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

["4. \u0110\u01b0\u1eddng ti\u1ec7m c\u1eadn Ta c\u00f3 lim y = lim 3x + 1 = 3. x\u2192\u00b1\u221e x\u2192\u00b1\u221e x \u2212 1 Do \u0111\u00f3 \u0111\u01b0\u1eddng th\u1eb3ng y = 3 l\u00e0 \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn ngang c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 9 (C\u00e2u 20 - M\u0110 101 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2019 - 2020). 2x + 2 Ti\u1ec7m c\u1eadn \u0111\u1ee9ng c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = x \u2212 1 l\u00e0 A x = 2. B x = \u22122. C x = 1. D x = \u22121. \u0253 L\u1eddi gi\u1ea3i. T\u1eadp x\u00e1c \u0111\u1ecbnh D = R \\\\ {1}. Ta c\u00f3 lim y = +\u221e, lim y = \u2212\u221e n\u00ean \u0111\u01b0\u1eddng th\u1eb3ng x = 1 l\u00e0 ti\u1ec7m c\u1eadn \u0111\u1ee9ng c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 x\u21921+ x\u21921\u2212 2x + 2 y= . x\u22121 Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 10 (C\u00e2u 12 - M\u0110 102 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2019 - 2020). x\u22121 Ti\u1ec7m c\u1eadn \u0111\u1ee9ng c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = x \u2212 3 l\u00e0 A x = \u22123. B x = \u22121. C x = 1. D x = 3. \u0253 L\u1eddi gi\u1ea3i. T\u1eadp x\u00e1c \u0111\u1ecbnh D = R \\\\ {3}. Ta c\u00f3 lim y = +\u221e v\u00e0 lim y = \u2212\u221e. x\u21923+ x\u21923\u2212 Suy ra \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111\u00e3 cho c\u00f3 \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn \u0111\u1ee9ng l\u00e0 x = 3. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 11 (C\u00e2u 9 - M\u0110 103 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2019 - 2020). Ti\u1ec7m c\u1eadn \u0111\u1ee9ng c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = 2x \u2212 2 l\u00e0 x+1 A x = \u22122. B x = 1. C x = \u22121. D x = 2. \u0253 L\u1eddi gi\u1ea3i. Ti\u1ec7m c\u1eadn \u0111\u1ee9ng c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = 2x \u2212 2 l\u00e0 x = \u22121. x+1 Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 12 (C\u00e2u 3 - M\u0110 102 - BGD&\u0110T - \u0110\u1ee3t 4 - N\u0103m 2019 - 2020). Ti\u1ec7m c\u1eadn \u0111\u1ee9ng c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = x+1 l\u00e0 x+3 A x = \u22121. B x = 1. C x = \u22123. D x = 3. \u0253 L\u1eddi gi\u1ea3i. T\u1eadp x\u00e1c \u0111\u1ecbnh c\u1ee7a h\u00e0m s\u1ed1 \u0111\u00e3 cho D = R \\\\ {\u22123}. Ta c\u00f3 lim y = lim x + 1 = +\u221e v\u00e0 lim y = lim x + 1 = \u2212\u221e. x\u2192\u22123\u2212 x\u2192\u22123\u2212 x + 3 x\u2192\u22123+ x\u2192\u22123+ x + 3 Khi \u0111\u00f3 \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn \u0111\u1ee9ng c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111\u00e3 cho l\u00e0 x = \u22123. Ch\u1ecdn \u0111\u00e1p \u00e1n C Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 98 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 \u0104 C\u00e2u 13 (C\u00e2u 20 - M\u0110 101 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2020 - 2021). 2x \u2212 1 Ti\u1ec7m c\u1eadn \u0111\u1ee9ng c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = x \u2212 1 l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh 1 A x = 1. B x = \u22121. C x = 2. D x= . 2 \u0253 L\u1eddi gi\u1ea3i. V\u00ec lim 2x \u2212 1 = +\u221e v\u00e0 lim 2x \u2212 1 = \u2212\u221e n\u00ean \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = 2x \u2212 1 c\u00f3 m\u1ed9t ti\u1ec7m c\u1eadn \u0111\u1ee9ng l\u00e0 x\u21921+ x \u2212 1 x\u21921\u2212 x \u2212 1 x\u22121 \u0111\u01b0\u1eddng th\u1eb3ng x = 1. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 14 (C\u00e2u 23 - M\u0110 102 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2020 - 2021). x+1 Ti\u1ec7m c\u1eadn \u0111\u1ee9ng c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = x \u2212 2 l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh A x = \u22121. B x = \u22122. C x = 2. D x = 1. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 lim x+1 = +\u221e ho\u1eb7c lim x+1 = \u2212\u221e. x\u21922+ x \u2212 2 x+1 x\u21922\u2212 x \u2212 2 V\u1eady \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = x\u22122 c\u00f3 ti\u1ec7m c\u1eadn \u0111\u1ee9ng l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng x = 2. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 15 (C\u00e2u 4 - M\u0110 104 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2020 - 2021). Ti\u1ec7m c\u1eadn \u0111\u1ee9ng c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = x\u22121 l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh x+2 A x = 2. B x = \u22121. C x = \u22122. D x = 1. