Huong dan on thi tot nghiep THPT Mon Toan hoc

Tags: Mon Toan, Bo GD, Phan Hinh, hai duong thang cheo nhau, cuc tri cua ham so, kien thuc co ban, phuong trinh tiep tuyen, gia tri lon nhat, the tich khoi, ve do thi, khoi da dien, bat phuong trinh, mat phang, dao ham, giua hai, 1


Bo GD-DT vua chinh thuc cong bo de cuong on tap cac mon thi tot nghiep THPT nam 2007. Toa Soan xin cung cap lan luot khung de cuong on tap nay. Duoi day la huong dan on tap chi tiet mon Toan hoc.

CHUONG TRINH KHONG PHAN BAN

Phan Giai tich gom ba chu de:

1. Dao ham va khao sat ham so.

2. Nguyen ham, tich phan va ung dung.

3. Dai so to hop.

Phan Hinh hoc gom hai chu de:

1. Phuong phap toa do trong mat phang.

2. Phuong phap toa do trong khong gian.

Trong moi chu de deu trinh bay noi dung, yeu cau on luyen nhung kien thuc trong tam, ky nang co ban, dang bai toan can luyen tap ma hoc sinh nao cung phai biet cach giai.

Chu de 1. Dao ham va khao sat ham so

Cac kien thuc co ban can nho

1. Tap xac dinh, tap gia tri cua ham so. Dau nhi thuc bac nhat, dau tam thuc bac hai. Ham so chan, ham so le, ham so tuan hoan. Cac quy tac tinh dao ham. Dao ham cua cac ham so so cap co ban. Dao ham ben trai, ben phai cua ham so. Dao ham tren khoang, tren doan. Quan he giua su ton tai cua dao ham va tinh lien tuc cua ham so. Y nghia cua dao ham cap mot. Phuong trinh tiep tuyen cua do thi cua ham so.

2. Diem toi han. Dieu kien de ham so dong bien, nghich bien; chieu bien thien, cac dinh ly (dinh ly Lagrang, dinh ly Fecma,...) va quy tac tim cuc dai va cuc tieu, gia tri lon nhat va gia tri nho nhat cua ham so trong mot khoang, mot doan. Tinh loi, lom va diem uon cua do thi. Tiem can. Tinh doi xung cua do thi (tam doi xung, truc doi xung).

3. Quy tac tinh dao ham va bang cac dao ham, dao ham bac cao va vi phan, tinh gan dung nho vi phan.

4. Cac dang gioi han co ban:

Huong dan on thi tot nghiep THPT Mon Toan hoc

5. Quy tac bon buoc tim cac diem cuc tri cua ham so.

6. Quy tac tim

Huong dan on thi tot nghiep THPT Mon Toan hoc

7. Cac cong thuc xac dinh cac he so a va b cua tiem can xien y =ax+b cua do thi ham so y=f(x).

8. So do khao sat ham so.

9. Cac bai toan ve tiep xuc va cat nhau cua hai do thi.

Cac dang toan can luyen tap

1. Cac ung dung cua dao ham: xet chieu bien thien, tim cuc tri, tim gia tri lon nhat nho nhat, xet nghiem cua phuong trinh, bat phuong trinh; lap phuong trinh tiep tuyen cua do thi (tiep tuyen tai mot diem, tiep tuyen di qua mot diem) biet he so goc cua tiep tuyen, dieu kien tiep xuc cua hai do thi; khong xet tiep tuyen song song voi truc tung Oy cua do thi.

2. Khao sat cac ham so y = ax3 + bx2 + cx + d (a 0) ; y = ax4 + bx2 + c (a 0)

Huong dan on thi tot nghiep THPT Mon Toan hoc

3. Cac ung dung do thi ham so, mien mat phang de giai toan bien luan nghiem phuong trinh, bat phuong trinh, tim gia tri lon nhat va nho nhat cua ham so hoac bieu thuc hai an, xet tinh dong bien, nghich bien, tim gia tri cuc tri khi ham so so cap thuong cho o dang co tham so m.

