Tuyển tập 45 đề thi học sinh giỏi Toán lớp 7 (có đáp án chi tiết)

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S GIO DC V O TO BC GIANG K THI CHN HC SINH GII VN HO CP TNH NM HC 2012-2013 MễN THI: TON; LP: PH THễNG THI CHNH THC Ngy thi: 30/3/2013 Thi gian lm bi 150 phỳt, khụng k thi gian giao thi cú 01 trang Cõu 1. (4,0 im) 1) Rỳt gn: A = + : + . 10 12 2) Tỡm giỏ tr nh nht ca biu thc P = x 2012 + x 2013 vi x l s t nhiờn. Cõu 2. (5,0 im) 1) Tỡm x bit x + 2.3x +1.5x = 10800 . 2) Ba bn An, Bỡnh v Cng cú tng s viờn bi l 74. Bit rng s viờn bi ca An v Bỡnh t l vi v 6; s viờn bi ca Bỡnh v Cng t l vi v 5. Tớnh s viờn bi ca mi bn. Cõu 3. (4,0 im) 1) Cho p l s nguyờn t ln hn 3. Chng minh rng p + 2012 l hp s. 2) Cho n l s t nhiờn cú hai ch s. Tỡm n bit n + v 2n u l cỏc s chớnh phng. Cõu 4. (6,0 im) Cho tam giỏc ABC cõn ti A v cú c ba gúc u l gúc nhn. 1) V phớa ngoi ca tam giỏc v tam giỏc ABE vuụng cõn B. Gi H l trung im ca BC, trờn tia i ca tia AH ly im I cho AI = BC . Chng minh hai tam giỏc ABI v BEC bng v BI CE . 2) Phõn giỏc ca cỏc gúc ABC , BDC ct AC, BC ln lt ti D, M. Phõn giỏc ca gúc BDA ct BC ti N. Chng minh rng: BD = MN . Cõu 5. (1,0 im) 1 Cho S = + + . + Tớnh ( S P ) 2013 1 1 1 + v P = + + . + + . 2011 2012 2013 1007 1008 2012 2013 . --------------Ht---------------Cỏn b coi thi khụng gii thớch gỡ thờm. H v tờn thớ sinh: .S bỏo danh: . Giỏm th (H tờn v ký) Giỏm th (H tờn v ký) S GIO DC V O TO BC GIANG HNG DN CHM K THI CHN HC SINH GII VN HO CP TNH MễN THI: TON; LP: PH THễNG CHNH THC Ngy thi: 30/3/2013 Bn hng dn cú 03 trang Phng phỏp-Kt qu Cõu Cõu 1 (2im) im ( im) 15 18 A = + : + 10 10 10 12 12 12 = 0.5 0.5 12 11 : 10 12 12 72 = . = 11 55 Vy A = (2im) 0.5 0.5 72 . 55 P = x 2012 + x 2013 0.5 + Nu x = 2012 hoc x = 2013 thỡ P = + Nu x > 2013 thỡ P = x 2012 + x 2013 > + x 2013 > 0.5 + Nu x < 2012 thỡ P = x 2012 + x 2013 > x 2012 + > 0.5 + Do ú giỏ tr nh nht ca P bng 1, t c x = 2012 hoc x = 2013 . 0.5 Cõu x+2 (2.5im) x +1 x x x (4im) 1.0 x Ta cú .3 .5 = 10800 .2 .3 .3.5 = 10800 x ( 2.3.5 ) = 900 0.5 x 30 = 30 x = (2.5im) Vy x = l kt qu cn tỡm. + Gi s viờn bi ca An, Bỡnh, Cng ln lt l a, b, c . Vỡ tng s viờn bi ca ba bn l 74 nờn a + b + c = 74 a b a b + Vỡ s viờn bi ca An v Bỡnh t l vi v nờn = = 10 12 + Vỡ s viờn bi ca Bỡnh v Cng t l vi v nờn + T ú ta cú a b c a+b+c 74 = = = = =2 10 12 15 10 + 12 + 15 37 b c b c = = 12 15 0.5 0.5 0.5 0.5 0.5 0.5 0.5 + Suy a = 20; b = 24; c = 30 Cõu (2im) + Vỡ p l s nguyờn t ln hn nờn p cú dng p = 3k 1( k , k 1) (4im) 0.5 +Vi p = 3k + 0.5 suy p + 2012 = ( 3k + 1) + 2012 = 9k + 6k + 2013 ( p + 2012 )M 0.5 +Vi p = 3k suy p + 2012 = ( 3k 1) + 2012 = 9k 6k + 2013 ( p + 2012 )M 0.5 Vy p + 2012 l hp s. (2im) + Vỡ n l s cú hai ch s nờn < n < 100 18 < 2n < 200 0.5 + Mt khỏc 2n l s chớnh phng chn nờn 2n cú th nhn cỏc giỏ tr: 0.5 36; 64; 100; 144; 196. + Vi 2n = 36 n = 18 n + = 22 khụng l s chớnh phng 2n = 64 n = 32 n + = 36 l s chớnh phng 2n = 100 n = 50 n + = 54 khụng l s chớnh phng 2n = 144 n = 72 n + = 76 khụng l s chớnh phng 2n = 196 n = 98 n + = 102 khụng l s chớnh phng + Vy s cn tỡm l n = 32 . Cõu 0.5 0.5 (6 im) (3im) + Xột hai tam giỏc AIB v BCE Cú AI=BC (gt) BE=BA( gt) 0.5 + Gúc IAB l gúc ngoi ca tam giỏc ABH nờn IAB = ABH + AHB = ABH + 900 0.5 + Ta cú EBC = EBA + ABC = ABC + 90 . Do ú IAB = EBC . + Do ú ABI = BEC (c g c) 0.5 + Do ABI = BEC (c g c) nờn AIB = BCE . 0.5 (3im) + Trong tam giỏc vuụng IHB vuụng ti H cú AIB + IBH = 900 . Do ú BCE + IBH = 900 . 0.5 KL: CE vuụng gúc vi BI. 0.5 + Do tớnh cht ca ng phõn giỏc, ta cú DM DN . 0.5 + Gi F l trung im ca MN. Ta cú FM = FD = FN . 0.5 + Tam giỏc FDM cõn ti F nờn FMD = MDF . FMD = MBD + BDM ( gúc ngoi tam giỏc) 0.5 = MBD + CDM Suy MBD = CDF (1) 0.5 Ta cú MCD = CDF + CFD (2) Do tam giỏc ABC cõn ti A nờn MCD = 2MBD (3) T (1), (2), (3) suy MBD = DFC hay tam giỏc DBF cõn ti D. Do ú 0.5 MN 1 1 1 Cho S = + + . + + v 2011 2012 2013 1 1 2013 P= + + . + + . Tớnh ( S P ) . 1007 1008 2012 2013 + Ta cú: 1 1 P= + + . + + 1007 1008 2012 2013 1 1 1 = + + + . + + + + . + + 1006 1007 1008 2012 2013 1 + + + . + 1006 1 1 1 = + + + . + + + + . + + 1006 1007 1008 2012 2013 1 + + + . + 2012 1 1 = + + + =S. 2012 2013 2013 Do ú ( S P ) =0 0.5 im ton bi (20im) BD = DF = Cõu (1 im) (1 im) 0.5 0.5 Lu ý chm bi: Trờn õy ch l s lc tng bc gii v cỏch cho im tng phn ca mi bi. Bi lm ca hc sinh yờu cu phi chi tit, lp lun cht ch. Nu hc sinh gii cỏch khỏc ỳng thỡ chm v cho im tng phn tng ng. PHềNG GD & T HO AN THI CHN HC SINH GII CP HUYN NM HC 2011-2012 Mụn: Toỏn - Lp Thi gian : 150 phỳt (khụng k thi gian chộp ) Cõu 1: (4 im) a, Tỡm x bit: 11 15 11 ( x) = ( ) 13 42 28 13 x b, Cho M = Tỡm x Z v x < 50 M cú giỏ tr nguyờn Cõu 2:(4 im) Mt i thu li cú 10 ngi lm ngy