Kinh nghiem hoc va lam bai thi tot nghiep THPT mon Toan

Tags: Nguyen Son Ha, Ha Noi, Truong THPT Chuyen DH Su, dang dai so cua so phuc, phuong trinh bac hai, gia tri tuyet doi, thi tot nghiep, vuong goc voi, Giai Phuong Trinh, the tich khoi, hoc sinh, duong thang, mat phang, lam bai, bieu thuc, dau


Kinh nghiem hoc va lam bai thi tot nghiep THPT mon Toan
Anh minh hoa
Thac si Nguyen Son Ha – Truong THPT Chuyen DH Su pham Ha Noi chia se kinh nghiem rat chi tiet giup cac em hoc sinh hoc va lam bai thi tot nghiep THPT mon Toan nam nay dat ket qua cao nhat.

I. Dinh huong chung khi on tap va lam bai thi

1. Kinh nghiem on tap

Hoc 7 chu de lon theo sach Huong dan On tap thi tot nghiep THPT nam hoc 2010 – 2011, mon Toan cua Nha xuat ban giao duc; tham khao them Cau truc de thi nam 2010, mon Toan; tham khao de thi tot nghiep THPT mon Toan nhung nam gan day.

Nho va hieu duoc tat ca cac cong thuc trong Sach giao khoa THPT lop 12, biet van dung vao cac bai tap cu the.

Mac du trong tam kien thuc thi tot nghiep tap trung o chuong trinh lop 12 nhung phan lon cac bai toan THPT deu lien quan den viec rut gon mot bieu thuc, giai phuong trinh va bat phuong trinh bac nhat, giai phuong trinh va bat phuong trinh bac hai, giai he phuong trinh, giai phuong trinh chua dau gia tri tuyet doi, giai phuong trinh chua an o mau, giai phuong trinh vo ti. Hoc sinh can phai nam vung cac kien thuc, ki nang noi tren va mot so kien thuc lien quan duoc hoc o cac lop 7, 8, 9, 10 nhu: quy tac pha ngoac, quy tac nhan hai da thuc, quy tac chia da thuc cho da thuc (tinh huong thuong gap la chia tam thuc bac hai cho nhi thuc bac nhat), dinh li ve dau cua nhi thuc bac nhat, dinh li ve dau cua tam thuc bac hai.

2. Kinh nghiem lam bai thi

Hoc sinh can phai chu y ‘tieu chi 3 D: Dung – Du - Dep’ trong mot bai thi: ket qua dung, du y, trinh bay dep.

+ Hoc sinh phai viet dung cac cong thuc toan, viet dung cac ki hieu toan,

rut gon dung cac bieu thuc va ket qua dung o tat ca cac phep toan.

+ Hoc sinh phai trinh bay du y; cac bai toan thi tot nghiep bam sat noi dung sach giao khoa va deu co quy trinh giai, vi vay hoc sinh phai trinh bay day du cac y trong quy trinh giai mot bai toan nhu: quy trinh khao sat va ve do thi ham so, quy trinh tim gia tri lon nhat va nho nhat cua ham so tren mot tap hop, quy trinh tinh tich phan bang phuong phap doi bien...Thang diem cua bai thi se can cu vao cac buoc trong quy trinh giai toan, neu hoc sinh trinh bay du cac y thi se khong bi mat diem. Ngoai ra, hoc sinh can phai co dap so hoac ket luan trong loi giai moi bai toan vi bieu diem thuong co 0,25 diem o phan ket luan, dap so.

+ De dat diem cao, hoc sinh phai trinh bay dep, dien dat tot, cac y ro rang. Thang diem cua bai thi thuong co sau moi suy luan logic hoac sau moi phep bien doi, tinh gia tri bieu thuc... Vi vay, sau moi suy luan logic hoac bien doi, tinh toan bieu thuc…; hoc sinh nen xuong dong, chia y ro rang. Tranh tinh trang viet loi giai mot bai toan nhu viet mot doan van, khi do neu hoc sinh sai o dong cuoi cung thi co the bi mat nhieu diem.

