dinh : Thi sinh trinh bay tom titt each giai, cong tlnrc ap dungjhoac quy trinh bam phim neu bai toan yeu cau va diSn ket qua vao 0 liSn kS.. Cac kSt qua tinh gftn dung, neu khong co chi[r]
Trang 1soGIAO Dl)C vA DAo T ';'0 LAo CAl cuoc THI cApTiNH GIAI ToAN TREN MAy
TiNH CASIO, VINACAL NAM HQC 2012-2013
HUONG nAN CHAM
DE THI cHiNH THUC
Mon fbi: Toan (Chuung trinh rHPn
Thai gian thi: 150 phut (kh6ng Jed thoi gian giao ai thi).
Ngay thi: 17/01/2013
Huang ddn chdm g6m co 10 cdu, 07trang, m6i cdu 05 iliim (Chuy: Thi sinh lam bai thi vaa ban ild thi nay)
(Ky va ghi roho ten) (Do Truong ban cham thi ghi)
1
.
2
* Quy dinh : Thi sinh trinh bay tom titt each giai, cong tlnrc ap dungjhoac quy trinh bam phim neu bai toan yeu cau) va diSn ket qua vao 0 liSn kS Cac kSt qua tinh gftn dung, neu khong co chi dinh cu thS thi duoc lay chinh xac toi 4 chtr s& thap phan
Bai 1 Cho ham s&f(x) = x 2 - 3~+1.Tim g~n dung tea dQ cac diem C1,IC tri cua ham s&
x+
Taco: f'(x)=x 2 +4x-7 (x;t:-2)
A(l, 3166; -0,3668)
1.5
B(-5,3 J 66; -13, 6332)
1.5 Bili 2: Cho da thirc P(x) b~c 4, h~ so cua X4 bang 1
1 (3.5 diemj'Iim da tlnrc P(x)
, , ~ , P(I)=-11,P(2)=6,
Tu gia thiet co (
P -1)=-2,P(-2)=4
Xet da thtrc b~c b6n Q( x) thoa
Trang 2-2=-a+b-c+d
4=-8a +4b - 2c+d
t ~276' a ~ ?_;c·~ ~37
2.0
Kdt (lud:
P ( x )= (x 2 - 1)(x 2 - 4)+%x 3
0.5
23 2 37 31
+-x
.
2 (1.5 diemj'I'inh : P(20) - P(10)
Bili 3: Giiii h~ phuong trinh : { :3+ ( - xy =6 (I)
x +y +x+y=5
{(x+ y)[ (x+y)' -3xy ] ~6+ xy 0.5
(I)~
(x +y)2 - 2xy +x+y::; 5
f'-3PS~6+P
S2+S-2P =5
¢::> S3 +4S2 - 14S+7=0
0.5
• Giai phuong trinh t 2 - Sf+P=0 'u'ng voi cac e~p
(SJ;Pi) tren ta dUQ'C cac nghiem cua h~ SI ~ ~6,3702;~ ~ 14,6046
S2 ~ 1,7379;Pz ~ -0,1209 1,5
S3 ~ 0, 6323; ~ ~ -1,9839
{x ~1,8049 {x ~-0,0670
y ~ -0,0670' Y ~ 1,8049 ' 2.0
{X~-1'1274 {X~I,7597
y~I,7597 ' y~-1,1274
{ Ul =1;». =-2
BAi 4: Cho day s6: _ 1 V6i n>O;nEN
Un+2 - 2u n+1 - 3un
1 ViSt quy trinh bfim phim tinh Un; Sn(T6ng cua n s6hang d~u cua day un)
2
Trang 3CACHGIAI DIEM
Gan: 1 -> A; -2 -> B ;
-1 -> C (tong hai s5 hang dAu)2 - >D (bien dem)
1
D = D + 1:A = 2B A: C= C+A:
3 1
D=D + 1: B=2A - - B : C= C+B
3
1.0
2.0
?