o p c 200m t. Mt i khỏc cú 12 ngi lm ngy thỡ o p c bao nhiờu t (gi thit nng sut ca mi ngi u nh nhau). Cõu 3: (2 im) x = Cho hm s f( x ) = Tỡm x1 bit f( x ) Cõu 4: (4 im) Tớnh giỏ tr ca biu thc A= a 3a b b+2 b+6 vi a - b = b 2; b Cõu 5: (6 im) Cho tam giỏc ABC cõn ti A (AB > BC). Trờn tia BC ly im M cho MA = MB v tia Bx // AM (Bx v AM cựng nm trờn na mt phng b AB). Trờn tia Bx ly im N cho BN = CM. Chng minh rng: a, ABN = ACM b, AMN cõn *****************Ht****************** HNG DN CHM THI HC SINH GII MễN TON - LP (2011-2012) Li gii Cõu a, 11 15 11 - ( - x) = - ( - ) 13 42 28 13 11 15 11 + x = + 13 42 28 13 15 x =+ 28 42 35 x =84 x =12 b, M cú giỏ tr nguyờn => x - M hay x - l s chn ú x l s l v l s chớnh phng => x {1;9; 25; 49} 11 =0 x = ta cú: M= =1 x = 25 ta cú: M= =2 x = 49 ta cú: M= =3 Vi x = ta cú: M = S cụng o c 200 m t ca 10 ngi o ngy l: 10 x = 80 (ngy cụng) S cụng o c x m t ca 12 ngi o ngy l: 12 x = 84 (ngy cụng) Vỡ nng sut ca mi ngi u nh nhau, thỡ s t o c t l thun vi s ngy cụng nờn ta cú: im 0,5 0,5 0,25 0,25 0,75 0,75 0,25 0,25 0,25 0,25 1 1,5 80 84 200 ì 84 = x= = 210 200 x 80 Vy i 12 ngi lm ngy thỡ o p c 210 m t Vỡ f( x ) = M f( x ) 3 => f( x1 ) = x x1 = => = x1 => x1 = 0,5 0,5 0,5 Vi a - b = => a = b + Thay a = b + vo biu thc A ta cú A= b + ì (b + 4) b b + 2b + 12 = b+2 b+6 b+2 b+6 = - = -1 Vi a - b = thỡ A = -1 0,5 2,5 0,5 0,5 V hỡnh, ghi GT-KL a, MAB cõn ti M nờn BAM = ABM (1) ABC cõn ti A nờn ACB = ABM (2) T (1) v (2) => BAM = ACB (3) Mt khỏc Bx // AM nờn ABN + BAM = 1800 (4) (gúc cựng phớa) Cú ACM + ACB = 1800 (k bự) (5) T (3);(4);(5) => ABN = ACM b, ABN = ACM (c. g. c) vỡ cú AB = AC; ABN = ACM; BN = CM => AM = AN => AMN cõn 0,5 0,5 0.5 0,5 0,5 0,5 1 0,5 0,5 * Lu ý: GV linh hot chm, nu HS cú cỏch gii khỏc nhng kt qu ỳng cho im ti a Phòng gd & đt sơn dơng đề thi chọn học sinh khiếu lớp Trờng thcs HồNG THáI Năm học 2011 - 2012 Môn thi : TON Thời gian : 120 phút ( không kể thời gian giao nhận đề ) Câu 1:(3điểm): a) So sánh hai số : 330 520 163.310 + 120.69 b) Tính : A = 12 11 .3 + Câu 2:(2điểm): Cho x, y, z số khác x2 = yz , y2 = xz , z = xy. Chứng minh rằng: x = y = z Câu 3:(4điểm) a) Tìm x biết : x x x x + = + 2009 2008 2007 2006 b) Cho hai đại lợng tỉ lệ nghịch x y ; x1, x hai giá trị x; y1, y2 hai giá trị tơng ứng y. Tính y1, y2 biết y12+ y22 = 52 x1=2 , x 2= 3. Câu 4:(2điểm) Cho hàm số : f(x) = a.x2 + b.x + c Biết với a, b, c, d Z f (1)M 3; f (0)M 3; f (1)M .Chứng minh a, b, c chia hết cho Câu 5:(3điểm) Cho đa thức A(x) = x + x2 + x3 + .+ x99 + x100 . a) Chứng minh x=-1 nghiệm A(x) b)Tính giá trị đa thức A(x) x = Câu 6:(6điểm) Cho tam giác ABC cân đỉnh A , cạnh BC lần lợt lấy hai điểm M N cho BM = MN = NC . Gọi H trung điểm BC . a) Chứng minh AM = AN AH BC b) Tính độ dài đoạn thẳng AM AB = 5cm , BC = 6cm c) Chứng minh MAN > BAM = CAN -------------------------------------------------Hết--------------------------------------------------Cán coi thi không giải thích thêm AK = AB BK = 16 = 12 AC => KC = AK = 12 KCM u => KC = KM = 12 M KC = Theo phn b) AB = BC = AH = BK = HM = BC ( HBCM l hỡnh ch nht) => AM = AH + HM = PHềNG GD T TP. TH DU MT K THI HC SINH GII TON THCS GII THNG LNG TH VINH NM HC: 2012-2013 MễN TON: LP Thi gian lm bi : 120 phỳt (Khụng k thi gian phỏt ) Ngy thi : 30/3/2013 Bi 1: 1 1 + ) + (1 + + 3) + (1 + + + ) + . + (1 + + + . + 16 ) ( 16 1 1 b) Cho a+b+c = 2010 v + + = a+b b+c c+a a b c Tớnh S = + + b+c c+a a+b a) Tớnh P = + Bi 2: Tỡm x bit: 30 31 . . . . = 2x 10 62 64 Bi 3: Chng minh tng bỡnh phng s t nhiờn liờn tip khng th l s chớnh phng. Bi 4: Tỡm a1, a2, a3 , .,a100 Bit: a 100 a1 a2 a3 = = = . = 100 100 99 98 v a1+ a2 + a3 + .+ a100 = 10100 Bi 5: Cho tam giỏc ABC B < 900 v B = 2C . K ng cao AH. Trờn tia i ca tia BA ly im E cho BE = EH, ng cao HE ct AC ti D. a) Chng minh : BEH = ACB b) Chng minh : DH = DE = DA c) Ly B cho H l trung im BB. Chng minh ABC cõn. d) Chng minh: AE = HC. ---------Ht--------- phòng gdgd-đt đức thọ Đề thi thức đề thi olympic toán năm học 20122012-2013 Thời gian làm 120 phút Câu 1: a) Thực phép tính A = 212.35 46.92 ( .3 ) + 4.35 510.73 25 5.492 (125.7 ) + 59.143 b) Chứng minh rằng, với số nguyên dơng n 3n + 2n+ + 3n 2n chia hết cho 10 212.35 46.92 510.73 25 5.492 212.3 4.3 212.3 510.73 510.73.7 Lời giải: a) A = = 212.35.3 + 212.35 9.7 + 59.73.23 22.3 + 4.35 (125.7 ) + .14 ( ) = 12 12 .3 ( 1) .3 ( + 1) b) Ta có n+ 510.73 (1 ) .7 (1 + ) n+2 = = + = + 3n 2n = 3n.9 2n.4 + 3n 2n.1 = 3n ( + 1) 2n ( + 1) = 10.3n 10.2n1 = 10. 