Dat dieu kien va kiem tra dieu kien: Khi viet moi bieu thuc toan hoc, neu gap bieu thuc chua an o mau, bieu thuc chua can bac hai, bieu thuc logarit, hoc sinh can co thoi quen dat dieu kien de cac bieu thuc co nghia. Ngoai ra, voi bieu dien dai so cua so phuc ta phai dieu kien a, b la cac so thuc. Truoc khi ket luan dap so bai toan, hoc sinh can co thoi quen kiem tra lai dieu kien.

Lam bai de de cung co tinh than: Hoc sinh can doc de thi vai luot, chon bai de lam truoc va viet ngay vao bai thi, khi trinh bay duoc vao bai thi, tinh than lam bai cua hoc sinh se tot hon. Bai khao sat va ve do thi ham so la bai co san quy trinh giai va luon xuat hien trong cac ki thi tot nghiep THPT, hoc sinh co the lam ngay bai khao sat truoc. Neu hoc sinh lam bai kho khong ra ket qua thi co the mat tinh than lam bai.

II. Dinh huong on tap tung chu de

1. Chu de Ung dung dao ham de khao sat va ve do thi ca ham so. Hoc sinh can nam vung cac van de sau day:

Quy trinh khao sat va ve do thi cac ham so: ham da thuc bac ba, ham trung phuong, ham phan thuc bac nhat tren bac nhat. Trong phan nay, hoc sinh can luyen tap nhieu ki nang tinh dao ham, xet dau dao ham, lap bang bien thien cua ham so.

Phuong phap lap phuong trinh tiep tuyen: tiep tuyen tai tiep diem cho truoc, tiep tuyen di qua mot diem cho truoc, tiep tuyen co he so goc cho truoc, tiep tuyen song song hoac vuong goc voi mot duong thang cho truoc.

Cac dang tiem can cua do thi ham so: tiem can dung, tiem can ngang.

Su lien he giua so giao diem cua duong thang va do thi ham so voi so nghiem thuc phan biet cua phuong trinh hoanh do giao diem.

Dau hieu nhan biet ham so dong bien, ham so nghich bien tren mot khoang xac dinh; dieu kien de ham so dong bien, nghich bien tren mot khoang xac dinh.

Cac dieu kien de ham so co cuc tri: Dieu kien can de ham so dat cuc tri, dieu kien du de ham so dat cuc dai, cuc tieu.

Phuong phap tim gia tri lon nhat va gia tri nho nhat cua ham so tren mot tap hop so (doan, khoang, nua khoang). Khao sat truc tiep ham so ban dau hoac hoac khao sat gian tiep ham so cua bien moi (doi bien).

Phuong phap van dung tinh don dieu cua ham so de chung minh bat dang thuc, giai phuong trinh.

2. Chu de Ham so luy thua, ham so mu va ham so logarit. Hoc sinh can nam vung cac van de sau:

Dieu kien xac dinh cua bieu thuc logarit.

Dao ham cua ham luy thua, ham so mu va ham so logarit.

Cac phuong phap bien doi tuong duong giai phuong trinh, bat phuong trinh mu, logarit: phuong phap logarit hoa, phuong phap dua ve cung co so.

Phuong phap dat an phu giai phuong trinh, bat phuong trinh mu, logarit.

Phuong phap the, phuong phap dat an phu giai he phuong trinh mu, logarit.

3. Chu de Nguyen ham, tich phan va ung dung. Hoc sinh can nam vung cac van de sau:

Cac cong thuc dao ham duoc gioi thieu trong Sach giao khoa lop 11.

Bang nguyen ham, tich phan cua mot so ham so thuong gap: Ham luy thua, ham so mu, ham so logarit, ham so luong giac

Phuong phap doi bien so tinh nguyen ham, tich phan: Chu y doi bien so dong thoi voi doi vi phan, voi bai toan tinh tich phan thi doi bien so dong thoi voi doi vi phan va doi can. Chu y: vi phan va can phai duoc viet tuong ung voi bien duoi dau nguyen ham.

