x- 5) ~ x = 35 c:> B9 dai do~ AB Ia 120 kmlh Bai X (phut) la thai gian chay cua voi nuac 1~ (35 - x) (phut) la thm gian chay cua voi nuac nong c:> PT: 30x + 40(35- x) = 1250 ~ x = 15 (tm) c:> K€t lu?n Bai ilCBD ~ ilCAB(g.g) => CB2 =CA CD ¢ CA =CD+ DA = 16 (em)=> CB = 144 => CB = 12cm =>DB=~ BA Bai LlABC ~ ilDEF theo ti s6 k => AB = BC = k DE , - BM EN EF BC EF BC=2BMvaEF=2EN=> - = - = k => MBM c.n LIDEN => AM DN -= k Bai a 6.BCD (/) ilHCB (g.g) 70 BC HC BC DC DC BC b -=-=:>HC=-=9(cm) HD=DC-HC= 16cm c BH = 12cm Ke AK DC=> MKD = => AB = HK = 7cm => ~BHC SABcD = => DK = CH = 9cm => KH = 7cm · (AB + DC).BH 2 192 (em ) -~ ~: - TUAN27 b.x= ~ ' a x=21 B a1 c 5 25 x=12 Bai a PT ~ 8(x + 5) = 6(3x- 5) ~ x = 7' b, c, d tuang t1)' i x= Bai a PT ~ (3x + 2).(-3)(x- 3)(2x + 1) = ~ x=3 x= b, c, d tuang t1)' Bai x (km/h) la v~ t6c c~n tim (x > 0) ,-"., J -240 ( gw ' ) '-,/ t d1J loen: X 240 ~ ~ duong: ' V o~ to~ sau lrl-, wl tang: x + 10 (km/h) => t d"1 hJ.et quang - - ( gw 0 ' ) x+10 ¢ PT: 240 _ 240 = 20 x x+ 10 [x = 80 (tm) 60 x = -90 (loai) ¢> K€t lu~n Bai a MDC (/) ~BEC (g.g) b MDC (/) ~EC => - = - => AC.EC = BC.DC ¢ '' DC EC AC BC c 6DEC (/) MBC (c.g.c) Bai a DE= 15cm 71 > DE AE =- ~ DE AE b LlliAD c.n LlliBK (g g) c MDE c.n 1CKD (g g}-> AP.=~ => A.Q = ~ - EK BE KC CD DE+EK ·AE+BE KC AD => AD ~ DK = 20cm =KC AE· · · ~ d ScKD = 96 cm2 Bai a MHB b dBMD c c.n c.n 1CAB (g.g) -> BC = 15cm; AH = 7,2cm dBAC (g.g) BM ~ 7,5cm; HM = ~,1~m; 1BMD c.n L\BAC (g~~): ·=? BD = 12,5cm =>AD=3,5cm d E Ia tqrc tam L\BCD nen BE l_ CD ~ - ~ TUAN28 x=-2 Bai a PT ~ (-x-2)(5x-2)=0~ x= r b, c, d tuang t\I Bai a f)K.Xf): X f- 1; X f- -l PT (3x2 + 4x + 1)- (3x2 - 5x + 2) = x =.!_ (tm) b, c, d tuang 1:\f Bai a BKXD: x f- - 1; x -:f PT (x - 1)(2x2 + 3x + 4) = x =1 (tm) b, c, d tuang 1:\f Bai V ngu di xe d?p: x (kmlh) (x > 0) Phuongtrinh : 20 60 60 - x x+4 60 x 1+ - + =- ~ [x=20 x= - 36(/oai) v~ t6c luc di cua nguai d6 la: 20 kmlh 72 Bai BK // AH => AH = BK.AC 18 (m) BC , Dh A·A'B'C' Bm A ADC ( g.g ) nen " A'B' B'C' ==.k => AB = -A'B' (/.) o.nJ.J AB BC k , Bai Chieu cao cua cay la 22,5m TUAN29 Bai b, c, d tuang tv a Sai vi (a+ 2)- (a- 2) = > Bai a B~ khing dinh x L~y X , + :::; 10 + 2x sai thi x + > 10 + 2x ~ x < - == -10 => X + =- 8; 10 + 2x = - 10 va -1 < - d L~yx =- c L~y X=- 40 b Layx=2 Bai a x > Vx > x + 2013 > Vx b, c, d tuang tl,l' Bai a L~y vi dv a= 2; b = 1; c =- 4~ d =- b L~y vi dv a = 3; b Bai a = - c L~y a= 2; b = -3 d L~y a = - 5; b = - 4 MBI (/) f: HCI (g.g) b LillHC (/.) f: CHI vi Fi chung va HBC = ICH = 10em, -=> AI_AB {AI=3cm c Be IC : " ·' · BC IC=5cm Bai a MBH (/.) f: CAH (g.g) AB BH BM BH ~ m'm ~ b - = - · -=-=> MBM c AM C/) f: CAN (c.a.c) o d.t CN t~i K MBM (/.) f: CAN·' JJrC = 90°=>AM LCN 73 Bai a AB II CD; MHB (/) ABCD (g.g) b AH = AB => AH = BC.AB va )3D= 15cm > AH = 7,2cm BC BD BD _ _ _ _ _ -· -·- c MHB (/) LlliCD > HB = AH.CD =9, (em) => SAHB = BC ~ AH.HB =_34,56 (cm2) - ; : Bai a s= · TUAN30 b S ={xI x 3} T~p nghi?m cua cac BPT l~i: V~y BPT (2) khong tuong duong v6i cac BPT l~i Bai a S1 = {0; 1; 2} d s4 = b s2.