3n 2n1 chia hết cho 10 ( Câu 2: Tìm x, biết a) x ) + = ( 3,2 ) + 5 b) ( x ) x +1 ( x 7) x +11 =0 x = x = 4 14 Lời giải: a) x + = ( 3,2 ) + x + = x =2 5 5 x = x = Vậy giá trị cần tìm x = ; x = 3 ( x ) x +1 = x +1 x +11 x +1 10 b) ( x ) ( x ) = ( x ) ( x ) = ( x )10 = x = x = x +1 10 Với ( x ) = x = . Với ( x ) = . Vậy giá trị cần tìm x {6;7;8} x = x = Câu 3: a) Số A đợc chia thành số tỉ lệ theo : : . Biết tổng bình phơng ba số 24309. Tìm số A 2x + 2y z 2x y + 2z x + 2y + 2z b) Cho x, y, z số hữu tỉ khác 0, cho . = = z y x ( x + y )( y + z )( z + x ) Tính giá trị số biểu thức M = 8xyz Lời giải: a) Gọi số đợc chia từ số A lần lợt x; y; z. x y z x2 y z2 x2 + y + z2 24309 Theo ta có = = = = = = = 32400 9 2701 + + 25 16 36 25 16 36 3600 x2 y2 = 32400 x = 5184 x = 72 ; = 32400 y = 18225 y = 135 25 16 z = 32400 z = 900 y = 30 36 Với x = 72; y = 135; z = 30 A = 237. Với x = -72; y = -135; z = -30 A = -237 2x + 2y z 2x y + 2z x + 2y + 2z ( x + y + z ) = = = =3 z y x x+y+z 2x + 2y z 2x y + 2z x + 2y + 2z = x + y = 2z ; = x + z = 2y ; = y + z = 2x z y x ( x + y )( y + z )( z + x ) = 2x.2y.2z = Do M = 8xyz 8xyz Câu 4: Cho tam giác ABC (AB < AC), M trung điểm BC. Trên tia đối tia MA lấy điểm E cho ME = MA. Chứng minh a) AC = EB AC // BE b) Gọi I điểm AC, K điểm EB cho AI = EK. Chứng minh ba điểm I, M, K thẳng hàng c) Từ M kẻ tia Mx cho MA tia phân giác BMx . Gọi D giao điểm Mx với AC. Chứng minh MB > MD Lời giải: a) Xét AMC EMB có A AM = ME (gt) x AMC = EMB (đối đỉnh) AMC = EMB (c g c) D MC=MB (gt) I AC = EB CAM = BEM mà CAM ; BEM C B hai góc vị trí so le nên AC // BE M b) Nối I với M K với M K Xét AMI EMK có AM = EM (gt) MAI = MEK (so le) AMI = EMK (c g c) E AI=EK (gt) b) Từ giả thiết ta có: AMI = EMK mà EMK + KMA = 180 (Hai góc kề bù) AMI + KMA = 1800 . Vậy ba điểm I, M, K thẳng hàng c) Ta có MDC > AMD (Góc AMD) MDC > AMB (Vì theo giả thiết AMB = AMD mà AMB > DCM (Góc AMC). Từ suy MDC > DCM MC > MD (Quan hệ cạnh góc DMC). Mặt khác MC = MB (gt). Vậy MB > MD (đpcm) Câu 5: Cho tam giác ABC có B$ = 600 , C$ = 450 . Trong ABC , vẽ tia Bx cho CBx = 150 . Đờng vuông góc với AB A cắt Bx I. Tính ICB A Lời giải: Lấy điểm M BC cho BM = BA ABM cân B có ABM = 600 nên ABM 150 AM = AB. Mặt khác ABI = ABM IBM = 600 150 = 450 x I ABI vuông cân A nên AI = AB AI = AM Ta lại có BAC = 1800 ABC ACB = 75 150 45 MAC = BAC BAM = 750 600 = 150 B C M MAC = IAC Xét AIC AMC có AI = AM 0 AC chung AIC = AMC ((c g c) ACI = ACM = 45 ICB = 90 IAC = MAC Lời giải: Nguyễn Ngọc Hùng THCS Hoàng Xuân Hãn TI LIU LUYN THI HSG LP FOR 7TH FORMS GIFTED STUDENTS Kè THI HSG 2013 2014 MễN : Anh - Thi gian : 120 phỳt H v tờn: . . . . . . . . . . . . Lp : . . . . . . . . . . . . . . im bng s im bng ch Ch kớ giỏm th Ch kớ giỏm kho Mó phỏch Mó phỏch I) Three words have the same vowel sound one word doesnt. Which one is it? (0) is an example for you. (1,5ms) 0) a-cat b-cat â-that d-hate 1) a-book b-look c-floor d-cook 2) a-nine b-fine c-kind d-thing 3) a-set b-between c-get d-met 4) a-husband b-busy c-must d-bus 5) a-do b-go c-so d-no II) Choose the correct answer for each sentence. (0) is an example for you (3ms) 0) My mother believes that my brother is __________ than me. a) good b) gooder â better d) best 1) Theyre getting married _____________ the end of June. a) on b) in c) at d) during 2) Im sorry but you have to cook dinner _____________ a) alone you b) himself c) yourself d) on you 3) You use a _______________ to cook rice. a) steamer b) rice cooker c) saucepan d) frying pan 4) Looks! Nam has become ________________. a) to be tall and taller. b) to be taller and taller. c) tall and taller d) taller and taller. 5) Because he didnt like the first pair of trousers, he asked for ____________. a) the other ones b) other trousers c) an other trousers d) an other pair 6) If a patient cant walk, he can use _____________ to move around. a) an eye chart b) a stretcher c) a wheelchair d) a scale 7) Would you mind _______ in the front seat of the taxi, Mark? a) to sit b) sit c) to sitting d) sitting 8) Lan is ________ and she has a flower shop in Hanoi. a) a flower seller b) a florist c) a flower girl d) a flower lady 9) The family _____________ when the mailman came. a) was sleeping b) is sleeping c) has slept d) have slept 10) Paul is said __________ the brightest student in class. a) was b) being c) to be d) he was PREPARED & RELEASED BY BèNH THPT LIN SN, LP THCH - VP TI LIU LUYN THI HSG LP FOR 7TH FORMS GIFTED STUDENTS III) Complete the following sentences with an appropriate form of the word in brackets. (0) is an example for you. (3ms) 0) They have all been absolutely (wonder) wonderful! 1) I dont like that film. Its very (bore) __________________. 2) Ho Chi Minh City is (large) _________________ city in Vietnam. 3) They boy fell asleep during (perform) __________________. 4) They waited for his (habit) _______________ response. 5) The male birds are more (colour) _________________ than the females. 