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 lim x\u22121 = \u2212\u221e, lim x\u22121 = +\u221e. x\u2192(\u22122)+ x + 2 x\u2192(\u22122)\u2212 x + 2 \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u00f3 ti\u1ec7m c\u1eadn \u0111\u1ee9ng l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh x = \u22122. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 16 (C\u00e2u 1 - M\u0110 101 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2020 - 2021). Ti\u1ec7m c\u1eadn ngang c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = 4x \u2212 1 l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh x+1 A y = \u22124. B y = 1. C y = 4. D y = \u22121. \u0253 L\u1eddi gi\u1ea3i. T\u1eadp x\u00e1c \u0111\u1ecbnh D = R\\\\{\u22121}. 4x \u2212 1 Ta c\u00f3 lim y = lim = 4 n\u00ean y = 4 l\u00e0 \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn ngang c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1. x\u2192\u00b1\u221e x\u2192\u00b1\u221e x + 1 Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 17 (C\u00e2u 7 - M\u0110 103 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2020 - 2021). Ti\u1ec7m c\u1eadn ngang c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = 2x \u2212 1 l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh x+1 A y = 1. B y = \u22121. C y = 2. D y = \u22122. Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t \u0253 L\u1eddi gi\u1ea3i. S\u0110T: 0905.193.688 99","4. \u0110\u01b0\u1eddng ti\u1ec7m c\u1eadn Ta c\u00f3 lim y = lim 2x \u2212 1 = 2, lim y = lim 2x \u2212 1 = 2. x\u2192+\u221e x\u2192+\u221e x + 1 x\u2192\u2212\u221e x\u2192\u2212\u221e x + 1 V\u1eady ti\u1ec7m c\u1eadn ngang c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = 2x \u2212 1 l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 y = 2. x+1 Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 18 (C\u00e2u 7 - M\u0110 104 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2020 - 2021). Ti\u1ec7m c\u1eadn ngang c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = 3x \u2212 1 l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh x+1 A y = \u22123. B y = \u22121. C y = 3. D y = 1. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 lim 3x \u2212 1 = 3 v\u00e0 lim 3x \u2212 1 = 3. x\u2192+\u221e x + 1 x\u2192\u2212\u221e x + 1 3x \u2212 1 Do \u0111\u00f3 \u0111\u01b0\u1eddng th\u1eb3ng y = 3 l\u00e0 ti\u1ec7m c\u1eadn ngang c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = x+1 . Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 19 (C\u00e2u 11 - M\u0110 101 - BGD&\u0110T - N\u0103m 2021 - 2022). Ti\u1ec7m c\u1eadn ngang c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = 2x\u22121 l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh 2x+4 A x = \u22122. B x = 1. C y = 1. D y = \u22122. \u0253 L\u1eddi gi\u1ea3i. Do lim y = 1 n\u00ean y = 1 l\u00e0 \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn ngang c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = 2x\u22121 \u00b7 2x+4 x\u2192\u221e Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 20 (C\u00e2u 5 - M\u0110 102 - BGD&\u0110T - N\u0103m 2021 - 2022). 2x \u2212 1 Ti\u1ec7m c\u1eadn ngang c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh 2x + 4 A y = \u22122. B x = \u22122. C x = 1. D y = 1. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 lim y = lim 2x \u2212 1 = 1 v\u00e0 lim y = lim 2x \u2212 1 = 1. x\u2192+\u221e x\u2192+\u221e 2x + 4 x\u2192\u2212\u221e x\u2192\u2212\u221e 2x + 4 V\u1eady \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u00f3 ti\u1ec7m c\u1eadn ngang l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh y = 1. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 21 (C\u00e2u 26 - M\u0110 103 - 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 \u22122 +\u221e f (x) \u22121 \u2212\u2212 \u22121 f (x) +\u221e \u2212\u221e Ti\u1ec7m c\u1eadn \u0111\u1ee9ng c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111\u00e3 cho l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: A x = \u22121. B y = \u22121. C y = \u22122. D x = \u22122. Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t \u0253 L\u1eddi gi\u1ea3i. S\u0110T: 0905.193.688 100","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 Ta th\u1ea5y: lim f (x) = +\u221e v\u00e0 lim f (x) = \u2212\u221e. x\u2192\u22122+ x\u2192\u22122\u2212 V\u1eady ti\u1ec7m c\u1eadn \u0111\u1ee9ng c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111\u00e3 cho l\u00e0 x = \u22122. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 22 (C\u00e2u 25 - M\u0110 104 - 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 \u22122 +\u221e f (x) \u22121 \u2212\u2212 \u22121 f (x) +\u221e \u2212\u221e Ti\u1ec7m c\u1eadn \u0111\u1ee9ng c\u1ee7a \u0111\u1ed3 th\u1ecb \u0111\u00e3 cho l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: A y = \u22121. B y = \u22122. C x = \u22122. D x = \u22121. \u0253 L\u1eddi gi\u1ea3i. T\u1eeb b\u1ea3ng bi\u1ebfn thi\u00ean ta c\u00f3 lim f (x) = \u2212\u221e v\u00e0 lim f (x) = +\u221e, suy ra \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111\u00e3 cho c\u00f3 x\u2192(\u22122)\u2212 x\u2192(\u22122)+ ti\u1ec7m c\u1eadn \u0111\u1ee9ng l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng x = \u22122. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 23 (C\u00e2u 22 - M\u0110 102 - BGD&\u0110\u221aT - N\u0103m 2017 - 2018). x+4\u22122 S\u1ed1 ti\u1ec7m c\u1eadn \u0111\u1ee9ng c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = l\u00e0 x2 + x A 3. B 0. C 2. D 1. \u0253 L\u1eddi gi\u1ea3i. T\u1eadp x\u00e1c \u0111\u1ecbnh h\u00e0m s\u1ed1 D = [\u22124; +\u221e) \\\\ {\u22121; 0}. Ta c\u00f3 lim y = +\u221e, lim y = 1 v\u00e0 lim y = 1. x\u2192\u22121+ x\u21920+ x\u21920\u2212 Suy ra \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 ch\u1ec9 c\u00f3 1 ti\u1ec7m c\u1eadn \u0111\u1ee9ng l\u00e0 x = \u22121. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 24 (C\u00e2u 43 - \u0110TK - BGD&\u0110T - l\u1ea7n 2 - N\u0103m 2019 - 2020). ax + 1 Cho h\u00e0m s\u1ed1 f (x) = bx + c (a, b, c \u2208 R) c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean nh\u01b0 sau: x \u2212\u221e 2 + +\u221e f (x) + 1 f (x) +\u221e 1 \u2212\u221e Trong c\u00e1c s\u1ed1 a, b v\u00e0 c c\u00f3 bao nhi\u00eau s\u1ed1 d\u01b0\u01a1ng? A 2. B 3. C 1. D 0. T\u1eeb b\u1ea3ng bi\u1ebfn thi\u00ean ta c\u00f3: \u0253 L\u1eddi gi\u1ea3i. S\u0110T: 0905.193.688 Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 101","4. \u0110\u01b0\u1eddng ti\u1ec7m c\u1eadn \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 f (x) c\u00f3 ti\u1ec7m c\u1eadn ngang y = 1, do \u0111\u00f3 a = 1 > 0 \u21d2 a v\u00e0 b c\u00f9ng d\u1ea5u. b \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 f (x) c\u00f3 ti\u1ec7m c\u1eadn \u0111\u1ee9ng x = 2, do \u0111\u00f3 \u2212c = 2 > 0 \u21d2 c < 0 \u21d2 c v\u00e0 b tr\u00e1i d\u1ea5u. bb Khi x < 2 th\u00ec f (x) lu\u00f4n d\u01b0\u01a1ng (f (x) > 1). Do \u0111\u00f3 v\u1edbi x = 0 th\u00ec f (0) = 1 > 0 \u21d2 c > 0. c V\u00ec c > 0, c v\u00e0 b tr\u00e1i d\u1ea5u n\u00ean b < 0. M\u00e0 a v\u00e0 b c\u00f9ng d\u1ea5u n\u00ean a < 0. V\u1eady ch\u1ec9 c\u00f3 1 s\u1ed1 d\u01b0\u01a1ng l\u00e0 c. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 25 (C\u00e2u 2 - \u0110MH - BGD&\u0110T - N\u0103m 2016 - 2017). Cho h\u00e0m s\u1ed1 y = f (x) c\u00f3 lim = 1 v\u00e0 lim = \u22121. Kh\u1eb3ng \u0111\u1ecbnh n\u00e0o sau \u0111\u00e2y l\u00e0 kh\u1eb3ng \u0111\u1ecbnh x\u2192+\u221e x\u2192\u2212\u221e \u0111\u00fang? A \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111\u00e3 cho kh\u00f4ng c\u00f3 ti\u1ec7m c\u1eadn ngang. B \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111\u00e3 cho c\u00f3 \u0111\u00fang m\u1ed9t ti\u1ec7m c\u1eadn ngang. C \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111\u00e3 cho c\u00f3 hai ti\u1ec7m c\u1eadn ngang l\u00e0 c\u00e1c \u0111\u01b0\u1eddng th\u1eb3ng y = 1 v\u00e0 y = \u22121. D \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111\u00e3 cho c\u00f3 hai ti\u1ec7m c\u1eadn ngang l\u00e0 c\u00e1c \u0111\u01b0\u1eddng th\u1eb3ng x = 1 v\u00e0 x = \u22121. \u0253 L\u1eddi gi\u1ea3i. Theo \u0111\u1ecbnh ngh\u0129a \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn, ta c\u00f3: lim = 1 suy ra y = 1 l\u00e0 \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn ngang. x\u2192+\u221e lim = \u22121 suy ra y = \u22121 l\u00e0 \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn ngang. x\u2192\u2212\u221e Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 26 (C\u00e2u 8 - \u0110TN - BGD&\u0110T - N\u0103m 2016 - 2017). \u221a 2x \u2212 1 \u2212 x2 + x + 3 T\u00ecm t\u1ea5t c\u1ea3 c\u00e1c ti\u1ec7m c\u1eadn \u0111\u1ee9ng c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = x2 \u2212 5x + 6 A x = \u22123 v\u00e0 x = \u22122. B x = \u22123. C x = 3 v\u00e0 x = 2. D x = 3. \u0253 L\u1eddi gi\u1ea3i. T\u1eadp x\u00e1c \u0111\u1ecbnh D\u221a= R\\\\ {2; 3} . (2x \u2212 1)2 \u2212 (x2 + x + 3) 2x \u2212 1 \u2212 x2 + x + 3 lim = lim \u00c4\u221a x2 \u2212 5x + 6 x\u21922+ (x \u2212 2)(x \u2212 3) 2x \u2212 1 + x2 + x + 3 \u00e4 x\u21922+ = lim (x \u2212 2)(3x + 1) \u00c4\u221a x\u21922+ (x \u2212 2)(x \u2212 3) 2x \u2212 1 + x2 + x + 3 \u00e4 = lim (3x + 1) \u00e4= \u22127 \u221a . \u00c4 6 x\u21922+ (x \u2212 3) 2x \u2212 1 + x2 + x + 3 \u221a 2x \u2212 1 \u2212 x2 + x + 3 \u22127 T\u01b0\u01a1ng