Cflu I . (2,0 diem) Cho tap hdp A = j x e Z,|x| < 3 ) ; B -{ x e N, l < x + 1 <5 1. Li$t ke cdc phan ti3f tap A, B. 1. Li$t ke cdc phan ti3f tap A, B.
2. T i m A n B , A u B , A \ B , B \ A .
Cfiu I I . (2,0 diem) Cho ham so y - x^ + 4x + 3 (1). 1. Ve d6 thi (P) cua ham so (1). 1. Ve d6 thi (P) cua ham so (1).
2. Tim giao diem cua (P) vdi diTdng thing d: y = x +13. Cfiu I I I . (2,0 diem) Giai cac phiTdng trinh sau: Cfiu I I I . (2,0 diem) Giai cac phiTdng trinh sau:
1. Vl5x + 16=2x + 3.
2. 2 = 3.
_ 1 x- 1
Cfiu I V . (1,0 diem) Cho tam giac ABC. Goi M , P Ian ItfcJt Ik trung diem cua AB
\k BC. Hay phan tich AC theo hai vectd AP C M .
n. P H A N R I E N G (3,0 diem)
Thi sink chi dUffc lam mgt trong haiphdn (phdn A hoQC phdn B)
Ạ Theo chrfofng t r i n h Chufín
Cfiu Vạ (2,0 diem) Trong mat phing Oxy, cho cic diem A ( l ; 3); B(4; 2). 1. T i m toa do diem D tren Ox cdch deu hai diem A B. 1. T i m toa do diem D tren Ox cdch deu hai diem A B.
2. T i m toa do di€m E de ttf giac OABE la hinh blnh h^nh. ChuTng minh OABE la hinh chxS nhat. OABE la hinh chxS nhat.
Cfiu V i a . (1,0 diem) Cho phiTcJng trinh x^ - 2(m - l)x + m^ - 3m = 0. Dinh m de phi/cJng trinh c6 2 nghiem X j , X j thoa man \\+x\= 8. phi/cJng trinh c6 2 nghiem X j , X j thoa man \\+x\= 8.
B . Theo chifcfng t r i n h Nfing Cao
Cfiu Vb. (2,0 diem) Trong mat ph^ng toa do Oxy cho ba diem A ( l ; 0), B(0; 3) v i C(-3; 2). v i C(-3; 2).
1. Tinh g6c BAC cua tam gidc ABC.
2. Tim toa do diem D de tiJ gi^c ABCD la hinh binh hanh. ChuTng minh ABCD la hinh vuong. ABCD la hinh vuong.
Cfiu V i b . (1,0 diem) Giai phiTdng trinh ( x - 3 ) ( x + 2 ) - - x + 4 + 10 = 0.
H i i d N G D A N - D A P s d
Cfiu I .
1. Li^t ke cdc phdn tii tap A, B.
A - { - 3 ; - 2 ; - 1 ; 0; 1; 2; 3 } . B = { l ; 2; 3; 4 } . ?2. 77w A r > B , A u B , A \ B , B . ?2. 77w A r > B , A u B , A \ B , B .
A n B - { l ; 2; 3 } , A u B = {-3; - 2 ; - 1 ; 0; 1; 2; 3; 4 A \ = {-3; - 2 ; - 1 ; O}. B \ A - { 4 . A \ = {-3; - 2 ; - 1 ; O}. B \ A - { 4 .
Cfiu H .
1. Ve do thi (P) cua ham scf (1).
Doc gia tiT giaị
2. 77m giao diem cua (P) vdi duclrng thdng d:y = x + \'ị
Toa do giao diem cija parabol (P) va diTdng thing d la nghi$m cua h$:
x ^ + 4 x + 3 = x + 13 f x ^ + 3 x - 1 0 = 0 1 <=>\> < 1 <=>\> < <=> y =:x + 13 hoac \ ^ • y - 8 • l y = 15 y = x + 13 x = -5 x = 2 y = x + 13
Vay c6 hai giao diem la A ( - 5 ; 8), B(2; 15).
Cfiu I I I . Giai cdc phU(fng trinh...
1. Taco Vl5x + 16=2x + 3 2x + 3 > 0 2x + 3 > 0 15x + 16 = (2x + 3)^ 2 o 4x2-3x-7 = 0 x = - l 7 • X = — 4
Vay phircJng trinh da cho c6 hai nghiem x = - 1 , x = - •
4
}. Dieu ki^n x ± 1 .
PhiTdng trinh da cho tifdng diTdng 3x - 7 + 2(x +1) = 3(x^ - 1 ) o 3 x ^ - 5 x + 2 - 0 « » x = l (loai)hoacx = - - o 3 x ^ - 5 x + 2 - 0 « » x = l (loai)hoacx = - -
3
w 2