6) Every pupil was very (excite ______________ about the holiday. 7) His parents are very proud of his (succeed) _______________. 8) David Beckham is my (favour) ______________. 9) I dont know how you (celebration) ______________ your birthday. 10) Some people feel that towns are too (noise) ______________ for them to live in. IV) Rewrite the following sentences without changing the meaning. (0) is an example for you. (3ms) 0) Tom wrote that letter. - That letter was written by Tom. 1) Is this bladder mended by Mr Green. - Does Mr Green ___________________________________________ 2) That girl is very intelligent. - What ________________________! 3)This living-room isnt as big as that kitchen. - That kitchen ______________________________________________ 4) Khanh said You ought to take a break, Huy - Khanh advised ____________________________________________ 5) Weve never met such a famous singer before. - Its the first time ___________________________________________ 6) Her hair is long and black. - She has __________________________________________________ V) Do as directed in parentheses. (0) is an example for you. (3ms) 0) I (go) to Dalat years ago. (Supply the correct verb form) - I went to Dalat years ago. 1) The weather was fine. We could go camping. (Combine into one sentence using enough . . . . . . . . to) - _______________________________________________________ 2) Everyone stopped (laugh) when we (come). (Supply the correct verb form) - _______________________________________________________ 3) He gave him back the money last Sunday. (Change into the passive voice) - _______________________________________________________ 4) Putting the knives __________ an electrical socket is dangerous. (Fill in the blank with the suitable preposition) 5) Jeans cant be worn at work. (Change into active voice) - _______________________________________________________ PREPARED & RELEASED BY BèNH THPT LIN SN, LP THCH - VP TI LIU LUYN THI HSG LP FOR 7TH FORMS GIFTED STUDENTS 6) The boy said to the girl Did you go out last night?. (Change into reported speech) - _______________________________________________________ VI) Complete the following sentences based on the given cues. (0) is an example for you. (1,5ms) 0) get up / six oclock / I / often / at. - I often get up at six oclock. 1) you / mind / the west lake / telling / would / us / about ? - _______________________________________________________ 2) could / I / visit / someday / wish / I - _______________________________________________________ 3) My brother / in central Vietnam / was / 1972 / in / born - _______________________________________________________ 4) Se you / to / I am / how glad / again ! - _______________________________________________________ 5) A parting meeting / have / before leaving / youd better - _______________________________________________________ VII) Read the article and choose the best answer. (0) is an example for you (3ms) TRAVELLING IN THE LAKE DISTRICT The Lake District is very popular (0) ___________ holidays all year round. Roads leading into the area have been improved in (1) ___________ years. Inside the area itself, however, many roads are (2) _____________ and winding with steep hills and it may not be safe to drive (3) ____________ roads like this when they are (4) _______________ in ice. For the mountain walker a word of warning every season visitors (5) ______________ lost or are injured and (6) _____________ to be rescued by the Mountain Rescue teams. This kind of problem can be (7) __________________ by following a few simple rules. When exploring the mountains, wear warm clothing, sensible boots, take a map, compass and whistle and a small (8) _________________ of food. Dont go (9) ______________ alone and always tell someone where you (10) __________ to go to. 0) a-to b-with â for d-as for 1) a-recent b-next c-last d-close 2) a-thin b-slim c-narrow d-shallow 3) a-along b-above c-by d-in 4) a-wrapped b-covered c-drowned d-filled 5) a-have b-be c-make d-get 6) a-must b-should c-need d-ought 7) a-encouraged b-prevented c-arranged d-organised 8) a-quantity b-weight c-length d-limit 9) a-for b-by c-with d-off 10) a-look b-seem c-plan d-know VIII) Read the following passage and choose the best answer: (2ms) Computing is now at the same stage as printing was when the first printing presses were used. Before printing presses were invented, only rich people like kings and dukes PREPARED & RELEASED BY BèNH THPT LIN SN, LP THCH - VP TI LIU LUYN THI HSG LP FOR 7TH FORMS GIFTED STUDENTS could afford to buy books. Often these people were unable to read and hadnt enough time to learn. In any case, the books