4. Bai toan tim giao diem hai duong, viet phuong trinh tiep tuyen.

Chu de 2. Nguyen ham, tich phan va ung dung

Cac kien thuc co ban can nho

1. Dinh nghia, tinh chat va bang cac nguyen ham.

2. Dinh nghia tich phan va cong thuc Niuton-Laibonit.

3. Cac tinh chat cua tich phan.

4. Hai phuong phap tinh tich phan: phuong phap doi bien so va phuong phap tinh tich phan tung phan.

5. Dien tich cua hinh thang cong, the tich cua vat the tron xoay.

Cac dang toan can luyen tap

1. Tim cac nguyen ham noi chung va tim nguyen ham thoa man dieu kien cho truoc.

2. Tim tich phan.

3. Cac ung dung cua tich phan: tinh dien tich hinh phang; tinh the tich khoi tron xoay theo cong thuc co ban.

Chu de 3. Dai so to hop

Cac kien thuc co ban can nho

Quy tac cong, quy tac nhan, cac khai niem va cong thuc tinh hoan vi, chinh hop, to hop, cong thuc nhi thuc Niuton.

Cac dang toan can luyen tap

1. Cac bai toan giai phuong trinh, bat phuong trinh co an so can tim lien quan cong thuc tinh so cac hoan vi, so cac chinh hop, so cac to hop.

2. Cac bai toan lien quan toi cong thuc khai trien nhi thuc Niuton: chung minh dang thuc, tinh he so cua mot luy thua trong mot khai trien.

Chu de 4. Phuong phap toa do trong mat phang

Cac kien thuc can nho

1. Toa do cua vecto, toa do cua diem trong he toa do Oxy. Bieu thuc toa do cua cac vecto cung phuong, cung huong; do dai cua vecto, vecto bang nhau. Lien he giua toa do vecto va toa do hai diem dau mut. Bieu thuc toa do cua cac phep tinh vecto, cua tich vo huong. Tinh cosin cua goc giua hai vecto, trung diem cua doan thang, trong tam cua tam giac, chia mot doan thang theo ty so cho truoc.

2. Khoang cach giua hai diem, tu mot diem toi mot duong thang, goc giua hai vecto, goc giua hai duong thang, dien tich tam giac.

3. Vecto phap tuyen, vecto chi phuong cua duong thang. Duong thang song song, vuong goc va vi tri tuong doi cua hai duong thang, chum duong thang.

4. Cac dang phuong trinh cua duong thang (dang tong quat, dang tham so, dang chinh tac), cua duong tron. Phuong trinh chinh tac cua 3 duong conic: elip, hypebol, parabol.

Cac dang toan can luyen tap

1. Viet cac dang phuong trinh cua duong thang khi biet di qua hai diem, di qua mot diem va song song hoac vuong goc voi mot duong thang, di qua mot diem va tiep xuc voi mot duong tron hoac mot conic.

2. Viet phuong trinh duong thang chua canh, duong cao, trung tuyen, trung truc, phan giac cua mot tam giac khi biet toa do ba dinh hoac phuong trinh ba canh.

3. Cac bai toan tinh toan: khoang cach (tim duong cao, chu vi, dien tich, tam va ban kinh duong tron ngoai tiep cua tam giac), goc (goc giua hai vecto, goc giua hai duong thang).

4. Cac bai toan ve duong tron: viet phuong trinh duong tron biet tam va ban kinh, biet hai diem dau duong kinh, tim phuong tich va truc dang phuong, viet phuong trinh tiep tuyen chung cua hai duong tron.

5. Cac bai toan ve duong conic: viet cac phuong trinh chinh tac cua elip, hypebol, parabol khi biet cac dieu kien xac dinh, tim cac yeu to (tam sai, tieu diem, duong chuan,…) cua mot duong conic khi biet phuong trinh cua no, viet phuong trinh tiep tuyen cua mot duong conic.

6. Cac bai toan ve xac dinh tap hop diem (quy tich).

Chu de 5. Phuong phap toa do trong khong gian

Cac kien thuc can nho

1. Toa do cua vecto, toa do cua diem trong he toa do Oxyz. Bieu thuc toa do cua cac vecto cung phuong, cung huong; do dai cua vecto, vecto bang nhau. Bieu thuc toa do cua cac phep tinh vecto, cua tich vo huong. Tinh cosin cua goc giua hai vecto, trung diem cua doan thang, trong tam cua tam giac, trong tam tu dien, chia mot doan thang theo ti so cho truoc.