t\u1ef1 ta c\u00f3 lim =. x\u21922\u2212 \u221ax2 \u2212 5x + 6 6\u221a 2x \u2212 1 \u2212 x2 + x + 3 2x \u2212 1 \u2212 x2 + x + 3 M\u1eb7t kh\u00e1c lim = lim = +\u221e x\u21923+ \u221a x2 \u2212 5x + 6 x\u21923+ (x \u2212 2)(x \u2212 3) v\u00e0 lim 2x \u2212 1 \u2212 x2 + x + 3 = \u2212\u221e. x\u21923\u2212 x2 \u2212 5x + 6 Suy ra \u0111\u01b0\u1eddng th\u1eb3ng x = 3 l\u00e0 ti\u1ec7m c\u1eadn \u0111\u1ee9ng c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111\u00e3 cho. Ch\u1ecdn \u0111\u00e1p \u00e1n D Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 102 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 \u0104 C\u00e2u 27 (C\u00e2u 18 - M\u0110 101 - BGD&\u0110\u221aT - N\u0103m 2017 - 2018). x+9\u22123 S\u1ed1 ti\u1ec7m c\u1eadn \u0111\u1ee9ng c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = x2 + x l\u00e0 A 3. B 2. C 0. D 1. \u0253 L\u1eddi gi\u1ea3i. T\u1eadp x\u00e1c \u0111\u1ecbnh D = [\u22129; +\u221e\u221a) \\\\ {\u22121; 0}. \uf8f1 x+9\u22123 \uf8f4 lim y = lim = +\u221e \uf8f4 x2 + x \u21d2 x = \u22121 l\u00e0 ti\u1ec7m c\u1eadn \u0111\u1ee9ng. \uf8f2 x\u2192\u22121+ x\u2192\u22121+ Ta c\u00f3 \u221ax+9\u22123 x2 + x = \u2212\u221e \uf8f4 lim y= lim \uf8f4 \uf8f3 x\u2192\u22121\u2212 x\u2192\u221a\u22121\u2212 Ngo\u00e0i ra lim y = lim x+9\u22123 1 = n\u00ean x = 0 kh\u00f4ng ph\u1ea3i l\u00e0 m\u1ed9t ti\u1ec7m c\u1eadn \u0111\u1ee9ng. x\u21920 x\u21920 x2 + x 6 Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 28 (C\u00e2u 18 - M\u0110 103 - BGD&\u0110\u221aT - N\u0103m 2017 - 2018). x + 25 \u2212 5 S\u1ed1 ti\u1ec7m c\u1eadn \u0111\u1ee9ng c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = x2 + x l\u00e0 A 2. B 0. C 1. D 3. \u0253 L\u1eddi gi\u1ea3i. T\u1eadp x\u00e1c \u0111\u1ecbnh: D = [\u221225; +\u221e) \\\\ {\u22121; 0}. Ta c\u00f3 lim y = lim \u221ax = lim \u221a1 1 = : h\u1eefu h\u1ea1n. x\u21920 x\u21920 x(x + 1) x + 25 + 5 x\u21920 (x + 1) x + 25 + 5 10 V\u00e0 lim y = lim \u221a1 = +\u221e. x\u2192(\u22121)+ x\u2192(\u22121)+ (x + 1) x + 25 + 5 V\u1eady \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111\u00e3 cho ch\u1ec9 c\u00f3 1 ti\u1ec7m c\u1eadn \u0111\u1ee9ng l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng x = \u22121. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 29 (C\u00e2u 19 - M\u0110 104 - BGD&\u0110\u221aT - N\u0103m 2017 - 2018). x + 16 \u2212 4 S\u1ed1 ti\u1ec7m c\u1eadn \u0111\u1ee9ng c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = l\u00e0 x2 + x A 0. B 3. C 2. D 1. \u0253 L\u1eddi gi\u1ea3i. Ph\u01b0\u01a1ng tr\u00ecnh x2 + x = 0 \u21d4 \u00f1x = 0 x = \u22121. Khi \u0111\u00f3 \u221a x + 16 \u2212 4 1 lim = . x\u21920\u00b1 x2 + x 8 \u221a x + 16 \u2212 4 lim = +\u221e. x\u2192(\u22121)+ x2 + x Suy ra \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u00f3 m\u1ed9t ti\u1ec7m c\u1eadn \u0111\u1ee9ng x = \u22121. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 30 (C\u00e2u 18 - \u0110MH - BGD&\u0110T - N\u0103m 2018 - 2019). Cho h\u00e0m s\u1ed1 y = f (x) c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean nh\u01b0 sau. Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 103 S\u0110T: 0905.193.688","4. \u0110\u01b0\u1eddng ti\u1ec7m c\u1eadn x \u2212\u221e 1 +\u221e + y+ 5 +\u221e y 23 T\u1ed5ng s\u1ed1 ti\u1ec7m c\u1eadn ngang v\u00e0 ti\u1ec7m c\u1eadn \u0111\u1ee9ng c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111\u00e3 cho l\u00e0 A 4. B 1. C 3. D 2. \u0253 L\u1eddi gi\u1ea3i. T\u1eeb b\u1ea3ng bi\u1ebfn thi\u00ean ta c\u00f3 lim y = 2 suy ra y = 2 l\u00e0 ti\u1ec7m c\u1eadn ngang. x\u2192\u2212\u221e lim y = 5 suy ra y = 5 l\u00e0 ti\u1ec7m c\u1eadn ngang. x\u2192+\u221e lim y = +\u221e suy ra x = 1 l\u00e0 ti\u1ec7m c\u1eadn \u0111\u1ee9ng. x\u21921\u2212 V\u1eady \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 t\u1ed5ng c\u1ed9ng c\u00f3 3 \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn ngang v\u00e0 ti\u1ec7m c\u1eadn \u0111\u1ee9ng. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 31 (C\u00e2u 28 - M\u0110 101 - BGD&\u0110T - N\u0103m 2018 - 2019). Cho h\u00e0m s\u1ed1 y = f (x) c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean nh\u01b0 sau: x \u2212\u221e 0 1 +\u221e y \u2212 \u22120+ y2 +\u221e +\u221e \u22122 \u22124 T\u1ed5ng s\u1ed1 ti\u1ec7m c\u1eadn \u0111\u1ee9ng v\u00e0 ti\u1ec7m c\u1eadn ngang c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111\u00e3 cho l\u00e0 A 4. B 1. C 3. D 2. \u0253 L\u1eddi gi\u1ea3i. H\u00e0m s\u1ed1 y = f (x) c\u00f3 t\u1eadp x\u00e1c \u0111\u1ecbnh D = R \\\\ {0}. Ta c\u00f3 lim f (x) = +\u221e suy ra kh\u00f4ng t\u1ed3n t\u1ea1i ti\u1ec7m c\u1eadn ngang khi x \u2192 +\u221e. x\u2192+\u221e lim f (x) = 2, suy ra \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = f (x) c\u00f3 ti\u1ec7m c\u1eadn ngang y = 2. x\u2192\u2212\u221e lim f (x) = +\u221e; lim f (x) = \u22124, suy ra \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = f (x) c\u00f3 ti\u1ec7m c\u1eadn \u0111\u1ee9ng x = 0. x\u21920+ x\u21920\u2212 V\u1eady t\u1ed5ng s\u1ed1 ti\u1ec7m c\u1eadn \u0111\u1ee9ng v\u00e0 ngang l\u00e0 2. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 32 (C\u00e2u 24 - M\u0110 102 - BGD&\u0110T - N\u0103m 2018 - 2019). Cho h\u00e0m s\u1ed1 f (x) c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean nh\u01b0 sau Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 104 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 0 1 +\u221e f (x) 0 \u2212 \u22120+ f (x) 2 +\u221e \u2212\u221e \u22122 T\u1ed5ng s\u1ed1 ti\u1ec7m c\u1eadn \u0111\u1ee9ng v\u00e0 ti\u1ec7m c\u1eadn ngang c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111\u00e3 cho l\u00e0 A 3. B 1. C 2. D 4. \u0253 L\u1eddi gi\u1ea3i. T\u1eeb b\u1ea3ng bi\u1ebfn thi\u00ean \u0111\u00e3 cho ta c\u00f3 lim f (x) = 0 n\u00ean \u0111\u01b0\u1eddng th\u1eb3ng y = 0 l\u00e0 m\u1ed9t ti\u1ec7m c\u1eadn ngang c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1. x\u2192\u2212\u221e lim f (x) = \u2212\u221e n\u00ean \u0111\u01b0\u1eddng th\u1eb3ng x = 0 l\u00e0 m\u1ed9t ti\u1ec7m c\u1eadn \u0111\u1ee9ng c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1. x\u21920\u2212 V\u1eady \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111\u00e3 cho c\u00f3 hai \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 33 (C\u00e2u 28 - M\u0110 103 - BGD&\u0110T - N\u0103m 2018 - 2019). Cho h\u00e0m s\u1ed1 y = f (x) c\u00f3 b\u00e1ng bi\u1ebfn thi\u00ean nh\u01b0 sau: x \u2212\u221e 0 3 +\u221e y\u2212 +0\u2212 12 3 y \u2212\u221e \u22123 T\u1ed5ng s\u1ed1 ti\u1ec7m c\u1eadn \u0111\u1ee9ng v\u00e0 ti\u1ec7m c\u1eadn ngang c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111\u00e3 cho l\u00e0 A 1. B 2. C 3. D 4. \u0253 L\u1eddi gi\u1ea3i. Nh\u00ecn b\u1ea3ng bi\u1ebfn thi\u00ean ta th\u1ea5y lim f (x) = \u2212\u221e \u21d2 x = 0 l\u00e0 TC\u0110 c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1. x\u21920\u2212 lim f (x) = 3 \u21d2 y = 3 l\u00e0 TCN c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1. x\u2192+\u221e lim f (x) = 1 \u21d2 y = 1 l\u00e0 TCN c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1. x\u2192\u2212\u221e V\u1eady h\u00e0m s\u1ed1 c\u00f3 3 ti\u1ec7m c\u1eadn. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 34 (C\u00e2u 27 - \u0110TK - BGD&\u0110T - l\u1ea7n 1 - N\u0103m 2019 - 2020). 5x2 \u2212 4x \u2212 1 T\u1ed5ng s\u1ed1 ti\u1ec7m c\u1eadn \u0111\u1ee9ng v\u00e0 ti\u1ec7m c\u1eadn ngang c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = l\u00e0 x2 \u2212 1 A 1. B 0. C 2. D 3. \u0253 L\u1eddi gi\u1ea3i. T\u1eadp x\u00e1c \u0111\u1ecbnh D = R\\\\ {\u22121; 1} Tr\u00ean D ta c\u00f3, y = 5x2 \u2212 4x \u2212 1 (5x + 1) (x \u2212 1) 5x + 1 = = x2 \u2212 1 (x \u2212 1) (x + 1) x + 1 Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 105 S\u0110T: 0905.193.688","4. \u0110\u01b0\u1eddng ti\u1ec7m c\u1eadn lim y = lim 5x + 1 = \u2212\u221e \u21d2 x = \u22121 l\u00e0 ti\u1ec7m c\u1eadn \u0111\u1ee9ng c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1. x\u2192(\u22121)+ x\u2192(\u22121)+ x + 1 lim y = lim 5x + 1 = 5 \u21d2 y = 5l\u00e0 ti\u1ec7m c\u1eadn ngang c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1. x\u2192\u00b1\u221e x\u2192\u00b1\u221e x + 1 V\u1eady \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111\u00e3 cho c\u00f3 2 ti\u1ec7m c\u1eadn. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 35 (C\u00e2u 24 - M\u0110 103 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2020 - 2021). 2x + 1 Ti\u1ec7m c\u1eadn \u0111\u1ee9ng c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = x \u2212 1 l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh C x = \u22121. A x = 2. B x = 1. 2 D x = \u22121. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 lim y = lim 2x + 1 = +\u221e n\u00ean ti\u1ec7m c\u1eadn \u0111\u1ee9ng c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng x = 1. x\u21921+ x\u21921+ x \u2212 1 Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 36 (C\u00e2u 9 - \u0110MH - 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 sao cho \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 y = \u221a x + 1 c\u00f3 hai \u0111\u01b0\u1eddng mx2 + 1 ti\u1ec7m c\u1eadn ngang. A Kh\u00f4ng c\u00f3 gi\u00e1 tr\u1ecb th\u1ef1c n\u00e0o c\u1ee7a m th\u1ecfa m\u00e3n y\u00eau c\u1ea7u \u0111\u1ec1 b\u00e0i. B m < 0. C m = 0. D m > 0. \u0253 L\u1eddi gi\u1ea3i. \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u00f3 hai ti\u1ec7m c\u1eadn ngang \u21d4 lim y, lim y t\u1ed3n t\u1ea1i v\u00e0 kh\u00e1c nhau. x\u2192\u2212\u221e x\u2192+\u221e Do \u0111\u00f3 h\u00e0m s\u1ed1 ph\u1ea3i x\u00e1c \u0111\u1ecbnh tr\u00ean kho\u1ea3ng (\u2212\u221e; +\u221e) t\u1ee9c l\u00e0 mx2 + 1 > 0, \u2200 \u21d4 m > 0.Do \u0111\u00f3 lo\u1ea1i B. m = 0 th\u00ec y = x + 1 n\u00ean h\u00e0m s\u1ed1 kh\u00f4ng c\u00f3 ti\u1ec7m c\u1eadn ngang. 