Toàn cảnh đề thi tốt nghiệp THPT môn Toán (2018 – 2022)

["5. Kh\u1ea3o s\u00e1t s\u1ef1 bi\u1ebfn thi\u00ean v\u00e0 v\u1ebd \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0104 C\u00e2u 102 (C\u00e2u 35 - \u0110MH - BGD&\u0110T - N\u0103m 2018 - 2019). Cho h\u00e0m s\u1ed1 y = f (x) li\u00ean t\u1ee5c tr\u00ean R v\u00e0 c\u00f3 \u0111\u1ed3 th\u1ecb nh\u01b0 h\u00ecnh v\u1ebd b\u00ean. y T\u1eadp h\u1ee3p t\u1ea5t c\u1ea3 c\u00e1c gi\u00e1 tr\u1ecb th\u1ef1c c\u1ee7a tham s\u1ed1 m \u0111\u1ec3 ph\u01b0\u01a1ng tr\u00ecnh 3 f (sin x) = m c\u00f3 nghi\u1ec7m thu\u1ed9c kho\u1ea3ng (0; \u03c0) l\u00e0 1 A [\u22121; 3). B (\u22121; 3). C (\u22121; 3). D [\u22121; 1). 1 \u22121 O x \u22121 \u0253 L\u1eddi gi\u1ea3i. \u0110\u1eb7t t = sin x. V\u1edbi x \u2208 (0; \u03c0) th\u00ec t \u2208 (0; 1]. y Do \u0111\u00f3 ph\u01b0\u01a1ng tr\u00ecnh f (sin x) = m c\u00f3 nghi\u1ec7m thu\u1ed9c kho\u1ea3ng (0; \u03c0) khi 3 v\u00e0 ch\u1ec9 khi ph\u01b0\u01a1ng tr\u00ecnh f (t) = m c\u00f3 nghi\u1ec7m thu\u1ed9c n\u1eeda kho\u1ea3ng (0; 1]. Quan s\u00e1t \u0111\u1ed3 th\u1ecb ta suy ra \u0111i\u1ec1u ki\u1ec7n c\u1ee7a tham s\u1ed1 m l\u00e0 m \u2208 [\u22121; 1). 1 x 1 y=m \u22121 O \u22121 Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 103 (C\u00e2u 38 - M\u0110 102 - BGD&\u0110T - N\u0103m 2018 - 2019). Cho h\u00e0m s\u1ed1 f (x), h\u00e0m s\u1ed1 y = f (x) li\u00ean t\u1ee5c tr\u00ean R v\u00e0 c\u00f3 \u0111\u1ed3 th\u1ecb nh\u01b0 h\u00ecnh y v\u1ebd. B\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh f (x) > x + m (m l\u00e0 tham s\u1ed1 th\u1ef1c) nghi\u1ec7m \u0111\u00fang 1 v\u1edbi m\u1ecdi x \u2208 (0; 2) khi v\u00e0 ch\u1ec9 khi O A m \u2264 f (2) \u2212 2. B m < f (2) \u2212 2. 2x C m \u2264 f (0). D m < f (0). \u0253 L\u1eddi gi\u1ea3i. X\u00e9t b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh f (x) > x + m \u21d4 m < f (x) \u2212 x. y 2x X\u00e9t h\u00e0m s\u1ed1 g(x) = f (x) \u2212 x v\u1edbi x \u2208 (0; 2). Ta c\u00f3 g (x) = f (x) \u2212 1. 1 g (x) = 0 \u21d4 f (x) = 1. T\u1eeb \u0111\u1ed3 th\u1ecb ta th\u1ea5y tr\u00ean (0; 2) \u0111\u01b0\u1eddng th\u1eb3ng y = 1 n\u1eb1m ph\u00eda tr\u00ean \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 O y = f (x) n\u00ean f (x) < 1, \u2200x \u2208 (0; 2) hay g (x) < 0, \u2200x \u2208 (0; 2). Ta c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean nh\u01b0 sau 148 S\u0110T: 0905.193.688 Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t","Ch\u01b0\u01a1ng 1. \u1ee8NG D\u1ee4NG \u0110\u1ea0O H\u00c0M \u0110\u1ec2 KH\u1ea2O S\u00c1T V\u00c0 V\u1ebc \u0110\u1ed2 TH\u1eca C\u1ee6A H\u00c0M S\u1ed0 x0 2 g (x) \u2212 g(0) g(x) g(2) T\u1eeb b\u1ea3ng bi\u1ebfn thi\u00ean ta th\u1ea5y b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh f (x) > x + m nghi\u1ec7m \u0111\u00fang v\u1edbi m\u1ecdi x \u2208 (0; 2) khi v\u00e0 ch\u1ec9 khi m < g(x) v\u1edbi \u2200x \u2208 (0; 2) \u21d4 m \u2264 g(2) \u21d4 m \u2264 f (2) \u2212 2. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 104 (C\u00e2u 50 - M\u0110 102 - BGD&\u0110T - N\u0103m 2018 - 2019). Cho hai h\u00e0m s\u1ed1 y = x + x + 1 + x + 2 + x + 3 v\u00e0 y = |x + 1| \u2212 x + m (m l\u00e0 tham s\u1ed1 th\u1ef1c) x+1 x+2 x+3 x+4 c\u00f3 \u0111\u1ed3 th\u1ecb l\u1ea7n l\u01b0\u1ee3t l\u00e0 (C1) v\u00e0 (C2). T\u1eadp h\u1ee3p t\u1ea5t c\u1ea3 c\u00e1c gi\u00e1 tr\u1ecb c\u1ee7a m \u0111\u1ec3 (C1) v\u00e0 (C2) c\u1eaft nhau t\u1ea1i \u0111\u00fang 4 \u0111i\u1ec3m ph\u00e2n bi\u1ec7t l\u00e0 A (3; +\u221e). B (\u2212\u221e; 3]. C (\u2212\u221e; 3). D [3; +\u221e). \u0253 L\u1eddi gi\u1ea3i. \uf8f1x = \u22121 \uf8f4 \uf8f4 \u0110i\u1ec1u ki\u1ec7n \uf8f4\uf8f2x = \u22122 \uf8f4x = \u22123 \uf8f4 \uf8f4 = \u22124. \uf8f3x Ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh ho\u00e0nh \u0111\u1ed9 giao \u0111i\u1ec3m x + x + 1 + x + 2 + x + 3 = |x + 1| \u2212 x + m x+1 x+2 x+3 x+4 \u00c5 1 \u00e3\u00c5 1 \u00e3\u00c5 1 \u00e3\u00c5 1 \u00e3 \u21d4 1\u2212 + 1\u2212 + 1\u2212 + 1\u2212 = |x \u2212 1| \u2212 x + m x+1 x+2 x+3 x+4 \u21d4 \u00c5 1 + 1 + 1 + 1 \u00e3 (\u2217). x \u2212 |x + 1| + 4 \u2212 =m x+1 x+2 x+3 x+4 \u0110\u1eb7t D1 = (\u22121; +\u221e) v\u00e0 D2 = (\u2212\u221e; \u22124) \u222a (\u22124; \u22123) \u222a (\u22123; \u22122) \u222a (\u22122; \u22121), ta c\u00f3 \uf8ee\u00c5 1 + 1 + 1 + 1\u00e3 khi x \u2208 D1 3\u2212 =m khi x \u2208 D2. x+1 x+2 x+3 x+4 (\u2217) \u21d4 \uf8ef \u00c5 1 1 1 1 \u00e3 \uf8ef =m + + + \uf8f02x + 5 \u2212 x+1 x+2 x+3 x+4 \uf8f1 \u2212 \u00c5 1 1 + x 1 2 + x 1 3 + x 1 \u00e3 khi x \u2208 D1 \uf8f4\uf8f43 x + + + + 4 khi x \u2208 D2. \uf8f2 \u0110\u1eb7t f (x) = \u00c5 1 1 1 1 \u00e3 x + + + + 4 \uf8f4\uf8f3\uf8f42x + 5 \u2212 1 + x 2 + x 3 + x \uf8f11 1 1 1 khi x \u2208 D1 + + + khi x \u2208 D2. \uf8f4 \uf8f4 (x + 1)2 (x + 2)2 (x + 3)2 (x + 4)2 \uf8f2 C\u00f3 f (x) = 1 1 1 1 \uf8f4\uf8f42 + + + + \uf8f3 (x + 1)2 (x + 2)2 (x + 3)2 (x + 4)2 V\u1eady h\u00e0m s\u1ed1 \u0111\u1ed3ng bi\u1ebfn tr\u00ean t\u1eebng kho\u1ea3ng x\u00e1c \u0111\u1ecbnh, ta c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean nh\u01b0 h\u00ecnh v\u1ebd Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 149 S\u0110T: 0905.193.688","5. Kh\u1ea3o s\u00e1t s\u1ef1 bi\u1ebfn thi\u00ean v\u00e0 v\u1ebd \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 x \u2212\u221e \u22124 \u22123 \u22122 \u22121 + +\u221e f (x) + + + + 3 f (x) +\u221e +\u221e +\u221e +\u221e \u2212\u221e \u2212\u221e \u2212\u221e \u2212\u221e \u2212\u221e Do \u0111\u00f3 \u0111\u1ec3 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 4 nghi\u1ec7m ph\u00e2n bi\u1ec7t th\u00ec m \u2265 3 \u21d2 m \u2208 [3; +\u221e). Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 105 (C\u00e2u 41 - M\u0110 101 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2020 - 2021). Cho h\u00e0m s\u1ed1 b\u1eadc ba y = f (x) c\u00f3 \u0111\u1ed3 th\u1ecb l\u00e0 \u0111\u01b0\u1eddng cong h\u00ecnh b\u00ean. S\u1ed1 nghi\u1ec7m y 3 th\u1ef1c ph\u00e2n bi\u1ec7t c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh f (f (x)) = 1 l\u00e0 A 9. B 3. C 6. D 7. O 1 1 \u2212\u221211 2 x \u0253 L\u1eddi gi\u1ea3i. D\u1ef1a v\u00e0o \u0111\u1ed3 th\u1ecb ta th\u1ea5y ph\u01b0\u01a1ng tr\u00ecnh y 3 \uf8eef (x) = a < \u22121 f (f (x)) = 1 \u21d4 \uf8eff (x) = 0 y=b 1 y=1 \uf8f0 O1 f (x) = b \u2208 (1; 2). \u2212\u22121 1 2y =x a Ph\u01b0\u01a1ng tr\u00ecnh f (x) = a, (a < \u22121) c\u00f3 m\u1ed9t nghi\u1ec7m. Ph\u01b0\u01a1ng tr\u00ecnh f (x) = 0 c\u00f3 3 nghi\u1ec7m ph\u00e2n bi\u1ec7t kh\u00f4ng tr\u00f9ng v\u1edbi nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh f (x) = a. Ph\u01b0\u01a1ng tr\u00ecnh f (x) = b c\u00f3 3 nghi\u1ec7m ph\u00e2n bi\u1ec7t kh\u00f4ng tr\u00f9ng v\u1edbi nghi\u1ec7m c\u1ee7a c\u00e1c ph\u01b0\u01a1ng tr\u00ecnh f (x) = 0 v\u00e0 f (x) = a. V\u1eady ph\u01b0\u01a1ng tr\u00ecnh f (f (x)) = 1 c\u00f3 7 nghi\u1ec7m ph\u00e2n bi\u1ec7t. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 106 (C\u00e2u 40 - \u0110MH - BGD&\u0110T - N\u0103m 2021 - 2022). Cho h\u00e0m s\u1ed1 y = f (x) c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean nh\u01b0 sau x \u2212\u221e \u22121 2 +\u221e +\u221e y +0\u22120+ D 6. 1 y \u2212\u221e \u22125 S\u1ed1 nghi\u1ec7m th\u1ef1c ph\u00e2n bi\u1ec7t c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh f (f (x)) = 0 l\u00e0 A 3. B 4. C 5. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 \u00f1f (x) = \u22121 f (f (x)) = 0 \u21d4 f (x) = 2 Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 150 S\u0110T: 0905.193.688","Ch\u01b0\u01a1ng 1. \u1ee8NG D\u1ee4NG \u0110\u1ea0O H\u00c0M \u0110\u1ec2 KH\u1ea2O S\u00c1T V\u00c0 V\u1ebc \u0110\u1ed2 TH\u1eca C\u1ee6A H\u00c0M S\u1ed0 V\u1edbi f (x) = \u22121, \u0111\u00e2y l\u00e0 ph\u01b0\u01a1ng tr\u00ecnh ho\u00e0nh \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = f (x) v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng y = \u22121. T\u1eeb b\u1ea3ng bi\u1ebfn thi\u00ean ta th\u1ea5y \u0111\u01b0\u1eddng th\u1eb3ng y = \u22121 c\u1eaft \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = f (x) t\u1ea1i ba \u0111i\u1ec3m ph\u00e2n bi\u1ec7t, suy ra ph\u01b0\u01a1ng tr\u00ecnh f (x) = \u22121 c\u00f3 3 nghi\u1ec7m th\u1ef1c ph\u00e2n bi\u1ec7t. V\u1edbi f (x) = 2, \u0111\u00e2y l\u00e0 ph\u01b0\u01a1ng tr\u00ecnh ho\u00e0nh \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = f (x) v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng y = 2. T\u1eeb b\u1ea3ng bi\u1ebfn thi\u00ean ta th\u1ea5y \u0111\u01b0\u1eddng th\u1eb3ng y = 2 c\u1eaft \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = f (x) t\u1ea1i m\u1ed9t \u0111i\u1ec3m duy nh\u1ea5t, suy ra ph\u01b0\u01a1ng tr\u00ecnh f (x) = 2 c\u00f3 1 nghi\u1ec7m th\u1ef1c (nghi\u1ec7m n\u00e0y kh\u00e1c 3 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh f (x) = 1). V\u1eady ph\u01b0\u01a1ng tr\u00ecnh f (f (x)) = 0 c\u00f3 4 nghi\u1ec7m th\u1ef1c ph\u00e2n bi\u1ec7t. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 107 (C\u00e2u 38 - M\u0110 103 - BGD&\u0110T - N\u0103m 2018 - 2019). Cho h\u00e0m s\u1ed1 y = f (x), h\u00e0m s\u1ed1 y = f (x) li\u00ean t\u1ee5c tr\u00ean R v\u00e0 c\u00f3 \u0111\u1ed3 y th\u1ecb nh\u01b0 h\u00ecnh v\u1ebd b\u00ean. B\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh f (x) < 2x + m (m l\u00e0 tham 2 y = f (x) s\u1ed1 th\u1ef1c) nghi\u1ec7m \u0111\u00fang v\u1edbi m\u1ecdi x \u2208 (0; 2) khi v\u00e0 ch\u1ec9 khi \u22121 O 1 2x A m > f (0). B m > f (2) \u2212 4. C m \u2265 f (0). D m \u2265 f (2) \u2212 4. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 f (x) < 2x + m \u21d4 m > f (x) \u2212 2x (1). \u0110\u1eb7t g(x) = f (x) \u2212 2x, x \u2208 (0; 2). \u2200x \u2208 (0; 2), g (x) = f (x) \u2212 2 < 0 \u21d2 h\u00e0m s\u1ed1 y = g(x) ngh\u1ecbch bi\u1ebfn tr\u00ean (0; 2). Do \u0111\u00f3 (1) \u0111\u00fang v\u1edbi m\u1ecdi x \u2208 (0; 2) khi v\u00e0 ch\u1ec9 khi m \u2265 g(0) = f (0). Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 108 (C\u00e2u 40 - M\u0110 101 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2020 - 2021). Cho h\u00e0m s\u1ed1 f (x) = ax4 + bx3 + cx2, (a, b, c \u2208 R). H\u00e0m s\u1ed1 y = f (x) y c\u00f3 \u0111\u1ed3 th\u1ecb nh\u01b0 trong h\u00ecnh b\u00ean. S\u1ed1 nghi\u1ec7m th\u1ef1c ph\u00e2n bi\u1ec7t c\u1ee7a ph\u01b0\u01a1ng O tr\u00ecnh 3f (x) + 4 = 0 l\u00e0 A 4. B 2. C 3. D 1. x \u0253 L\u1eddi gi\u1ea3i. \uf8eex = x1 < 0 T\u1eeb \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 y = f (x), ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh f (x) = 0 \u21d4 \uf8efx = 0 \uf8f0 x = x2 > 0. Theo gi\u1ea3i thi\u1ebft, ta c\u00f3 f (x) = ax4 + bx3 + cx2 n\u00ean f (0) = 0. B\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a h\u00e0m s\u1ed1 y = f (x) x \u2212\u221e x1 0 x2 +\u221e f (x) +0\u22120+0\u2212 f (x1) f (x2) f (x) \u2212\u221e 0 \u2212\u221e Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 151 S\u0110T: 0905.193.688","5. Kh\u1ea3o s\u00e1t s\u1ef1 bi\u1ebfn thi\u00ean v\u00e0 v\u1ebd \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 Ta c\u00f3 3f (x) + 4 = 0 \u21d4 f (x) = \u22124. 3 Do \u0111\u00f3, s\u1ed1 nghi\u1ec7m th\u1ef1c ph\u00e2n bi\u1ec7t c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh 3f (x) + 4 = 0 \u0111\u00fang b\u1eb1ng s\u1ed1 giao \u0111i\u1ec3m chung c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = f (x) v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng y = \u22124 (song song v\u1edbi tr\u1ee5c ho\u00e0nh Ox). 3 T\u1eeb b\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a h\u00e0m s\u1ed1 y = f (x), ta k\u1ebft lu\u1eadn s\u1ed1 nghi\u1ec7m th\u1ef1c ph\u00e2n bi\u1ec7t c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh 3f (x) + 4 = 0 l\u00e0 2. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 109 (C\u00e2u 41 - M\u0110 102 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2020 - 2021). Cho h\u00e0m s\u1ed1 f (x) = ax4 + bx3 + cx2, (a, b, c \u2208 R). H\u00e0m s\u1ed1 y y = f (x) c\u00f3 \u0111\u1ed3 th\u1ecb nh\u01b0 h\u00ecnh b\u00ean. S\u1ed1 nghi\u1ec7m th\u1ef1c ph\u00e2n bi\u1ec7t c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh 3f (x) \u2212 4 = 0 l\u00e0 A 1. B 2. C 3. D 4. MDD-109 x O y = f (x) \u0253 L\u1eddi gi\u1ea3i. D\u1ec5 th\u1ea5y f (0) = 0 v\u00e0 h\u1ec7 s\u1ed1 a > 0. y \uf8eex = m < 0 T\u1eeb \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 y = f (x) ta c\u00f3 f (x) = 0 \u21d4 \uf8efx = 0 \uf8f0 x = n > 0. m n MDD-109 x O y = f (x) T\u1eeb \u0111\u00e2y ta c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a y = f (x) nh\u01b0 sau MDD-10x9 \u2212\u221e m 0 n +\u221e f (x) \u22120+0\u22120+ +\u221e 0 +\u221e f (x) f (m) f (n) X\u00e9t ph\u01b0\u01a1ng tr\u00ecnh 3f (x) \u2212 4 = 0 \u21d4 f (x) = 4 (1). 3 T\u1eeb b\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a h\u00e0m s\u1ed1 y = f (x) ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh (1) c\u00f3 2 nghi\u1ec7m ph\u00e2n bi\u1ec7t. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 110 (C\u00e2u 40 - M\u0110 103 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2020 - 2021). Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 152 S\u0110T: 0905.193.688","Ch\u01b0\u01a1ng 1. \u1ee8NG D\u1ee4NG \u0110\u1ea0O H\u00c0M \u0110\u1ec2 KH\u1ea2O S\u00c1T V\u00c0 V\u1ebc \u0110\u1ed2 TH\u1eca C\u1ee6A H\u00c0M S\u1ed0 Cho h\u00e0m s\u1ed1 f (x) = ax4 + bx3 + cx2 (a, b \u2208 R). H\u00e0m s\u1ed1 y y = f (x) c\u00f3 \u0111\u1ed3 th\u1ecb nh\u01b0 trong h\u00ecnh b\u00ean. S\u1ed1 nghi\u1ec7m ph\u00e2n bi\u1ec7t c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh 2f (x) \u2212 3 = 0 l\u00e0 A 2. B 3. C 1. D 4. Ox \u0253 L\u1eddi gi\u1ea3i. \u0110\u1eb7t h(x) = 2f (x) \u2212 3, ta c\u00f3 h (x) = 2f (x). \uf8eex = x0 h (x) = 0 \u21d4 f (x) = 0 \u21d4 \uf8efx = 0 d\u1ef1a v\u00e0o \u0111\u1ed3 th\u1ecb \u0111\u00e3 cho v\u1edbi x0 < 0 < x1 . \uf8f0 x = x1 Ta c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a h\u00e0m s\u1ed1 h(x) nh\u01b0 sau x \u2212\u221e x0 0 x1 +\u221e +\u221e h (x) \u22120+0\u22120+ +\u221e \u22123 h(x) h0 h1 D\u1ef1a v\u00e0o b\u1ea3ng bi\u1ebfn thi\u00ean ta th\u1ea5y ph\u01b0\u01a1ng tr\u00ecnh h(x) = 0 c\u00f3 2 nghi\u1ec7m ph\u00e2n bi\u1ec7t. Do \u0111\u00f3 ph\u01b0\u01a1ng tr\u00ecnh 2f (x) \u2212 3 = 0 c\u00f3 2 c\u00f3 hai nghi\u1ec7m ph\u00e2n bi\u1ec7t. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 111 (C\u00e2u 40 - M\u0110 104 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2020 - 2021). Cho h\u00e0m s\u1ed1 f (x) = ax4+bx3+cx2 (a, b, c \u2208 R). H\u00e0m s\u1ed1 y = f (x) y c\u00f3 \u0111\u1ed3 th\u1ecb nh\u01b0 trong h\u00ecnh b\u00ean. S\u1ed1 nghi\u1ec7m th\u1ef1c ph\u00e2n bi\u1ec7t c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh 2f (x) \u2212 3 = 0 l\u00e0 A 2. B 3. C 1. D 4. Ox \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 f (x) = 4ax3 + 3bx2 + 2cx v\u00e0 t\u1eeb h\u00ecnh d\u00e1ng \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 f (x) y suy ra f (x) l\u00e0 h\u00e0m s\u1ed1 \u0111a th\u1ee9c b\u1eadc ba v\u00e0 lim f (x) = +\u221e \u21d2 a > 0. m O nx x\u2192+\u221e \uf8eex = m < 0 C\u0169ng t\u1eeb h\u00ecnh v\u1ebd ta c\u00f3 f (x) = 0 \u21d4 \uf8efx = 0 \uf8f0 x = n > 0. B\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a h\u00e0m s\u1ed1 f (x) nh\u01b0 sau Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 153 S\u0110T: 0905.193.688","5. Kh\u1ea3o s\u00e1t s\u1ef1 bi\u1ebfn thi\u00ean v\u00e0 v\u1ebd \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 x \u2212\u221e m 0 n +\u221e +\u221e f (x) \u22120+0\u22120+ +\u221e 0 f (x) f (m) f (n) D\u1ef1a v\u00e0o b\u1ea3ng bi\u1ebfn thi\u00ean th\u00ec ph\u01b0\u01a1ng tr\u00ecnh 2f (x) \u2212 3 = 0 \u21d4 f (x) = 3 c\u00f3 hai nghi\u1ec7m th\u1ef1c ph\u00e2n bi\u1ec7t. 2 Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 112 (C\u00e2u 40 - M\u0110 103 - BGD&\u0110T - N\u0103m 2017 - 2018). x\u22122 Cho h\u00e0m s\u1ed1 y = c\u00f3 \u0111\u1ed3 th\u1ecb (C). G\u1ecdi I l\u00e0 giao \u0111i\u1ec3m c\u1ee7a hai ti\u1ec7m c\u1eadn c\u1ee7a (C). X\u00e9t tam gi\u00e1c x+2 \u0111\u1ec1u AB\u221aI c\u00f3 hai \u0111\u1ec9nh A, B thu\u1ed9c (C), \u0111o\u1ea1n th\u1eb3ng AB c\u00f3 \u0111\u1ed9 d\u00e0i b\u1eb1ng \u221a A 2 2. B 4. C 2. D 2 3. \u0253 L\u1eddi gi\u1ea3i. \u0110\u1ed3 th\u1ecb (C) : y = x \u2212 2 = 1 \u2212 4 c\u00f3 I(\u22122; 1) l\u00e0 giao \u0111i\u1ec3m c\u1ee7a 2 \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn. x+2 x+2 \uf8f1\u00c5 4 \u00e3 \u2208 (C) \uf8f1\uf8f4\uf8f4I#A\u00bb \u00c5 \u22124\u00e3 \uf8f4\uf8f4A a \u2212 2; 1 \u2212 a \uf8f2 = a; a \uf8f1 16 \uf8f2 4 \u00e3 \u2208 (C) \uf8f2\uf8f4IA2 = a2 + X\u00e9t b (a = b) ta c\u00f3 \uf8f4\uf8f4\uf8f3I#B\u00bb \u00c5 \u22124\u00e3 v\u00e0 a2 \u00c5 b; b \uf8f4\uf8f3IB2 = b2 + 16 \uf8f4\uf8f3\uf8f4B b \u2212 2; 1 \u2212 = . b2 \uf8f1IA = IB \u00aeIA = IB (1) \uf8f2 Tam gi\u00e1c IAB \u0111\u1ec1u \u21d4 #\u00bb #\u00bb 1 \u21d4 IA2 = 2I#A\u00bb \u00b7 I#B\u00bb. (2) \uf8f3 cos(IA, IB) = 2 16 32 (2) \u21d4 a2 + a2 = 2ab + ab \u21d2 ab > 0. (1) \u21d4 a2 + 16 = b2 + 16 \u21d4 (a2 \u2212 b2)(a2b2 \u2212 16) = 0 \u21d4 ab = 4 (do a = b v\u00e0 ab > 0). a2 b2 Nh\u01b0 v\u1eady IA2 = a2 + 16 = 2ab + 32 = 16 \u21d2 AB = IA = 4. a2 ab Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 113 (C\u00e2u 38 - M\u0110 101 - BGD&\u0110T - N\u0103m 2016 - 2017). Cho h\u00e0m s\u1ed1 y = \u2212x3 \u2212 mx2 + (4m + 9)x + 5 v\u1edbi m l\u00e0 tham s\u1ed1. C\u00f3 bao nhi\u00eau gi\u00e1 tr\u1ecb nguy\u00ean c\u1ee7a m \u0111\u1ec3 h\u00e0m s\u1ed1 ngh\u1ecbch bi\u1ebfn tr\u00ean kho\u1ea3ng (\u2212\u221e; +\u221e)? A 7. B 4. C 6. D 5. \u0253 L\u1eddi gi\u1ea3i. \u0110\u00e2y l\u00e0 h\u00e0m s\u1ed1 b\u1eadc 3 c\u00f3 h\u1ec7 s\u1ed1 a = \u22123 < 0 n\u00ean h\u00e0m s\u1ed1 ngh\u1ecbch bi\u1ebfn tr\u00ean R \u21d4 b2 \u2212 3ac \u2264 0 \u21d4 m2 + 12m + 27 \u2264 0 \u21d4 \u22129 \u2264 m \u2264 \u22123. Suy ra c\u00f3 7 gi\u00e1 tr\u1ecb nguy\u00ean c\u1ee7a m tho\u1ea3 m\u00e3n y\u00eau c\u1ea7u b\u00e0i to\u00e1n. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 114 (C\u00e2u 39 - M\u0110 101 - BGD&\u0110T - N\u0103m 2016 - 2017). T\u00ecm gi\u00e1 tr\u1ecb th\u1ef1c c\u1ee7a tham s\u1ed1 m \u0111\u1ec3 ph\u01b0\u01a1ng tr\u00ecnh log32 x \u2212 m log3 x + 2m \u2212 7 = 0 c\u00f3 hai nghi\u1ec7m th\u1ef1c x1,x2 th\u1ecfa m\u00e3n x1x2 = 81. A m = \u22124. B m = 4. C m = 81. D m = 44. Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t \u0253 L\u1eddi gi\u1ea3i. S\u0110T: 0905.193.688 154","Ch\u01b0\u01a1ng 1. \u1ee8NG D\u1ee4NG \u0110\u1ea0O H\u00c0M \u0110\u1ec2 KH\u1ea2O S\u00c1T V\u00c0 V\u1ebc \u0110\u1ed2 TH\u1eca C\u1ee6A H\u00c0M S\u1ed0 Ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00e3 cho c\u00f3 hai nghi\u1ec7m th\u1ef1c x1,x2 th\u1ecfa m\u00e3n x1x2 = 81 suy ra log3(x1.x2) = 4 hay log3 x1 + log3 x2 = 4. Do \u0111\u00f3 theo \u0111\u1ecbnh l\u00fd Vi\u00e9t ta suy ra m = 4. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 115 (C\u00e2u 40 - M\u0110 101 - BGD&\u0110T - N\u0103m 2016 - 2017). \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = x3 \u2212 3x2 \u2212 9x + 1 c\u00f3 hai \u0111i\u1ec3m c\u1ef1c tr\u1ecb A v\u00e0 B. \u0110i\u1ec3m n\u00e0o d\u01b0\u1edbi \u0111\u00e2y thu\u1ed9c \u0111\u01b0\u1eddng th\u1eb3ng AB? A P (1; 0). B M (0; \u22121). C N (1; \u221210). D Q(\u22121; 10). \u0253 L\u1eddi gi\u1ea3i. D\u00f9ng m\u00e1y t\u00ednh t\u00ednh \u0111\u01b0\u1ee3c \u0111\u01b0\u1eddng th\u1eb3ng AB : y = \u22128x \u2212 2. T\u1eeb \u0111\u00f3 ta th\u1ea5y ch\u1ec9 c\u00f3 N (1; \u221210) thu\u1ed9c AB. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 116 (C\u00e2u 24 - M\u0110 103 - BGD&\u0110T - N\u0103m 2016 - 2017). \u0110\u01b0\u1eddng cong \u1edf h\u00ecnh b\u00ean y ax + b 1 l\u00e0 \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 y = O2 cx + d v\u1edbi a, b, c, d l\u00e0 c\u00e1c s\u1ed1 th\u1ef1c. M\u1ec7nh \u0111\u1ec1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y \u0111\u00fang? A y < 0, \u2200x = 2. B y < 0, \u2200x = 1. C y > 0, \u2200x = 2. D y > 0, \u2200x = 1. x \u0253 L\u1eddi gi\u1ea3i. Theo h\u00ecnh v\u1ebd ta c\u00f3 h\u00e0m s\u1ed1 ngh\u1ecbch bi\u1ebfn tr\u00ean c\u00e1c kho\u1ea3ng x\u00e1c \u0111\u1ecbnh v\u00e0 c\u00f3 ti\u1ec7m c\u1eadn \u0111\u1ee9ng l\u00e0 x = 2 \u21d2 y < 0, \u2200x = 2. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 117 (C\u00e2u 45 - M\u0110 103 - BGD&\u0110T - N\u0103m 2016 - 2017). T\u00ecm t\u1ea5t c\u1ea3 c\u00e1c gi\u00e1 tr\u1ecb th\u1ef1c c\u1ee7a tham s\u1ed1 m \u0111\u1ec3 \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 y = x4 \u2212 2mx2 c\u00f3 ba \u0111i\u1ec3m c\u1ef1c tr\u1ecb t\u1ea1o th\u00e0nh m\u1ed9t tam gi\u00e1c c\u00f3 di\u1ec7n t\u00edch nh\u1ecf h\u01a1n 1. \u221a A m > 0. B m < 1. C 0 < m < 3 4. D 0 < m < 1. \u0253 L\u1eddi gi\u1ea3i. y = 4x3 \u2212 4mx = 0 \u21d4 4x(x2 \u2212 m) = 0. H\u00e0m s\u1ed1 c\u00f3 ba \u0111i\u1ec3m c\u1ef1c tr\u1ecb khi v\u00e0 ch\u1ec9 Akh(\u221ai mm;>\u22120m. 2), \u221a \u2212m2). \u221a T\u00ecm \u0111\u01b0\u1ee3c ba \u0111i\u1ec3m c\u1ef1c tr\u1ecb l\u00e0 O(0; 0), B(\u2212 m; 2m G\u1ecdi H l\u00e0 trung \u0111i\u1ec3m AB th\u00ec di\u1ec7n t\u00edch tam gi\u00e1c OAB l\u00e0 1 \u00b7 AB = 1 \u00b7 \u00b7 m2. Di\u1ec7n t\u00edch tam OH 22 gi\u00e1c ph\u1ea3i l\u1edbn h\u01a1n 0 v\u00e0 nh\u1ecf h\u01a1n 1 theo y\u00eau c\u1ea7u b\u00e0i to\u00e1n, suy ra 0 < m < 1. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 118 (C\u00e2u 49 - M\u0110 104 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2020 - 2021). Cho h\u00e0m s\u1ed1 f (x) = x4 \u2212 10x3 + 24x2 + (3 \u2212 m)x, v\u1edbi m l\u00e0 s\u1ed1 th\u1ef1c. C\u00f3 bao nhi\u00eau gi\u00e1 tr\u1ecb nguy\u00ean c\u1ee7a m \u0111\u1ec3 h\u00e0m s\u1ed1 g(x) = f (|x|) c\u00f3 \u0111\u00fang 7 \u0111i\u1ec3m c\u1ef1c tr\u1ecb? A 21. B 25. C 24. D 22. Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t \u0253 L\u1eddi gi\u1ea3i. S\u0110T: 0905.193.688 155","5. Kh\u1ea3o s\u00e1t s\u1ef1 bi\u1ebfn thi\u00ean v\u00e0 v\u1ebd \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 Ta c\u00f3 f (0) = 0 v\u00e0 \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 f (|x|) \u0111\u1ed1i x\u1ee9ng qua Oy n\u00ean h\u00e0m s\u1ed1 f (|x|) lu\u00f4n c\u00f3 m\u1ed9t c\u1ef1c tr\u1ecb t\u1ea1i x = 0. V\u1eady f (|x|) c\u00f3 7 \u0111i\u1ec3m c\u1ef1c tr\u1ecb khi v\u00e0 ch\u1ec9 khi f (x) c\u00f3 3 \u0111i\u1ec3m c\u1ef1c tr\u1ecb d\u01b0\u01a1ng. \u21d4 f (x) = 0 c\u00f3 3 nghi\u1ec7m d\u01b0\u01a1ng ph\u00e2n bi\u1ec7t \u21d4 4x3 \u2212 30x2 + 48x + 3 \u2212 m = 0 c\u00f3 3 nghi\u1ec7m d\u01b0\u01a1ng ph\u00e2n bi\u1ec7t. \u21d4 4x3 \u2212 30x2 + 48x + 3 = m c\u00f3 3 nghi\u1ec7m d\u01b0\u01a1ng ph\u00e2n bi\u1ec7t. (1) \u0110\u1eb7t g(x) = 4x3 \u2212 30x2 + 48x + 3, D = R. g (x) = 12x2 \u2212 60x + 48, g (x) = 0 \u21d4 \u00f1x = 4 x = 1. B\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a g(x) x \u2212\u221e 0 1 4 +\u221e g (x) + | +0\u22120+ +\u221e g(x) 25 3 \u221229 \u2212\u221e T\u1eeb b\u1ea3ng bi\u00ean thi\u00ean ta c\u00f3 (1) \u21d4 3 < m < 25. Do m nguy\u00ean suy ra m \u2208 {4; 5; 6; . . . ; 24}. V\u1eady c\u00f3 t\u1ea5t c\u1ea3 21 s\u1ed1 nguy\u00ean m tho\u1ea3 m\u00e3n. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 119 (C\u00e2u 50 - M\u0110 102 - BGD&\u0110T - N\u0103m 2021 - 2022). C\u00f3 bao nhi\u00eau gi\u00e1 tr\u1ecb nguy\u00ean \u00e2m c\u1ee7a tham s\u1ed1 a \u0111\u1ec3 h\u00e0m s\u1ed1 y = |x4 + 2ax2 + 8x| c\u00f3 \u0111\u00fang ba \u0111i\u1ec3m c\u1ef1c tr\u1ecb? A 2. B 6. C 5. D 3. \u0253 L\u1eddi gi\u1ea3i. X\u00e9t h\u00e0m s\u1ed1 f (x) = x4 + 2ax2 + 8x tr\u00ean R. Ta c\u00f3 f (x) = 4x3 + 4ax + 8. f (x) = 0 \u21d4 4x3 + 4ax + 8 = 0 \u21d4 a = \u2212x2 \u2212 2 \u00b7 x (do x = 0 kh\u00f4ng th\u1ecfa m\u00e3n f (x) = 0 n\u00ean x = 0). X\u00e9t h\u00e0m s\u1ed1 g(x) = \u2212x2 \u2212 2 tr\u00ean R \\\\ {0} c\u00f3 g (x) = \u22122x + 2 x . x2 g (x) = 0 \u21d4 \u22122x + 2 = 0 \u21d4 x = 1. x2 B\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a h\u00e0m s\u1ed1 g(x) : x \u2212\u221e 0 1 +\u221e g (x) + +0\u2212 +\u221e \u22123 g(x) \u2212\u221e \u2212\u221e \u2212\u221e Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 156 S\u0110T: 0905.193.688","Ch\u01b0\u01a1ng 1. \u1ee8NG D\u1ee4NG \u0110\u1ea0O H\u00c0M \u0110\u1ec2 KH\u1ea2O S\u00c1T V\u00c0 V\u1ebc \u0110\u1ed2 TH\u1eca C\u1ee6A H\u00c0M S\u1ed0 D\u1ec5 th\u1ea5y ph\u01b0\u01a1ng tr\u00ecnh f (x) = 0 c\u00f3 \u00edt nh\u1ea5t hai nghi\u1ec7m ph\u00e2n bi\u1ec7t, trong \u0111\u00f3 c\u00f3 \u00edt nh\u1ea5t m\u1ed9t nghi\u1ec7m \u0111\u01a1n x = 0 n\u00ean y\u00eau c\u1ea7u c\u1ee7a b\u00e0i to\u00e1n \u21d4 h\u00e0m s\u1ed1f (x)c\u00f3 \u0111\u00fang m\u1ed9t \u0111i\u1ec3m c\u1ef1c tr\u1ecb \u21d4 ph\u01b0\u01a1ng tr\u00ecnha = g(x)c\u00f3 m\u1ed9t nghi\u1ec7m \u0111\u01a1n duy nh\u1ea5t \u21d4 a \u2265 \u22123. Do a nguy\u00ean \u00e2m n\u00ean a \u2208 {\u22123; \u22122; \u22121}. V\u1eady c\u00f3 3 gi\u00e1 tr\u1ecb nguy\u00ean \u00e2m c\u1ee7a tham s\u1ed1 a th\u1ecfa m\u00e3n y\u00eau c\u1ea7u b\u00e0i to\u00e1n. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 120 (C\u00e2u 43 - M\u0110 101 - BGD&\u0110T - N\u0103m 2018 - 2019). Cho h\u00e0m s\u1ed1 b\u1eadc ba y = f (x) c\u00f3 \u0111\u1ed3 th\u1ecb nh\u01b0 h\u00ecnh v\u1ebd b\u00ean. S\u1ed1 y 2 nghi\u1ec7m th\u1ef1c c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh |f (x3 \u2212 3x)| = 4 l\u00e0 3 A 3. B 8. C 7. D 4. \u22122 2 Ox \u22121 \u0253 L\u1eddi gi\u1ea3i. \u0110\u1eb7t t = x3 \u2212 3x \u21d2 t = 3x2 \u2212 3. Ta c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean x \u2212\u221e \u22121 1 +\u221e t +0\u22120+ 2 +\u221e \u22122 t \u2212\u221e Khi \u0111\u00f3 |f (t)| = 4 (1). \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = |f (t)| \u0111\u01b0\u1ee3c v\u1ebd th\u00e0nh 2 ph\u1ea7n 3 Ph\u1ea7n 1 gi\u1eef nguy\u00ean \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = f (x) ph\u00eda tr\u00ean tr\u1ee5c Ox khi f (x) \u2265 0. Ph\u1ea7n 2 l\u1ea5y \u0111\u1ed1i x\u1ee9ng c\u1ee7a ph\u1ea7n c\u00f2n l\u1ea1i qua tr\u1ee5c Ox. y 2 2 4 y= \u22122 O 3 x D\u1ef1a v\u00e0o \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 |f (t)| ta th\u1ea5y ph\u01b0\u01a1ng tr\u00ecnh (1) c\u00f3 4 nghi\u1ec7m ph\u00e2n bi\u1ec7t t1 < \u22122, \u22122 < t2 < 0, 0 < t3 < 2, t4 > 2. M\u1ed7i nghi\u1ec7m t c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh (1), ta thay v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh t = x3 \u2212 3x \u0111\u1ec3 t\u00ecm nghi\u1ec7m x. Khi \u0111\u00f3 t1 < \u22122 \u21d2 ph\u01b0\u01a1ng tr\u00ecnh t = x3 \u2212 3x c\u00f3 1 nghi\u1ec7m. \u22122 < t2 < 0 \u21d2 ph\u01b0\u01a1ng tr\u00ecnh t = x3 \u2212 3x c\u00f3 3 nghi\u1ec7m. Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 157 S\u0110T: 0905.193.688","5. Kh\u1ea3o s\u00e1t s\u1ef1 bi\u1ebfn thi\u00ean v\u00e0 v\u1ebd \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 0 < t3 < 2 \u21d2 ph\u01b0\u01a1ng tr\u00ecnh t = x3 \u2212 3x c\u00f3 3 nghi\u1ec7m. t4 > 2 \u21d2 ph\u01b0\u01a1ng tr\u00ecnh t = x3 \u2212 3x c\u00f3 1 nghi\u1ec7m. V\u1eady ph\u01b0\u01a1ng tr\u00ecnh |f (x3 \u2212 3x)| = 4 c\u00f3 8 nghi\u1ec7m. 3 Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 121 (C\u00e2u 41 - M\u0110 102 - BGD&\u0110T - N\u0103m 2018 - 2019). Cho h\u00e0m s\u1ed1 b\u1eadc ba y = f (x) c\u00f3 \u0111\u1ed3 th\u1ecb nh\u01b0 h\u00ecnh v\u1ebd b\u00ean. S\u1ed1 y 2 nghi\u1ec7m th\u1ef1c c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh |f (x3 \u2212 3x)| = 1 l\u00e0 2 A 6. B 10. C 12. D 3. \u22122 O 2 x \u22121 \u0253 L\u1eddi gi\u1ea3i. 1 Ta c\u00f3 |f (x3 \u2212 3x)| = 1 \u21d4 \uf8ee \u2212 3x) = (1) 2 f (x3 \u2212 3x) = 2 (2). \u22121 \uf8ef 2 \uf8f0 f (x3 T\u1eeb \u0111\u1ed3 th\u1ecb ta c\u00f3 y 2 \u22122 O 2 1 y= 2 x \u22121 y = \u22121 2 (1) \u21d4 f (x3 \u2212 3x) = 1 \u21d4 \uf8eex3 \u2212 3x = \u03b11 (\u22122 < \u03b11 < 0) 2 \uf8efx3 \u2212 3x = \u03b12 (0 < \u03b12 < 2) \uf8f0 \u2212 3x = \u03b13 (\u03b13 > 2) . x3 (2) \u21d4 f (x3 \u2212 3x) = \u22121 \u21d4 \uf8eex3 \u2212 3x = \u03b14 (\u03b14 < \u22122) 2 \uf8efx3 \u2212 3x = \u03b15 (\u03b15 > 2) \uf8f0 \u2212 3x = \u03b16 (\u03b16 > 2) . x3 X\u00e9t h\u00e0m s\u1ed1 y = x3 \u2212 3x x\u00e1c \u0111\u1ecbnh tr\u00ean R v\u00e0 c\u00f3 y = 3x2 \u2212 3. Ta c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean x \u2212\u221e \u22121 1 +\u221e f (x) +0\u22120+ 2 +\u221e \u22122 f (x) \u2212\u221e Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 158 S\u0110T: 0905.193.688","Ch\u01b0\u01a1ng 1. \u1ee8NG D\u1ee4NG \u0110\u1ea0O H\u00c0M \u0110\u1ec2 KH\u1ea2O S\u00c1T V\u00c0 V\u1ebc \u0110\u1ed2 TH\u1eca C\u1ee6A H\u00c0M S\u1ed0 D\u1ef1a v\u00e0o b\u1ea3ng bi\u1ebfn thi\u00ean ta c\u00f3 Ph\u01b0\u01a1ng tr\u00ecnh x3 \u2212 3x = \u03b11 c\u00f3 3 nghi\u1ec7m. Ph\u01b0\u01a1ng tr\u00ecnh x3 \u2212 3x = \u03b12 c\u00f3 3 nghi\u1ec7m. M\u1ed7i ph\u01b0\u01a1ng tr\u00ecnh x3 \u2212 3x = \u03b13, x3 \u2212 3x = \u03b14, x3 \u2212 3x = \u03b15, x3 \u2212 3x = \u03b16 \u0111\u1ec1u c\u00f3 m\u1ed9t nghi\u1ec7m. T\u1eeb \u0111\u00f3 suy ra ph\u01b0\u01a1ng tr\u00ecnh |f (x3 \u2212 3x)| = 1 c\u00f3 10 nghi\u1ec7m. 2 Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 122 (C\u00e2u 45 - M\u0110 103 - BGD&\u0110T - N\u0103m 2018 - 2019). Cho h\u00e0m s\u1ed1 b\u1eadc ba y = f (x) c\u00f3 \u0111\u1ed3 th\u1ecb nh\u01b0 h\u00ecnh v\u1ebd d\u01b0\u1edbi y 2 \u0111\u00e2y. S\u1ed1 nghi\u1ec7m th\u1ef1c c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh |f (x3 \u2212 3x)| = 3 2 l\u00e0 A 8. B 4. C 7. D 3. 2 \u22122 O x \u22121 \u0253 L\u1eddi gi\u1ea3i. \u0110\u1eb7t t = x3 \u2212 3x ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh |f (t)| = 3 (*). 2 y y = |f (t)| 2 2 3 y= \u22122 O \u22121 2 x T\u1eeb \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = |f (t)| v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng y = 3 ta suy ra ph\u01b0\u01a1ng tr\u00ecnh (*) 2 c\u00f3 4 nghi\u1ec7m t1 < \u22122 < t2 < 0 < t3 < 2 < t4. X\u00e9t h\u00e0m t = x3 \u2212 3x. Ta c\u00f3 t = 3x2 \u2212 3 = 0 \u21d4 \u00f1x = 1 x = \u22121. Ta c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean x \u2212\u221e 1 0 1 +\u221e t +0\u2212 | \u22120+ 2 +\u221e t0 \u2212\u221e \u22122 Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 159 S\u0110T: 0905.193.688","5. Kh\u1ea3o s\u00e1t s\u1ef1 bi\u1ebfn thi\u00ean v\u00e0 v\u1ebd \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 V\u1edbi t1 < \u22122 ph\u01b0\u01a1ng tr\u00ecnh: t1 = x3 \u2212 3x cho ta 1 nghi\u1ec7m. V\u1edbi \u22122 < t2 < 0 ph\u01b0\u01a1ng tr\u00ecnh: t2 = x3 \u2212 3x cho ta 3 nghi\u1ec7m. V\u1edbi 0 < t3 < 2 ph\u01b0\u01a1ng tr\u00ecnh: t3 = x3 \u2212 3x cho ta 3 nghi\u1ec7m. V\u1edbi 2 < t4 ph\u01b0\u01a1ng tr\u00ecnh: t4 = x3 \u2212 3x cho ta 1 nghi\u1ec7m. V\u1eady ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00e3 cho c\u00f3 t\u1ea5t c\u1ea3 8 nghi\u1ec7m. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 123 (C\u00e2u 37 - M\u0110 104 - BGD&\u0110T - N\u0103m 2018 - 2019). Cho h\u00e0m s\u1ed1 f (x), h\u00e0m s\u1ed1 y = f (x) li\u00ean t\u1ee5c tr\u00ean R v\u00e0 c\u00f3 y y = f (x) \u0111\u1ed3 th\u1ecb nh\u01b0 h\u00ecnh v\u1ebd b\u00ean. B\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh f (x) > 2x + m 2 (m l\u00e0 tham s\u1ed1 th\u1ef1c) nghi\u1ec7m \u0111\u00fang v\u1edbi m\u1ecdi x \u2208 (0; 2) khi v\u00e0 ch\u1ec9 khi O 2x A m \u2264 f (2) \u2212 4. B m \u2264 f (0). C m < f (0). D m < f (2) \u2212 4. \u0253 L\u1eddi gi\u1ea3i. H\u00e0m s\u1ed1 g(x) = f (x) \u2212 2x ngh\u1ecbch bi\u1ebfn tr\u00ean kho\u1ea3ng (0; 2) v\u00ec y g (x) = f (x) \u2212 2 < 0, \u2200x \u2208 (0; 2) (quan s\u00e1t tr\u00ean kho\u1ea3ng y = f (x) (0; 2), \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 f (x) n\u1eb1m d\u01b0\u1edbi \u0111\u01b0\u1eddng th\u1eb3ng y = 2). Suy ra g(2) < g(x) < g(0), \u2200x \u2208 (0; 2). 2 y=2 B\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00e3 cho nghi\u1ec7m \u0111\u00fang v\u1edbi m\u1ecdi x \u2208 (0; 2) khi v\u00e0 ch\u1ec9 khi O 2x m < g(x), \u2200x \u2208 (0; 2) \u21d4 m \u2264 g(2) \u21d4 m \u2264 f (2) \u2212 4. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 124 (C\u00e2u 42 - M\u0110 104 - BGD&\u0110T - N\u0103m 2018 - 2019). Cho h\u00e0m s\u1ed1 b\u1eadc ba y = f (x) c\u00f3 \u0111\u1ed3 th\u1ecb nh\u01b0 h\u00ecnh v\u1ebd b\u00ean. S\u1ed1 nghi\u1ec7m th\u1ef1c c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh |f (x3 \u2212 3x)| = 2 l\u00e0 y 3 2 A 6. B 10. C 3. D 9. \u22122 O \u22121 2 x Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t \u0253 L\u1eddi gi\u1ea3i. S\u0110T: 0905.193.688 160","Ch\u01b0\u01a1ng 1. \u1ee8NG D\u1ee4NG \u0110\u1ea0O H\u00c0M \u0110\u1ec2 KH\u1ea2O S\u00c1T V\u00c0 V\u1ebc \u0110\u1ed2 TH\u1eca C\u1ee6A H\u00c0M S\u1ed0 \u0110\u1eb7t t = g(x) = x3 \u2212 3x (1). Ta c\u00f3 g (x) = 3x2 \u2212 3 = 0 \u21d4 x \u00b1 1. B\u1ea3ng bi\u1ebfn thi\u00ean x \u2212\u221e \u22121 1 +\u221e g (x) +0\u22120+ g(x) 2 +\u221e \u2212\u221e \u22122 D\u1ef1a v\u00e0o b\u1ea3ng bi\u1ebfn thi\u00ean ta c\u00f3 t \u2208 (\u22122; 2) cho ta 3 gi\u00e1 tr\u1ecb x th\u1ecfa m\u00e3n (1). t \u2208 {\u22122; 2} cho ta 2 gi\u00e1 tr\u1ecb x th\u1ecfa m\u00e3n (1). t \u2208 (\u2212\u221e; \u22122) \u222a (2; +\u221e) cho ta 1 gi\u00e1 tr\u1ecb x th\u1ecfa m\u00e3n (1). \uf8ee2 f (t) = Ph\u01b0\u01a1ng tr\u00ecnh |f (x3 \u2212 3x)| = 2 (2) tr\u1edf th\u00e0nh |f (t)| = 2 \u21d4 \uf8ef = 3 3 3 \uf8f0 \u22122. f (t) 3 D\u1ef1a v\u00e0o \u0111\u1ed3 th\u1ecb ta c\u00f3: Ph\u01b0\u01a1ng tr\u00ecnh f (t) = 2 c\u00f3 3 nghi\u1ec7m th\u1ecfa m\u00e3n \u22122 < t1 < t2 < 2 < t3. Suy ra c\u00f3 7 nghi\u1ec7m c\u1ee7a 3 ph\u01b0\u01a1ng tr\u00ecnh (2). Ph\u01b0\u01a1ng tr\u00ecnh f (t) = \u22122 c\u00f3 3 nghi\u1ec7m th\u1ecfa m\u00e3n t4 < \u22122 < 2 < t5 < t6. Suy ra c\u00f3 3 nghi\u1ec7m c\u1ee7a 3 ph\u01b0\u01a1ng tr\u00ecnh (2). V\u1eady ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00e3 cho c\u00f3 10 nghi\u1ec7m. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 125 (C\u00e2u 46 - \u0110TK - BGD&\u0110T - l\u1ea7n 2 - N\u0103m 2019 - 2020). Cho h\u00e0m s\u1ed1 y = f (x) c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean nh\u01b0 sau x \u2212\u221e \u22121 0 1 +\u221e f (x) +0\u22120+0\u2212 22 f (x) \u2212\u221e 0 \u2212\u221e \u00ef 5\u03c0 \u00f2 S\u1ed1 nghi\u1ec7m thu\u1ed9c \u0111o\u1ea1n 0; c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh f (sin x) = 1 l\u00e0 2 A 7. B 4. C 5. D 6. \u0253 L\u1eddi gi\u1ea3i. \u0110\u1eb7t t = sin x \u21d2 t = cos x. t =0\u21d4x= \u03c0 + k\u03c0, k\u2208Z\u21d2x= \u03c0 x= 3\u03c0 x= 5\u03c0 \u2208 \u00ef 5\u03c0 \u00f2 2 ; ; 2 0; . 2 2 2 Ta c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 161 S\u0110T: 0905.193.688","5. Kh\u1ea3o s\u00e1t s\u1ef1 bi\u1ebfn thi\u00ean v\u00e0 v\u1ebd \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 x0 \u03c0 3\u03c0 5\u03c0 222 t +0\u22120+ 11 t0 \u22121 T\u1eeb b\u1ea3ng bi\u1ebfn thi\u00ean suy ra x \u2208 \u00ef 5\u03c0 \u00f2 th\u00ec t \u2208 [\u22121; 1]. Khi \u0111\u00f3 s\u1ed1 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh f (sin x) = 1 0; 2 hay f (t) = 1 ch\u00ednh l\u00e0 s\u1ed1 giao \u0111i\u1ec3m c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = f (t) v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng y = 1 v\u1edbi t \u2208 [\u22121; 1]. t \u22121 b 0 a 1 22 f (t) y = 1 0 D\u1ef1a v\u00e0o b\u1ea3ng bi\u1ebfn thi\u00ean, suy ra tr\u00ean \u0111o\u1ea1n [\u22121; 1] th\u00ec ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 2 nghi\u1ec7m M\u1ed9t nghi\u1ec7m t = b \u2208 (\u22121; 0) cho 2 nghi\u1ec7m x, m\u1ed9t nghi\u1ec7m thu\u1ed9c \u00c5 3\u03c0 \u00e3 v\u00e0 m\u1ed9t nghi\u1ec7m thu\u1ed9c \u03c0; 2 \u00c53\u03c0 \u00e3 m\u1ed9t nghi\u1ec7m thu\u1ed9c ; 2\u03c0 . 2 M\u1ed9t nghi\u1ec7m t = a \u2208 (0; 1) cho 3 nghi\u1ec7m x, m\u1ed9t nghi\u1ec7m thu\u1ed9c \u03c0 \u03c0 \u00c5 5\u03c0 \u00e3 0; ; m\u1ed9t nghi\u1ec7m thu\u1ed9c ;\u03c0 v\u00e0 m\u1ed9t nghi\u1ec7m thu\u1ed9c 2\u03c0; . 2 2 2 V\u1eady ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00e3 cho c\u00f3 5 nghi\u1ec7m. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 126 (C\u00e2u 50 - M\u0110 101 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2019 - 2020). Cho h\u00e0m s\u1ed1 b\u1eadc ba y = f (x) c\u00f3 \u0111\u1ed3 th\u1ecb l\u00e0 \u0111\u01b0\u1eddng cong trong h\u00ecnh y b\u00ean. S\u1ed1 nghi\u1ec7m th\u1ef1c ph\u00e2n bi\u1ec7t c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh f (x3f (x)) + 1 = O \u22121 0 l\u00e0 x A 8. B 5. C 6. D 4. \u0253 L\u1eddi gi\u1ea3i. T\u1eeb \u0111\u1ed3 th\u1ecb (C) c\u1ee7a h\u00e0m s\u1ed1 f (x), ta suy ra y b cx \uf8eex = 0 Oa Ph\u01b0\u01a1ng tr\u00ecnh f (x) = \u22121 \u21d4 \uf8efx = a \u2208 (2; 3) \u22121 \uf8f0 x = b \u2208 (5; 6). Ph\u01b0\u01a1ng tr\u00ecnh f (x) = 0 \u21d4 x = c \u2208 (5; 6). Do \u0111\u00f3, ta c\u00f3 \uf8eex3f (x) = 0 (1) f x3f (x) + 1 = 0 \u21d4 \uf8efx3f (x) = a (2) (3) \uf8f0 x3f (x) = b. S\u0110T: 0905.193.688 Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 162","Ch\u01b0\u01a1ng 1. \u1ee8NG D\u1ee4NG \u0110\u1ea0O H\u00c0M \u0110\u1ec2 KH\u1ea2O S\u00c1T V\u00c0 V\u1ebc \u0110\u1ed2 TH\u1eca C\u1ee6A H\u00c0M S\u1ed0 Khi \u0111\u00f3 Ph\u01b0\u01a1ng tr\u00ecnh (1) \u21d4 \u00f1x = 0 \u21d4 \u00f1x = 0 f (x) = 0 x = c. a Ph\u01b0\u01a1ng tr\u00ecnh (2) \u21d4 f (x) = ax3 . S\u1ed1 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh (2) b\u1eb1ng s\u1ed1 giao \u0111i\u1ec3m c\u1ee7a \u0111\u1ed3 th\u1ecb (C) v\u1edbi \u0111\u1ed3 th\u1ecb (C1) : g(x) = x3 . 3a V\u1edbi a \u2208 (2; 3) ta c\u00f3 g (x) = \u2212 < 0, \u2200x = 0. x4 a T\u1eeb \u0111\u00f3 suy ra b\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a h\u00e0m s\u1ed1 g(x) = x3 l\u00e0 x \u2212\u221e 0 +\u221e g (x) \u2212 \u2212 g(x) 0 +\u221e \u2212\u221e 0 T\u1eeb b\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a h\u00e0m s\u1ed1 g(x) v\u00e0 \u0111\u1ed3 th\u1ecb (C), ta suy ra \u2014 Tr\u00ean kho\u1ea3ng (\u2212\u221e; 0), ta th\u1ea5y x \u2212\u221e 0 0 \u2212\u221e g(x) \u22121 f (x) \u2212\u221e Suy ra ph\u01b0\u01a1ng tr\u00ecnh (2) c\u00f3 \u0111\u00fang 1 nghi\u1ec7m x = x1 \u2208 (\u2212\u221e; 0). \u2014 Tr\u00ean kho\u1ea3ng (0; c), ta th\u1ea5y \u00aef (x) < 0 n\u00ean ph\u01b0\u01a1ng tr\u00ecnh (2) v\u00f4 nghi\u1ec7m. g(x) > 0 \u2014 Tr\u00ean n\u1eeda kho\u1ea3ng [c; +\u221e), ta th\u1ea5y xc +\u221e a 0 g(x) c3 +\u221e f (x) 0 Suy ra ph\u01b0\u01a1ng tr\u00ecnh (2) c\u00f3 \u0111\u00fang 1 nghi\u1ec7m x = x2 \u2208 (c; +\u221e). Do \u0111\u00f3, ph\u01b0\u01a1ng tr\u00ecnh (2) c\u00f3 hai nghi\u1ec7m ph\u00e2n bi\u1ec7t kh\u00e1c c\u00e1c nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh (1). Ph\u01b0\u01a1ng tr\u00ecnh (3) \u21d4 f (x) = b . x3 T\u01b0\u01a1ng t\u1ef1 nh\u01b0 tr\u00ean, ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh (3) c\u00f3 hai nghi\u1ec7m ph\u00e2n bi\u1ec7t kh\u00e1c c\u00e1c nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh (1) v\u00e0 (2). V\u1eady ph\u01b0\u01a1ng tr\u00ecnh f (x3f (x)) + 1 = 0 c\u00f3 6 nghi\u1ec7m ph\u00e2n bi\u1ec7t. Ch\u1ecdn \u0111\u00e1p \u00e1n C Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 163 S\u0110T: 0905.193.688","5. Kh\u1ea3o s\u00e1t s\u1ef1 bi\u1ebfn thi\u00ean v\u00e0 v\u1ebd \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0104 C\u00e2u 127 (C\u00e2u 50 - M\u0110 104 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2019 - 2020). Cho h\u00e0m s\u1ed1 b\u1eadc b\u1ed1n y = f (x) c\u00f3 \u0111\u1ed3 th\u1ecb l\u00e0 \u0111\u01b0\u1eddng cong trong y 2 h\u00ecnh b\u00ean. S\u1ed1 nghi\u1ec7m th\u1ef1c c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh f (x2f (x)) \u2212 2 = 0 Ox l\u00e0 A 6. B 12. C 8. D 9. \u0253 L\u1eddi gi\u1ea3i. T\u1eeb \u0111\u1ed3 th\u1ecb ta th\u1ea5y \uf8eex2f (x) = 0 (1) f (x2f (x)) \u2212 2 = 0 \u21d4 f (x2f (x)) = 2 \u21d4 \uf8efx2f (x) = a (\u22121 < a < 0) (2) \uf8ef = b (\u22123 < b < \u22122) (3) \uf8ef\uf8f0x2f (x) x2f (x) = c (\u22124 < c < \u22123) . (4) \u00f1x = 0 \uf8eex = 0 (1) \u21d4 f (x) = 0 \u21d4 \uf8efx = x1 (3 nghi\u1ec7m ph\u00e2n bi\u1ec7t). y \uf8f0 O a x = x2 y = f (x) (2) \u21d4 f (x) = x2 . a V\u1ebd \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = l\u00ean h\u1ec7 t\u1ecda \u0111\u1ed9 Oxy \u0111\u00e3 c\u00f3 \u0111\u1ed3 th\u1ecb x2 a h\u00e0m s\u1ed1 y = f (x). Ta th\u1ea5y \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = c\u1eaft \u0111\u1ed3 x2 x th\u1ecb h\u00e0m s\u1ed1 y = f (x) t\u1ea1i 2 nghi\u1ec7m ph\u00e2n bi\u1ec7t. m y = x2 (m < 0) T\u01b0\u01a1ng t\u1ef1, m\u1ed7i ph\u01b0\u01a1ng tr\u00ecnh (3) v\u00e0 (4) \u0111\u1ec1u c\u00f3 2 nghi\u1ec7m ph\u00e2n bi\u1ec7t v\u00e0 b\u1ed1n ph\u01b0\u01a1ng tr\u00ecnh tr\u00ean kh\u00f4ng c\u00f3 nghi\u1ec7m chung. V\u1eady ph\u01b0\u01a1ng tr\u00ecnh f (x2f (x)) = 2 c\u00f3 9 nghi\u1ec7m ph\u00e2n bi\u1ec7t. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 128 (C\u00e2u 49 - M\u0110 101 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2019 - 2020). Cho h\u00e0m s\u1ed1 f (x) c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean nh\u01b0 sau x \u2212\u221e \u22124 \u22122 0 +\u221e f (x) \u22120+0\u22120+ +\u221e +\u221e 2 f (x) \u22122 \u22123 C\u00f3 bao nhi\u00eau gi\u00e1 tr\u1ecb nguy\u00ean c\u1ee7a m \u0111\u1ec3 ph\u01b0\u01a1ng tr\u00ecnh 5f (x2 \u2212 4x) = m c\u00f3 \u00edt nh\u1ea5t 3 nghi\u1ec7m th\u1ef1c ph\u00e2n bi\u1ec7t thu\u1ed9c kho\u1ea3ng (0; +\u221e)? A 24. B 21. C 25. D 20. Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t \u0253 L\u1eddi gi\u1ea3i. S\u0110T: 0905.193.688 164","Ch\u01b0\u01a1ng 1. \u1ee8NG D\u1ee4NG \u0110\u1ea0O H\u00c0M \u0110\u1ec2 KH\u1ea2O S\u00c1T V\u00c0 V\u1ebc \u0110\u1ed2 TH\u1eca C\u1ee6A H\u00c0M S\u1ed0 \u0110\u1eb7t g(x) = 5f (x2 \u2212 4x), v\u1edbi x \u2208 (0; +\u221e). Ta c\u00f3 g (x) = 10(x \u2212 2)f (x2 \u2212 4x). \uf8eex = 2 \u221a \uf8eex = 2 \uf8eex = 2 \uf8efx = 2 \u22122 \uf8ef = 2 \u221a \u00f1x \u2212 2 = 0 = 0 \u21d4 \uf8efx2 \u2212 4x = \u22124 \u21d4 \uf8efx2 \u2212 4x + 4 = 0 \u21d4 g (x) = 0 \u21d4 f x2 \u2212 4x \uf8ef \u2212 4x = \u22122 \uf8ef \u2212 4x + 2 = 0 \uf8ef +2 \uf8f0\uf8efx2 \uf8ef\uf8f0x2 \uf8efx \uf8ef x2 \u2212 4x = 0 x2 \u2212 4x = 0 \uf8f0\uf8efx = 0 x = 4. B\u1ea3ng bi\u1ebfn thi\u00ean \u221a\u221a +\u221e x 0 2\u2212 2 2 2+ 2 4 g (x) 0 + 0 \u2212 0 + 0 \u2212 0 + +\u221e 10 10 g(x) \u221210 \u221215 \u221215 T\u1eeb b\u1ea3ng bi\u1ebfn thi\u00ean suy ra ph\u01b0\u01a1ng tr\u00ecnh g(x) = m c\u00f3 \u00edt nh\u1ea5t 3 nghi\u1ec7m th\u1ef1c ph\u00e2n bi\u1ec7t thu\u1ed9c kho\u1ea3ng (0; +\u221e) khi v\u00e0 ch\u1ec9 khi \u221215 < m \u2264 10. M\u00e0 m nguy\u00ean n\u00ean c\u00f3 25 gi\u00e1 tr\u1ecb m th\u1ecfa m\u00e3n. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 129 (C\u00e2u 50 - M\u0110 102 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2019 - 2020). Cho h\u00e0m s\u1ed1 f (x) c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean nh\u01b0 sau x \u2212\u221e \u22124 \u22122 0 +\u221e f (x) \u22120+0\u22120+ +\u221e +\u221e 2 f (x) \u22122 \u22123 C\u00f3 bao nhi\u00eau gi\u00e1 tr\u1ecb nguy\u00ean c\u1ee7a tham s\u1ed1 m \u0111\u1ec3 ph\u01b0\u01a1ng tr\u00ecnh 6f (x2 \u2212 4x) = m c\u00f3 \u00edt nh\u1ea5t 3 nghi\u1ec7m th\u1ef1c ph\u00e2n bi\u1ec7t thu\u1ed9c kho\u1ea3ng (0; +\u221e)? A 25. B 30. C 29. D 24. \u0253 L\u1eddi gi\u1ea3i. \u0110\u1eb7t g(x) = 6f (x2 \u2212 4x), v\u1edbi x \u2208 (0; +\u221e). Ta c\u00f3 g (x) = 12(x \u2212 2)f (x2 \u2212 4x). \uf8eex = 2 \u221a \uf8eex = 2 \uf8eex = 2 \uf8efx = 2 \u22122 \uf8ef = 2 \u221a \u00f1x \u2212 2 = 0 = 0 \u21d4 \uf8efx2 \u2212 4x = \u22124 \u21d4 \uf8efx2 \u2212 4x + 4 = 0 \u21d4 g (x) = 0 \u21d4 f x2 \u2212 4x \uf8ef \u2212 4x = \u22122 \uf8ef \u2212 4x + 2 = 0 \uf8ef +2 \uf8f0\uf8efx2 \uf8ef\uf8f0x2 \uf8efx \uf8ef x2 \u2212 4x = 0 x2 \u2212 4x = 0 \uf8f0\uf8efx = 0 x = 4. B\u1ea3ng bi\u1ebfn thi\u00ean Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 165 S\u0110T: 0905.193.688","5. Kh\u1ea3o s\u00e1t s\u1ef1 bi\u1ebfn thi\u00ean v\u00e0 v\u1ebd \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 +\u221e \u221a\u221a +\u221e x 0 2\u2212 2 2 2+ 2 4 g (x) 0 + 0 \u2212 0 + 0 \u2212 0 + 12 12 g(x) \u221212 \u221218 \u221218 T\u1eeb b\u1ea3ng bi\u1ebfn thi\u00ean suy ra ph\u01b0\u01a1ng tr\u00ecnh g(x) = m c\u00f3 \u00edt nh\u1ea5t 3 nghi\u1ec7m th\u1ef1c ph\u00e2n bi\u1ec7t thu\u1ed9c kho\u1ea3ng (0; +\u221e) khi v\u00e0 ch\u1ec9 khi \u221218 < m \u2264 12. M\u00e0 m nguy\u00ean n\u00ean c\u00f3 30 gi\u00e1 tr\u1ecb m th\u1ecfa m\u00e3n. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 130 (C\u00e2u 49 - M\u0110 102 - BGD&\u0110T - \u0110\u1ee3t 4 - N\u0103m 2019 - 2020). Cho h\u00e0m s\u1ed1 f (x) c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean nh\u01b0 sau: x \u2212\u221e \u22124 \u22122 0 +\u221e f (x) \u22120+0\u22120+ +\u221e +\u221e 2 f (x) \u22122 \u22123 C\u00f3 bao nhi\u00eau gi\u00e1 tr\u1ecb nguy\u00ean c\u1ee7a tham s\u1ed1 m \u0111\u1ec3 ph\u01b0\u01a1ng tr\u00ecnh 4f (x2 \u2212 4x) = m c\u00f3 \u00edt nh\u1ea5t 3 nghi\u1ec7m th\u1ef1c ph\u00e2n bi\u1ec7t thu\u1ed9c kho\u1ea3ng (0; +\u221e)? A 16. B 19. C 20. D 17. \u0253 L\u1eddi gi\u1ea3i. \u0110\u1eb7t g(x) = 4f (x2 \u2212 4x), v\u1edbi x \u2208 (0; +\u221e). Ta c\u00f3 g (x) = 8(x \u2212 2)f (x2 \u2212 4x). T\u1eeb b\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a h\u00e0m s\u1ed1 f (x), suy ra \uf8eex = 2 \u221a \uf8eex = 2 \uf8eex = 2 \uf8efx = 2 \u22122 \uf8ef = 2 \u221a \u00f1x \u2212 2 = 0 = 0 \u21d4 \uf8efx2 \u2212 4x = \u22124 \u21d4 \uf8efx2 \u2212 4x + 4 = 0 \u21d4 g (x) = 0 \u21d4 f x2 \u2212 4x \uf8ef \u2212 4x = \u22122 \uf8ef \u2212 4x + 2 = 0 \uf8ef +2 \uf8ef\uf8f0x2 \uf8ef\uf8f0x2 \uf8efx \uf8ef x2 \u2212 4x = 0 x2 \u2212 4x = 0 \uf8ef\uf8f0x = 0 x = 4. \u221a\u221a Ta c\u00f3 g(0) = g(4) = 4f (0) = \u221212, g(2 \u2212 2) = g(2 + 2) = 4f (\u22122) = 8, g(2) = 4f (\u22124) = \u22128. B\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a h\u00e0m s\u1ed1 g(x): \u221a\u221a +\u221e x 0 2\u2212 2 2 2+ 2 4 g (x) 0 + 0 \u2212 0 + 0 \u2212 0 + +\u221e 88 g(x) \u22128 \u221212 \u221212 Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 166 S\u0110T: 0905.193.688","Ch\u01b0\u01a1ng 1. \u1ee8NG D\u1ee4NG \u0110\u1ea0O H\u00c0M \u0110\u1ec2 KH\u1ea2O S\u00c1T V\u00c0 V\u1ebc \u0110\u1ed2 TH\u1eca C\u1ee6A H\u00c0M S\u1ed0 T\u1eeb b\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a g(x), suy ra ph\u01b0\u01a1ng tr\u00ecnh g(x) = m c\u00f3 \u00edt nh\u1ea5t 3 nghi\u1ec7m th\u1ef1c ph\u00e2n bi\u1ec7t thu\u1ed9c kho\u1ea3ng (0; +\u221e) khi v\u00e0 ch\u1ec9 khi \u221212 < m \u2264 8. M\u00e0 m nguy\u00ean n\u00ean c\u00f3 20 gi\u00e1 tr\u1ecb m th\u1ecfa m\u00e3n. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 131 (C\u00e2u 49 - M\u0110 101 - BGD&\u0110T - N\u0103m 2018 - 2019). x\u22123 x\u22122 x\u22121 x Cho hai h\u00e0m s\u1ed1 y = x\u22122 + x\u22121 + x + x+1 v\u00e0 y = |x + 2| \u2212 x + m (m l\u00e0 tham s\u1ed1 th\u1ef1c) c\u00f3 \u0111\u1ed3 th\u1ecb l\u1ea7n l\u01b0\u1ee3t l\u00e0 (C1) v\u00e0 (C2). T\u1eadp h\u1ee3p t\u1ea5t c\u1ea3 c\u00e1c gi\u00e1 tr\u1ecb c\u1ee7a m \u0111\u1ec3 (C1) v\u00e0 (C2) c\u1eaft nhau t\u1ea1i \u0111\u00fang b\u1ed1n \u0111i\u1ec3m ph\u00e2n bi\u1ec7t l\u00e0 A (\u2212\u221e; 2]. B [2; +\u221e). C (\u2212\u221e; 2). D (2; +\u221e). \u0253 L\u1eddi gi\u1ea3i. X\u00e9t ph\u01b0\u01a1ng tr\u00ecnh x \u2212 3 + x \u2212 2 + x \u2212 1 + x = |x + 2| \u2212 x + m x \u2212 2 x \u2212 1 x + x 1 \u21d4 x \u2212 3 + x \u2212 2 + x \u2212 1 + x \u2212 |x + 2| + x = m (1) x \u2212 2 x \u2212 1 x + x 1 H\u00e0m s\u1ed1 g(x) = x\u22123 + x \u2212 2 + x\u22121 + x x \u2212 |x + 2| + x x\u22122 x \u2212 1 x +1 \uf8f1x \u2212 3 x \u2212 2 x \u2212 1 x + + + \u2212 2 n\u1ebfu x \u2265 \u22122 \uf8f4 x \u2212 2 x \u2212 1 x x + 1 n\u1ebfu x < \u22122. \uf8f2 \u2212 3 x \u2212 2 \u2212 x = x x 1 \uf8f4 + + + + 2x + 2 \uf8f3 x\u22122 x\u22121 x x+1 \uf8f11 111 \u2200x \u2208 (\u22122; +\u221e) \\\\ {\u22121; 0; 1; 2} + + + > 0, \uf8f4 \uf8f4 (x \u2212 2)2 (x \u2212 1)2 x2 (x + 1)2 \uf8f2 Ta c\u00f3 g (x) = 1 1 1 1 ++ \uf8f4 + + 2 > 0, \u2200x < \u22122. \uf8f4 \uf8f3 (x \u2212 2)2 (x \u2212 1)2 x2 (x + 1)2 N\u00ean h\u00e0m s\u1ed1 y = g(x) \u0111\u1ed3ng bi\u1ebfn tr\u00ean m\u1ed7i kho\u1ea3ng (\u2212\u221e; \u22121), (\u22121; 0), (0; 1), (1; 2), (2; +\u221e). M\u1eb7t kh\u00e1c ta c\u00f3 lim g(x) = 2 v\u00e0 lim g(x) = \u2212\u221e. x\u2192+\u221e x\u2192\u2212\u221e B\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a h\u00e0m s\u1ed1 y = g(x) x \u2212\u221e \u22122 \u22121 0 1 2 +\u221e y ++++++ +\u221e +\u221e +\u221e +\u221e 2 49 y 12 \u2212\u221e \u2212\u221e \u2212\u221e \u2212\u221e \u2212\u221e Do \u0111\u00f3 \u0111\u1ec3 (C1) v\u00e0 (C2) c\u1eaft nhau t\u1ea1i \u0111\u00fang b\u1ed1n \u0111i\u1ec3m ph\u00e2n bi\u1ec7t th\u00ec ph\u01b0\u01a1ng tr\u00ecnh (1) ph\u1ea3i c\u00f3 4 nghi\u1ec7m ph\u00e2n bi\u1ec7t. \u0110i\u1ec1u n\u00e0y x\u1ea3y ra khi v\u00e0 ch\u1ec9 khi \u0111\u01b0\u1eddng th\u1eb3ng y = m c\u1eaft \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = g(x) t\u1ea1i 4 \u0111i\u1ec3m ph\u00e2n bi\u1ec7t \u21d4 m \u2265 2. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 132 (C\u00e2u 50 - M\u0110 103 - BGD&\u0110T - N\u0103m 2018 - 2019). x\u22121 x + x + 1 + x + 2 v\u00e0 y = |x + 2| \u2212 x \u2212 m (m l\u00e0 tham s\u1ed1 th\u1ef1c) c\u00f3 Cho hai h\u00e0m s\u1ed1 y = + x x+1 x+2 x+3 \u0111\u1ed3 th\u1ecb l\u1ea7n l\u01b0\u1ee3t l\u00e0 (C1), (C2). T\u1eadp h\u1ee3p t\u1ea5t c\u1ea3 c\u00e1c gi\u00e1 tr\u1ecb c\u1ee7a m \u0111\u1ec3 (C1) v\u00e0 (C2) c\u1eaft nhau t\u1ea1i \u0111\u00fang b\u1ed1n \u0111i\u1ec3m ph\u00e2n bi\u1ec7t l\u00e0 A [\u22122; +\u221e). B (\u2212\u221e; \u22122). C (\u22122; +\u221e). D (\u2212\u221e; \u22122]. Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t \u0253 L\u1eddi gi\u1ea3i. S\u0110T: 0905.193.688 167","5. Kh\u1ea3o s\u00e1t s\u1ef1 bi\u1ebfn thi\u00ean v\u00e0 v\u1ebd \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 X\u00e9t ph\u01b0\u01a1ng tr\u00ecnh ho\u00e0nh \u0111\u1ed9 giao \u0111i\u1ec3m x\u22121 x\u22121 + x x +1 x+2 = |x + 2| \u2212 x \u2212 m \u21d4 + x + x + 1 + x + 2 \u2212|x+2|+x = \u2212m(1) + + x x+1 x+2 x+3 x x+1 x+2 x+3 x\u22121 x x+ 1 x+ 2 X\u00e9t f (x) = x + x + 1 + x+ 2 + x+ 3 \u2212 |x + 2| + x, x \u2208 D = R\\\\ {\u22123; \u22122; \u22121; 0} \uf8f1x \u2212 1 x x + 1 x + 2 \u2212 2, x \u2208 (\u22122; +\u221e) \u222a D = D1 + + + + 2x + 2, x \u2208 (\u2212\u221e; \u22122) \u222a D = Ta c\u00f3 f (x) = \uf8f4 x 1 + x + 1 + x + 2 + x + 3 \uf8f2 \u2212 x x 1 x + 1 x + 2 D2. x x + x + 2 x + 3 \uf8f4 \uf8f3 \uf8f11 + 1 + 1 + 1 \u2200x \u2208 D1 + + , \uf8f4 + 3)2 \uf8f4 x2 (x 1)2 (x 2)2 (x \uf8f2 C\u00f3 f (x) = 1 + 1 + 1 + 1 + 2, \u2200x \u2208 D2. \uf8f4 \uf8f4 (x + 1)2 (x + 2)2 (x + 3)2 \uf8f3 x2 D\u1ec5 th\u1ea5y f (x) > 0, \u2200x \u2208 D1 \u222a D2, ta c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean x \u2212\u221e \u22123 \u22122 0 1 +\u221e f (x) + + + + + +\u221e +\u221e +\u221e +\u221e 2 f (x) \u2212\u221e \u2212\u221e \u2212\u221e \u2212\u221e \u2212\u221e Hai \u0111\u1ed3 th\u1ecb c\u1eaft nhau t\u1ea1i \u0111\u00fang 4 \u0111i\u1ec3m ph\u00e2n bi\u1ec7n khi v\u00e0 ch\u1ec9 khi ph\u01b0\u01a1ng tr\u00ecnh (1) c\u00f3 \u0111\u00fang 4 nghi\u1ec7m ph\u00e2n bi\u1ec7t, t\u1eeb b\u1ea3ng bi\u1ebfn thi\u00ean ta c\u00f3: \u2212m \u2265 2 \u21d4 m \u2264 \u22122. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 133 (C\u00e2u 47 - M\u0110 104 - BGD&\u0110T - N\u0103m 2018 - 2019). x\u22122 x\u22121 x x+1 Cho hai h\u00e0m s\u1ed1 y = x\u22121 + x + x+1 + x+2 v\u00e0 y = |x + 1| \u2212 x \u2212 m (m l\u00e0 tham s\u1ed1 th\u1ef1c) c\u00f3 \u0111\u1ed3 th\u1ecb l\u1ea7n l\u01b0\u1ee3t l\u00e0 (C1) v\u00e0 (C2). T\u1eadp h\u1ee3p t\u1ea5t c\u1ea3 c\u00e1c gi\u00e1 tr\u1ecb c\u1ee7a m \u0111\u1ec3 (C1) v\u00e0 (C2) c\u1eaft nhau t\u1ea1i \u0111\u00fang b\u1ed1n \u0111i\u1ec3m ph\u00e2n bi\u1ec7t l\u00e0 A (\u22123; +\u221e). B (\u2212\u221e; \u22123). C [\u22123; +\u221e). D (\u2212\u221e; \u22123]. \u0253 L\u1eddi gi\u1ea3i. X\u00e9t ph\u01b0\u01a1ng tr\u00ecnh ho\u00e0nh \u0111\u1ed9 x \u2212 2 + x\u22121 + x x + x +1 = |x + 1| \u2212 x \u2212 m x \u2212 1 x +1 x +2 \u21d4 x\u22122 x\u22121 x + x + 1 \u2212 |x + 1| + x = \u2212m (1). ++ x\u22121 x x+1 x+2 S\u1ed1 nghi\u1ec7m c\u1ee7a (1) l\u00e0 s\u1ed1 giao \u0111i\u1ec3m c\u1ee7a F (x) = x \u2212 2x \u2212 1 x x + 1 \u2212|x+1|+x = \uf8f1x \u2212 2 + x \u2212 1 + x x 1 + x + 1 \u2212 1, x > \u22121 x \u2212 + x + + + + 2 + x 1 + x 1 + + 2x x < \u22121. x 1x \uf8f4 \u2212 1 x + x + 2 + 1, 1 \uf8f2x \u2212 2 \u2212 x x + 1 \uf8f11 1 1 1 x \u2212 1 x + x + 2 \uf8f4 \uf8f3 x \uf8f4 + + + 2)2 , x \u2208 (\u22121; +\u221e) \\\\ {0; 1} x \u2208 (\u2212\u221e; \u22121) \\\\ {\u22122}. \uf8f4 (x \u2212 1)2 x2 (x + 1)2 (x + \uf8f2 Ta c\u00f3 F (x) = 1 1 1 1 \uf8f4 ++ + + 2, \uf8f4 \uf8f3 (x \u2212 1)2 x2 (x + 1)2 (x + 2)2 M\u1eb7t kh\u00e1c lim F (x) = +\u221e; lim F (x) = 3. x\u2192+\u221e x\u2192\u2212\u221e lim F (x) = +\u221e; lim F (x) = \u2212\u221e; lim F (x) = \u2212\u221e; lim F (x) = +\u221e. x\u2192\u22122+ x\u2192\u22122\u2212 x\u2192\u22121+ x\u2192\u22121\u2212 lim F (x) = \u2212\u221e; lim F (x) = +\u221e; lim F (x) = \u2212\u221e; lim F (x) = +\u221e. x\u21920+ x\u21920\u2212 x\u21921+ x\u21921\u2212 B\u1ea3ng bi\u1ebfn thi\u00ean Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 168 S\u0110T: 0905.193.688","Ch\u01b0\u01a1ng 1. \u1ee8NG D\u1ee4NG \u0110\u1ea0O H\u00c0M \u0110\u1ec2 KH\u1ea2O S\u00c1T V\u00c0 V\u1ebc \u0110\u1ed2 TH\u1eca C\u1ee6A H\u00c0M S\u1ed0 x \u2212\u221e \u22122 \u22121 0 1 +\u221e f (x) + + + + + +\u221e +\u221e +\u221e +\u221e +\u221e f (x) 3 \u2212\u221e \u2212\u221e \u2212\u221e \u2212\u221e \u0110\u1ec3 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 4 nghi\u1ec7m th\u00ec \u2212m \u2264 3 \u21d4 m \u2265 \u22123. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 134 (C\u00e2u 50 - M\u0110 102 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2019 - 2020). Cho h\u00e0m s\u1ed1 b\u1eadc ba y = f (x) c\u00f3 \u0111\u1ed3 th\u1ecb l\u00e0 \u0111\u01b0\u1eddng cong y trong h\u00ecnh b\u00ean. S\u1ed1 nghi\u1ec7m th\u1ef1c ph\u00e2n bi\u1ec7t c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh f (x3f (x)) + 1 = 0 l\u00e0 A 6. B 4. C 5. D 8. O x \u22121 \u0253 L\u1eddi gi\u1ea3i. \uf8ee x3f (x) = a (\u22123 < a < \u22121) (1) (2) , v\u1edbi a, b < 0. Ta c\u00f3 f (x3f (x)) + 1 = 0 \u21d4 f (x3f (x)) = \u22121 \u21d4 \uf8f0 x3f (x) = b (\u22125 < b < \u22123) (3) x3f (x) = 0 m +V\u1edbi m < 0, x\u00e9t ph\u01b0\u01a1ng tr\u00ecnh x3f (x) = m \u21d4 f (x) = x3 . \u0110\u1eb7t g(x) = m g (x) = \u22123m > 0, \u2200x = 0. , x3 x4 lim g(x) = lim g(x) = 0, lim g(x) = +\u221e, lim g(x) = \u2212\u221e. x\u2192\u2212\u221e x\u2192+\u221e x\u21920\u2212 x\u21920+ Ta c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean x 0 1 +\u221e g (x) + + +\u221e 0 g(x) \u2212\u221e 0 D\u1ef1a v\u00e0o b\u1ea3ng bi\u1ebfn thi\u00ean v\u00e0 \u0111\u1ec1 b\u00e0i, suy ra trong m\u1ed7i kho\u1ea3ng (\u2212\u221e; 0) v\u00e0 (0; +\u221e) ph\u01b0\u01a1ng tr\u00ecnh f (x) = g(x) c\u00f3 \u0111\u00fang m\u1ed9t nghi\u1ec7m. Suy ra m\u1ed7i ph\u01b0\u01a1ng tr\u00ecnh (1) v\u00e0 (2) c\u00f3 2 nghi\u1ec7m. +X\u00e9t ph\u01b0\u01a1ng tr\u00ecnh (3) : x3f (x) = 0 \u21d4 \u00f1x = 0 \u00f1x = 0 , v\u1edbi c kh\u00e1c c\u00e1c nghi\u1ec7m c\u1ee7a (1) v\u00e0 \u21d4 f (x) = 0 x = c < 0 (2). V\u1eady ph\u01b0\u01a1ng tr\u00ecnh f (x3f (x)) + 1 = 0 c\u00f3 \u0111\u00fang 6 nghi\u1ec7m. Ch\u1ecdn \u0111\u00e1p \u00e1n A Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 169 S\u0110T: 0905.193.688","5. Kh\u1ea3o s\u00e1t s\u1ef1 bi\u1ebfn thi\u00ean v\u00e0 v\u1ebd \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0104 C\u00e2u 135 (C\u00e2u 50 - M\u0110 103 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2019 - 2020). Cho h\u00e0m s\u1ed1 b\u1eadc b\u1ed1n y = f (x) c\u00f3 \u0111\u1ed3 th\u1ecb l\u00e0 \u0111\u01b0\u1eddng cong y O trong h\u00ecnh b\u00ean. S\u1ed1 nghi\u1ec7m th\u1ef1c ph\u00e2n bi\u1ec7t c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh f (x2f (x)) + 2 = 0 l\u00e0 A 8. B 12. C 6. D 9. x \u22122 \u0253 L\u1eddi gi\u1ea3i. \uf8eex2f (x) = a (1) (2) Ta c\u00f3 f (x2f (x)) + 2 = 0 \u21d4 f (x2f (x)) = \u22122 \u21d4 \uf8efx2f (x) = b \uf8ef (x) = c , v\u1edbi a, b, c > 0. \uf8f0\uf8efx2f (3) (4) x2f (x) = 0 V\u1edbi m > 0, x\u00e9t ph\u01b0\u01a1ng tr\u00ecnh x2f (x) = m \u21d4 f (x) = m (\u2217) . x2 m \u22122m, \u2200x X\u00e9t h\u00e0m s\u1ed1 g (x) = , m > 0, ta c\u00f3 g (x) = = 0. x2 x3 lim g (x) = lim g (x) = 0; lim g (x) = +\u221e ; lim g (x) = +\u221e. x\u2192\u2212\u221e x\u2192+\u221e x\u21920\u2212 x\u21920+ B\u1ea3ng bi\u1ebfn thi\u00ean x \u2212\u221e 0 +\u221e g (x) +\u2212 0 g(x) +\u221e +\u221e 0 D\u1ef1a v\u00e0o b\u1ea3ng bi\u1ebfn thi\u00ean v\u00e0 h\u00ecnh v\u1ebd, suy ra trong m\u1ed7i kho\u1ea3ng (\u2212\u221e; 0) v\u00e0 kho\u1ea3ng (0; +\u221e) ph\u01b0\u01a1ng tr\u00ecnh f (x) = g (x) c\u00f3 \u0111\u00fang m\u1ed9t nghi\u1ec7m. Do \u0111\u00f3 ph\u01b0\u01a1ng tr\u00ecnh (\u2217) c\u00f3 \u0111\u00fang 2 nghi\u1ec7m. T\u1eeb \u0111\u00f3 suy ra m\u1ed7i ph\u01b0\u01a1ng tr\u00ecnh (1), (2), (3) c\u00f3 2 nghi\u1ec7m ph\u00e2n bi\u1ec7t. Ph\u01b0\u01a1ng tr\u00ecnh (4) t\u01b0\u01a1ng \u0111\u01b0\u01a1ng v\u1edbi \u00f1x = 0 . T\u1eeb \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = f (x) suy ra ph\u01b0\u01a1ng tr\u00ecnh f (x) = 0 (4) c\u00f3 3 nghi\u1ec7m ph\u00e2n bi\u1ec7t. V\u1eady ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00e3 cho c\u00f3 9 nghi\u1ec7m ph\u00e2n bi\u1ec7t. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 136 (C\u00e2u 42 - \u0110MH - BGD&\u0110T - N\u0103m 2018 - 2019). Cho h\u00e0m s\u1ed1 f (x) = mx4 + nx3 + px2 + qx + r (m, n, p, q, r \u2208 R). Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 170 S\u0110T: 0905.193.688","Ch\u01b0\u01a1ng 1. \u1ee8NG D\u1ee4NG \u0110\u1ea0O H\u00c0M \u0110\u1ec2 KH\u1ea2O S\u00c1T V\u00c0 V\u1ebc \u0110\u1ed2 TH\u1eca C\u1ee6A H\u00c0M S\u1ed0 H\u00e0m s\u1ed1 y = f (x) c\u00f3 \u0111\u1ed3 th\u1ecb nh\u01b0 h\u00ecnh v\u1ebd b\u00ean. T\u1eadp nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng y tr\u00ecnh f (x) = r c\u00f3 s\u1ed1 ph\u1ea7n t\u1eed l\u00e0 A 4. B 3. C 1. D 2. 5 4 x \u22121 O 3 y = f (x) \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 f (x) = 4mx3 + 3nx2 + 2px + q (1). D\u1ef1a v\u00e0o \u0111\u1ed3 th\u1ecb y =f (x) ta th\u1ea5y ph\u01b0\u01a1ng tr\u00ecnh f (x) = 0 c\u00f3 ba nghi\u1ec7m \u0111\u01a1n l\u00e0 \u22121, 5 3. , 4 Do \u0111\u00f3 f (x) = m (x + 1) (4x \u2212 5) (x \u2212 3) v\u00e0 m = 0 hay f (x) = 4mx3 \u2212 13mx2 \u2212 2mx + 15m (2). T\u1eeb (1) v\u00e0 (2) suy ra n = \u221213m, p = \u2212m v\u00e0 q = 15m. Khi \u0111\u00f3 3 f (x) = r \u21d4 mx4 + nx3 + px2 + qx = 0 \u21d4 x4 \u2212 13 x3 \u2212 x2 + 15x = 0 3 \uf8eex = 0 \u21d4 \uf8efx = 3 \uf8ef \uf8f0 = \u2212 5 . x 3 V\u1eady t\u1eadp nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh f (x) = r l\u00e0 S = \u00df 5 ; 0; \u2122 \u2212 3. 3 Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 137 (C\u00e2u 48 - M\u0110 102 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2019 - 2020). Cho h\u00e0m s\u1ed1 f (x) c\u00f3 f (0) = 0. Bi\u1ebft y = f (x) l\u00e0 h\u00e0m s\u1ed1 b\u1eadc b\u1ed1n y v\u00e0 c\u00f3 \u0111\u1ed3 th\u1ecb l\u00e0 \u0111\u01b0\u1eddng cong trong h\u00ecnh b\u00ean. S\u1ed1 \u0111i\u1ec3m c\u1ef1c tr\u1ecb c\u1ee7a Ox h\u00e0m s\u1ed1 g(x) = |f (x3) + x| l\u00e0 y = f (x) A 4. B 5. C 3. D 6. \u0253 L\u1eddi gi\u1ea3i. \u0110\u1eb7t h(x) = f (x3) + x \u21d2 h (x) = 3x2f (x3) + 1 = 0 \u21d4 f (x3) = \u2212 1 . 3x2 \u0110\u1eb7t t = x3 \u21d2x= \u221a th\u1ebf v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh tr\u00ean ta \u0111\u01b0\u1ee3c f (t) = \u2212 \u221a1 . 3t 3 3 t2 X\u00e9t h\u00e0m s\u1ed1 y = \u2212 \u221a1 \u21d2 y = \u221a2 \u0111\u1ed5i d\u1ea5u khi qua 0 v\u00e0 \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u00f3 ti\u1ec7m c\u1eadn ngang y = 0. 3 3 t2 9 3 t5 Khi v\u1ebd \u0111\u1ed3 th\u1ecb tr\u00ean c\u00f9ng m\u1ed9t m\u1eb7t ph\u1eb3ng t\u1ecda \u0111\u1ed9 v\u1edbi \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = f (t) ta th\u1ea5y hai \u0111\u1ed3 th\u1ecb c\u1eaft nhau t\u1ea1i 2 \u0111i\u1ec3m ph\u00e2n bi\u1ec7t thu\u1ed9c g\u00f3c ph\u1ea7n t\u01b0 th\u1ee9 3 v\u00e0 4\u221a. \u221a G\u1ecdi 2 giao \u0111i\u1ec3m l\u1ea7n l\u01b0\u1ee3t l\u00e0 t1 < 0, t2 > 0 \u21d2 x1 = 3 t1, x2 = 3 t2. Nh\u01b0 v\u1eady ta c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a h\u00e0m s\u1ed1 h(x) nh\u01b0 sau Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 171 S\u0110T: 0905.193.688","5. Kh\u1ea3o s\u00e1t s\u1ef1 bi\u1ebfn thi\u00ean v\u00e0 v\u1ebd \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 x \u2212\u221e x1 0 x2 +\u221e y \u22120+0+ y0 D\u1ef1a v\u00e0o b\u1ea3ng bi\u1ebfn thi\u00ean ta th\u1ea5y ph\u01b0\u01a1ng tr\u00ecnh h(x) = 0 c\u00f3 3 nghi\u1ec7m ph\u00e2n bi\u1ec7t v\u00e0 h\u00e0m s\u1ed1 h(x) c\u00f3 2 \u0111i\u1ec3m c\u1ef1c tr\u1ecb kh\u00f4ng n\u1eb1m tr\u00ean tr\u1ee5c ho\u00e0nh, do \u0111\u00f3 h\u00e0m s\u1ed1 g(x) = |h(x)| c\u00f3 5 \u0111i\u1ec3m c\u1ef1c tr\u1ecb. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 138 (C\u00e2u 45 - M\u0110 102 - BGD&\u0110T - \u0110\u1ee3t 4 - N\u0103m 2019 - 2020). Cho h\u00e0m s\u1ed1 f (x) c\u00f3 f (0) = 0. Bi\u1ebft y = f (x) l\u00e0 h\u00e0m s\u1ed1 b\u1eadc b\u1ed1n v\u00e0 y Ox c\u00f3 \u0111\u1ed3 th\u1ecb l\u00e0 \u0111\u01b0\u1eddng cong trong h\u00ecnh b\u00ean. S\u1ed1 \u0111i\u1ec3m c\u1ef1c tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1 g(x) = |f (x4) + x2| l\u00e0 A 3. B 6. C 5. D 4. \u0253 L\u1eddi gi\u1ea3i. X\u00e9t h\u00e0m s\u1ed1 h(x) = f (x4) + x2, ta c\u00f3 h (x) = 4x3 \u00b7 f (x4) + 2x. \uf8eex = 0 Ph\u01b0\u01a1ng tr\u00ecnh h (x) = 0 \u21d4 4x3 \u00b7 f (x4) + 2x = 0 \u21d4 \uf8f0 1 (x = 0) (1). f (x4) = \u2212 2x2 \u221a \u221a1 \u0110\u1eb7t t = x4 \u21d2 x2 = t, t\u1eeb (1) suy ra f (t) = \u2212 2t . (2) X\u00e9t k(t) = \u2212 \u221a1 , c\u00f3 k (t) = 1 >0 , \u2200t \u2208 (0; +\u221e). 2t 4t 3 2 B\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a k(t) nh\u01b0 sau t0 +\u221e k (t) + 0 k(t) \u2212\u221e D\u1ef1a v\u00e0o \u0111\u1ed3 th\u1ecb f (x) suy ra ph\u01b0\u01a1ng tr\u00ecnh (2) c\u00f3 m\u1ed9t nghi\u1ec7m d\u01b0\u01a1ng hay ph\u01b0\u01a1ng tr\u00ecnh (1) c\u00f3 hai nghi\u1ec7m tr\u00e1i d\u1ea5u x1 < 0 < x2. B\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a h(x) nh\u01b0 sau x \u2212\u221e x1 0 x2 +\u221e h (x) \u22120+0\u22120+ +\u221e 0 +\u221e h(x) h(x1) h(x2) Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 172 S\u0110T: 0905.193.688","Ch\u01b0\u01a1ng 1. \u1ee8NG D\u1ee4NG \u0110\u1ea0O H\u00c0M \u0110\u1ec2 KH\u1ea2O S\u00c1T V\u00c0 V\u1ebc \u0110\u1ed2 TH\u1eca C\u1ee6A H\u00c0M S\u1ed0 T\u1eeb b\u1ea3ng bi\u1ebfn thi\u00ean tr\u00ean suy ra h\u00e0m s\u1ed1 g(x) = |h(x)| c\u00f3 5 \u0111i\u1ec3m c\u1ef1c tr\u1ecb. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 139 (C\u00e2u 50 - M\u0110 102 - BGD&\u0110T - N\u0103m 2017 - 2018). Cho h\u00e0m s\u1ed1 y = 1 x4 \u2212 7 x2 c\u00f3 \u0111\u1ed3 th\u1ecb l\u00e0 (C). C\u00f3 bao nhi\u00eau \u0111i\u1ec3m A thu\u1ed9c (C) sao cho ti\u1ebfp tuy\u1ebfn 84 c\u1ee7a (C) t\u1ea1i A c\u1eaft (C) t\u1ea1i hai \u0111i\u1ec3m ph\u00e2n bi\u1ec7t M (x1; y1); N (x2; y2) (M , N kh\u00e1c A) th\u1ecfa m\u00e3n y1 \u2212 y2 = 3(x1 \u2212 x2)? A 0. B 2. C 3. D 1. \u0253 L\u1eddi gi\u1ea3i. Ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng th\u1eb3ng M N c\u00f3 d\u1ea1ng x \u2212 x2 = y \u2212 y2 \u21d2 h\u1ec7 s\u1ed1 g\u00f3c c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng M N l\u00e0 x1 \u2212 x2 y1 \u2212 y2 y1 \u2212 y2 k = x1 \u2212 x2 = 3. Suy ra ti\u1ebfp tuy\u1ebfn c\u1ee7a (C ) t\u1ea1i A \u00c5 1 x40 \u2212 7 \u00e3 c\u00f3 h\u1ec7 s\u1ed1 g\u00f3c b\u1eb1ng 3. Suy ra x0; 8 4 x02 f (x0) = 3 \u21d4 1 x03 \u2212 7 = 3 \u21d4 \uf8eex0 = \u22121 2 2 x0 \uf8ef\uf8f0x0 = 3 x0 = \u22122. V\u1edbi x0 = \u22121, ta c\u00f3 A \u00c5 13 \u00e3 Ph\u01b0\u01a1ng tr\u00ecnh ti\u1ebfp tuy\u1ebfn l\u00e0 y = 3x + 11 \u22121; . . 8 8 X\u00e9t ph\u01b0\u01a1ng tr\u00ecnh ho\u00e0nh \u0111\u1ed9 giao \u0111i\u1ec3m \uf8eex = \u22121 \u221a 1 x4 \u2212 7 x2 11 \u21d4 \uf8efx = 1 + 3 \u00c5 13 \u00e3 \u22121; 84 = 3x + 8\uf8f0 \u221a \u21d2 A 8 th\u1ecfa y\u00eau c\u1ea7u b\u00e0i to\u00e1n. x=1\u2212 3 V\u1edbi x0 = 3 ta c\u00f3 A \u00c5 \u2212 171 \u00e3 Ph\u01b0\u01a1ng tr\u00ecnh ti\u1ebfp tuy\u1ebfn y = 3x \u2212 195 3; . . 8 8 X\u00e9t ph\u01b0\u01a1ng tr\u00ecnh ho\u00e0nh \u0111\u1ed9 giao \u0111i\u1ec3m 1 x4 \u2212 7 x2 195 \u00c5 171 \u00e3 3; 84 = 3x \u2212 8 \u21d4 x = 3 \u21d2 A \u2212 8 kh\u00f4ng th\u1ecfa m\u00e3n y\u00eau c\u1ea7u b\u00e0i to\u00e1n. V\u1edbi x0 = \u22122, ta c\u00f3 A (\u22122; \u22125). Ph\u01b0\u01a1ng tr\u00ecnh ti\u1ebfp tuy\u1ebfn y = 3x + 1. X\u00e9t ph\u01b0\u01a1ng tr\u00ecnh ho\u00e0nh \u0111\u1ed9 giao \u0111i\u1ec3m \uf8eex = \u22122 \u221a 1 x4 \u2212 7 x2 = 3x \u2212 195 \u21d4 \uf8efx = 2 +6 \u21d2 A(\u22122; \u22125) th\u1ecfa m\u00e3n y\u00eau c\u1ea7u b\u00e0i to\u00e1n. 84 8\uf8f0 \u221a x=2\u2212 6 V\u1eady c\u00f3 2 \u0111i\u1ec3m A th\u1ecfa m\u00e3n y\u00eau c\u1ea7u b\u00e0i to\u00e1n. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 140 (C\u00e2u 50 - M\u0110 103 - BGD&\u0110T - N\u0103m 2017 - 2018). Cho h\u00e0m s\u1ed1 y = 1 x4 \u2212 14 x2 c\u00f3 \u0111\u1ed3 th\u1ecb (C). C\u00f3 bao nhi\u00eau \u0111i\u1ec3m A thu\u1ed9c (C) sao cho ti\u1ebfp tuy\u1ebfn 33 c\u1ee7a (C) t\u1ea1i A c\u1eaft (C) t\u1ea1i hai \u0111i\u1ec3m ph\u00e2n bi\u1ec7t M (x1; y1), N (x2; y2) (M , N kh\u00e1c A) th\u1ecfa m\u00e3n Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 173 S\u0110T: 0905.193.688","5. Kh\u1ea3o s\u00e1t s\u1ef1 bi\u1ebfn thi\u00ean v\u00e0 v\u1ebd \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y1 \u2212 y2 = 8(x1 \u2212 x2)? B 2. C 0. D 3. A 1. \u0253 L\u1eddi gi\u1ea3i. H\u00e0m s\u1ed1 y = 1 x4 \u2212 14 x2 c\u00f3 y = 4 x3 \u2212 28 x2. Cho y =0\u21d4 \u00f1x = 0 \u221a 33 33 x = \u00b1 7. Do y1 \u2212 y2 = 8(x1 \u2212 x2) \u21d4 y1 \u2212 y2 = 8 n\u00ean ti\u1ebfp tuy\u1ebfn c\u1ee7a (C ) t\u1ea1i A c\u00f3 h\u1ec7 s\u1ed1 g\u00f3c k = 8. x1 \u2212 x2 \uf8eexA Cho y (xA) = 8 ta \u0111\u01b0\u1ee3c 4 xA3 \u2212 28 x2A = 8 \u21d4 \uf8f0\uf8efxA = 3 (\u0111\u1ebfn \u0111\u00e2y c\u00f3 3 \u0111i\u1ec3m A c\u1ea7n x\u00e9t). 3 3 = \u22121 xA = \u22122 Ti\u1ebfp tuy\u1ebfn c\u1ee7a (C) t\u1ea1i m\u1ed7i \u0111i\u1ec3m A t\u00ecm \u0111\u01b0\u1ee3c c\u00f3 d\u1ea1ng d : y = 8x + b. Ph\u01b0\u01a1ng tr\u00ecnh ho\u00e0nh \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a (C) v\u00e0 ti\u1ebfp tuy\u1ebfn d: 1 x4 \u2212 14 x2 = 8x + b \u21d4 b = 1 x4 \u2212 14 x2 \u2212 8x = g(x). 33 33 Cho g (x) = 0 ta \u0111\u01b0\u1ee3c x = 3 \u2228 x = \u22121 \u2228 x = \u22122. B\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a g(x): x \u2212\u221e \u22122 \u22121 3 +\u221e g (x) \u22120+0\u22120+ +\u221e 11 +\u221e g(x) 8 3 3 \u221239 Nh\u01b0 v\u1eady (C ) v\u00e0 d c\u00f3 3 \u0111i\u1ec3m chung khi b = 8 ho\u1eb7c b = 11 \u1ee9ng v\u1edbi xA = \u22122 ho\u1eb7c xA = \u22121. 3 3 V\u1eady c\u00f3 2 \u0111i\u1ec3m A tho\u1ea3 m\u00e3n y\u00eau c\u1ea7u b\u00e0i to\u00e1n. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 141 (C\u00e2u 45 - M\u0110 104 - BGD&\u0110T - N\u0103m 2017 - 2018). Cho h\u00e0m s\u1ed1 y = 1 x4 \u2212 7 x2 c\u00f3 \u0111\u1ed3 th\u1ecb (C). C\u00f3 bao nhi\u00eau \u0111i\u1ec3m A thu\u1ed9c (C) sao cho ti\u1ebfp tuy\u1ebfn c\u1ee7a 63 (C) t\u1ea1i A c\u1eaft (C) t\u1ea1i hai \u0111i\u1ec3m ph\u00e2n bi\u1ec7t M (x1; y1), N (x2; y2) th\u1ecfa m\u00e3n y1 \u2212y2 = 4 (x1 \u2212 x2)? A 3. B 0. C 1. D 2. \u0110\u01b0\u1eddng th\u1eb3ng M N c\u00f3 v\u00e9c-t\u01a1 ch\u1ec9 ph\u01b0\u01a1ng l\u00e0 M# \u0253N\u00bbL=\u1eddi(xg1i\u1ea3\u2212i.x2; y#n\u00bb1 \u2212 y2) = (x1 \u2212 x2; 4(x1 \u2212 x2)). Ch\u1ecdn v\u00e9c-t\u01a1 ch\u1ec9 ph\u01b0\u01a1ng l\u00e0 #u\u00bb = (1; 4) \u21d2 v\u00e9c-t\u01a1 ph\u00e1p tuy\u1ebfn = (4; \u22121). Ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng th\u1eb3ng MN : 4(x \u2212 x1) \u2212 (y \u2212 y1) = 0 \u21d4 y = 4x \u2212 4x1 + 1 x41 \u2212 7 x21 . 6 3 \u0110\u01b0\u1eddng th\u1eb3ng M N ti\u1ebfp x\u00fac v\u1edbi (C) t\u1ea1i \u0111i\u1ec3m A. Nh\u01b0 v\u1eady, n\u1ebfu A c\u00f3 ho\u00e0nh \u0111\u1ed9 l\u00e0 x0 th\u00ec x0 l\u00e0 nghi\u1ec7m 2 x3 14 \uf8eex = \u22121 x c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh \u2212 = 4 \u21d4 x3 \u2212 7x \u2212 6 \u21d4 \uf8efx = \u22122 33 \uf8f0 x = 3. V\u1edbi x= \u22121 \u21d2 A \u00c5 \u2212 13 \u00e3 V\u00ec \u0111\u01b0\u1eddng th\u1eb3ng MN ti\u1ebfp x\u00fac v\u1edbi \u0111\u1ed3 th\u1ecb (C ) t\u1ea1i A n\u00ean ta c\u00f3 \u22121; . 6 \u2212 13 = \u22124 + 1 x41 \u2212 7 x12 \u2212 4x1 \u21d4 (x1 + 1)2(x12 \u2212 2x1 \u2212 11) = 0 (1). 6 6 3 Ph\u01b0\u01a1ng tr\u00ecnh (1) c\u00f3 nghi\u1ec7m k\u00e9p v\u00e0 hai nghi\u1ec7m \u0111\u01a1n ph\u00e2n bi\u1ec7t n\u00ean \u0111\u01b0\u1eddng th\u1eb3ng M N ti\u1ebfp x\u00fac v\u1edbi \u0111\u1ed3 th\u1ecb (C) t\u1ea1i A v\u00e0 c\u1eaft \u0111\u1ed3 th\u1ecb t\u1ea1i hai \u0111i\u1ec3m ph\u00e2n bi\u1ec7t M , N kh\u00e1c A. Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 174 S\u0110T: 0905.193.688","Ch\u01b0\u01a1ng 1. \u1ee8NG D\u1ee4NG \u0110\u1ea0O H\u00c0M \u0110\u1ec2 KH\u1ea2O S\u00c1T V\u00c0 V\u1ebc \u0110\u1ed2 TH\u1eca C\u1ee6A H\u00c0M S\u1ed0 V\u1edbi x = \u22122 \u21d2 A \u00c5 \u2212 20 \u00e3 V\u00ec \u0111\u01b0\u1eddng th\u1eb3ng MN ti\u1ebfp x\u00fac v\u1edbi \u0111\u1ed3 th\u1ecb (C ) t\u1ea1i A n\u00ean ta c\u00f3 \u22122; . 3 \u2212 20 = \u22128 + 1 x14 \u2212 7 x12 \u2212 4x1 \u21d4 (x1 + 2)2(x21 \u2212 4x1 \u2212 4) = 0 (2). 3 6 3 Ph\u01b0\u01a1ng tr\u00ecnh (2) c\u00f3 m\u1ed9t nghi\u1ec7m k\u00e9p v\u00e0 hai nghi\u1ec7m \u0111\u01a1n n\u00ean \u0111\u01b0\u1eddng th\u1eb3ng M N ti\u1ebfp x\u00fac v\u1edbi \u0111\u1ed3 th\u1ecb (C) t\u1ea1i A v\u00e0 c\u1eaft \u0111\u1ed3 th\u1ecb t\u1ea1i 2 \u0111i\u1ec3m ph\u00e2n bi\u1ec7t M , N kh\u00e1c A. V\u1edbi x= 3\u21d2 A \u00c5 \u2212 15 \u00e3 V\u00ec MN ti\u1ebfp x\u00fac v\u1edbi (C ) t\u1ea1i A n\u00ean ta c\u00f3 3; . 2 \u2212 15 = 12 + 1 x41 \u2212 7 x12 \u2212 4x1 \u21d4 (x1 \u2212 3)2(x21 + 6x1 + 13) = 0 (3). 2 6 3 Ph\u01b0\u01a1ng tr\u00ecnh (3) ch\u1ec9 c\u00f3 m\u1ed9t nghi\u1ec7m k\u00e9p n\u00ean \u0111\u01b0\u1eddng th\u1eb3ng M N ch\u1ec9 ti\u1ebfp x\u00fac v\u1edbi \u0111\u1ed3 th\u1ecb (C) t\u1ea1i A n\u00ean tr\u01b0\u1eddng h\u1ee3p n\u00e0y lo\u1ea1i. V\u1eady c\u00f3 hai \u0111i\u1ec3m A th\u1ecfa m\u00e3n y\u00eau c\u1ea7u. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 142 (C\u00e2u 48 - M\u0110 102 - BGD&\u0110T - N\u0103m 2017 - 2018). x\u22121 Cho h\u00e0m s\u1ed1 y = c\u00f3 \u0111\u1ed3 th\u1ecb (C). G\u1ecdi I l\u00e0 giao \u0111i\u1ec3m c\u1ee7a hai ti\u1ec7m c\u1eadn c\u1ee7a (C). X\u00e9t tam gi\u00e1c x+1 \u0111\u1ec1u ABI c\u00f3 hai \u0111\u1ec9nh A, B thu\u1ed9c (C), \u0111o\u1ea1n AB c\u00f3 \u0111\u1ed9 d\u221a\u00e0i b\u1eb1ng \u221a A 3. B 2. C 2 2. D 2 3. \u0253 L\u1eddi gi\u1ea3i. Giao \u0111i\u1ec3m hai \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn c\u1ee7a (C) l\u00e0 I(\u22121; 1). H\u00e0m s\u1ed1 \u0111\u00e3 cho \u0111\u01b0\u1ee3c vi\u1ebft l\u1ea1i y = 1 \u2212 2 . x+1 \u00c5 2 \u00e3\u00c5 2 \u00e3 I#A\u00bb \u00c5 2 \u00e3 I#B\u00bb Gi\u1ea3 s\u1eed A a; 1 \u2212 \u2208 (C), A b; 1 \u2212 a + 1; \u2212 , a+1 b+1 \u2208 (C ). Ta c\u00f3 = a+1 = \u00c5 2 \u00e3 b + 1; \u2212 . b+1 \u0110\u1eb7t a1 = a + 1, b1 = b + 1 (hi\u1ec3n nhi\u00ean a1 = 0, b1 = 0 v\u00e0 a1 = b1). Tam gi\u00e1c ABI \u0111\u1ec1u khi ch\u1ec9 khi \uf8f1 \u00c5 4 \u00e3 1 a12b12 \u00aeIA2 = IB2 \uf8f1 4 = b21 + 4 \uf8f4\uf8f4\uf8f4(a21 \u2212 b21) \u2212 = 0 (1) cos(I#A\u00bb, I#B\u00bb) = cos 60\u25e6 \uf8f2\uf8f4\uf8f4a21 + #a12\u00bb 1 b21 \uf8f2 (2) IB \u21d4 \uf8f4I#A\u00bb \u00b7 = \u21d4 a1b1 + 4 1 \uf8f4 \uf8f4 a1 b1 2 \uf8f3 = \uf8f4 a21 + 4 IA \u00b7 IB 2 \uf8f4 a21 \uf8f3 \uf8eea1 = b1, lo\u1ea1i v\u00ec A \u2261 B. Ph\u01b0\u01a1ng tr\u00ecnh (1) \u21d4 \uf8ef\uf8efa1 = \u2212b1, lo\u1ea1i v\u00ec kh\u00f4ng th\u1ecfa m\u00e3n (2). \uf8ef \uf8f0\uf8efa1b1 = \u22122, lo\u1ea1i v\u00ec kh\u00f4ng th\u1ecfa m\u00e3n (2). a1b1 = 2. V\u1edbi a1b1 = 2, thay v\u00e0o (2), ta \u0111\u01b0\u1ee3c 2 + 4 = 1 \u21d4 a12 + 4 = 8. 2 2 a12 a21 + 4 a12 V\u1eady AB = IA = \u00a0 + 4 = \u221a = \u221a a12 a21 8 2 2. Ch\u1ecdn \u0111\u00e1p \u00e1n C Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 175 S\u0110T: 0905.193.688","5. Kh\u1ea3o s\u00e1t s\u1ef1 bi\u1ebfn thi\u00ean v\u00e0 v\u1ebd \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0104 C\u00e2u 143 (C\u00e2u 48 - M\u0110 101 - BGD&\u0110T - N\u0103m 2016 - 2017). T\u00ecm t\u1ea5t c\u1ea3 c\u00e1c gi\u00e1 tr\u1ecb th\u1ef1c c\u1ee7a tham s\u1ed1 m \u0111\u1ec3 \u0111\u01b0\u1eddng th\u1eb3ng y = mx \u2212 m + 1 c\u1eaft \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 y = x3 \u2212 3x2 + x + 2 t\u1ea1i ba \u0111i\u1ec3m A, B, C ph\u00e2n bi\u1ec7t sao cho AB = BC. A m \u2208 (\u2212\u221e; 0] \u222a [4; +\u221e). B m \u2208 R. C m \u2208 \u2212 5; +\u221e . D m \u2208 (\u22122; +\u221e). 4 \u0253 L\u1eddi gi\u1ea3i. Nh\u1eadn th\u1ea5y \u0111\u01b0\u1eddng th\u1eb3ng y = mx \u2212 m + 1 lu\u00f4n \u0111i qua \u0111i\u1ec3m u\u1ed1n B(1; 1) c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = x3 \u2212 3x2 + x + 2, do v\u1eady n\u1ebfu n\u00f3 c\u1eaft \u0111\u1ed3 th\u1ecb t\u1ea1i 3 \u0111i\u1ec3m ph\u00e2n bi\u1ec7t A, B, C th\u00ec lu\u00f4n tho\u1ea3 m\u00e3n AB = BC. Th\u1eed m = \u22123 th\u00ec \u0111\u01b0\u1eddng th\u1eb3ng kh\u00f4ng c\u1eaft \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111\u00e3 cho t\u1ea1i 3 \u0111i\u1ec3m ph\u00e2n bi\u1ec7t n\u00ean lo\u1ea1i tr\u1eeb c\u00e1c ph\u01b0\u01a1ng \u00e1n A, B. Th\u1eed m = \u22123 th\u00ec \u0111\u01b0\u1eddng th\u1eb3ng c\u1eaft \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111\u00e3 cho t\u1ea1i 3 \u0111i\u1ec3m ph\u00e2n bi\u1ec7t n\u00ean lo\u1ea1i tr\u1eeb c\u00e1c ph\u01b0\u01a1ng 2 \u00e1n C. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 144 (C\u00e2u 45 - M\u0110 102 - BGD&\u0110T - N\u0103m 2016 - 2017). T\u00ecm t\u1ea5t c\u1ea3 c\u00e1c gi\u00e1 tr\u1ecb th\u1ef1c c\u1ee7a tham s\u1ed1 m \u0111\u1ec3 \u0111\u01b0\u1eddng th\u1eb3ng y = \u2212mx c\u1eaft \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = x3 \u2212 3x2 \u2212 m + 2 t\u1ea1i ba \u0111i\u1ec3m ph\u00e2n bi\u1ec7t A, B, C sao cho AB = BC. A m \u2208 (\u2212\u221e; 3). B m \u2208 (\u2212\u221e; \u22121). C m \u2208 (\u2212\u221e; +\u221e). D m \u2208 (1; +\u221e). \u0253 L\u1eddi gi\u1ea3i. - \u0110\u1ec3 \u0111\u01b0\u1eddng th\u1eb3ng y = \u2212mx c\u1eaft \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 (C) : y = x3 \u2212 3x2 \u2212 m + 2 t\u1ea1i ba \u0111i\u1ec3m ph\u00e2n bi\u1ec7t l\u00e0 ph\u01b0\u01a1ng tr\u00ecnh ho\u00e0nh \u0111\u1ed9 giao \u0111i\u1ec3m (x \u2212 1)(x2 \u2212 2x \u2212 2 + m) = 0 c\u00f3 ba nghi\u1ec7m ph\u00e2n bi\u1ec7t, gi\u1ea3i ra ra \u0111\u01b0\u1ee3c m < 3. - Nh\u1eadn th\u1ea5y (C) c\u00f3 \u0111i\u1ec3m u\u1ed1n U (1; \u2212m) lu\u00f4n thu\u1ed9c \u0111\u01b0\u1eddng th\u1eb3ng y = \u2212mx n\u00ean \u0111\u1ec3 th\u1ecfa m\u00e3n y\u00eau c\u1ea7u \u0111\u1ec1 b\u00e0i th\u00ec m < 3. Ch\u1ecdn \u0111\u00e1p \u00e1n A Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 176 S\u0110T: 0905.193.688","Ch\u01b0\u01a1ng H\u00c0M S\u1ed0 L\u0168Y TH\u1eeaA. H\u00c0M S\u1ed0 M\u0168 V\u00c0 H\u00c0M S\u1ed0 L\u00d4GARIT 2 B\u00c0I 1. L\u0168Y TH\u1eeaA \u0104 C\u00e2u 1 \u221a(C\u00e2u 19 - M\u0110 104\u221a - BGD&\u0110T - N\u0103m 2021 - 2022). Cho a = 3 5, b = 32 v\u00e0 c = 3 6. M\u1ec7nh \u0111\u1ec1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y \u0111\u00fang? A a < b < c. B a < c < b. C c < a < b. D b < a < c. \u221a\u221a \u0253 L\u1eddi gi\u1ea3i. \u221a\u221a Ta c\u00f3 2 < 5 < 6 m\u00e0 c\u01a1 s\u1ed1 3 > 1 n\u00ean 32 < 3 5 < 3 6 hay b < a < c. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 2 (C\u00e2u 12 - \u0110TK - BGD&\u0110T \u221a- N\u00e4\u01032m0172\u00c401\u221a6 - 2017). \u00c4 \u00e42016 4 3\u22127 . T\u00ednh gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c P = 7 + 4 3 \u221a\u221a D \u00c4 \u221a \u00e42016 A P = 1. B P = 7 \u2212 4 3. C P = 7 + 4 3. 7+4 3 . \u0253 L\u1eddi gi\u1ea3i. \u00c4 \u221a \u00e4 \u00c4 \u221a \u00e42016 \u00c4 \u221a \u00e42016 \u00c4 \u221a \u00e4 \u00c4\u00c4 \u221a \u00e4 \u00c4 \u221a \u00e4\u00e42016 Ta vi\u1ebft l\u1ea1i P = 7 + 4 3 7 + 4 3 4 3\u22127 = 7+4 3 7+4 3 4 3\u22127 . S\u1eed \u221a\u00e4 \u00c4\u221a \u221a\u00e4 \u221a\u00e4 d\u1ee5ng m\u00e1y t\u00ednh, t\u00ednh \u0111\u01b0\u1ee3c \u00c4 + 43 43 \u2212 \u00e4 = \u22121. Suy ra P = \u00c4 43 (\u22121)2016 = \u00c4 4 3. 7 7 7+ 7+ Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 3 (C\u00e2u 15 - \u0110TN - BGD&\u0110T - N\u0103m 2016 - 2017). \u221a Cho bi\u1ec3u th\u1ee9c P = \u00bb 3 x2. x3, v\u1edbi x > 0. M\u1ec7nh \u0111\u1ec1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y \u0111\u00fang ? 4 x. A P = x1 . B P = x .13 C P = x1 . D P = x 2 . 2 24 4 3 \u0253 L\u1eddi gi\u1ea3i. \u00bb\u00bb 4 4 Ta c\u00f3 P = x. 3 x2.x 3 = x. 3 x7 = 4 x.x 7 = 4 x 13 = x 13 . 2 2 6 6 24 Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 4 \u221a(C\u00e2u 6 - M\u0110 103 \u221a- BGD&\u0110T - N\u0103m 2021 - 2022). Cho a = 3 5, b = 32 v\u00e0 c = 3 6 m\u1ec7nh \u0111\u1ec1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y \u0111\u00fang? A a < c < b. B a < b < c. C b < a < c. D c < a < b. \u0253 L\u1eddi gi\u1ea3i. \u221a\u221a\u221a \u221a \u221a \u221a\u00ae 4< 5< 6 \u21d2 b < a < c. Ta c\u00f3 a = 3 5, b = 32 = 3 4, c = 3 6 v\u00e0 3>1 Ch\u1ecdn \u0111\u00e1p \u00e1n C Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 177 S\u0110T: 0905.193.688","1. L\u0169y th\u1eeba \u0104 C\u00e2u 5 (C\u00e2u 13 - =M\u0110x 131.\u221a06 2x - BGD&\u0110T - N\u0103m 2016 - 2017). R\u00fat g\u1ecdn v\u1edbi x > 0. \u221a bi\u1ec3u th\u1ee9c P AP C P = x. = x1 . B P = x2. D P = x 2 . 