were so big that it was difficult for anyone to relax with a book as we today. They wanted booked because they were expensive and there was something magical about them. Only a few people were able to write, and it took an extremely long time to write a book. Monks and other people who could write said ordinary people could not learn to read. The position with computers is very similar today. A few years ago, computers were very large and expensive. Business managers and rich people ordered them but they didnt know how to use them. In many countries, however, the situation has now completely changed. Lots of people not only own microcomputer but also know how to use them. Questions: 1) What happened before printing presses were invented? - _____________________________________________________________ 2) Why were books wanted before printing presses were invented? - _____________________________________________________________ 3) What is common feature of a book and a computer? - _____________________________________________________________ 4) What situation has thoroughly changed nowadays? - _____________________________________________________________ _____ THE END_____ PREPARED & RELEASED BY BèNH THPT LIN SN, LP THCH - VP TI LIU LUYN THI HSG LP FOR 7TH FORMS GIFTED STUDENTS P N V HNG DN CHM TETS 27 I) Mi cõu ỳng 0,3 1-c 2-d 3-b 4-d 5-a II) Mi cõu ỳng 0,3 1-c 2-c 6-c 7-d 3b 8-b 4-d 9-a 5-a 10-c III) Mi cõu ỳng 0,3 1-boring 2-the largest 5-colourful 6-excited 9-celebration 10-noisy 3-performance 8-success 4-dicussion 8-favourite IV) Mi cõu ỳng 0,5 1) Does Mr Green mend this bladder? 2) What an intelligent girl! 3) That kitchen is bigger than this living-room. 4) Khanh advised Huy to take a break. 5) Its the first time we met such a famous singer. 6) She has long black hair. V) Mi cõu ỳng 0,5 1) The weather was fine enough for us to go camping. 2) . . . . . . laughing . . . . . . . came 3) He was given the money back last Sunday. 4) into PREPARED & RELEASED BY BèNH THPT LIN SN, LP THCH - VP TI LIU LUYN THI HSG LP FOR 7TH FORMS GIFTED STUDENTS 5) They cant wear jeans at work. 6) The boy asked the girl if she had gone out the night before. VI) Mi cõu ỳng 0,3 1) Would you mind telling us about the west lake? 2) I wish I could visit Hue someday. 3) My brother was born in central Vietnam in 1972. 4) How glad I am to see you again! 5) Youd better have a parting meeting before leaving. VII) Mi cõu ỳng 0,3 1-a 2-c 6-d 7-b 3-a 8-a 4-b 9-d 5-d 10-c VIII) Mi cõu ỳng 0,5. 1) Only kings and dukes had enough money to buy books. 2) Because books were expensive and magical. 3) They were large and expensive at first 4) A person who buys a computer knows how to use it. PREPARED & RELEASED BY BèNH THPT LIN SN, LP THCH - VP TI LIU LUYN THI HSG LP FOR 7TH FORMS GIFTED STUDENTS Kè THI HSG 2013 2014 MễN : Anh - Thi gian : 120 phỳt H v tờn: . . . . . . . . . . . . . . . . . Lp : . . . . . . . . . . . . . . im bng s im bng ch Ch kớ giỏm th Ch kớ giỏm kho Mó phỏch Mó phỏch I.Choose the word or phrase which best completes each of the following sentences. Write your answers in the table below(2pts) 1. Jack is. His jokes often make his friends laugh a lot. A. generous B. humorous C.easy-going D. unusual 2. Im sorry. Im notto help you lift the table. A. enough strong B. too strong C. strong enough D. enough strength. 3. We.in our present house for years. A. live B. have lived C. are living D. lived. 4. We used to wash clothes by hand. Now we have a. A. washing machine B. dishwasher C. hair dryer D. refrigerator. 5. It took me a long time to get used glasses. A. to wear B. to wearing C. wear D. wore. 6.Last night he didnt go home 10 oclock. A. until B. at C. after D. in front of 7."Dont shout", I said to Jim. A. I told Jim don't shout B. I told to Jim not to shout C. I told Jim not to shout D. I said to Jim don't shout. 8. Hoa was very surprised when she looked at in the mirror. A. she B. hers C. herself D. her 9. She went to market without. anything. A. buy B. to buy C. bought D. buying 10. Since we have to be there by 8.30, we. take a taxi. A. had better B. may C. ought D. are able to 11. Ive never seen such an interesting A. performing B. performer C. performance D. performed 12. Its at least a month since.John. A. I last seen B. I have last seen C. I last see D. I last saw 13. I like my sisters house. It is a A. new beautiful house B. beautiful house new C. beautiful new house D. new house beautiful 14. Living in the country is not expensive. And it isnt complex . A. either B. too C. neither D. so 15. The new shopping mall is quite the present shopping area. A. different from B. the same C. like to D. similar 16. What ? She is very nice. PREPARED & RELEASED BY BèNH THPT LIN SN, LP THCH - VP TI LIU LUYN THI HSG LP FOR 7TH FORMS GIFTED STUDENTS A. did Sandra like B. is Sandra like C. does Sandra like D. was Sandra like 17. Thank you very much the Christmas gift . A. of B. with C. for D. about 18. she plays the piano! A. How well B. How good C. What well D. What good 19. Life here is very . A. peace B. peacefully C. peaceful D. peacefulness 20. It is raining outside, and Tom brought his umbrella with him he wouldnt get wet. A. so as to B. in order C. so that D. in order to ANSWERS: 1. 