DIEM
CACHGIAI
Bai 5: 0Tim gia tri 1611nhat, gia tri nho nhat cua ham so : f(x) =3x - 2+~4- 3x 2
DIEM KETQUA
BK : - Jj2 5,x 5,T3 2 X' h'et am so;
I(x) =3x-2+ }4-3x' tren doan [- Jj;~]
f'(X):::: 0<=>X =1
Thuc hien tren may tinh
f'(x)=O<=>x=l
f(1) =2;
2
/(Jj) ~1,4641;
2
f(- v13) ~ -5,4641
Max/(x) =f(1):::: 2
[-}~J
Min/(x) =/C-1):::: -5,4641
II
0.5
0.5 1.0
1.0
1.0
1.0
Trang 41 (3di~m)Tinh do dai BM, CN
BC= AB = 13 =213
sin C sin 30°
AC+BC
2 (2 diemj'Ifnh dien tich tam giac MMN
nen l la tam duong trong ngoai tiep
AB+BC+AC
BIC=NIM
2
Bili 7:
1.(2 di~m) Tinh gia tri eua bi~u thirc
A= ~I+.l)1 +.l + ]_. 1+.l +.!_+i ''-1+-_-1-+-.!_-+- -+-= -1
?
DIEM KETQUA
Gan A= 0, B ::;::0, C = 1
A
,
¢::?n.x(l+xy-l =xC~ +2C;X2 + +nC;xn
0.5
¢::? n(1+xy-I +n(n -I)x.(l +xy-2 ",,}2 C! + 22C;x + +n2c;xn-1
~ S= f (_1_) =2013(1 +_1_)2012 +2013.2012.-1 -(1 +_1_)2011
4
Trang 5I Sd0930,2233 I 0.5
SO L (ABeD); SO=%a ;mat phang (a) chua AD va (a) vuong goc voi (SBC)
s
1.(1.5di6m) Tinh VSABCD
c
0.5
a 2J3
=-.-2
1
V SABCD=-SO,SABCD
0.5
,
2 (3.5 diem) Thill dien tich thiet dien tao boi (a) va hinh ch6p SABeD
+Til J ke JH lS1; tir H ke EF IIBC c~t SB, SC
+IJ=201
+ S/l.)lJ =-.SO.lJ ; S/l.)'1J =-.JH.SI Suy ra JH = SO = - 0.5
Trang 6Bai 9: B6 ban A tang ban mot may tinh tri gia 5.000.000 d6ng bang each cho ban tien hang thang thea phirong thirc nhu sau: thang dftu tien ban nhan duoc 100.000 d6ng, cac thang ill thang thir hai tro di m6i thang nhan duoc 8<3tien han thang tnroc 20.000 d6ng
tiSn b<3cho voi 1ffi sudt 0,7%-1 thang, thi sau bao nhieu thang ban tra h~t n9'?(ViSt quy
20 thang S6 tiSn tra thang cu6i cung 1.0 1a 85392 dong
Thang thu nhat sau khi gop con no:
A = 5.000.000 - 100.000 = 4.900.000(d6ng)
Gan: A =4.900.000 ; B =100.000
Thi thang sau gop: B =B +20.000(gia tri trong
A =A x 1.007 - B
KETQUA
0.5 0.5 0.5
2.0
0.5
7,69cm , BC =6,96cm , CD =3,85cm Tinh ti l~ phan tram dien tich giira phan to mau
c
6
Trang 7CACH GIAI KETQUA DIEM
- Sin
-2R COB-2. - SIn. -I-CB
DoA =360° - Doc' - CoB - AoB
i50A R: 60°59'22"
I 2 - - . -
1.0
=> Dien tich phdn to mau la S Im=lr.R2 -SABCIJ R: 25,8374
T' l~ 1 y s ; - 25,8374 100~ 0 S /mR: 25,8374
1.0
Shin 29,5803
S1m R: 87 3466%,
s.;