8 3 \u221a \u0253 L\u1eddi gi\u1ea3i. x. Ta c\u00f3: P = x x1 1 = x1 + 1 = x1 = 36 3 6 2 Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 6 (C\u00e2u 5 - M\u0110 104 - BGD&\u0110T - N\u0103m 2016 - 2017). T\u00ecm nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh log2 (x \u2212 5) = 4. A x = 21. B x = 3. C x = 11. D x = 13. \u0253 L\u1eddi gi\u1ea3i. \u0110i\u1ec1u ki\u1ec7n: x \u2212 5 > 0 \u21d4 x > 5. Pt \u21d4 x \u2212 5 = 24 \u21d4 x = 21 (th\u1ecfa \u0111i\u1ec1u ki\u1ec7n). Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 7 (C\u00e2u 29 - M\u0110 10\u221a3 - BGD&\u0110T - N\u0103m 2016 - 2017). R\u00fat g\u1ecdn bi\u1ec3u th\u1ee9c Q : 3b v\u1edbi b > 0. = b5 3 A Q = b2. B Q = b5 . C Q = b\u2212 4 . D Q = b4 . 9 3 3 \u221a \u0253 L\u1eddi gi\u1ea3i. 3b Ta c\u00f3 Q = b5 : = b5 : b1 = b5 \u2212 1 = b4 3 3 3 3 3 3 Ch\u1ecdn \u0111\u00e1p \u00e1n D Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 178 S\u0110T: 0905.193.688","Ch\u01b0\u01a1ng 2. H\u00c0M S\u1ed0 L\u0168Y TH\u1eeaA. H\u00c0M S\u1ed0 M\u0168 V\u00c0 H\u00c0M S\u1ed0 L\u00d4GARIT B\u00c0I 2. H\u00c0M S\u1ed0 L\u0168Y TH\u1eeaA \u0104 C\u00e2u 1 (C\u00e2u 9 - \u0110MH - BGD\u221a&\u0110T - N\u0103m 2021 - 2022). T\u1eadp x\u00e1c \u0111\u1ecbnh c\u1ee7a h\u00e0m s\u1ed1 y = x 2 l\u00e0 A R. B R\\\\{0}. C (0; +\u221e). D (2; +\u221e). \u0253 L\u1eddi gi\u1ea3i. \u221a H\u00e0m s\u1ed1 y = x 2 x\u00e1c \u0111\u1ecbnh khi v\u00e0 ch\u1ec9 khi x > 0. V\u1eady D = (0; +\u221e). Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 2 (C\u00e2u 10 - M\u0110 101 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2020 - 2021). 5 Tr\u00ean kho\u1ea3ng (0; +\u221e), \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 y = x 2 l\u00e0 A y = 27 B y 23 C y = 53 D y = 5 x\u2212 3 . x2. = x2. x2. 2 7 5 2 2 \u0253 L\u1eddi gi\u1ea3i. Tr\u00ean kho\u1ea3ng (0; +\u221e), ta c\u00f3 y \u00c5 5\u00e3 = 5 x 5 \u22121 = 53 = x2 2 x2. 22 Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 3 (C\u00e2u 1 - M\u0110 102 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2020 - 2021). Tr\u00ean kho\u1ea3ng (0; +\u221e), \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 y = x5 l\u00e0 4 A y = 4 x 9 . B y = 4 x 1 . C y = 5 x 1 . D y = 5 x\u2212 1 . 4 4 4 4 9 5 4 4 \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 y = 5 x 1 . 4 4 Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 4 (C\u00e2u 17 - M\u0110 103 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2020 - 2021). 4 Tr\u00ean kho\u1ea3ng (0; +\u221e), \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 y = x 3 l\u00e0 A y = 4 x\u2212 1 . B y 41 C y = 37 D y 31 3 = x3. x3. = x3. 3 3 7 4 \u0253 L\u1eddi gi\u1ea3i. Tr\u00ean kho\u1ea3ng (0; +\u221e), ta c\u00f3 y = 41 x3. 3 Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 5 (C\u00e2u 8 - M\u0110 104 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2020 - 2021). 5 Tr\u00ean kho\u1ea3ng (0; +\u221e), \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 y = x 3 l\u00e0 A y = 38 B y 52 C y = 5 x\u2212 2 . D y 32 x3. = x3. 3 = x3. 8 3 3 5 \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 y = 5 x 5 \u22121 = 52 3 x3. 33 Ch\u1ecdn \u0111\u00e1p \u00e1n B Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 179 S\u0110T: 0905.193.688","2. H\u00e0m s\u1ed1 l\u0169y th\u1eeba \u0104 C\u00e2u 6 (C\u00e2u 1 - M\u0110 102 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2020 - 2021). Tr\u00ean kho\u1ea3ng (0; +\u221e), \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 y = x5 l\u00e0 4 A y = 4 x 9 . B y = 4 x 1 . C y = 5 x 1 . D y = 5 x\u2212 1 . 4 4 4 4 9 5 4 4 5 \u0253 L\u1eddi gi\u1ea3i. Tr\u00ean kho\u1ea3ng (0; +\u221e), ta c\u00f3 y = x 1 . 4 4 Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 7 (C\u00e2u 24 - M\u0110 101 - BGD&\u0110T - N\u0103m 2016 - 2017). T\u00ecm t\u1eadp x\u00e1c \u0111\u1ecbnh c\u1ee7a h\u00e0m s\u1ed1 y = (x \u2212 1) 1 . 3 A D = (\u2212\u221e; 1). B D = (1; +\u221e). C D = R. D D = R \\\\ {1}. 1 \u0253 L\u1eddi gi\u1ea3i. 3 \u0110i\u1ec1u ki\u1ec7n: x\u22121 > 0 (v\u00ec kh\u00f4ng nguy\u00ean) \u21d2 x > 1 \u21d2 t\u1eadp x\u00e1c \u0111\u1ecbnh D = (1; +\u221e). Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 8 (C\u00e2u 22 - M\u0110 103 - BGD&\u0110T - N\u0103m 2016 - 2017). Cho hai h\u00e0m s\u1ed1 y = ax, y = bx v\u1edbi a, b l\u00e0 hai s\u1ed1 th\u1ef1c d\u01b0\u01a1ng kh\u00e1c 1, l\u1ea7n l\u01b0\u1ee3t c\u00f3 \u0111\u1ed3 th\u1ecb l\u00e0 (C1) v\u00e0 (C2) y nh\u01b0 h\u00ecnh b\u00ean.M\u1ec7nh \u0111\u1ec1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y \u0111\u00fang? (C2) (C1) A 0 < a < b < 1. B 0 < b < 1 < a. C 0 < a < 1 < b. D 0 < b < a < 1. Ox \u0253 L\u1eddi gi\u1ea3i. Theo h\u00ecnh v\u1ebd ta c\u00f3 h\u00e0m y = ax \u0111\u1ed3ng bi\u1ebfn \u21d2 a > 1 v\u00e0 h\u00e0m s\u1ed1 y = bx ngh\u1ecbch bi\u1ebfn \u21d2 b < 1. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 9 (C\u00e2u 11 - M\u0110 104 - BGD&\u0110T - N\u0103m 2016 - 2017). T\u00ecm t\u1eadp x\u00e1c \u0111\u1ecbnh D c\u1ee7a h\u00e0m s\u1ed1 y = (x2 \u2212 x \u2212 2)\u22123. A D = R. B D = (0; +\u221e). C D = (\u2212\u221e; \u22121) \u222a (2; +\u221e). D D = R \\\\ {\u22121; 2}. \u0253 L\u1eddi gi\u1ea3i. \u0110i\u1ec1u ki\u1ec7n x\u00e1c \u0111\u1ecbnh: x2 \u2212 x \u2212 2 = 0 \u21d4 x = \u22121 v\u00e0 x = 2. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 10 (C\u00e2u 32 - M\u0110 103 - BGD&\u0110T - N\u0103m 2016 - 2017). T\u00ecm t\u1ea5t c\u1ea3 c\u00e1c gi\u00e1 tr\u1ecb th\u1ef1c c\u1ee7a tham s\u1ed1 m \u0111\u1ec3 h\u00e0m s\u1ed1 y = log (x2 \u2212 2x \u2212 m + 1) c\u00f3 t\u1eadp x\u00e1c \u0111\u1ecbnh l\u00e0 R. B m < 0. C m \u2264 2. D m > 2. A m \u2265 0. \u0253 L\u1eddi gi\u1ea3i. H\u00e0m s\u1ed1 y = log (x2 \u2212 2x \u2212 m + 1) x\u00e1c \u0111\u1ecbnh \u21d4 x2 \u2212 2x \u2212 m + 1 > 0 H\u00e0m s\u1ed1 c\u00f3 t\u1eadp x\u00e1c \u0111\u1ecbnh l\u00e0 R \u21d4 b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh x2 \u2212 2x \u2212 m + 1 > 0 x\u1ea3y ra v\u1edbi m\u1ecdi x \u21d4 \u2206 = 4 + 4 (m \u2212 1) < 0 \u21d4 m < 0. Ch\u1ecdn \u0111\u00e1p \u00e1n B Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 180 S\u0110T: 0905.193.688","Ch\u01b0\u01a1ng 2. H\u00c0M S\u1ed0 L\u0168Y TH\u1eeaA. H\u00c0M S\u1ed0 M\u0168 V\u00c0 H\u00c0M S\u1ed0 L\u00d4GARIT \u0104 C\u00e2u 11 (C\u00e2u 47 - M\u0110 104 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2019 - 2020). X\u00e9t c\u00e1c s\u1ed1 th\u1ef1c kh\u00f4ng \u00e2m x v\u00e0 y th\u1ecfa m\u00e3n 2x + y4x+y\u22121 \u2265 3. Gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a bi\u1ec3u th\u1ee9c P = x2 + y2 + 6x + 4y b\u1eb1ng A 33 B 9 C 21 D 41 . . .. . 8 8 4 8 1 \u0253 L\u1eddi gi\u1ea3i. N\u1ebfu x + y < 3 th\u00ec 2x + y4x+y\u22121 < 2x + y4 2 = 2x + 2y < 3 (lo\u1ea1i). V\u1eady t\u1eeb gi\u1ea3 thi\u1ebft suy ra 2x + 2y \u2265 3. 2 \u00ae2x + 2y \u2265 3 Tr\u00ean m\u1eb7t ph\u1eb3ng t\u1ecda \u0111\u1ed9 mi\u1ec1n nghi\u1ec7m c\u1ee7a h\u1ec7 l\u00e0 ph\u1ea7n kh\u00f4ng b\u1ecb g\u1ea1ch nh\u01b0 h\u00ecnh v\u1ebd x \u2265 0; y \u2265 0 y 2x + 2y = 3 H x O I Ta c\u00f3 P = x2 + y2 + 4x + 2y \u21d4 (x + 2)2 + (y + 1)2 = 5 + P (\u2217) \u221a T\u1eadp h\u1ee3p c\u00e1c \u0111i\u1ec3m (x; y) th\u1ecfa m\u00e3n (\u2217) l\u00e0 \u0111\u01b0\u1eddng tr\u00f2n t\u00e2m I (\u22122; \u22121) b\u00e1n k\u00ednh R = 5 + P , (P > \u22125). \u0110\u1ec3 t\u1ed3n t\u1ea1i c\u1eb7p (x; y) th\u00ec \u0111\u01b0\u1eddng tr\u00f2n ph\u1ea3i c\u00f3 \u0111i\u1ec3m chung v\u1edbi ph\u1ea7n m\u1eb7t ph\u1eb3ng kh\u00f4ng b\u1ecb g\u1ea1ch \u1edf h\u00ecnh tr\u00ean. \u0110i\u1ec1u \u0111\u00f3 x\u1ea3y ra khi b\u00e1n k\u00ednh \u0111\u01b0\u1eddng tr\u00f2n kh\u00f4ng b\u00e9 h\u01a1n kho\u1ea3ng c\u00e1ch t\u1eeb t\u00e2m I \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh d : 2x + 2y \u2212 3 = 0. \u221a \u00c7 \u221a \u00e52 41 B\u1edfi v\u00ec d (I; d) = |\u22122.2 \u2212\u221a1.2 \u2212 3| = 9 2 92 . n\u00ean ta ph\u1ea3i c\u00f3 5+P \u2265 \u21d4 P \u2265 22 4 48 D\u1ea5u b\u1eb1ng x\u1ea3y ra khi c\u1eb7p (x; y) l\u00e0 t\u1ecda \u0111\u1ed9 c\u1ee7a \u0111i\u1ec3m H tr\u00ean h\u00ecnh v\u1ebd. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 12 (C\u00e2u 50 - M\u0110 103 - BGD&\u0110T - N\u0103m 2016 - 2017). 9t X\u00e9t h\u00e0m s\u1ed1 f (t) = v\u1edbi m l\u00e0 tham s\u1ed1 th\u1ef1c. G\u1ecdi S l\u00e0 t\u1eadp h\u1ee3p t\u1ea5t c\u1ea3 c\u00e1c gi\u00e1 tr\u1ecb c\u1ee7a m sao 9t + m2 cho f (x) + f (y) = 1 v\u1edbi m\u1ecdi s\u1ed1 th\u1ef1c x, y th\u1ecfa m\u00e3n ex+y \u2264 e(x + y). T\u00ecm s\u1ed1 ph\u1ea7n t\u1eed c\u1ee7a S. A 0. B 1. C V\u00f4 s\u1ed1. D 2. \u0253 L\u1eddi gi\u1ea3i. ex+y \u2264 e(x + y) \u21d4 ex+y\u22121 \u2264 x + y \u21d4 ex+y\u22121 \u2212 1 \u2264 x + y \u2212 1 X\u00e9t g(t) = et \u2212 t \u2212 1 v\u1edbi t \u2208 R g (t) = et \u2212 1 = 0 \u21d4 t = 0. B\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a g(t) nh\u01b0 sau. t \u2212\u221e 0 +\u221e +\u221e g (t) \u2212 0 + +\u221e g(t) 0 Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 181 S\u0110T: 0905.193.688","2. H\u00e0m s\u1ed1 l\u0169y th\u1eeba T\u1eeb b\u1ea3ng bi\u1ebfn thi\u00ean ta th\u1ea5y g(t) \u2265 0 \u2200t \u2208 R, t\u1ee9c l\u00e0 ex+y\u22121 \u2212 1 \u2265 x + y \u2212 1, k\u1ebft h\u1ee3p v\u1edbi gi\u1ea3 thi\u1ebft suy ra ex+y\u22121 = x+y \u21d4 x+y = 1. T\u1eeb \u0111\u00f3, v\u1edbi x+y = 1, f (x)+f (y) = f (x)+f (1\u2212x) = 9x 9x 91\u2212x = + m2 + 91\u2212x + m2 9x m2u2 + 18u + 9m2 = 9x + m2 + 9 \u00b7 m2 = m2u2 + (m4 + 9)u + 9\u221am2 v\u1edbi u = 9x > 0. 9 + 9x f (x) + f (1 \u2212 x) = 1 \u2200x \u21d4 m4 + 9 = 18 \u21d4 m = \u00b1 3. Ch\u1ecdn \u0111\u00e1p \u00e1n D Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 182 S\u0110T: 0905.193.688","Ch\u01b0\u01a1ng 2. H\u00c0M S\u1ed0 L\u0168Y TH\u1eeaA. H\u00c0M S\u1ed0 M\u0168 V\u00c0 H\u00c0M S\u1ed0 L\u00d4GARIT B\u00c0I 3. L\u00d4GARIT \u0104 C\u00e2u 1 (C\u00e2u 1 - M\u0110 103 - BGD&\u0110T - N\u0103m 2017 - 2018). V\u1edbi a l\u00e0 s\u1ed1 th\u1ef1c d\u01b0\u01a1ng t\u00f9y \u00fd, ln(7a) \u2212 ln(3a) b\u1eb1ng A ln(7a) B ln 7 C 7 D ln(4a). . . ln . ln(3a) ln 3 3 \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 ln(7a) \u2212 ln(3a) = ln \u00c5 7a \u00e3 = ln 7 . 3a 3 Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 2 (C\u00e2u 2 - M\u0110 101 - BGD&\u0110T - N\u0103m 2018 - 2019). V\u1edbi a l\u00e0 s\u1ed1 th\u1ef1c d\u01b0\u01a1ng t\u00f9y \u00fd, log5 a2 b\u1eb1ng 1 1 2 + log5 a. 2 log5 a. A 2 log5 a. B 2 + log5 a. C D \u0253 L\u1eddi gi\u1ea3i. V\u00ec a l\u00e0 s\u1ed1 th\u1ef1c d\u01b0\u01a1ng n\u00ean ta c\u00f3 log5 a2 = 2 log5 a. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 3 (C\u00e2u 14 - M\u0110 103 - BGD&\u0110T - N\u0103m 2018 - 2019). V\u1edbi a l\u00e0 s\u1ed1 th\u1ef1c d\u01b0\u01a1ng t\u00f9y \u00fd, log2 a3 b\u1eb1ng 1 1 A 3 log2 a. B 3 log2a. C 3 + log2 a. D 3 + log2 a. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 log2 a3 = 3 log2 a. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 4 (C\u00e2u 28 - M\u0110 104 - BGD&\u0110T - N\u0103m 2018 - 2019). Cho a v\u00e0 b l\u00e0 hai s\u1ed1 th\u1ef1c d\u01b0\u01a1ng th\u1ecfa m\u00e3n ab3 = 8. Gi\u00e1 tr\u1ecb c\u1ee7a log2 a + 3 log2 b b\u1eb1ng A 8. B 6. C 2. D 3. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 log2 a + 3 log2 b = log2 a + log2 b3 = log2(ab3) = log2 8 = 3. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 5 (C\u00e2u 12 - M\u0110 102 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2019 - 2020). V\u1edbi a, b l\u00e0 c\u00e1c s\u1ed1 th\u1ef1c d\u01b0\u01a1ng t\u00f9y \u00fd v\u00e0 a = 1, loga2 b b\u1eb1ng 11 A 2 + loga b. B 2 logab. C 2 + loga b. D 2 loga b. \u0253 L\u1eddi gi\u1ea3i. 1 Ta c\u00f3 loga2 b = 2 logab. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 6 (C\u00e2u 6 - M\u0110 102 - BGD&\u0110T - \u0110\u1ee3t 4 - N\u0103m 2019 - 2020). V\u1edbi a l\u00e0 s\u1ed1 th\u1ef1c d\u01b0\u01a1ng t\u00f9y \u00fd, log3 (3a) b\u1eb1ng Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 183 S\u0110T: 0905.193.688","3. L\u00f4garit A 3 \u2212 log3 (a). B 1 \u2212 log3 (a). C 3 + log3 (a). D 1 + log3 (a). \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 log3 (3a) = 1 + log3 (a). Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 7 (C\u00e2u 21 - M\u0110 101 - \u221aBGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2020 - 2021). Cho a > 0 v\u00e0 a = 1, khi \u0111\u00f3 loga 4 a b\u1eb1ng 1 C \u22121. A 4. B . D \u22124. 44 \u0253 L\u1eddi gi\u1ea3i. \u221a 11 Ta c\u00f3 loga 4 a = loga a 4 = . 4 Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 8 (C\u00e2u 11 - M\u0110 102 - BG\u221aD&\u0110T - N\u0103m 2021 - 2022). V\u1edbi a l\u00e0 s\u1ed1 th\u1ef1c d\u01b0\u01a1ng t\u00f9y \u00fd, 4 log a b\u1eb1ng A \u22124 log a. B 8 log a. C 2 log a. D \u22122 log a. \u221a \u0253 L\u1eddi gi\u1ea3i. 4 log a Ta c\u00f3 = 4 log a 1 = 2 log a. 2 Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 9 (C\u00e2u 12 - \u0110TN - BGD&\u0110T - N\u0103m 2016 - 2017). V\u1edbi c\u00e1c s\u1ed1 th\u1ef1c d\u01b0\u01a1ng a, b b\u1ea5t k\u00ec. M\u1ec7nh \u0111\u1ec1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y \u0111\u00fang ? A ln(ab) = ln a + ln b. B ln(ab) = ln a. ln b. D ln a = ln b \u2212 ln a. C a = ln a ln . b b ln b \u0253 L\u1eddi gi\u1ea3i. V\u1edbi m\u1ecdi s\u1ed1 d\u01b0\u01a1ng a, b ta c\u00f3: ln(ab) = ln a + ln b. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 10 (C\u00e2u 8 - \u0110TK - BGD&\u0110T - N\u0103m 2017 - 2018). D 1 log(3a) = log a. V\u1edbi a l\u00e0 s\u1ed1 th\u1ef1c d\u01b0\u01a1ng b\u1ea5t k\u00ec, m\u1ec7nh \u0111\u1ec1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y \u0111\u00fang? 3 A log(3a) = 3 log a. B log(a3) = 1 log a. C log(a3) = 3 log a. 3 \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 log(a3) = 3 log a. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 11 (C\u00e2u 6 - M\u0110 101 - BGD&\u0110T - N\u0103m 2017 - 2018). V\u1edbi a l\u00e0 s\u1ed1 th\u1ef1c d\u01b0\u01a1ng t\u00f9y \u00fd, ln(5a) \u2212 ln(3a) b\u1eb1ng A ln(5a) B ln(2a). C 5 D ln 5 . ln . . ln(3a) 3 ln 3 Ta c\u00f3 ln(5a) \u2212 ln(3a) = ln 5a = ln 5 \u0253 L\u1eddi gi\u1ea3i. . 3a 3 184 Ch\u1ecdn \u0111\u00e1p \u00e1n C Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t S\u0110T: 0905.193.688","Ch\u01b0\u01a1ng 2. H\u00c0M S\u1ed0 L\u0168Y TH\u1eeaA. H\u00c0M S\u1ed0 M\u0168 V\u00c0 H\u00c0M S\u1ed0 L\u00d4GARIT \u0104 C\u00e2u 12 (C\u00e2u 11 - M\u0110 102 - BGD&\u0110T - N\u0103m 2017 - 2018). V\u1edbi a l\u00e0 s\u1ed1 th\u1ef1c d\u01b0\u01a1ng tu\u1ef3 \u00fd, log3(3a) b\u1eb1ng A 3 log3 a. B 3 + log3 a. C 1 + log3 a. D 1 \u2212 log3 a. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 log3(3a) = log3 3 + log3 a = 1 + log3 a. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 13 (C\u00e2u 43 - \u0110MH - BGD&\u0110T - N\u0103m 2018 - 2019). V\u1edbi a v\u00e0 b l\u00e0 hai s\u1ed1 th\u1ef1c d\u01b0\u01a1ng t\u00f9y \u00fd, log (ab2) b\u1eb1ng A 2 log a + log b. B log a + 2 log b. C 2 (log a + log b). D 1 log a + log b. 2 \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 log (ab2) = log a + log b2 = log a + 2 log b. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 14 (C\u00e2u 5 - M\u0110 102 - BGD&\u0110T - N\u0103m 2018 - 2019). V\u1edbi a l\u00e0 s\u1ed1 th\u1ef1c d\u01b0\u01a1ng t\u00f9y \u00fd, log5 a3 b\u1eb1ng 1 1 A 3 log5 a. B 3 + log5 a. C 3 + log5 a. D 3 log5 a. \u0253 L\u1eddi gi\u1ea3i. log5 a3 = 3 log5 a. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 15 (C\u00e2u 12 - M\u0110 104 - BGD&\u0110T - N\u0103m 2018 - 2019). V\u1edbi a l\u00e0 s\u1ed1 th\u1ef1c d\u01b0\u01a1ng t\u00f9y \u00fd, log2 a2 b\u1eb1ng 1 1 A 2 log2 a. B 2 + log2 a. C 2 log2 a. D 2 + log2 a. \u0253 L\u1eddi gi\u1ea3i. V\u00ec a l\u00e0 s\u1ed1 th\u1ef1c d\u01b0\u01a1ng t\u00f9y \u00fd n\u00ean log2 a2 = 2 log2 a. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 16 (C\u00e2u 11 - \u0110TK - BGD&\u0110T - l\u1ea7n 2 - N\u0103m 2019 - 2020). V\u1edbi a l\u00e0 s\u1ed1 th\u1ef1c d\u01b0\u01a1ng t\u00f9y \u00fd, log2 (a3) b\u1eb1ng 3 1 A 2 log2 a. B 3 log2 a. C 3 + log2 a. D 3 log2 a. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 log2 (a3) = 3 log2 a. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 17 (C\u00e2u 9 - M\u0110 101 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2019 - 2020). V\u1edbi a, b l\u00e0 c\u00e1c s\u1ed1 th\u1ef1c d\u01b0\u01a1ng t\u00f9y \u00fd v\u00e0 a = 1, loga5 b b\u1eb1ng 1 1 A 5 loga b. B 5 + loga b. C 5 + loga b. D 5 loga b. \u0253 L\u1eddi gi\u1ea3i. 1 loga5 b = 5 loga b. Ch\u1ecdn \u0111\u00e1p \u00e1n D Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 185 S\u0110T: 0905.193.688","3. L\u00f4garit \u0104 C\u00e2u 18 (C\u00e2u 24 - M\u0110 103 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2019 - 2020). V\u1edbi a, b l\u00e0 c\u00e1c s\u1ed1 th\u1ef1c d\u01b0\u01a1ng t\u00f9y \u00fd v\u00e0 a = 1, loga3 b b\u1eb1ng 1 1 3 logab. A 3 + loga b. B 3 loga b. C 3 + loga b. D \u0253 L\u1eddi gi\u1ea3i. 1 Ta c\u00f3 loga3 b = 3 logab. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 19 (C\u00e2u 11 - M\u0110 104 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2019 - 2020). V\u1edbi a, b l\u00e0 c\u00e1c s\u1ed1 th\u1ef1c d\u01b0\u01a1ng t\u00f9y \u00fd v\u00e0 a = 1 th\u00ec loga4 b b\u1eb1ng 1 1 A 4 + loga b. B 4 loga b. C 4logab. D 4 + loga b. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 log4a b = 1 loga b. 4 Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 20 (C\u00e2u 23 - M\u0110 101 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2019 - 2020). V\u1edbi a l\u00e0 s\u1ed1 th\u1ef1c d\u01b0\u01a1ng t\u00f9y \u00fd, log4(4a) b\u1eb1ng A 1 + log4 a. B 4 \u2212 log4 a. C 4 + log4 a. D 1 \u2212 log4 a. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 log4(4a) = log4 4 + log4 a = 1 + log4 a. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 21 (C\u00e2u 33 - M\u0110 101 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2019 - 2020). V\u1edbi a, b l\u00e0 c\u00e1c s\u1ed1 th\u1ef1c d\u01b0\u01a1ng t\u00f9y \u00fd th\u1ecfa m\u00e3n log2 a\u22122 log4 b = 3, m\u1ec7nh \u0111\u1ec1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y \u0111\u00fang? A a = 8b2. B a = 8b. C a = 6b. D a = 8b4. \u0253 L\u1eddi gi\u1ea3i. a a b Ta c\u00f3 log2 a \u2212 2 log4 b = 3 \u21d4 log2 a \u2212 log2 b = 3 \u21d4 log2 b = 3 \u21d4 = 23 \u21d4 a = 8b. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 22 (C\u00e2u 1 - M\u0110 103 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2019 - 2020). V\u1edbi a l\u00e0 s\u1ed1 th\u1ef1c d\u01b0\u01a1ng t\u00f9y \u00fd, log2(2a) b\u1eb1ng A 1 + log2 a. B 1 \u2212 log2 a. C 2 \u2212 log2 a. D 2 + log2 a. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 log2(2a) = log2 2 + log2 a = 1 + log2 a. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 23 (C\u00e2u 17 - M\u0110 102 -\u221aBGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2020 - 2021). Cho a > 0 v\u00e0 a = 1. Khi \u0111\u00f3 loga 3 a b\u1eb1ng 1 C \u22121. A \u22123. B . D 3. 33 \u221a 11 \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 loga 3 a = loga a 3 = . 3 Ch\u1ecdn \u0111\u00e1p \u00e1n B Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 186 S\u0110T: 0905.193.688","Ch\u01b0\u01a1ng 2. H\u00c0M S\u1ed0 L\u0168Y TH\u1eeaA. H\u00c0M S\u1ed0 M\u0168 V\u00c0 H\u00c0M S\u1ed0 L\u00d4GARIT \u0104 C\u00e2u 24 (C\u00e2u 36 - M\u0110 104 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2020 - 2021). V\u1edbi m\u1ecdi a, b th\u1ecfa m\u00e3n log2 a3 + log2 b = 5, kh\u1eb3ng \u0111\u1ecbnh n\u00e0o d\u01b0\u1edbi \u0111\u00e2y \u0111\u00fang? A a3b = 32. B a3b = 25. C a3 + b = 25. D a3 + b = 32. \u0253 L\u1eddi gi\u1ea3i. T\u1eeb gi\u1ea3 thi\u1ebft suy ra a > 0, b > 0. Do \u0111\u00f3 log2 a3 + log2 b = 5 \u21d4 log2(a3b) = 5 \u21d4 a3b = 32. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 25 (C\u00e2u 3 - M\u0110 101 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2020 - 2021). V\u1edbi m\u1ecdi s\u1ed1 th\u1ef1c a d\u01b0\u01a1ng, log4(4a) b\u1eb1ng A 1 + log4 a. B 1 \u2212 log4 a. C log4 a. D 4 log4 a. \u0253 L\u1eddi gi\u1ea3i. V\u1edbi a > 0 ta c\u00f3 log4(4a) = log4 4 + log4 a = 1 + log4 a. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 26 (C\u00e2u 21 - M\u0110 102 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2020 - 2021). V\u1edbi m\u1ecdi s\u1ed1 th\u1ef1c d\u01b0\u01a1ng a, log3(3a) b\u1eb1ng A 3 log3 a. B 1 \u2212 log3 a. C log3 a. D 1 + log3 a. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 log3(3a) = log3 3 + log3 a = 1 + log3 a. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 27 (C\u00e2u 4 - M\u0110 103 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2020 - 2021). V\u1edbi m\u1ecdi s\u1ed1 th\u1ef1c a d\u01b0\u01a1ng, log2 (2a) b\u1eb1ng A 1 \u2212 log2 a. B 1 + log2 a. C 2 log2 a. D log2 a. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 log2 (2a) = log2 2 + log2 a = 1 + log2 a. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 28 (C\u00e2u 12 - M\u0110 104 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2020 - 2021). V\u1edbi m\u1ecdi s\u1ed1 th\u1ef1c a d\u01b0\u01a1ng, log5 (5a) b\u1eb1ng A 5 log5 a. B 1 \u2212 log5 a. C 1 + log5 a. D log5 a. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 log5 (5a) = log5 5 + log5 a = 1 + log5 a. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 29 (C\u00e2u 17 - M\u0110 101 - B\u221aGD&\u0110T - N\u0103m 2021 - 2022). V\u1edbi a l\u00e0 s\u1ed1 th\u1ef1c d\u01b0\u01a1ng t\u00f9y \u00fd, 4 log a b\u1eb1ng A \u22122 log a. B 2 log a. C \u22124 log a. D 8 log a. \u221a \u0253 L\u1eddi gi\u1ea3i. 4 log a Ta c\u00f3 = 4 log a 1 = 4. 1 log a = 2 log a. 2 2 Ch\u1ecdn \u0111\u00e1p \u00e1n B Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 187 S\u0110T: 0905.193.688","3. L\u00f4garit \u0104 C\u00e2u 30 (C\u00e2u 7 - M\u0110 104 - BGD&\u0110T - N\u0103m 2021 - 2022). V\u1edbi a l\u00e0 s\u1ed1 th\u1ef1c d\u01b0\u01a1ng tu\u1ef3 \u00fd, log(100a) b\u1eb1ng A 2 \u2212 log a. B 2 + log a. C 1 \u2212 log a. D 1 + log a. \u0253 L\u1eddi gi\u1ea3i. V\u1edbi a > 0, ta c\u00f3 log(100a) = log 100 + log a = log 102 + log a = 2 + log a. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 31 (C\u00e2u 31 - M\u0110 104 - BGD&\u0110T - N\u0103m 2021 - 2022). 1 V\u1edbi a, b l\u00e0 c\u00e1c s\u1ed1 th\u1ef1c d\u01b0\u01a1ng t\u00f9y \u00fd v\u00e0 a = 1, log 1 b\u1eb1ng b3 a 1 3 loga b. A loga b. B \u22123 loga b. C D 3 loga b. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 log 1 1 = loga\u22121 b\u22123 = 3 loga b. b3 a Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 32 (C\u00e2u 6 - M\u0110 102 - BGD&\u0110T - N\u0103m 2016 - 2017). Cho a l\u00e0 s\u1ed1 th\u1ef1c d\u01b0\u01a1ng kh\u00e1c 1. M\u1ec7nh \u0111\u1ec1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y \u0111\u00fang v\u1edbi m\u1ecdi s\u1ed1 th\u1ef1c d\u01b0\u01a1ng x, y? x x A loga y = loga x \u2212 loga y. B loga y = loga x + loga y. C x = loga(x \u2212 y). D loga x = loga x loga y y loga . y \u0253 L\u1eddi gi\u1ea3i. \u00c1p d\u1ee5ng c\u00f4ng th\u1ee9c s\u00e1ch gi\u00e1o khoa loga x = loga x \u2212 loga y . y Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 33 (C\u00e2u 26 - M\u0110 104 - BGD&\u0110T - N\u0103m 2016 - 2017). T\u00ecm t\u1eadp x\u00e1c \u0111\u1ecbn\u221ah D c\u1ee7a h\u00e0m s\u1ed1\u221ay = log3(x2 \u2212 4x + 3). A D = (2 \u2212 2; 1) \u222a (3; 2 + 2). B D = (1; 3). \u221a \u221a C D = (\u2212\u221e; 1) \u222a (3; +\u221e). D D = (\u2212\u221e; 2 \u2212 2) \u222a (2 + 2; +\u221e). \u0253 L\u1eddi gi\u1ea3i. \u0110i\u1ec1u ki\u1ec7n x\u00e1c \u0111\u1ecbnh x2 \u2212 4x + 3 > 0 \u21d4 x \u2208 (\u2212\u221e; 1) \u222a (3; +\u221e) Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 34 (C\u00e2u 24 - M\u0110 101 - BGD&\u0110T - N\u0103m 2018 - 2019). Cho a v\u00e0 b l\u00e0 hai s\u1ed1 th\u1ef1c d\u01b0\u01a1ng th\u1ecfa m\u00e3n a4b = 16. Gi\u00e1 tr\u1ecb c\u1ee7a 4 log2 a + log2 b b\u1eb1ng A 4. B 2. C 16. D 8. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 4 log2 a + log2 b = log2 a4 + log2 b = log2(a4b) = log2 16 = log2 24 = 4. Ch\u1ecdn \u0111\u00e1p \u00e1n A Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 188 S\u0110T: 0905.193.688","Ch\u01b0\u01a1ng 2. H\u00c0M S\u1ed0 L\u0168Y TH\u1eeaA. H\u00c0M S\u1ed0 M\u0168 V\u00c0 H\u00c0M S\u1ed0 L\u00d4GARIT \u0104 C\u00e2u 35 (C\u00e2u 25 - M\u0110 102 - BGD&\u0110T - N\u0103m 2018 - 2019). Cho a v\u00e0 b l\u00e0 hai s\u1ed1 th\u1ef1c d\u01b0\u01a1ng th\u1ecfa m\u00e3n a3b2 = 32. Gi\u00e1 tr\u1ecb c\u1ee7a 3 log2 a + 2 log2 b b\u1eb1ng A 5. B 2. C 32. D 4. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3: log2 a3b2 = log2 32 \u21d4 3 log2 a + 2 log2 b = 5. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 36 (C\u00e2u 21 - M\u0110 103 - BGD&\u0110T - N\u0103m 2018 - 2019). Cho a v\u00e0 b l\u00e0 hai s\u1ed1 th\u1ef1c d\u01b0\u01a1ng th\u1ecfa m\u00e3n a2b3 = 16. Gi\u00e1 tr\u1ecb c\u1ee7a 2 log2 a + 3 log2 b b\u1eb1ng A 8. B 16. C 4. D 2. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 2 log2 a + 3 log2 b = log2(a2b3) = log2 16 = 4. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 37 (C\u00e2u 3 - M\u0110 102 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2019 - 2020). V\u1edbi a l\u00e0 s\u1ed1 th\u1ef1c d\u01b0\u01a1ng tu\u1ef3 \u00fd, log5(5a) b\u1eb1ng A 5 + log5 a. B 5 \u2212 log5 a. C 1 + log5 a. D 1 \u2212 log5 a. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 log5(5a) = log5 5 + log5 a = 1 + log5 a. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 38 (C\u00e2u 27 - M\u0110 102 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2019 - 2020). V\u1edbi a, b l\u00e0 c\u00e1c s\u1ed1 th\u1ef1c d\u01b0\u01a1ng t\u00f9y \u00fd th\u1ecfa m\u00e3n log3 a\u22122 log9 b = 2, m\u1ec7nh \u0111\u1ec1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y \u0111\u00fang? A a = 9b3. B a = 9b. C a = 6b. D a = 9b2. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 log3 a \u2212 2 log9 b = 2 \u21d4 log3 a \u2212 log3 b = 2 \u21d4 log3 a = 2 \u21d4 a = 9b. b Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 39 (C\u00e2u 18 - M\u0110 103 -\u221aBGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2020 - 2021). Cho a > 0 v\u00e0 a = 1, khi \u0111\u00f3 loga a b\u1eb1ng C \u22121. 1 A 2. B \u22122. D . 22 \u0253 L\u1eddi gi\u1ea3i. \u221a a 11 1 V\u1edbi a > 0 v\u00e0 a = 1, ta c\u00f3 loga = loga a 2 = loga a = . 2 2 Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 40 (C\u00e2u 12 - M\u0110 103 - BGD&\u0110T - N\u0103m 2021 - 2022). V\u1edbi a l\u00e0 s\u1ed1 th\u1ef1c d\u01b0\u01a1ng t\u00f9y \u00fd, log(100a) b\u1eb1ng A 1 \u2212 log a. B 2 + log a. C 2 \u2212 log a. D 1 + log a. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 log(100a) = log(100) + log a = 2 + log a. Ch\u1ecdn \u0111\u00e1p \u00e1n B Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 189 S\u0110T: 0905.193.688","3. L\u00f4garit \u0104 C\u00e2u 41 (C\u00e2u 17 - \u0110MH - BGD&\u0110T - N\u0103m 2016 - 2017). Cho c\u00e1c s\u1ed1 th\u1ef1c d\u01b0\u01a1ng a, b, v\u1edbi a = 1. Kh\u1eb3ng \u0111\u1ecbnh n\u00e0o sau \u0111\u00e2y l\u00e0 kh\u1eb3ng \u0111\u1ecbnh \u0111\u00fang? A loga2(ab) = 1 B loga2(ab) = 2 + 2 loga b. 2 loga b. 1 11 C loga2(ab) = 4 loga b. D loga2(ab) = 2 + 2 loga b. \u0253 L\u1eddi gi\u1ea3i. 11 11 Ta c\u00f3 loga2(ab) = 2 loga(ab) = 2 (1 + loga b) = 2 + 2 loga b, n\u00ean c\u00e2u D \u0111\u00fang. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 42 (C\u00e2u 19 - \u0110MH - BGD&\u0110T - N\u0103m 2016 - 2017). \u0110\u1eb7t a = log2 3, b = log5 3. H\u00e3y bi\u1ec3u di\u1ec5n log6 45 theo a v\u00e0 b. 2a2 \u2212 2ab A log6 45 = a + 2ab B log6 45 = . . ab 2a2 \u2212 2ab ab a + 2ab C log6 45 = . D log6 45 = . ab + b ab + b \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 1 = log3 5 \u21d2 a = log2 3. log3 5 = log2 5. V\u1eady ta \u0111\u01b0a v\u1ec1 c\u01a1 s\u1ed1 2. b b log2 (32.5) 2a + a 2ab + a log6 45 = log23 + 1 = b = . a+1 ab + b Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 43 (C\u00e2u 16 - \u0110TN - BGD&\u0110T - N\u0103m 2016 - 2017). V\u1edbi c\u00e1c s\u1ed1 th\u1ef1c d\u01b0\u01a1ng a, b b\u1ea5t k\u00ec. M\u1ec7nh \u0111\u1ec1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y \u0111\u00fang ? \u00c5 2a3 \u00e3 \u00c5 2a3 \u00e3 1 b b 3 log2a A log2 = 1 + 3log2a \u2212 log2b. B log2 = 1 + \u2212 log2b. C \u00c5 2a3 \u00e3 D \u00c5 2a3 \u00e3 1 log2 b = 1 + 3log2a + log2b. log2 b = 1 + 3 log2a + log2b. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 log2 \u00c5 2a3 \u00e3 = log2 (2a3) \u2212 log2 (b) = log2 (2) + log2 (a3) \u2212 log2 (b) = 1 + 3log2a \u2212 log2b b Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 44 (C\u00e2u 13 - \u0110TK - BGD&\u0110T - N\u0103m 2016 - 2017). Cho a l\u00e0 s\u1ed1 th\u1ef1c d\u01b0\u01a1ng, a = 1 v\u00e0 P = log \u221a3 a a3. M\u1ec7nh \u0111\u1ec1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y \u0111\u00fang? A P = 1. B P = 1. C P = 9. D P 1 =. 3 \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 P = P = loga1\/3 a3 = 9 loga a = 9. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 45 (C\u00e2u 33 - \u0110TK - BGD&\u0110T - N\u0103m 2016 - 2017). Cho a, b l\u00e0 c\u00e1c s\u1ed1 th\u1ef1c d\u01b0\u01a1ng th\u1ecfa m\u00e3n a = 1, a = \u221a\u221a 3. P = log \u2026b b v\u00e0 loga b = T\u00ednh \u221a . b a\u221a \u221a\u221a \u221aa A P = \u22125 + 3 3. B P = \u22121 + 3. C P = \u22121 \u2212 3. D P = \u22125 \u2212 3 3. Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t \u0253 L\u1eddi gi\u1ea3i. S\u0110T: 0905.193.688 190","Ch\u01b0\u01a1ng 2. H\u00c0M S\u1ed0 L\u0168Y TH\u1eeaA. H\u00c0M S\u1ed0 M\u0168 V\u00c0 H\u00c0M S\u1ed0 L\u00d4GARIT C\u00e1ch 1: Ph\u01b0\u01a1ng ph\u00e1p t\u1ef1 lu\u1eadn. \u2026b 1 (loga b \u2212 1) 1 \u00c4\u221a \u2212 \u00e4 \u221a \u221a loga \u221aa 2 \u221a 3 1 \u221a3 \u2212 1 = \u22121 \u2212 3. 2 P = b = = = 3\u22122 loga a loga b \u2212 1 1 2 loga b \u2212 1 C\u00e1ch 2: Ph\u01b0\u01a1ng\u221aph\u00e1p tr\u1eafc nghi\u1ec7m. \u221a Ch\u1ecdn a = 2, b = 2 3. B\u1ea5m m\u00e1y t\u00ednh ta \u0111\u01b0\u1ee3c P = \u22121 \u2212 3. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 46 (C\u00e2u 5 - M\u0110 104 - BGD&\u0110T - N\u0103m 2017 - 2018). \u00c53\u00e3 V\u1edbi a l\u00e0 s\u1ed1 th\u1ef1c d\u01b0\u01a1ng t\u00f9y \u00fd, log3 a b\u1eb1ng A 1 \u2212 log3 a. B 3 \u2212 log3 a. C 1 D 1 + log3 a. . log3 a \u0253 L\u1eddi gi\u1ea3i. \u00c53\u00e3 Ta c\u00f3 log3 a = log3 3 \u2212 log3 a = 1 \u2212 log3 a. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 47 (C\u00e2u 12 - \u0110MH - BGD&\u0110T - N\u0103m 2018 - 2019). \u0110\u1eb7t log3 2 = a, khi \u0111\u00f3 log16 27 b\u1eb1ng 4a 3a 3 4 . A . B . C . D 4 4a 3a 3 \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 log16 27 = log24 33 = 3 log2 3 = 3 \u00b7 1 2 = 3 4 4 log3 . 4a Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 48 (C\u00e2u 10 - \u0110TK - BGD&\u0110T - l\u1ea7n 1 - N\u0103m 2019 - 2020). V\u1edbi a l\u00e0 s\u1ed1 th\u1ef1c d\u01b0\u01a1ng t\u00f9y \u00fd, log2 (a2) b\u1eb1ng 1 1 2 log2 a. A 2 + log2 a. B 2 + log2 a. C 2 log2 a. D \u0253 L\u1eddi gi\u1ea3i. V\u1edbi a l\u00e0 s\u1ed1 th\u1ef1c d\u01b0\u01a1ng t\u00f9y \u00fd, ta c\u00f3 log2 (a2) = 2 log2 a. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 49 (C\u00e2u 20 - \u0110TK - BGD&\u0110T - l\u1ea7n 1 - N\u0103m 2019 - 2020). X\u00e9t t\u1ea5t c\u1ea3 c\u00e1c s\u1ed1 th\u1ef1c d\u01b0\u01a1ng a v\u00e0 b th\u1ecfa m\u00e3n log2 a = log8(ab). M\u1ec7nh \u0111\u1ec1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y \u0111\u00fang? A a = b2. B a3 = b. C a = b. D a2 = b. \u0253 L\u1eddi gi\u1ea3i. log2 a = log8 (ab) \u21d4 log2 a = log23 (ab) 1 \u21d4 log2 a = 3 log2 (ab) \u21d4 3 log2 a = log2 (ab) \u21d4 log2 a3 = log2 (ab) \u21d4 a3 = ab \u21d4 a2 = b. Ch\u1ecdn \u0111\u00e1p \u00e1n D Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 191 S\u0110T: 0905.193.688","3. L\u00f4garit \u0104 C\u00e2u 50 (C\u00e2u 29 - \u0110TK - BGD&\u0110T - l\u1ea7n 2 - N\u0103m 2019 - 2020). X\u00e9t c\u00e1c s\u1ed1 th\u1ef1c a v\u00e0 b th\u1ecfa m\u00e3n log3(3a \u00b7 9b) = log9 3. M\u1ec7nh \u0111\u1ec1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y \u0111\u00fang? A a + 2b = 2. B 4a + 2b = 1. C 4ab = 1. D 2a + 4b = 1. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 log3(3a \u00b7 9b) = log9 3 \u21d4 log3(3a \u00b7 32b) = 1 \u21d4 log3 3a+2b = 1 \u21d4 a + 2b = 1 \u21d4 2a + 4b = 1. 2 log9 9 2 log9 9 2 Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 51 (C\u00e2u 30 - M\u0110 102 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2019 - 2020). Cho a v\u00e0 b l\u00e0 hai s\u1ed1 th\u1ef1c d\u01b0\u01a1ng tho\u1ea3 m\u00e3n 4log2(ab) = 3a. Gi\u00e1 tr\u1ecb c\u1ee7a ab2 b\u1eb1ng A 3. B 6. C 2. D 12. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 4log2(ab) = 2log2(ab) 2 = (ab)2 n\u00ean 4log2(ab) = 3a \u21d4 (ab)2 = 3a \u21d4 ab2 = 3. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 52 (C\u00e2u 30 - M\u0110 103 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2019 - 2020). Cho a v\u00e0 b l\u00e0 hai s\u1ed1 th\u1ef1c d\u01b0\u01a1ng th\u1ecfa m\u00e3n 9log3(ab) = 4a. Gi\u00e1 tr\u1ecb c\u1ee7a ab2 b\u1eb1ng A 3. B 6. C 2. D 4. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 9log3(ab) = 4a \u21d4 (ab)2 = 4a \u21d4 ab2 = 4. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 53 (C\u00e2u 35 - M\u0110 103 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2019 - 2020). V\u1edbi a, b l\u00e0 c\u00e1c s\u1ed1 th\u1ef1c d\u01b0\u01a1ng t\u00f9y \u00fd th\u1ecfa m\u00e3n log3 a\u22122 log9 b = 3, m\u1ec7nh \u0111\u1ec1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y \u0111\u00fang? A a = 27b. B a = 9b. C a = 27b4. D a = 27b2. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 log3 a \u2212 2 log9 b = 3 \u21d4 log3 a \u2212 log3 b = 3 \u21d4 log3 a = 3 \u21d4 a = 27 \u21d4 a = 27b. b b V\u1eady a = 27b. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 54 (C\u00e2u 29 - M\u0110 102 - BGD&\u0110T - \u0110\u1ee3t 4 - N\u0103m 2019 - 2020). V\u1edbi a, b l\u00e0 c\u00e1c s\u1ed1 th\u1ef1c d\u01b0\u01a1ng t\u00f9y \u00fd th\u1ecfa m\u00e3n log2 a\u22122 log4 b = 4, m\u1ec7nh \u0111\u1ec1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y \u0111\u00fang? A a = 16b2. B a = 8b. C a = 16b. D a = 16b4. \u0253 L\u1eddi gi\u1ea3i. V\u1edbi a, b l\u00e0 c\u00e1c s\u1ed1 th\u1ef1c d\u01b0\u01a1ng ta c\u00f3 log2 a \u2212 2 log4 b = 4 \u21d4 log2 a = log2 b + log2 16 \u21d4 log2 a = log2(16b) \u21d4 a = 16b. Ch\u1ecdn \u0111\u00e1p \u00e1n C 192 S\u0110T: 0905.193.688 Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t","Ch\u01b0\u01a1ng 2. H\u00c0M S\u1ed0 L\u0168Y TH\u1eeaA. H\u00c0M S\u1ed0 M\u0168 V\u00c0 H\u00c0M S\u1ed0 L\u00d4GARIT \u0104 C\u00e2u 55 (C\u00e2u 37 - M\u0110 101 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2020 - 2021). V\u1edbi m\u1ecdi a, b th\u1ecfa m\u00e3n log2 a3 + log2 b = 6, kh\u1eb3ng \u0111\u1ecbnh n\u00e0o d\u01b0\u1edbi \u0111\u00e2y \u0111\u00fang? A a3b = 64. B a3b = 36. C a3 + b = 64. D a3 + b = 36. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 log2 a3 + log2 b = 6 \u21d4 log2 (a3 \u00b7 b) = log2 26 \u21d4 a3b = 26 = 64. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 56 (C\u00e2u 38 - M\u0110 102 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2020 - 2021). V\u1edbi m\u1ecdi a, b th\u1ecfa m\u00e3n log2 a3 + log2 b = 8, kh\u1eb3ng \u0111\u1ecbnh n\u00e0o d\u01b0\u1edbi \u0111\u00e2y \u0111\u00fang? A a3 + b = 64. B a3b = 256. C a3b = 64. D a3 + b = 256. \u0253 L\u1eddi gi\u1ea3i. V\u1edbi a, b > 0, ta c\u00f3 log2 a3 + log2 b = 8 \u21d4 log2 (a3b) = 8 \u21d4 a3b = 28 = 256. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 57 (C\u00e2u 34 - M\u0110 103 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2020 - 2021). V\u1edbi m\u1ecdi a, b th\u1ecfa m\u00e3n log2 a3 + log2 b = 7, kh\u1eb3ng \u0111\u1ecbnh n\u00e0o d\u01b0\u1edbi \u0111\u00e2y \u0111\u00fang? A a3 + b = 49. B a3b = 128. C a3 + b = 128. D a3b = 49. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 log2 a3 + log2 b = 7 \u21d4 log2 a3b = 7 \u21d4 a3b = 27 = 128. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 58 (C\u00e2u 19 - M\u0110 104 -\u221aBGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2020 - 2021). Cho a > 0 v\u00e0 a = 1, khi \u0111\u00f3 loga 5 a b\u1eb1ng 1 B \u22121. A . C 5. D \u22125. 55 \u221a \u0253 L\u1eddi gi\u1ea3i. 5a Ta c\u00f3 loga = loga a 1 = 1 loga a = 1 5 5 . 5 Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 59 (C\u00e2u 37 - M\u0110 101 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2020 - 2021). V\u1edbi a > 0, \u0111\u1eb7t log2(2a) = b, khi \u0111\u00f3 log2 (8a4) b\u1eb1ng A 4b + 7. B 4b + 3. C 4b. D 4b \u2212 1. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 log2 8a4 = log2 16a4 = log2 (2a)4 = log2(2a)4 \u2212 log2 2 = 4 log2(2a) \u2212 1 = 4b \u2212 1. 2 2 Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 60 (C\u00e2u 31 - M\u0110 102 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2020 - 2021). V\u1edbi a > 0, \u0111\u1eb7t log2(2a) = b, khi \u0111\u00f3 log2 (4a3) b\u1eb1ng A 3b + 5. B 3b. C 3b + 2. D 3b \u2212 1. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 log2(2a) = b \u21d4 1 + log2 a = b suy ra log2 a = b \u2212 1. Khi \u0111\u00f3 log2 (4a3) = log2 4 + log2 a3 = 2 + 3 log2 a = 2 + 3(b \u2212 1) = 3b \u2212 1. Ch\u1ecdn \u0111\u00e1p \u00e1n D Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 193 S\u0110T: 0905.193.688","3. L\u00f4garit \u0104 C\u00e2u 61 (C\u00e2u 33 - M\u0110 103 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2020 - 2021). V\u1edbi a > 0, \u0111\u1eb7t log3 (3a) = b, khi \u0111\u00f3 log3 (9a3) b\u1eb1ng A 3b. B 3b \u2212 1. C 3b + 5. D 3b + 2. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 log3 (3a) = b \u21d4 log3 a = b \u2212 1. Suy ra log3 (9a3) = log3 9 + log3 a3 = 2 + 3 log3 a = 2 + 3(b \u2212 1) = 3b \u2212 1. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 62 (C\u00e2u 34 - M\u0110 104 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2020 - 2021). V\u1edbi a > 0, \u0111\u1eb7t log3(3a) = b, khi \u0111\u00f3 log3(27a4) b\u1eb1ng A 4b + 3. B 4b. C 4b \u2212 1. D 4b + 7. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 log3(3a) = b \u21d4 log3 3 + log3 a = b \u21d4 log3 a = b \u2212 1. M\u1eb7t kh\u00e1c log3(27a4) = log3 27 + log3 a4 = 3 + 4 log3 a = 3 + 4(b \u2212 1) = 4b \u2212 1. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 63 (C\u00e2u 34 - M\u0110 103 - BGD&\u0110T - N\u0103m 2021 - 2022). 1 V\u1edbi a, b l\u00e0 c\u00e1c s\u1ed1 th\u1ef1c d\u01b0\u01a1ng t\u00f9y \u00fd v\u00e0 a = 1, log 1 b\u1eb1ng b3 a 1 3 loga b. A 3 loga b. B loga b. C \u22123 loga b. D \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 log 1 1 = \u2212 loga b\u22123 = 3 loga b. b3 a Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 64 (C\u00e2u 31 - \u0110MH - BGD&\u0110T - N\u0103m 2021 - 2022). V\u1edbi m\u1ecdi a, b th\u1ecfa m\u00e3n log2 a \u2212 3 log2 b = 2, kh\u1eb3ng \u0111\u1ecbnh n\u00e0o d\u01b0\u1edbi \u0111\u00e2y \u0111\u00fang? 4 a = b3 . A a = 4b3. B a = 3b + 4. C a = 3b + 2. D \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 log2 a \u2212 3 log2 b = 2 \u21d4 log2 a = 2 \u21d4 a = 22 \u21d4 a = 4b3. b3 b3 Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 65 (C\u00e2u 20 - \u0110MH - BGD&\u0110T - N\u0103m 2016 - 2017). Cho hai s\u1ed1 th\u1ef1c a v\u00e0 b, v\u1edbi 1 < a < b. Kh\u1eb3ng \u0111\u1ecbnh n\u00e0o d\u01b0\u1edbi \u0111\u00e2y l\u00e0 kh\u1eb3ng \u0111\u1ecbnh \u0111\u00fang? A loga b < 1 < logb a. B 1 < loga b < logb a. C logb a < loga b < 1. D logb a < 1 < loga b. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 1 < a < b \u21d2 \u00ae loga 1 < loga a < loga b \u21d2 \u00ae0 < 1 < loga b \u21d2 logb a < 1 < loga b. logb 1 < logb a < logb b 0 < logb a < 1 Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 66 (C\u00e2u 15 - M\u0110 101 - BGD&\u0110T - N\u0103m 2016 - 2017). V\u1edbi a, b l\u00e0 c\u00e1c s\u1ed1 th\u1ef1c d\u01b0\u01a1ng t\u00f9y \u00fd v\u00e0 a kh\u00e1c 1, \u0111\u1eb7t P = loga b3 + loga2 b6. M\u1ec7nh \u0111\u1ec1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 194 S\u0110T: 0905.193.688","Ch\u01b0\u01a1ng 2. H\u00c0M S\u1ed0 L\u0168Y TH\u1eeaA. H\u00c0M S\u1ed0 M\u0168 V\u00c0 H\u00c0M S\u1ed0 L\u00d4GARIT \u0111\u00fang? B P = 27 loga b. C P = 15 loga b. D P = 6 loga b. A P = 9 loga b. D P = 108. \u0253 L\u1eddi gi\u1ea3i. P = loga b3 + loga2 b6 = 3 loga b + 1 = 6 loga b. 2 .6 loga b Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 67 (C\u00e2u 29 - M\u0110 102 - BGD&\u0110T - N\u0103m 2016 - 2017). Cho loga b = 2 v\u00e0 loga c = 3. T\u00ednh P = loga (b2c3). A P = 31. B P = 13. C P = 30. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 P = loga (b2c3) = 2 loga b + 3 loga c = 2.2 + 3.3 = 13. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 68 (C\u00e2u 10 - M\u0110 103 - BGD&\u0110T - N\u0103m 2016 - 2017). \u00c5 a2 \u00e3 Cho a l\u00e0 s\u1ed1 th\u1ef1c d\u01b0\u01a1ng kh\u00e1c 2. T\u00ednh I = log a . 24 A I= 1 B I = 2. C I = \u22121. D I = \u22122. . 2 2 \u0253 L\u1eddi gi\u1ea3i. I = log a a2 a = 2 (v\u00ec a = 2) = 2 log a 22 22 Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 69 (C\u00e2u 8 - M\u0110 104 - BGD&\u0110T - N\u0103m 2016 - 2017). Cho a l\u00e0 s\u1ed1 th\u1ef1c d\u01b0\u01a1ng t\u00f9y \u00fd kh\u00e1c 1. M\u1ec7nh \u0111\u1ec1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y \u0111\u00fang? A log2 a = loga 2. B log2 a = 1 . C log2 a = 1 D log2 a = \u2212 loga 2. a . log2 loga 2 \u0253 L\u1eddi gi\u1ea3i. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 70 (C\u00e2u 29 - M\u0110 104 - BGD&\u0110T - N\u0103m 2016 - 2017). V\u1edbi m\u1ecdi a, b, x l\u00e0 c\u00e1c s\u1ed1 th\u1ef1c d\u01b0\u01a1ng th\u1ecfa m\u00e3n log2 x = 5 log2 a + 3 log2 b, m\u1ec7nh \u0111\u1ec1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y \u0111\u00fang? A x = 3a + 5b. B x = 5a + 3b. C x = a5 + b3. D x = a5b3. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 log2 x = 5 log2 a + 3 log2 b = log2 a5 + log2 b3 = log2(a5b3) \u21d2 x = a5b3. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 71 (C\u00e2u 38 - M\u0110 101 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2019 - 2020). (a2b) Cho a, b l\u00e0 hai s\u1ed1 th\u1ef1c d\u01b0\u01a1ng th\u1ecfa m\u00e3n 4log2 = 3a3. Gi\u00e1 tr\u1ecb c\u1ee7a ab2 b\u1eb1ng A 3. B 6. C 12. D 2. Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t \u0253 L\u1eddi gi\u1ea3i. S\u0110T: 0905.193.688 195","Ta c\u00f3 3. L\u00f4garit 4log(2a2b) = 3a3 \u21d4 a2b log42 = 3a3 \u21d4 a2b 2 = 3a3 \u21d4 a4b2 = 3a3 \u21d4 ab2 = 3. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 72 (C\u00e2u 41 - \u0110TK - BGD&\u0110T - l\u1ea7n 1 - N\u0103m 2019 - 2020). x Cho x, y l\u00e0 c\u00e1c s\u1ed1 th\u1ef1c d\u01b0\u01a1ng th\u1ecfa m\u00e3n log9x = log6y = log4 (2x + y). Gi\u00e1 tr\u1ecb c\u1ee7a y b\u1eb1ng A 2. B 1 C log2 \u00c53\u00e3 D log 3 2. . . 2 2 2 \u0253 L\u1eddi gi\u1ea3i. \uf8f1x = 9t \uf8f4 \uf8f2 \u0110\u1eb7t log9x = log6y = log4 (2x + y) = t \u21d2 y = 6t \uf8f4\uf8f32x + y = 4t Khi \u0111\u00f3 ta c\u00f3: x = 9t = \u00c5 3 \u00e3t 2.9t + 6t = 4t (1). v\u00e0 y 6t 2 \uf8ee\u00c5 3 \u00e3t = \u22121 (loai) 1 Ta c\u00f3 (1) \u21d4 \u00c5 3 \u00e32t + \u00c5 3 \u00e3t \u2212 1 = 0 \u21d4 \uf8ef2 2 2 \uf8ef 3 \u00e3t 2 \uf8f0\u00c5 = (t\/man) 22 x \u00c5 3 \u00e3t 1 V\u1eady = =. y2 2 Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 73 (C\u00e2u 37 - M\u0110 103 - BGD&\u0110T - N\u0103m 2017 - 2018). Cho a > 0, b > 0 th\u1ecfa m\u00e3n log4a+5b+1(16a2 + b2 + 1) + log8ab+1(4a + 5b + 1) = 2. Gi\u00e1 tr\u1ecb c\u1ee7a a + 2b b\u1eb1ng A 9. B 6. C 27 D 20 . . 4 3 \u221a \u0253 L\u1eddi gi\u1ea3i. Do a, b > 0 n\u00ean \u00ae16a2 + b2 2 16a2b2 \u21d2 log4a+5b+1(16a2 + b2 + 1) log4a+5b+1(8ab + 1). 4a + 5b + 1 > 1 Do \u0111\u00f3 log4a+5b+1(16a2 + b2 + 1) + log8ab+1(4a + 5b + 1) log4a+5b+1(8ab + 1) + log8ab+1(4a + 5b + 1) 2 (\u00e1p d\u1ee5ng B\u0110T C\u00f4-si). D\u1ea5u b\u1eb1ng x\u1ea3y ra \u21d4 \u00ae16a2 = b2 ; a > 0, b > 0 \u00ae4a = b > 0 \u21d4 \uf8f13 \u21d4 \uf8f2a = 4 8ab + 1 = 4a + 5b + 1 2b2 + 1 = 6b + 1 \uf8f3b = 3. 27 V\u1eady a + 2b = . 4 Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 74 (C\u00e2u 42 - M\u0110 101 - BGD&\u0110T - N\u0103m 2016 - 2017). Cho loga x = 3, logb x = 4 v\u1edbi a, b l\u00e0 c\u00e1c s\u1ed1 th\u1ef1c l\u1edbn h\u01a1n 1. T\u00ednh P = logab x. Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 196 S\u0110T: 0905.193.688","Ch\u01b0\u01a1ng 2. H\u00c0M S\u1ed0 L\u0168Y TH\u1eeaA. H\u00c0M S\u1ed0 M\u0168 V\u00c0 H\u00c0M S\u1ed0 L\u00d4GARIT A P= 7 B P= 1 C P = 12. D P 12 . . =. 12 12 7 \u0253 L\u1eddi gi\u1ea3i. 1 1 1 12 Ta c\u00f3 P = logab x = logx ab = logx a + logx b = = . 1 + 1 7 3 4 Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 75 (C\u00e2u 37 - M\u0110 102 - BGD&\u0110T - N\u0103m 2016 - 2017). Cho x, y l\u00e0 c\u00e1c s\u1ed1 th\u1ef1c l\u1edbn h\u01a1n 1 th\u1ecfa m\u00e3n x2 + 9y2 = 6xy. T\u00ednh M = 1+ log12 x + log12 y . 2 log12(x + 3y) 1 1 1 A M =. B M = 1. C M= . D M= . 4 23 \u0253 L\u1eddi gi\u1ea3i. - Ta c\u00f3 x2 + 9y2 = 6xy \u21d4 (x + 3y)2 = 12xy n\u00ean M = 1 + log12 x + log12 y = log12(12xy) = 1. 2 log12(x + 3y) log12(x + 3y)2 Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 76 (C\u00e2u 28 - M\u0110 103 - BGD&\u0110T - N\u0103m 2016 - 2017). 1 Cho log3 a = 2 v\u00e0 log2 b = . T\u00ednh I = 2 log3 [log3 (3a)] + log 1 b2. 4 2 5 3 A I= . B I = 4. C I = 0. D I= . 4 2 \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 I = 2 log3 [log3 (3a)] + log 1 b2 = 2 log3 (log3 3 + log3 a) + log2\u22122 b2 4 1 13 \u21d2 I = 2 log3 (1 + 2) \u2212 2 .2 log2 b = 2 log3 3 \u2212 log2 b = 2\u2212 = . 2 2 Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 77 (C\u00e2u 43 - M\u0110 103 - BGD&\u0110T - N\u0103m 2016 - 2017). V\u1edbi m\u1ecdi s\u1ed1 th\u1ef1c d\u01b0\u01a1ng a v\u00e0 b th\u1ecfa m\u00e3n a2 + b2 = 8ab, m\u1ec7nh \u0111\u1ec1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y \u0111\u00fang? A log(a + b) = 1 B log(a + b) = 1 + log a + log b. (log a + log b). 2 1 1 C log(a + b) = (1 + log a + log b). D log(a + b) = + log a + log b. 2 2 \u0253 L\u1eddi gi\u1ea3i. a2 + b2 = 8ab \u21d4 (a + b)2 = 10ab \u21d4 log(a + b)2 = log(10ab) \u21d4 log(a + b) = 1 + log a + log b) (1 2 Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 78 (C\u00e2u 43 - M\u0110 104 - BGD&\u0110T - N\u0103m 2016 - 2017). V\u1edbiCAc\u00e1clloosgg\u1ed12277t\u00c5\u00c5h\u1ef1\u221a\u221ayycxxd\u00e3\u00e3\u01b033\u01a1n==g99x, y t\u00f9y \u00fd, \u0111\u1eb7t log3 x = \u03b1, log3 y = \u03b2.\u00c5M\u221a\u1ec7xn\u00e3h3\u0111\u1ec1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y \u0111\u00fang? \u03b1 \u2212\u03b2 . B \u03b1 2 log27 \u221ay = \u03b1 +\u03b2 . D x + \u03b2. 2 \u00c5 \u00e33 2 \u03b1 \u2212 \u03b2. log27 y = 2 Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0253 L\u1eddi gi\u1ea3i. S\u0110T: 0905.193.688 Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 197"]