2. 11. 12. 3. 13. 4. 14. 5. 15. 6. 16. 7. 17. 8. 18. 9. 19. 10. 20. II. Use the correct form of the words in brackets to complete sentences (2pts) 1. Bell experimented with ways of transmiting .over a long distance. (SPEAK) 2. The tiger wanted to see the farmer's . (WISE) 3. The scouts the work (VOLUNTEER) 4. Nowadays, scouting is popular (WORLD) 5. After his parents died, he was sent to an. ( ORPHAN) 6. Huy makes friends very easily because he is very ( SOCIAL) 7. Cook the meat in the for at least 30 minutes. ( STEAM) 8. My friend, Nga plays the piano. ( BEAUTIFUL). 9. The lost shoe is one of the . stories I like best. ( TRADITION) 10. Our teacher always. us to work hard. (COURAGE) ANSWERS: 1. 5. 6. 7. 8. 10 III. Complete the sentences using the correct form of the verbs in the brackets (2pts) 1. They (watch) their favorite TV programmes at the moment. 2. Mary and John are neighbors. They ( know) each other for a long time. 3. They ( arrive) in New york yesterday? 4. I havent met him since he ( move ) to Ho Chi Minh City 5. My mother is tired enough ( cook) tonight. 6. The teacher asked me ( not make) noise in class. 7. The boys like ( play ) games but hate doing lessons. 8. His doctor advised him ( give) up smoking. 9. Look at those black clouds. It( rain). 10. This is the first time I (be) to Ha Noi. ANSWERS: 1. 5. 6. 7. 8. 10 IV. Fill in each numbered blank with a suitable word (2pts) PREPARED & RELEASED BY BèNH THPT LIN SN, LP THCH - VP TI LIU LUYN THI HSG LP FOR 7TH FORMS GIFTED STUDENTS The country is (1) .beautiful than a town and more pleasant to live in. Many people think so, and go to the country (2) the summer holiday though they can't live (3) . all the year round. Some have cottage built in a village (4) that they can go there whenever they (5) find the time. English villages are not alike, but (6) . some ways they are not very different from (7) .other. Almost every village (8) .a church, the round or square tower of which can (9) seen from many miles around. Surrounding the church is the church yard, (10) people are buried. ANSWERS: 1. 5. 6. 7. 8. 10 V. The following sentences belong to a passage about Cinderella, but they are not in the correct order. Put them in their correct order to make a full passage. There are examples for you. Write your answers in the spaces below. ( 2,0 pts ) A.Once upon a time there was a girl called Cinderella who did all the work in the kitchen while her lazy sisters did nothing. B. So she went to the ball in a beautiful dress and a wonderful coach. C. She danced with the prince but at midnight she ran back home, leaving one of her shoes on the dance floor. D. One night her sisters went to a ball at the palace. E. The prince wanted to see her again and went to every house in the capital until he found that the shoe was the right size for Cinderella. F. Cinderella was left at home, very sad. After a time her fairy godmother appeared and told Cinderella that she could go to the ball - but to return home by midnight. G. She and the prince were married and lived happily ever after. ANSWERS: 1.A 2. 3. 4. . 5. 6. 7. G VI. Read the following passage and choose the best answer(2pts) Every year students in many countries learn Enghlish . Some of these students are young children . Others are teenagers . Many are adults. Some learn at school , others study by themselves. A few learn English just by hearing the language , in film , on television , in the office , or among their friends . But not many are lucky enough to that . Most people must work hard to learn another language . Learning another language ! Learning English ! Why all these people want to learn English ? It is difficult to answer that quetion . Many boys and girls learn English at school because it is one of their subjects . They study their own language , and mathematics and English . ( In England , or America , or Australia , many boys and girls study their own language , which is English and mathematics and another language , perhaps French , or German , or Spainish ) Many adults learn English because it is useful for their work . Teenagers often learn English for their high studies , because some of their books are in English at the college or university . Other people learn English because they want to read newspapers or magazines in English . 