C. Khai quat hoa, trim tugng hoa, dac biet hoa trong day hoc giai toan
Chuyen de 1: Cac bai toan ve hinh hoc giai tich
Cac bai toan hinh hgc giai tich dugc dua vao chuang trinh toan d THPT bit diu tir lap 10 va dugc kit thuc d lap 12. Tuy nhien, viec dua ngi dung nay
vao day d timg Idp trong chuang trinh toan CCGD, chuang trinh toan nang
cao va chuang trinh toan co ban cd nhimg diem khac nhau. Song, cho den
cuoi Idp 12 khi budc vao dn tap chuin bi cho cac ky thi, hgc sinh deu phai co dugc nhirng kiln thirc, ky nang, tu duy toan hgc nhat dinh thi mdi eo the giai
dugc cac dang toan trong cac ky thi. Tren thuc tl d nha trudng phd thong ta
thirc toan hpc dugc trang bj trude dd. Chinh vi thi, trude khi chudn bi ndi dung day thuc nghiem chuyen de ndy, cdng trinh da xdc muc tieu cdn day Id: L Muc tieu can dat
. .
- Dinh hudng cho hgc sinh bilt each tu dn tap, tu kilm tra cac kiln thirc ly thuyet da dugc trang bi lien quan den cdc bdi todn hinh hpc gidi tich .
- He thdng cac dang bai tap, phuang phap giai cho timg dang ciing vdi
^ f \ f
nhimg luu y can thiet ve kien thiie, ky nang cho timg dang bdi tap trong chuyen de.
- Gido vien vd hpc sinh tu kiem sodt dupe kit qud hpc tap eua hpc sinh ed ly thuyet ldn thire hdnh gidi cdc bdi todn hinh hpc gidi tich.
- Gay dupe niem tin, tao cdm gidc thu vi cho hpc sinh trong qud trinh dn
f f
tap, cung ed cdc kien thiic da hpc
t r
De dat dupe muc tieu tren cdng trinh tien hdnh cdc hoat ddng trong bdi day
thuc nghiem nhu sau:
Buac 1: GV Gioi thieu tong quan noi dung can on tap Noi dung can on
,. — . . ... —. ,
Hinh gidi tich trong mat phdng
1. Dudng thang trong mat phang 2. Dudng trdn trong mat phang
3.Elip(E), Hypebol(H), Parabol(P)
Hinh gidi tich trong khong gian
1. Dudng thang, mat phang trong khdng gian 2. Mat cdu
3. Khdi da dien, khdi trdn xo3.y{kh6 xet trong hinh gidi tich)
Birdc 2: Hu-dng dan hoc sinh he thong cac kien thu'c quan trong
0 budc nay, giao vien da chuan bi cho hoc sinh mgt bang he thong kien
A.Mot s6 ki6n thiic ckn nhd v6 ly thuyet
I.Cac kien thuc can hieu va nhd ve vee ta
Xet trong mat phang Xet trong khdng gian
7. Khdi niem ve vie ta
' {din, phuang hudng, dp ddi, cdch ky hieu vee to)
- Mot so loai vee ta dac biet: ( vee to khdng, vee to cimg phuang, ciing hudng, vee ta bang nhau)
2. Toa dp ciia vee ta
- Toa dp ciia mdt diem (Xet tren mdt true, tren he true toa dp)
- Cdch tinh toa dp ciia vee to trong mf A(xi,y,)); B(x2,y2))
>«5=(x2-xi;y2-yi)
- Toa dp cua mdt diem tren doan thang
A(xi, yi)); B(x2, y2)) . M Id diem thude doan thdng AB vd chia AB theo ty so k. Khi dd
X M Xl .
yu- yr^y:
\-k •"" 1-^
Chu y trudmg hop M Id trung diem
- Diing tpa dp dk tinh dp ddi vee to hay khodng cdch
giira hai dilm bode gdc giira hai vee ta( nhd cdng thiic)
3. Cdc phep todn tren vee to vd tinh chat
- Phep cdng (Quy tdc HBH, he thirc Salo ciing t/c
—>
giao hoan, kit hgp,cdng vdi vee to Q) - Phep trir
- Phep nhan vdi mdt so ( k>0 va k< 0) - Tieh vd hudng cua hai vee to
Chu y cae ket qua sau:
- A, B, C thdng hdng khi vd chi khi AB - k, AC
-1 Id trung dilm cua AB
<:>MA +MB =2MI VM
- G Id trpng tam tam gidc ABC
7. Khdi niem ve vee ta
Gidng nhu trong mat phang
2, Toa dp ciia vee to - Toa dp eiia mdt diem
- Cdch tinh toa dp ciia vee to trong KG
A(xi,y,),Z,); B(x2, y2, Z2)) ^5=(x2-xi;y2-yi;Z2-Zi) -Toa dp ciia mot diem tren doan thang
Cdch suy tuomg tu
- Diing tpa dp de tinh dp ddi vee to hay khodng cdch giira hai diem hoac gdc giira hai vee to (suy tuomg tu)
Chu y cdc ket qua sau:
-Ba vecta a '^b 'C <^P
khi aS] =0
-1 la trung diem cua AB c^ Z4 + 75 = 0
c^MA +MB =2MI \fM
- G la trgng tam cua tir dien ABCD
<>GA +GB + GC = 0
Xg= 1/3 (XA+XB+XC)
yg= l/3(yA+yB+yc)
- a;b;c tuy y ludn tdn tai n. kde
c = na-\-kb
<^GA +GS + G C + G D - 0
Xg= 1/3(XA+XB+XC)
yg= i/3(yA+yB+yc)