Dieu kien de hai vecto cung phuong, hai vecto vuong goc, de ba vecto dong phang. Toa do diem doi xung qua mot diem voi diem cho truoc. Vecto phap tuyen, vecto chi phuong cua duong thang.

2. Khoang cach giua hai diem, tu mot diem toi mot mat phang, toi mot duong thang; khoang cach giua hai duong thang cheo nhau. Goc giua hai vecto, goc giua hai duong thang, goc giua hai mat phang, goc giua duong thang va mat phang. Dien tich tam giac, the tich hinh hop va hinh tu dien.

3. Cac dang phuong trinh cua mat phang, cua duong thang, cua mat cau.

Cac dang toan can luyen tap

1. Dung vecto (cung phuong, tich vo huong, bieu dien vectoqua hai hoac ba vecto khac) de chung minh mot he thuc vecto, chung minh tinh thang hang, song song, vuong goc, dong phang.

2. Cac bai toan tinh toan: khoang cach; (khoang cach giua hai diem, tu mot diem toi mot mat phang, toi mot duong thang, khoang cach giua hai duong thang cheo nhau); goc (goc giua hai vecto, goc giua hai duong thang, goc giua hai mat phang, goc giua duong thang va mat phang), tinh dien tich tam giac, the tich hinh hop va hinh tu dien.

3. Cac bai toan ve mat phang: tim vecto phap tuyen, viet phuong trinh tong quat, phuong trinh theo doan chan, phuong trinh mat phang di qua ba diem khong thang hang, xac dinh vi tri tuong doi cua hai mat phang, chum mat phang, mat phang song song, vuong goc, cac vi tri dac biet cua mat phang.

4. Cac bai toan ve duong thang: tim vecto chi phuong, viet phuong trinh tong quat, phuong trinh tham so, phuong trinh chinh tac; xac dinh cac he thuc vecto, he thuc toa do bieu dien vi tri tuong doi cua duong thang va mat phang, vi tri tuong doi giua hai duong thang (dong phang, cat nhau, song song, trung nhau, cheo nhau), vi tri tuong doi giua duong thang va mat phang (cat nhau, song song, nam tren, vuong goc), chum duong thang.

5. Cac bai toan ve mat cau: viet phuong trinh mat cau biet tam va ban kinh, biet hai diem dau duong kinh, biet bon diem khong dong phang, biet tam va mat phang tiep dien, viet phuong trinh mat phang tiep dien, tim tam va ban kinh khi biet phuong trinh mat cau. Xac dinh vi tri tuong doi giua mat cau va mat phang (cat nhau, tiep xuc, khong cat nhau).

6. Cac bai toan co ap dung phuong phap toa do de giai (ke tu khau thiet lap he toa do vuong goc, xac dinh toa do cac yeu to cho trong bai toan nhu diem, vecto, duong thang, goc, khoang cach,… trong he toa do do; toi khau ap dung cac he thuc, cac phuong trinh ve duong thang, mat phang, mat cau, goc, khoang cach, dien tich, the tich).

CHUONG TRINH PHAN BAN (THI DIEM)

BAN KHOA HOC TU NHIEN

Phan Dai so va Giai tich gom bon chu de:

1. Ung dung dao ham de khao sat va ve do thi cua ham so.

2. Nguyen ham, tich phan va ung dung.

3. Ham so luy thua, ham so mu va ham so logarit.

4. So phuc.

Phan Hinh hoc gom hai chu de:

1. Khoi da dien, mat cau va mat tron xoay.

2. Phuong phap toa do trong khong gian.

Trong moi chu de deu trinh bay noi dung, yeu cau on luyen nhung kien thuc trong tam, ky nang co ban, dang bai toan can luyen tap ma hoc sinh nao cung phai biet cach giai.

Chu de 1. Ung dung dao ham de khao sat va ve do thi cua ham so

Cac kien thuc co ban can nho

1. Ham so, tinh don dieu cua ham so; moi lien he giua su dong bien, nghich bien cua mot ham so va dau dao ham cap mot cua no.

2. Diem cuc dai, diem cuc tieu, diem cuc tri cua ham so. Cac dieu kien du de co diem cuc tri cua ham so.

3. Gia tri lon nhat, gia tri nho nhat cua ham so tren mot tap hop so.

4. Cac phep bien doi don gian do thi cua ham so (phep tinh tien song song voi truc toa do, phep doi xung qua truc toa do).