1. According to the writer , A. only adults learn English . B. no children like learning English C. English is only useful to teenagers . D. English is popular in much of the world . 2. Many people learn English by PREPARED & RELEASED BY BèNH THPT LIN SN, LP THCH - VP TI LIU LUYN THI HSG LP FOR 7TH FORMS GIFTED STUDENTS A. watching videos only . B. hearing the language in the office . C. talking with the film star D. working hard on their lesson. 3. Many boys and girls learn English because A. English can give them a job. B. it's included in their study courses. C.their parents make them . D.they have to study their own language . 4. In America or Australia many school children study A. English as a foreign language . B. English and Mathematics only . C. such foreign languages as French , German , and Spanish . D. their own language and no foreign language . 5. Many adults learn English because A. their work is useful . B. they want to go abroad . C. most of their books are in English D. it helps them in their work . ANSWERS 1. 2. 3. 4. 5. VII. There are five mistakes in the passage. Find and correct them (1pt) Everyone know that in studying foreign languages, practice is the key of fluency. All foreign language learner even the advanced ones need practice. There has a fact that a learner can know a lot of grammar rules and vocabulary, however, they cant speaking well yet. So the learners must know how use what they have learned apart from the ability to explain grammar rules. ANSWERS 1. 2. 3. 4. 5. VIII. Rewrite the sentences so that it has the same meaning as the sentence printed before (4pts) 1. Its a long time since we became close friends. We have 2. No one is more intelligent than her in our school. She 3. Can I borrow your bike, Nga?, Nam asked. Nam asked Nga 4. Lan is 1.60m tall and Hoa is 1.60 tall, too. Lan 5. Apples are usually cheaper than oranges. Apples are not 6. Hed rather play golf than tennis. He prefers 7. You shouldnt translate each sentence into Vietnamese, my brother told me My brother told 8. When did you start playing the piano? How long? 9. Your younger brother is too weak to lift that box Your brother is not . 10. Hung is interested in collecting stamps Hungs PREPARED & RELEASED BY BèNH THPT LIN SN, LP THCH - VP TI LIU LUYN THI HSG LP FOR 7TH FORMS GIFTED STUDENTS IX-Choose the words that has the underline pronounced differently from the others. Identify your answer by writing the corresponding word or phrase on your answer paper. 1.A. though B. enough C. cough D. rough 2.A. chair B. cheap C. chorus D. child 3.A. missed B. closed C. called D. planned 4.A. fat B. any C. gas D. hat 5.A physics B. basic C. sailor D. subject X. Use the suggested words and phrases to make a full sentence. 1. Those buses / not going / airport / neither / taxis. 2. You / not / want / sell / house last year ? 3. He / stop / smoke / save / money . 4. My brother / not drive / carefully / I. 5. It / difficult / prevent / people / park here. 6) watching/ the living room/ father/ in/ at the moment/ My/ is/ TV. 7) interested/ history/ John/ the/ of/ is/ Vietnam/ in. 8) is/ the/ to/ She/ strong/ suitcase/ not/ lift/ enough 9) time/ your/ will/ What/ be/ here/ aunt/ ? TETS 26 KEYS I. 1B 2C 3B 4A 5B 6A 7C 8C 9D 10A 11C 12D 13A 14A 15A 16B 17C 18A 19C 20C II. 1. SPEECH 2. WISDOM 3. VOLUNTARY 4. WORLDWIDE 5. ORPHANAGE 6. SOCIABLE 7. STEAMER 8. BEAUTIFULLY 9. TRADITIONAL 10. ENCOURAGES III. 1. are watching 2. have known 3. Did they arrive 4. moved 5. to cook 6. not to make 7. playing 8. to give 9. is going to rain 10. have been IV. 1. more 2. for 3. there 4. so 5. can 6. in 7. each 8. has 9. be 10. where V. 1A 2D 3F 4B 5C 6E 7G VI. 1D 2D 3B 4C 5D VII. 1. know knows 2. learner learners 3. has is 4. speaking speak 5. use to u se VIII. 1. We have become/have been close friends for a long time 2. She is the most intelligent student/girl in our school. 3. Nam asked Nga to lend him her bike./Nam asked Nga if he could borrow her bike. 4. Lan is the same height as Hoa/ Lan is as tall as Hoa/ Lan and Hoa are the same height. PREPARED & RELEASED BY BèNH THPT LIN SN, LP THCH - VP TI LIU LUYN THI HSG LP FOR 7TH FORMS GIFTED STUDENTS 5. Apples are not as expensive as oranges. 6. He prefers golf to tennis/ He prefers playing golf to (playing) tennis 7. My brother told me not to translate each sentence into Vietnamese. 8. How long have you played the piano 9. Your brother is not strong enough to lift that box. 10. Hungs hobby is collecting stamps. . Those buses are not going to the airport and neither are taxis. 