De thi thu DHCD mon Toan 2013 truong DHKHTN chuyen KHTN

Thứ ba, 04 Tháng sáu 2013, 14:51 GMT+7

Moi cac ban tham khao de thi thu Dai hoc cao dang nam 2013 mon Toan truong Dai hoc khoa hoc tu nhien truong THPT chuyen KHTN.


TRUONG DAI HOC KHOA HOC TU NHIEN
TRUONG THPT CHUYEN KHTN
DE THI THU DAI HOC DOT 1 NAM HOC 2012 – 2013
Mon: Toan hoc
Thoi gian lam bai: 180 phut

Cau I. Cho ham so y = x3 + (m + 3)x2 + 2(m + 1)x + m2 + 2m .

1) Khao sat su bien thien va ve do thi khi m = – 1.

2) Hay tim gia tri cua tham so m de ham so co cuc tri thoa man ymax.ymin < 0.

Cau II. Giai phuong trinh

De thi thu DH-CD mon Toan 2013 truong DHKHTN chuyen KHTN

Cau III.

De thi thu DH-CD mon Toan 2013 truong DHKHTN chuyen KHTN
.
2) Tim so cac so co 3 chu so sao cho tong cua 3 chu so do bang 11.

Cau IV

1) Trong khong gian voi he truc toa do Oxyz cho 2 diem A(0; – 2; 1); B(2; 0; 3) va mat phang (P): 2x – y – z + 4 = 0. Tim M ∈ (P) sao cho MA = MB va (ABM) vuong goc (P).

2) Cho khoi chop S.ABC, tam giac ABC vuong can tai B, AB = BC = 2a. Mat phang (SAB) va (SAC) cung vuong goc voi mat phang (ABC). Goc giua SC va mat phang (SAB) bang 300. Tinh the tich khoi chop S.ABC va khoang cach giua SA va BC.

3) Trong mat phang toa do Oxy cho hinh chu nhat ABCD co dien tich bang 12. Tam I cua hinh chu nhat la giao diem cua duong thang d1: x – y – 3 = 0 va duong thang d2: x + y – 6 = 0. Trung diem mot canh la giao diem cua d1 voi truc hoanh. Xac dinh toa do bon dinh cua hinh chu nhat.

Cau V. Voi a, b, c la cac so thuc duong thoa man dieu kien a2 + b2 + c2 + 2abc = 1. Chung minh rang: a2 + b2 + c2 ≥ 4(a2b2 + b2c2 + c2a2).


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