5. Duong tiem can dung, duong tiem can ngang, tiem can xien cua do thi.

6. So do tong quat de khao sat ham so (tim tap xac dinh, xet chieu bien thien, tim cuc tri, tim tiem can, lap bang bien thien, ve do thi).

Cac dang toan can luyen tap

1. Xet su dong bien, nghich bien cua mot ham so tren mot khoang dua vao dau dao ham cap mot cua no.

2. Tim diem cuc tri cua ham so; tim gia tri lon nhat, gia tri nho nhat cua ham so tren mot doan, mot khoang.

3. Van dung cac phep bien doi don gian do thi cua ham so (phep tinh tien song song voi truc toa do, phep doi xung qua truc toa do).

4. Tim duong tiem dung, tiem can ngang, tiem can xien cua do thi ham so.

5. Khao sat va ve do thi cua cac ham so

Huong dan on thi tot nghiep THPT Mon Toan hoc

trong do a, b, c, m, n la cac so cho truoc, am 0.

6. Dung do thi ham so de bien luan so nghiem cua mot phuong trinh.

7. Viet phuong trinh tiep tuyen cua do thi ham so tai mot diem thuoc do thi ham so, viet phuong trinh tiep tuyen chung cua hai duong cong tai diem chung.

Chu de 2. Nguyen ham, tich phan va ung dung

Cac kien thuc co ban can nho

1. Dinh nghia, tinh chat cua nguyen ham. Bang nguyen ham cua mot so ham so so cap. Phuong phap doi bien so. Tinh nguyen ham tung phan.

2. Dinh nghia va cac tinh chat cua tich phan. Tich phan cua ham so lien tuc bang cong thuc Niuton - Laibonit. Phuong phap tich phan tung phan va phuong phap doi bien so de tinh tich phan.

3. Dien tich hinh thang cong. Cac cong thuc tinh dien tich, the tich nho tich phan.

Cac dang toan can luyen tap

1. Tinh nguyen ham cua mot so ham so tuong doi don gian dua vao bang nguyen ham va cach tinh nguyen ham tung phan.

2. Su dung phuong phap doi bien so (khi da chi ro cach doi bien so va khong doi bien so qua mot lan) de tinh nguyen ham.

3. Tinh tich phan cua mot so ham so tuong doi don gian bang dinh nghia hoac phuong phap tinh tich phan tung phan.

4. Su dung phuong phap doi bien so (khi da chi ro cach doi bien so va khong doi bien so qua mot lan) de tinh tich phan.

5. Tinh dien tich mot so hinh phang, the tich mot so khoi nho tich phan.

Chu de 3. Ham so luy thua, ham so mu va ham so Logarit

Cac kien thuc co ban can nho

1. Luy thua. Luy thua voi so mu nguyen, so mu huu ti, so mu thuc. Cac tinh chat.

2. Logarit. Logarit co so a cua mot so duong (a > 0, a ≠ 1). Cac tinh chat co ban cua Logarit. Logarit thap phan. So e va Logarit tu nhien.

3. Ham so luy thua. Ham so mu. Ham so Logarit (dinh nghia, tinh chat, dao ham va do thi).

4. Phuong trinh, he phuong trinh, bat phuong trinh mu va logarit.

Cac dang toan can luyen tap

1. Dung cac tinh chat cua luy thua de don gian bieu thuc, so sanh nhung bieu thuc co chua luy thua.

2. Dung dinh nghia de tinh mot so bieu thuc chua Logarit don gian.

3. Dung cac tinh chat cua logarit vao cac bai tap bien doi, tinh toan cac bieu thuc chua Logarit.

4. Dung tinh chat cua cac ham so mu, ham so Logarit vao viec so sanh hai so, hai bieu thuc chua mu va Logarit.

5. Ve do thi cac ham so luy thua, ham so mu, ham so logarit.

6. Tinh dao ham cac ham so luy thua, mu va logarit.

7. Giai phuong trinh, bat phuong trinh mu: phuong phap dua ve luy thua cung co so, phuong phap Logarit hoa, phuong phap dung an so phu, phuong phap su dung tinh chat cua ham so.

8. Giai phuong trinh, bat phuong trinh logarit: phuong trinh dua ve Logarit cung co so, phuong phap mu hoa, phuong phap dung an so phu, phuong phap su dung tinh chat cua ham so.