Phuong phap tinh nguyen ham tung phan, tich phan tung phan. Neu bieu thuc duoi dau nguyen ham tich phan co mot trong dang

voi la ham da thuc, ta chon neu bieu thuc trong nguyen ham tich phan co dang voi la ham da thuc, ta chon neu bieu thuc duoi dau nguyen ham tich phan co dang hoac ta chon trong cac truong hop tren, chon dv la thanh phan con lai duoi dau nguyen ham tich phan.

Voi nguyen ham, tich phan cua ham luong giac, hoc sinh can chu y cong thuc luong giac bien tich thanh tong, cong thuc nhan doi (Sach giao khoa lop 10). Chu y:

Ung dung tich phan tich dien tich hinh phang. De lam tot phan nay, hoc sinh can ren ki nang tinh tich phan cua ham chua dau gia tri tuyet doi; ki nang xet dau bieu thuc bac nhat, bieu thuc bac hai, phan thuc huu ti bac nhat tren bac nhat. Hoc sinh co the bi 0 diem phan nay neu viet nham cong thuc dien tich cong thuc chinh xac phai la sau khi giai thich ve dau cua hoc sinh moi duoc pha dau gia tri tuyet doi.

Ung dung tich phan tich the tich khoi tron xoay.

4.Chu de so phuc. Hoc sinh can nam vung nhung van de sau:

Dang dai so cua so phuc, phan thuc va phan ao cua so phuc, so phuc lien hop cua mot so phuc, mo dun cua so phuc, dieu kien de mot so phuc la so thuc, dieu kien de mot so phuc la so thuan ao. Chu y: Khi viet dang dai so ta phai co dieu kien a, b la cac so thuc.

Phep toan giua hai so phuc. Chu y: voi cac so thuc a, b, c, d ta co

Ta co the ap dung hang dang thuc dang nho doi voi cac so phuc.

Phuong trinh bac nhat doi voi so phuc: su dung phep toan giua cac so phuc hoac su dung dang dai so cua so phuc de giai phuong trinh.

Phuong trinh bac hai nghiem phuc: . Neu hoac thi co the su dung cong thuc nghiem nhu cong thuc nghiem cua phuong trinh bac hai da hoc o lop 9, neu thi Neu khong phai la so thuc thi phai chon cac so thuc m, n de ta co

Su dung dang dai so cua so phuc de tim can bac hai cua so phuc.

Bieu dien hinh hoc cua so phuc: Tim tap hop diem bieu dien so phuc thoa man mot tinh chat xac dinh. Tinh huong thuong gap la viet voi x, y la cac so thuc, bien doi tinh chat cua z tuong duong voi x, y thoa man mot phuong trinh duong thang hoac duong tron.

Dang luong giac cua so phuc (danh cho hoc sinh ban nang cao): Cho so phuc duoi dang dai so, bieu dien so phuc duoi dang luong giac, tim acgumen, su dung cong thuc Moa-vro tim luy thua bac n cua so phuc; su dung dang luong giac de thuc hien phep toan giua hai so phuc.

5. Chu de Khoi da dien. Hoc sinh can chu y nhung van de sau

Cong thuc tinh dien tich tam giac, dien tich hinh thang, dien tich hinh chu nhat, the tich khoi chop, the tich khoi lang tru tam giac va lang tru tu giac.

Trong phan the tich, hoc sinh thuong phai tinh duong cao cua hinh chop hoac hinh lang tru. Cac tinh huong thuong gap: hinh chop hoac hinh lang tru co mot mat ben vuong goc voi mat day, khi do duong cao cua hinh chop hoac hinh lang tru la duong cao cua mat ben; hinh chop deu co duong cao di qua tam cua mat day, hinh lang tru dung co duong cao bang canh ben.

De lam tot chu de nay, hoc sinh phai nho dinh li Pytago trong tam giac vuong, dinh li cosin trong tam giac, he thuc lien he giua goc va canh trong tam giac vuong. Ngoai ra, hoc sinh can nam vung dau hieu nhan biet duong thang vuong goc voi mat phang, dau hieu nhan biet hai duong thang vuong goc, goc giua duong thang va mat phang, goc giua hai mat phang.