= {O; ±I} e Ss = {0; 1; 2; 3; 4} C = Ai5E = Ki5B => L:lFBD (/) L:lFEC (g.g) {1; 2} c s~ = Bai a MBC (/) L:lAED (c.g.c) b c TLr y a va b thay vao ti Bai a C/m ABD s6.d6ng d?llg d~ tinh ED va FB = CED => MDB c.n.MCE(g.g) b MBD (/) L:lCED (g.g) c AD.AE=AB.AC } =>AD = AB.AC - DB.DC AD.DE =DB CD · Bai a AB = CD; AD= BC AB II CD=> AM/ICDvaMB II CD AD II BC=> AD 1/CN 74 {± 1; ± 2; 3; 4} AM II CD=> AM CD IA AD IC' II CN => -=-· AD CN IA IC · -=- => AM_CB_DM -AB CN DN AM CB AB va' CB co.t dinh => AM-CN kh"ong d _01 b -=-=>AM.CN=AB.CB·, AB ,, CN 1M IA · ID ID IC IN ? c -=-=-=>ID- =IM.IN IH AH IH HD lli IH HD AH ·• · · · d.-.- = - · - = - = > - + - = - + - :=!:.f - CD AD' AM AD · AM CD AD AD · 1 =>-+-=AM CD IH Bai a 2x- < - ~ 2x < - ~ TUAN31 x-2_ Bai Sxq = 2.(15 + 25).8 = 640 (cm2) V = 25.15.8 = 3000 (cm3) 75 Bai a: ThS tich cua bS: 1,2.2.1 = 2,4 (m3) b ThS tich cua nu6c: 60.20 = 1200 (I)= 1,2 m A cao cua •· , 1, = 0, ( m ) Ch teu m\fc nuac: 24 ' Bai a HS t\1' ch1lng minh b Stp = 2352 (cm2); V = 7760 (cm3) Bai a Di~n tich day:_2.3.4 = 24 (cm2) Di~n tich xung quanh: 6.2.(3 + 4) = 84.(cm2) Di~n tich toan phfui: 24 + 84 = 108 ( cm2 ) b V = Sda.y.h = 6.3.4 = 72 (cm3) - TUAN32 b, c, d tuang tt;r ' a -x+-< 2 -9 - x~ x< B at 70 b, c, d tuang tlJ Bai a ¢:::> ! x- x(2x- 1) > 25 - 2x(x + 3) -x - 2x2 +x+2x +6x>25 ¢!> ¢!> !~7 31 x> 3- HS tt.r biSu di~n nghi~m tren h~ t:rvc·tQa d9 b, c, d tuang tt;r , Bat4 a 3x + 16 X - X X X ~ +- ~ -x +2~ - + 58 425 X X ~ -x ~ - ¢) 100 x :::;;- 76 2x2 + x > 25- 2x2 - 6x b, c, d tuang tv Bai MBC vuong A=> BC = 3-Ji(cm) Sxq = 2.p.h = 24 + 12Ji (cm2) V = S.h = ~ 3.3.4 = 18 (em-') Bai Sxq = 3.4.10 = 120· (cm2); AH = Sday =.::! .AH.BC = 4J3 2J3 (em) (cm2) V = Sday.h = 40.J3 ( cm3) b Sxq = _(3 + + 5).9 = 108 (cm2) c Stp = Sxq + 2.Sday = 108 + 3.4 = 120 (cm2) Bai a BC = 5cm d V = S.h = ! 3.4.9 =54 ( cm3) Bai a B'MDN la hinh thoi :!· ; , TUAN33 Bai a Khi m 2>:.! thi A = - Khi m < m+1 ! thi A = 5m - b, c, d tuang tl! Bai a N~u 2x - < N~u 2x- ~ ¢> x < ~ thi J2x- 5J = - 2x + x = (tm) x ~ ~ thi J2x- 5J = 2x- x = (tm) b tucmgtt.r Bai a x ~ - 1; PT tr& 5- (x + 1) = 3x - 10 77 ¢> x = 3,5 (tm) X< - 1; PT tr& thrum + (x + 1) = 3x -10 ¢?X= (k thoa man) b, c, d tuong tt,r - - , B a1 I a X- 21-1 - X - 3X +.21 - [x-2 =-(xz -3x+2) x-2 =x -3x+2 b, c, d tuong tt,r b OA = Bai a AC = 10.J2 em J1l9 em c Trung do:;m SH = Stp = Sxq + Sday = d V = !._ S.h = Bai a AH = s.J2 em; SO = J94 em 20M+ 100 ( cm2) 100J94 (cm3) AB.Ji =6.J3 (em) V = !