9. Giai mot so he phuong trinh, he bat phuong trinh mu, logarit don gian.

Chu de 4. So phuc

Cac kien thuc co ban can nho

1. So phuc. Dang dai so cua so phuc. Bieu dien hinh hoc cua so phuc, modun cua so phuc, so phuc lien hop.

2. Can bac hai cua so phuc. Cong thuc tinh nghiem cua phuong trinh bac hai voi he so phuc.

3. Dang luong giac cua so phuc. Cong thuc Moa-vro va ung dung.

Cac dang toan can luyen tap

1. Tinh can bac hai cua so phuc. Giai phuong trinh bac hai voi he so phuc.

2. Cac phep tinh cong, tru, nhan, chia so phuc. Cach nhan, chia cac so phuc duoi dang luong giac.

3. Bieu dien cos3α, sin4α,... qua cosα va sinα.

Chu de 5. Khoi da dien, Mat cau va mat tron xoay

Cac kien thuc can nho

1. Khoi lang tru, khoi chop, khoi chop cut. Khoi da dien, phan chia va lap ghep cac khoi da dien.

2. Khoi da dien deu. Nam loai khoi da dien deu.

3. The tich khoi da dien. The tich khoi hop chu nhat. Cong thuc the tich khoi lang tru va khoi chop.

4. Mat cau. Giao cua mat cau va mat phang. Mat phang kinh, duong tron lon. Mat phang tiep xuc voi mat cau. Giao cua mat cau voi duong thang. Tiep tuyen cua mat cau. Dien tich mat cau.

5. Mat tron xoay. Mat non, giao cua mat non voi mat phang. Dien tich xung quanh cua hinh non. Mat tru, giao cua mat tru voi mat phang, dien tich xung quanh cua hinh tru.

Cac dang toan can luyen tap

1. Tinh the tich khoi lang tru va khoi chop.

2. Tinh dien tich mat cau, the tich khoi cau.

3. Tinh dien tich xung quanh cua hinh non, dien tich xung quanh cua hinh tru.

Chu de 6. Phuong phap toa do trong khong gian

Cac kien thuc can nho

1. He toa do trong khong gian, toa do cua mot vecto, toa do cua diem, bieu thuc toa do cua cac phep toan vecto, khoang cach giua hai diem. Mot so ung dung cua tich vecto (tich co huong cua hai vecto). Phuong trinh mat cau.

2. Phuong trinh mat phang. Vecto phap tuyen cua mat phang. Phuong trinh tong quat cua mat phang. Dieu kien de hai mat phang song song, vuong goc. Khoang cach tu mot diem den mot mat phang.

3. Phuong trinh duong thang. Phuong trinh tham so cua duong thang. Dieu kien de hai duong thang cheo nhau, cat nhau, song song hoac vuong goc voi nhau.

Cac dang toan can luyen tap

1. Tinh toa do cua tong, hieu, tich vecto voi mot so; tinh duoc tich vo huong cua hai vecto, tich co huong cua hai vecto. Tinh duoc dien tich hinh binh hanh, the tich khoi hop bang cach dung tich co huong cua hai vecto.

2. Tinh khoang cach giua hai diem co toa do cho truoc. Xac dinh toa do tam va ban kinh cua mat cau co phuong trinh cho truoc. Viet phuong trinh mat cau.

3. Xac dinh vecto phap tuyen cua mat phang. Viet phuong trinh mat phang. Tinh khoang cach tu mot diem den mot mat phang.

4. Viet phuong trinh tham so cua duong thang. Su dung phuong trinh cua hai duong thang de xac dinh vi tri tuong doi cua hai duong thang do.

BAN KHOA HOC XA HOI VA NHAN VAN

Phan Dai so va Giai tich gom bon chu de

1. Ung dung dao ham de khao sat va ve do thi cua ham so.

2. Nguyen ham, tich phan va ung dung.

3. Ham so luy thua, ham so mu va ham so logarit.

4. So phuc.

Phan Hinh hoc gom hai chu de

1. Khoi da dien, mat cau va mat tron xoay.

2. Phuong phap toa do trong khong gian.

Trong moi chu de deu trinh bay noi dung, yeu cau on luyen nhung kien thuc trong tam, ky nang co ban, dang baμi toan can luyen tap ma hoc sinh nao cung phai biet cach giai.