6.Chu de Hinh cau, hinh tru, hinh non

Nam vung cong thuc dien tich mat cau, the tich khoi cau, dien tich xung quanh cua hinh tru, the tich khoi tru, dien tich xung quanh cua hinh non va the tich khoi non.

Voi dang toan hinh cau, hoc sinh phai biet xac dinh tam mat cau ngoai tiep da dien. Mot so truong hop thuong gap: cac dinh da dien cung nhin hai diem co dinh duoi mot goc vuong, khi do tam mat cau la trung diem doan noi hai diem co dinh; hinh chop deu co tam mat cau ngoai tiep thuoc duong cao. Nhu vay, de nam vung dang toan nay, hoc sinh phai nam vung cac loai quan he vuong goc: duong thang vuong goc voi duong thang, duong thang vuong goc voi mat phang, hai mat phang vuong goc.

7.Phuong phap toa do trong khong gian

Nam vung cong thuc toa do tich co huong cua hai vec to. Biet su dung

tich co huong cua hai vec to de tinh dien tich tam giac, tinh the tich khoi hop, the tich khoi tu dien (ban nang cao). Su dung tich co huong cua hai vec to de xac dinh vec to chi phuong cua duong thang khi vec to chi phuong vuong goc voi hai vec to cho truoc, su dung tich co huong cua hai vec to de xac dinh vec to phap tuyen cua hai mat phang khi vec to phap tuyen vuong goc voi hai vec to cho truoc.

Nam vung cac dang phuong trinh duong thang: phuong trinh tham so va phuong trinh chinh tac, nam vung phuong trinh mat phang va phuong trinh mat cau. Chu y cac dang mat phang dac biet (song song voi cac mat phang toa do, chua cac truc toa do,…).

Lap phuong trinh mat phang thoa man mot trong cac dieu kien: mat

phang chua ba diem phan biet, chua mot duong thang va mot diem ngoai duong thang, di qua mot diem va vuong goc voi mot duong thang cho truoc, di qua mot diem va song song voi mot mat phang cho truoc, di qua mot diem va song song voi hai duong thang cho truoc, tiep xuc mat cau tai mot diem cho truoc, mat phang chua mot duong thang va song song voi mot duong thang khac.

Lap phuong trinh duong thang thoa man mot trong cac dieu kien sau: duong thang di qua hai diem cho truoc, di qua mot diem va song song voi mot duong thang cho truoc, di qua mot diem va vuong goc voi mot mat phang cho truoc, di qua mot diem vuong goc voi hai duong cho truoc, di qua mot diem dong thoi vuong goc va cat mot duong cho truoc, duong thang la giao tuyen cua hai mat phang cho truoc.

Lap phuong trinh mat cau thoa man mot trong cac dieu kien sau: mat cau co tam va ban kinh cho truoc, co tam va di qua mot diem cho truoc, co tam va tiep xuc voi mot mat phang cho truoc, co tam va tiep xuc voi mot duong thang cho truoc (ban nang cao), chua bon diem cho truoc.

Goc giua hai duong thang, goc giua hai mat phang (ban nang cao).

Khoang cach tu mot diem den mat phang, khoang cach tu mot diem den duong thang, khoang cach giua hai duong thang cheo nhau.

Vi tri tuong doi cua hai duong thang, vi tri tuong doi cua duong thang va mat phang, vi tri tuong doi cua hai mat phang.

Theo Ths. Nguyen Son Ha (Giao duc)
Viet Bao

Tìm hiểu: Nguyen Son Ha, Ha Noi, Truong THPT Chuyen DH Su, dang dai so cua so phuc, phuong trinh bac hai, gia tri tuyet doi, thi tot nghiep, vuong goc voi, Giai Phuong Trinh, the tich khoi, hoc sinh, duong thang, mat phang, lam bai, bieu thuc, dau
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