_ SABc.SO = 180 J3 (cm3) ' stp -B at 62 sxq + sday -3 • + - J3 - =36 + 9-vr:; - Bai a OA = Ji; SA= b V = c Sxq = => Sxq Jso + OA 2 (_em2_ ) =Jl94(cm) ! S.h = 400 (cm3) 4.Sm~tben = = - .sH.BC; SH = 13cm 260 cm2 78 TUAN34 b, 9, d tuong 1:lJ Bai a x~ 1; pt ¢> 3x- (x-1)"= X< 1; pt ¢> 3x +X- = ¢> x = ~ (lo~i) ¢>X= (tm) · b tucmg tg Bai a x~ x< j thipt ¢> 3x-5 = 1-2x ¢> x=% (lo?i) %thi pt ¢> -3x + = - 2x ¢> x = (lo?i) btuongtlJ · Bai a x2 < => S = {x 1- < x < 2} b, e, d tuong tv Bai Stp = Sxq + Sctay = :.fj ~ 3.30~25 + 30 = 1125 + 225.J3 (mm) v 1500 ' a V = S.h => l1 = -=-=12,5 Bm (em) s 120 b a, b la d9 dai day eua hinh h9p ehfr nh?t a.b =120 {a= 4.J6 => Sxo = 225-v6cmr; , s.J6 ' } => a :b = 4:5 b= Bai AC = 12em ,; i' ! Chu vi day = 36 em ' ¢ Stp = 2.p.h + 2S = 576 + 9.12 = 684 (em 2) V = S.h = l - ~ 9.12.16 = 864 (em"') 79 · Bfli a Hinh chop SABCD c6 day ABCD Ia hinh vuong G9i la giao diSm du SABCD la hinh chop d~~b _ V _,SAB=C=D- =_!_ VABCD.A'B'C'D' TUAN 35 Bai a y + 2y + ~ ~ y + 2y + + > ~ (y + I ) + ~ 2 Dung vi (y + 1? ~ Vy b, c, d tuong tv Bai a (m + I)2 > 4m; (n + I) > 4ri; (p + I)2 > 4p ¢ ¢ (m + 1) (n + I? (p + I? ~ 64mnp = 64 (m + 1) (n +I) (p +I)~ , b Ap d\ffig (x + y) ~ 4xy · {(a+b) > 4ab (ab+Ii ~ 4ab Dfiu ''=" xay ~ a= b va a.b = ~ a= b = , a x - , I m+n B al -+-~ ., ~ ., m n m+n ~ (m-n) ~ Bai a ~MIN mn m+n dung 'v'm,n > (/) L\KIP (g.g) b Vi L1MIN (/) L\KIP nen = MIMN ' IP NP 5cm· -=-=> • MNi = iPK Do-NI la phan giac cua g6c N => c NP , (m+n) -~4mn :MN1 = iNP MI - MN -:Ml+IP MN+NP 80 =>:Ml = MP.MN = ~ MN+NP Bai a 3+5 AEi5 = BEH =.AD£=> b MBE (/) ~CBD = ~=>:Ml = ~em 2 MDE can A (g.g) => AE.BD =BE.CD c AEKD la hlnh binh hanh Ma AE =AD nen AEKD la hinh thoi ' \ n i Bai a L1BHC (/) L1MBC (g.g) => BH.BC = CH.BM b BM = BN; HBN = HCD => L1BHN (/) L1CHD (c.g.c) => BHN = EH1) => DHN = 90° => DH L HN Bai a IC = 9cm; DC= DI + IC = 25cm; BD = 20cm BD + BC = DC => WCD vuong B -> BD l BC b SABcD = _!_(AB ~ CD).BI = 192 (cm2) KB KC KD KB c L1BCK (/) L1DBK (g.g) > - = - => KB =KD.KC l i d i ~ j ; ··~ i I :~ ' I 81 p, v ~· :: ... Tinh s6 cac g6c ngil giac I6i Bai 6: Tinh s6 cac g6c da giac 12 qmh Bai 7: Tinh s6 qmh cta m9t da giac bi~t rkg t6ng s& cac g6c cua n6 bing 360 ° Bai 8: Tinh s6 qmh cua m9t da giac bi~t rkg t6ng... 1: M6i khkg dinh sau dung hay sai? Vi sao? a)a + ~a- v6i m9i s6 thvc a b)3( a+ 2) ~ 3(a- 2)- v6i mQi s6 thvc a c)a-15~a-20 v6im9i s6 thvc a d)a(-a+2)~a(2-a) v6in:tQis6thgca Bai 2: Tim m9t gia... n = 24 ,6 ; p = 10 ,6; q = -31, b)B =(a-b )(b +c)+ b(b -a) v&i a= 0, 86; b = 0, 26; c =1,5 Bai 5: Cho riJY < 90 °, diem A nfun g6c d6 G9i B la diem d6i xilng v&i A qua diSm Ox, C la diSm d6i xilng