Chu de 1. Ung dung dao ham de khao sat va ve do thi cua ham so

Cac kien thuc co ban can nho

1. Ung dung dao ham cap mot de xet tinh don dieu cua ham so. Moi lien he giua su dong bien, nghich bien cua mot ham so va dau dao ham cap mot cua no.

2. Cuc tri cua ham so. Dieu kien du de co cuc tri. Diem cuc dai, diem cuc tieu, diem cuc tri cua ham so. Cac dieu kien du de co diem cuc tri cua ham so.

3. Gia tri lon nhat, gia tri nho nhat cua ham so. Gia tri lon nhat, gia tri nho nhat cua ham so tren mot tap hop so.

4. Duong tiem can cua do thi hμm so. Duong tiem can dung, duong tiem can ngang.

5. Khao sat ham so. Su tuong giao cua hai do thi. Phuong trinh tiep tuyen cua do thi ham so. Cac buoc khao sat va ve do thi ham so (tim tap xac dinh, xet chieu bien thien, tim cuc tri, tim tiem can, lap bang bien thien, ve do thi).

Cac dang toan can luyen tap

1. Xet su dong bien, nghich bien cua mot ham so tren mot khoang dua vao dau dao ham cap mot cua no.

2. Tim diem cuc tri cua hμm so.

3. Tim gia tri lon nhat, gia tri nho nhat cua ham so tren mot doan, mot khoang.

4. Tim duong tiem dung, tiem can ngang cua do thi ham so.

5. Khao sat va ve do thi cua cac ham so

Huong dan on thi tot nghiep THPT Mon Toan hoc

6. Dung do thi ham so de bien luan so nghiem cua mot phuong trinh.

7. Viet phuong trinh tiep tuyen cua do thi ham so tai mot diem thuoc do thi ham so.

Chu de 2. Nguyen ham, tich phan va ung dung

Cac kien thuc co ban can nho

1. Dinh nghia va cac tinh chat cua nguyen ham. Ky hieu ho cac nguyen ham cua mot ham so. Bang nguyen ham cua mot so ham so so cap. Phuong phap doi bien so. Tinh nguyen ham tung phan.

2. Dinh nghia tich phan va cong thuc Niuton-Laibonit. Cac tinh chat cua tich phan. Phuong phap doi bien so. Phuong phap tinh tich phan tung phan.

5. Dien tich cua hinh thang cong, the tich cua vat the tron xoay

Cac dang toan can luyen tap

1. Tim nguyen ham cua mot so ham so tuong doi don gian dua vao bang nguyen ham va cach tinh nguyen ham tung phan.

2. Su dung phuong phap doi bien so (khi da chi ro cach doi bien so va khong doi bien so qua mot lan) de tinh nguyen ham.

3. Tinh tich phan cua mot so ham so tuong doi don gian bang dinh nghia hoac phuong phap tinh tich phan tung phan.

4. Su dung phuong phap doi bien so (khi da chi ro cach doi bien so va khong doi bien so qua mot lan) de tinh tich phan.

5. Tinh dien tich mot so hinh phang, the tich mot so khoi nho tich phan.

Chu de 3. Ham so luy thua, ham so mu va ham so logarit

Cac kien thuc co ban can nho

1. Luy thua. Luy thua voi so mu nguyen, so mu huu ti, so mu thuc cua so thuc duong. Cac tinh chat cua luy thua voi so mu nguyen, luy thua voi so mu huu ti va luy thua voi so mu thuc.

2. Logarit. Logarit co so a (a > 0, a ≠ 1) cua mot so duong. Cac tinh chat co ban cua logarit. Logarit thap phan. So e va logarit tu nhien. (So sanh hai logarit cung co so, quy tac tinh logarit, doi co so cua logarit).

3. Dinh nghia, tinh chat, dao ham va do thi ham so luy thua. Ham so mu. Ham so logarit.

4. Phuong trinh, bat phuong trinh mu va logarit.

Cac dang toan can luyen tap

1. Dung cac tinh chat cua luy thua de don gian bieu thuc, so sanh nhung bieu thuc co chua luy thua.

2. Van dung dinh nghia de tinh mot so bieu thuc chua logarit don gian. Van dung cac tinh chat cua logarit vao cac bai tap bien doi, tinh toan cac bieu thuc chua logarit.