62. Didnt you want to sell the house last year ? 63. He stops smoking to save money 64. My brother doesnt drive carefully as I do. 65. It is difficult to prevent people from parking here PREPARED & RELEASED BY BèNH THPT LIN SN, LP THCH - VP [...]... 1 x =2 3 x1=2 3 3 x=2+1= 7 3 3 x=2+1= 5 3 3 0,5 i m 0,5 i m 0,5 i m 0,5 i m b) (2 i m) 0,5 i m ( x 7) x +1 ( x 7) x +11 0,5 i m =0 1 ( x 7 )10 = 0 10 ( x +1) 1 x 7 ) = 0 ( x 7) ( x 7 x +1=0 1( x 7) 10 =0 x 7= 0 x =7 10 ( x 7) =1 x =8 ( x 7) x +1 Bi 3: (4 i m) ỏp ỏn a) (2,5 i m) G i a, b, c l ba s Theo 0,5 i m 0,5 i m Thang i m c chia ra t s A bi ta cú: a : b... ========= 3 Bi 1:(4 i m): Thang i m ỏp ỏn a) (2 i m) 212.35 46.92 510 .73 255.492 10 212.35 212.34 510 .73 5 74 A= = 6 3 2 4 5 (125 .7) + 59.143 212.36 + 212.35 59 .73 + 59.23 .73 ( 2 3) + 8 3 0,5 i m 212.34 ( 3 1) 510 .73 (1 7 ) = 12 5 2 3 ( 3 + 1) 59 .73 (1 + 23 ) 0,5 i m 10 3 212.34.2 5 7 ( 6) = 12 5 9 3 2 3 4 5 7 9 1 10 7 = = 6 3 2 b) (2 i m) 3 n + 2 - V i m i s nguyờn dng n ta cú: 3n+ 2 ... 4 7 Ta cú : + x= 5 3 2 3 15 6 2 5 4 7 + x= 5 2 9 6 4 7 2 5 x= + 9 6 5 2 4 49 x= 9 15 49 4 x= : 15 9 49 9 x= 15 4 1 47 x= 20 1 2 5 Ta cú : x 1 + x 2 x 1 = 5 4 3 8 1 2 5 + x = 5 ( 1 2 1) 4 3 8 4 x =9 27 7 x = 9: 24 24 x = 9 7 216 x= 7 Trong ABC ta cú : A + B + C = 1800 Theo gi thi t ta cú : A B C = = 2 3 4 i m 0.5 0.25 0.25 0.25 0.25 0.25 0.25 0.5 0.5 0.25 0.25 0.25 0.25 0 .75 0 .75 ... 111(a+b+c) = 37. 3(a+b+c) / Vì 0 < a+b+c 27 nên a+b+c M 37 Mặt khác( 3; 37) =1 nên 3(a+b+c) M 37 => S không thể l số chính phơng Câu 3: Qu ng đờng AB d i 540 Km; nửa quảng dờng AB d i 270 Km Gọi qu ng đờng ô tô v xe máy đ đi l S1, S2 Trong cùng M B 1 thời gian thì qu ng đờng tỉ lệ thuận với A vận tốc do đó t= S1 S 2 = = t (t chính l thời gian cần tìm) V1 V2 270 a 270 2a 540 2a 270 2a (540 2a ) ( 270 2a... 6=1+5=2+4=3+3=4+2=5+1 7= 1+6=2+5=3+4= 4+3=5+2=-6+1 8= 2+6=3+5=4+4=5+3=6+2 9=3+6=4+5=5+4=6+3 10=4+6=5+5=6+4 11=5+6=6+5 12=6+6 Điểm số (x) 2 Tần số( n) 1 Tần suất (f) 2,8% 3 2 5,6% 4 3 5 4 6 5 7 6 8 5 9 4 10 3 8,3% 11,1% 13,9% 16 ,7% 13,9% 11,1% 8,3% 11 2 12 1 5,6% 2,8% Nh vậy tổng số 7 điểm có khả năng xảy ra nhất tới 16 ,7% - TUY N CH N THI H C SINH GI I TON 7 2: Mụn: Toỏn 7 Bi 1: (3... - TUY N CH N THI H C SINH GI I TON 7 3 Bi 1:(4 i m) a) Th c hi n phộp tớnh: A= 212.35 46.92 ( 2 3) 2 6 4 5 + 8 3 510 .73 255.492 (125 .7 ) 3 + 59.143 b) Ch ng minh r ng : V i m i s nguyờn dng n thỡ : 3n+ 2 2n+ 2 + 3n 2n chia h t cho 10 Bi 2:(4 i m) Tỡm x bi t: a x 1 4 2 + = ( 3, 2 ) + 3 5 5 b ( x 7 ) Bi 3: (4 i m) x +1 ( x 7) x +11 =0 a) S A c chia thnh 3 s t l theo c a ba...Hớng dẫn chấm toán 7 Câu Nội dung 3 10 ( ) a)330 = ( 3) 4 3 2 10 ( ) = 271 0 ;520 = ( 5 ) (( 2) ) 3 + 3.2.5.2 ( 2.3) b) A = (( 2 ) ) 3 + ( 2.3) 1 10 2 6 = 2 11 12 9 = 2510 < 271 0 330 > 520 12 10 212.310 + 310.212.5 2 3 (1 + 5) = 12 12 11 11 = 11 11 2 3 + 2 3 2 3 ( 2.3 + 1) 2 z y x z x z y x y z = ; = ; = 1.5đ 1.5đ 6.212.310 4.211.311 4 = = 7. 211.311 7. 211.311 7 Vì x, y, z l các số khác... AM : AM2 = AH2 + MH2 = 42 + 12 = 17 AM = 17 cm Trên tia AM lấy điểm K sao cho AM = MK ,suy ra AMN= KMB ( c- c 2đ g- c) MAN = BKM v AN = AM =BK Do BA > AM BA > BK BKA > BAK MAN >BAM=CAN Duyệt BGH P Hiệu trởng Thân thị thuý ho n Ngời ra đề TĂNG Bá DũNG 2đ TR NG THCS HNG M T TON Lí ( chớnh th c) THI H C SINH GI I VềNG TR NG NM H C :2013 2014 MễN THI: TON KH I 7 Th i gian : 90 phỳt (Khụng k th i... EAN M t khỏc : AE n m gi a hai tia AB v AN nờn AE l tia phõn giỏc c a gúc trong t i nh A c a ABC 0.5 0.5 0.25 0.25 0.5 0.5 0.25 0.25 0.5 0.25 0.25 0.5 0.5 TUY N CH N THI H C SINH GI I TON 7 1 Bi 1 (4 i m) a) Ch ng minh r ng 76 + 75 74 chia h t cho 55 b) Tớnh A = 1 + 5 + 52 + 53 + + 549 + 55 0 Bi 2 (4 i m) a) Tỡm cỏc s a, b, c bi t r ng : a b c = = v a + 2b 3c = -20 2 3 4 b) Cú 16 t gi y b c lo... d cd c cd a b cd a c a b a+b b a+b a+b c+d b = = = = = b d c d c+d d c+d b d 2 a Từ (0 ,75 điểm) (0 ,75 điểm) Câu 2: Vì tích của 4 số : x2 1 ; x2 4; x2 7; x2 10 l số âm nên phải có 1 số âm hoặc 3 số âm Ta có : x2 10< x2 7 . VÀ ĐÀO TẠO BẮC GIANG ĐỀ THI CHÍNH THỨC Đề thi có 01 trang KỲ THI CHỌN HỌC SINH GIỎI VĂN HOÁ CẤP TỈNH NĂM HỌC 2012-2013 MÔN THI: TOÁN; LỚP: 7 PHỔ THÔNG Ngày thi: 30/3/2013 Thời gian. của góc trong tại đỉnh A của ∆ABC. 0.5 TUYỂN CHỌN ĐỀ THI HỌC SINH GIỎI TOÁN 7 Đề 1 Bài 1. (4 điểm) a) Chứng minh rằng 7 6 + 7 5 – 7 4 chia hết cho 55 b) Tính A = 1 + 5 + 5 2 . SỞ GIÁO DỤC VÀ ĐÀO TẠO BẮC GIANG ĐỀ CHÍNH THỨC HƯỚNG DẪN CHẤM KỲ THI CHỌN HỌC SINH GIỎI VĂN HOÁ CẤP TỈNH MÔN THI: TOÁN; LỚP: 7 PHỔ THÔNG Ngày thi: 30/3/2013 Bản hướng dẫn có 03 trang
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