3. Van dung tinh chat cua cac ham so mu, ham so logarit vao viec so sanh hai so, hai bieu thuc chua mu va logarit.

4. Ve do thi cac ham so luy thua, ham so mu, ham so logarit.

5. Tinh duoc dao ham cac ham so y = ex, y = lnx.

6. Giai duoc phuong trinh, bat phuong trinh mu: phuong phap dua ve luy thua cung co so, phuong phap logarit hoa, phuong phap dung an so phu, phuong phap su dung tinh chat cua ham so.

7. Giai duoc phuong trinh, bat phuong trinh logarit: phuong phap dua ve logarit cung co so, phuong phap mu hoa, phuong phap dung an so phu.

Chu de 4. So phuc

Cac kien thuc co ban can nho

1. Dang dai so cua so phuc. Bieu dien hinh hoc cua so phuc, modun cua so phuc, so phuc lien hop. Cac phep tinh cong, tru, nhan, chia so phuc.

2. Giai phuong trinh bac hai voi he so thuc.

Cac dang toan can luyen tap

1. Thuc hien duoc cac phep tinh cong, tru, nhan, chia so phuc.

2. Biet tim nghiem phuc cua phuong trinh bac hai voi he so thuc (neu Δ < 0).

Chu de 5. Khoi da dien, mat cau va mat tron xoay

Cac kien thuc can nho

1. Khoi lang tru, khoi chop, khoi chop cut. Khoi da dien, phan chia va lap ghep cac khoi da dien.

2. Khoi da dien deu, tu dien deu, lap phuong, bat dien deu.

3. The tich khoi hop chu nhat. Cong thuc the tich khoi lang tru vμ khoi chop, the tich khoi da dien.

4. Mat cau, mat phang kinh, duong tron lon. Mat phang tiep xuc voi mat cau. Tiep tuyen cua mat cau, cong thuc tinh dien tich mat cau.

5. Mat tron xoay. Mat non, giao cua mat non voi mat phang, dien tich xung quanh cua hinh non. Mat tru, giao cua mat tru voi mat phang, dien tich xung quanh cua hinh tru.

Cac dang toan can luyen tap

1. Tinh the tich khoi lang tru vμ khoi chop.

2. Tinh dien tich mat cau, the tich khoi cau. Tinh dien tich xung quanh cua hinh non. Dien tich xung quanh cua hinh tru.

Chu de 6. Phuong phap toa do trong khong gian

Cac kien thuc can nho

1. He toa do trong khong gian. Toa do cua mot vecto. Bieu thuc toa do cua cac phep toan vecto. Toa do cua diem. Khoang cach giua hai diem. Phuong trinh mat cau. Tich vo huong cua hai vecto.

2. Phuong trinh mat phang. Vecto phap tuyen cua mat phang. Phuong trinh tong quat cua mat phang. Dieu kien de hai mat phang song song, vuong goc. Khoang cach tu mot diem den mot mat phang.

3. Phuong trinh duong thang. Phuong trinh tham so cua duong thang. Dieu kien de hai duong thang cheo nhau, cat nhau, song song hoac vuong goc voi nhau.

Cac dang toan can luyen tap

1. Tinh toa do cua tong, hieu, tich vecto voi mot so; tinh duoc tich vo huong cua hai vecto.

2. Tinh khoang cach giua hai diem co toa do cho truoc.

3. Xac dinh toa do tam va ban kinh cua mat cau co phuong trinh cho truoc.

4. Viet phuong trinh mat cau.

5. Xac dinh vecto phap tuyen cua mat phang, viet phuong trinh mat phang va tinh khoang cach tu mot diem den mot mat phang.

6. Viet phuong trinh tham so cua duong thang. Su dung phuong trinh cua hai duong thang de xac dinh vi tri tuong doi cua hai duong thang do.

(Nguon: Tuoi Tre/Bo GD-DT)

Viet Bao

Tìm hiểu: Mon Toan, Bo GD, Phan Hinh, hai duong thang cheo nhau, cuc tri cua ham so, kien thuc co ban, phuong trinh tiep tuyen, gia tri lon nhat, the tich khoi, ve do thi, khoi da dien, bat phuong trinh, mat phang, dao ham, giua hai, 1

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