1+ 1 m > 0 th\u00ec lim y = lim \u221a x + 1 = lim \u2026 x = \u2212\u221a1 . x\u2192\u2212\u221e x\u2192\u2212\u221e mx2 + 1 \u2212m + 1 m x\u2192\u2212\u221e x2 1 + 1 \u2026 v\u00e0 lim y = lim \u221ax+1 1 = lim x = \u221a1 . mx2 + 1 m x\u2192+\u221e x\u2192+\u221e x\u2192+\u221e m + x2 \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u00f3 hai ti\u1ec7m c\u1eadn ngang l\u00e0 y = \u00b1\u221a1 . m Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 37 (C\u00e2u 11 - \u0110TK - BGD&\u0110T - N\u0103m 2016 - 2017). Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 106 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 y = f (x) c\u00f3 b\u1ea3ng x \u2212\u221e \u22122 0 +\u221e bi\u1ebfn thi\u00ean nh\u01b0 h\u00ecnh d\u01b0\u1edbi \u0111\u00e2y. H\u1ecfi y + \u2212 \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 \u0111\u00e3 cho c\u00f3 bao +\u221e nhi\u00eau ti\u1ec7m c\u1eadn? y 1 0 A 1. B 3. C 2. D \u2212\u221e 4. \u0253 L\u1eddi gi\u1ea3i. C\u0103n c\u1ee9 v\u00e0o b\u1ea3ng bi\u1ebfn thi\u00ean ta th\u1ea5y: lim y = \u2212\u221e n\u00ean \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u00f3 ti\u1ec7m c\u1eadn \u0111\u1ee9ng l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng x = \u22122. x\u2192(\u22122)+ lim y = +\u221e n\u00ean \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u00f3 ti\u1ec7m c\u1eadn \u0111\u1ee9ng l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng x = 0. x\u21920\u2212 lim y = 0 n\u00ean \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u00f3 ti\u1ec7m c\u1eadn ngang l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng y = 0. x\u2192+\u221e T\u00f3m l\u1ea1i, \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111\u00e3 cho c\u00f3 ba \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 38 (C\u00e2u 12 - M\u0110 101 - BGD&\u0110T - N\u0103m 2016 - 2017). x2 \u2212 3x \u2212 4 T\u00ecm s\u1ed1 ti\u1ec7m c\u1eadn \u0111\u1ee9ng c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = . x2 \u2212 16 A 2. B 3. C 1. D 0. \u0253 L\u1eddi gi\u1ea3i. x2 \u2212 3x \u2212 4 (x + 1)(x \u2212 4) y= = . x2 \u2212 16 (x + 4)(x \u2212 4) lim y = +\u221e \u21d2 x = \u22124 l\u00e0 ti\u1ec7m c\u1eadn \u0111\u1ee9ng c\u1ee7a \u0111\u1ed3 th\u1ecb. x\u2192\u22124+ lim y = 5 \u21d2 x = \u22124 kh\u00f4ng l\u00e0 ti\u1ec7m c\u1eadn \u0111\u1ee9ng c\u1ee7a \u0111\u1ed3 th\u1ecb. x\u21924 8 V\u1eady \u0111\u1ed3 th\u1ecb c\u00f3 1 ti\u1ec7m c\u1eadn \u0111\u1ee9ng. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 39 (C\u00e2u 15 - M\u0110 102 - BGD&\u0110T - N\u0103m 2016 - 2017). x2 \u2212 5x + 4 T\u00ecm s\u1ed1 ti\u1ec7m c\u1eadn c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = . x2 \u2212 1 A 3. B 1. C 0. D 2. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 lim y = 1; lim y = 1 do \u0111\u00f3 \u0111\u01b0\u1eddng th\u1eb3ng y = 1 l\u00e0 ti\u1ec7m c\u1eadn ngang c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111\u00e3 cho. x\u2192+\u221e x\u2192\u2212\u221e L\u1ea1i c\u00f3: lim y = \u22123; lim y = \u22123 x\u21921+ 2 x\u21921\u2212 2 lim y = +\u221e; lim y = \u2212\u221e x\u2192\u22121+ x\u2192\u22121\u2212 Do \u0111\u00f3 \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u00f3 m\u1ed9t ti\u1ec7m c\u1eadn \u0111\u1ee9ng l\u00e0 x = \u22121. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 40 (C\u00e2u 27 - M\u0110 103 - BGD&\u0110T - N\u0103m 2016 - 2017). \u0110\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 n\u00e0o trong c\u00e1c h\u00e0m s\u1ed1 d\u01b0\u1edbi \u0111\u00e2y c\u00f3 ti\u1ec7m c\u1eadn \u0111\u1ee9ng? Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 107 S\u0110T: 0905.193.688","4. \u0110\u01b0\u1eddng ti\u1ec7m c\u1eadn A y = \u221a1 . B y= 1 C y= 1 D y= 1 x . . . x2 + x + 1 x4 + 1 x2 + 1 \u0253 L\u1eddi gi\u1ea3i. H\u00e0m s\u1ed1 y = \u221a1 c\u00f3 m\u1eabu th\u1ee9c c\u00f3 nghi\u1ec7m x = 0 \u21d2 \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u00f3 ti\u1ec7m c\u1eadn \u0111\u1ee9ng. x Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 41 (C\u00e2u 16 - \u0110TK - BGD&\u0110T - N\u0103m 2017 - 2018). \u0110\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y c\u00f3 ti\u1ec7m c\u1eadn \u0111\u1ee9ng? \u221a A y= x2 \u2212 3x + 2 B y= x2 C y = x2 \u2212 1. D y= x . . . x\u22121 x2 + 1 x+1 \u0253 L\u1eddi gi\u1ea3i. x xx H\u00e0m s\u1ed1 y = c\u00f3 ti\u1ec7m c\u1eadn \u0111\u1ee9ng x = \u22121 v\u00ec lim = \u2212\u221e; lim = +\u221e. x+1 x\u2192\u22121+ x + 1 x\u2192\u22121\u2212 x + 1 H\u00e0m s\u1ed1 y = x2 \u2212 3x + 2 x\u00e1c \u0111\u1ecbnh tr\u00ean D = (\u2212\u221e; 1) \u222a (1; +\u221e), nh\u01b0ng kh\u00f4ng c\u00f3 ti\u1ec7m c\u1eadn \u0111\u1ee9ng x\u22121 x2 v\u00ec lim \u2212 3x + 2 = lim(x \u2212 2) = \u22121. x\u22121 x\u21921 x\u21921 x2 H\u00e0m s\u1ed1 y = x2 + 1 x\u00e1c \u0111\u1ecbnh v\u00e0 li\u00ean t\u1ee5c tr\u00ean R n\u00ean kh\u00f4ng c\u00f3 ti\u1ec7m c\u1eadn. \u221a H\u00e0m s\u1ed1 y = x2 \u2212 1 x\u00e1c \u0111\u1ecbnh tr\u00ean D = (\u2212\u221e; \u22121] \u222a [1; +\u221e) v\u00e0 \u221a\u221a lim x2 \u2212 1 = lim x2 \u2212 1 = 0 x\u2192\u22121\u2212 x\u21921+ n\u00ean kh\u00f4ng c\u00f3 ti\u1ec7m c\u1eadn. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 42 (C\u00e2u 43 - M\u0110 104 - 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+1 \u0111\u1ec1u AB\u221aI c\u00f3 hai \u0111\u1ec9nh A, B thu\u1ed9\u221ac (C), \u0111o\u1ea1n th\u1eb3ng AB\u221ac\u00f3 \u0111\u1ed9 d\u00e0i b\u1eb1ng \u221a A 2 3. B 2 2. C 3. D 6. \u0253 L\u1eddi gi\u1ea3i. \u22123 v\u00e9c-t\u01a1 O# \u00bbI = (\u22121; 1) \u21d2 I(0; 0) v\u00e0 . T\u1ecbnh ti\u1ebfn h\u1ec7 tr\u1ee5c theo (C) : Y = X G\u1ecdi \u00c5 \u22123 \u00e3 B \u00c5 \u22123 \u00e3 \u2208 (C ), \u0111i\u1ec1u ki\u1ec7n a = b. A a; , b; ab Tam gi\u00e1c IAB \u0111\u1ec1u \uf8f1 + 9 = b2 + 9 (1) \uf8f4a2 a2 b2 \uf8f4 \uf8f4 \u00aeIA = IB \uf8f4 \uf8f4 9 \uf8f2 cos(I#A\u00bb; I#B\u00bb) = cos 60\u25e6 \u21d4 ab + ab 1 2 \uf8f4 = (2). \uf8f4\u2026 9 \u2026 9 \uf8f4 a2 b2 b2 \uf8f4 a2 + \u00b7 + \uf8f4 \uf8f3 T\u1eeb (2) \u21d2 ab > 0 do \u0111\u00f3 (1) \u21d4 (a2 \u2212 b2)(a2b2 \u2212 9) = 0 \u21d2 ab = 3. \u221a Suy ra AB2 = 2 \u00c5 + 9\u00e3 = 12 \u21d2 AB = 2 3. 3 3 Ch\u1ecdn \u0111\u00e1p \u00e1n A Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 108 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 B\u00c0I 5. KH\u1ea2O S\u00c1T S\u1ef0 BI\u1ebeN THI\u00caN V\u00c0 V\u1ebc \u0110\u1ed2 TH\u1eca H\u00c0M S\u1ed0 \u0104 C\u00e2u 1 (C\u00e2u 1 - \u0110MH - BGD&\u0110T - N\u0103m 2016 - 2017). \u0110\u01b0\u1eddng cong trong h\u00ecnh b\u00ean l\u00e0 \u0111\u1ed3 th\u1ecb c\u1ee7a m\u1ed9t h\u00e0m s\u1ed1 trong b\u1ed1n h\u00e0m y s\u1ed1 \u0111\u01b0\u1ee3c li\u1ec7t k\u00ea \u1edf b\u1ed1n ph\u01b0\u01a1ng \u00e1n A, B, C, D d\u01b0\u1edbi \u0111\u00e2y. H\u1ecfi h\u00e0m s\u1ed1 \u0111\u00f3 l\u00e0 h\u00e0m s\u1ed1 n\u00e0o? B y = \u2212x3 + 3x + 1. A y = \u2212x2 + x \u2212 1. C y = x3 \u2212 3x + 1. D y = x4 \u2212 x2 + 1. x \u0253 L\u1eddi gi\u1ea3i. \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u00f3 2 c\u1ef1c tr\u1ecb v\u00e0 lim y = +\u221e, lim y = \u2212\u221e. x\u2192+\u221e x\u2192\u2212\u221e Lo\u1ea1i A: v\u00ec l\u00e0 parapol ch\u1ec9 c\u00f3 1 c\u1ef1c tr\u1ecb. Lo\u1ea1i B: v\u00ec lim y = \u2212\u221e. x\u2192+\u221e Lo\u1ea1i D: v\u00ec h\u00e0m h\u00e0m tr\u00f9ng ph\u01b0\u01a1ng nh\u1eadn Oy l\u00e0m tr\u1ee5c \u0111\u1ed1i x\u1ee9ng. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 2 (C\u00e2u 6 - M\u0110 103 - BGD&\u0110T - N\u0103m 2017 - 2018). \u0110\u01b0\u1eddng cong trong h\u00ecnh v\u1ebd b\u00ean l\u00e0 \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y? y Ox A y = \u2212x4 + x2 \u2212 1. B y = x4 \u2212 3x2 \u2212 1. C y = \u2212x3 \u2212 3x \u2212 1. D y = x3 \u2212 3x \u2212 1. \u0253 L\u1eddi gi\u1ea3i. \u0110\u01b0\u1eddng cong tr\u00ean h\u00ecnh l\u00e0 \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 b\u1eadc ba v\u1edbi h\u1ec7 s\u1ed1 a > 0 n\u00ean ch\u1ec9 c\u00f3 y = x3 \u2212 3x \u2212 1 l\u00e0 \u0111\u00fang. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 3 (C\u00e2u 7 - \u0110MH - BGD&\u0110T - N\u0103m 2018 - 2019). Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 109 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 \u0110\u01b0\u1eddng cong trong h\u00ecnh v\u1ebd b\u00ean l\u00e0 \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 n\u00e0o d\u01b0\u1edbi y 1 \u0111\u00e2y? 2x \u2212 1 x\u22121 . A y= B y = x+1 . x \u2212 1 C y = x4 + x2 + 1. D y = x3 \u2212 3x \u2212 1. O1 x \u0253 L\u1eddi gi\u1ea3i. \u0110\u01b0\u1eddng cong c\u00f3 \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn \u0111\u1ee9ng x = 1 v\u00e0 ti\u1ec7m c\u1eadn ngang y = 1 n\u00ean n\u00f3 kh\u00f4ng th\u1ec3 l\u00e0 \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m \u0111a th\u1ee9c. Ta x\u00e9t c\u00e1c tr\u01b0\u1eddng h\u1ee3p sau: 2x \u2212 1 a) X\u00e9t y = x \u2212 1 , c\u00f3 2x \u2212 1 2x \u2212 1 lim = lim = 2 \u21d2 y = 2 l\u00e0 ti\u1ec7m c\u1eadn ngang c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1. Do \u0111\u00f3 \u0111\u01b0\u1eddng x\u22121 x\u2192+\u221e x\u22121 x\u2192\u2212\u221e cong tr\u00ean kh\u00f4ng th\u1ec3 l\u00e0 \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 y = 2x \u2212 1 . x\u22121 x+1 b) X\u00e9t y = x \u2212 1 , c\u00f3 x+1 x + 1 lim x\u22121 = lim x \u2212 1 = 1 \u21d2 y = 1 l\u00e0 ti\u1ec7m c\u1eadn ngang c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1. x\u2192\u2212\u221e x\u2192+\u221e x+1 x+1 lim = +\u221e v\u00e0 lim = \u2212\u221e \u21d2 x = 1 l\u00e0 ti\u1ec7m c\u1eadn \u0111\u1ee9ng c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1. x\u21921+ x \u2212 1 x\u21921\u2212 x \u2212 1 x+1 Do \u0111\u00f3 \u0111\u01b0\u1eddng cong tr\u00ean l\u00e0 \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 y = . x \u2212 1 Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 4 (C\u00e2u 6 - M\u0110 101 - BGD&\u0110T - N\u0103m 2018 - 2019). \u0110\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y c\u00f3 d\u1ea1ng nh\u01b0 \u0111\u01b0\u1eddng cong trong h\u00ecnh y v\u1ebd b\u00ean? B y = \u2212x3 + 3x2 + 3. A y = x3 \u2212 3x2 + 3. C y = x4 \u2212 2x2 + 3. D y = \u2212x4 + 2x2 + 3. Ox \u0253 L\u1eddi gi\u1ea3i. \u0110\u01b0\u1eddng cong \u0111\u00e3 cho l\u00e0 \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = ax3 + bx2 + cx + d v\u1edbi a > 0. V\u1eady h\u00e0m s\u1ed1 th\u1ecfa m\u00e3n l\u00e0 y = x3 \u2212 3x2 + 3. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 5 (C\u00e2u 2 - M\u0110 103 - BGD&\u0110T - N\u0103m 2018 - 2019). Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 110 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 \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y c\u00f3 d\u1ea1ng nh\u01b0 \u0111\u01b0\u1eddng cong trong h\u00ecnh v\u1ebd y b\u00ean? B y = x4 \u2212 2x2 \u2212 2. O A y = x3 \u2212 3x2 \u2212 2. C y = \u2212x3 + 3x2 \u2212 2. D y = \u2212x4 + 2x2 \u2212 2. x \u0253 L\u1eddi gi\u1ea3i. Quan s\u00e1t \u0111\u1ed3 th\u1ecb ta th\u1ea5y \u0111\u1ed3 th\u1ecb c\u00f3 d\u1ea1ng b\u1eadc 4 v\u00e0 a > 0 n\u00ean y = x4 \u2212 2x2 \u2212 2. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 6 (C\u00e2u 9 - M\u0110 104 - BGD&\u0110T - N\u0103m 2018 - 2019). \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y c\u00f3 d\u1ea1ng nh\u01b0 \u0111\u01b0\u1eddng cong trong h\u00ecnh v\u1ebd y b\u00ean? B y = \u22122x4 + 4x2 + 1. A y = 2x3 \u2212 3x + 1. C y = 2x4 \u2212 4x2 + 1. D y = \u22122x3 + 3x + 1. O x \u0253 L\u1eddi gi\u1ea3i. D\u1ea1ng \u0111\u1ed3 th\u1ecb h\u00ecnh b\u00ean l\u00e0 \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 tr\u00f9ng ph\u01b0\u01a1ng y = ax4 + bx2 + c c\u00f3 h\u1ec7 s\u1ed1 a < 0. Do \u0111\u00f3, ch\u1ec9 c\u00f3 \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = \u22122x4 + 4x2 + 1 l\u00e0 th\u1ecfa m\u00e3n. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 7 (C\u00e2u 1 - M\u0110 101 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2019 - 2020). \u0110\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y c\u00f3 d\u1ea1ng \u0111\u01b0\u1eddng cong trong h\u00ecnh v\u1ebd? y Ox A y = x3 \u2212 3x2 + 1. B y = \u2212x3 + 3x2 + 1. C y = \u2212x4 + 2x2 + 1. D y = x4 \u2212 2x2 + 1. \u0253 L\u1eddi gi\u1ea3i. \u0110\u1ed3 th\u1ecb trong h\u00ecnh v\u1ebd c\u1ee7a h\u00e0m b\u1eadc b\u1ed1n, c\u00f3 h\u1ec7 s\u1ed1 a < 0. Ch\u1ecdn \u0111\u00e1p \u00e1n C Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 111 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 8 (C\u00e2u 20 - M\u0110 102 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2019 - 2020). \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 n\u00e0o c\u00f3 d\u1ea1ng nh\u01b0 \u0111\u01b0\u1eddng cong trong h\u00ecnh b\u00ean? y O A y = \u2212x4 + 2x2. B y = \u2212x3 + 3x. C y = x4 \u2212 2x2. D y = x3 \u2212 3x. x \u0253 L\u1eddi gi\u1ea3i. T\u1eeb h\u00ecnh d\u00e1ng \u0111\u1ed3 th\u1ecb ta th\u1ea5y \u0111\u00f3 l\u00e0 \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 b\u1eadc b\u1ed1n tr\u00f9ng ph\u01b0\u01a1ng c\u00f3 h\u1ec7 s\u1ed1 a < 0. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 9 (C\u00e2u 10 - M\u0110 104 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2019 - 2020). \u0110\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y c\u00f3 d\u1ea1ng nh\u01b0 \u0111\u01b0\u1eddng cong trong y h\u00ecnh b\u00ean? A y = x4 \u2212 2x2 + 1. B y = \u2212x3 + 3x2 + 1. O x C y = x3 \u2212 3x2 + 1. D y = \u2212x4 + 2x2 + 1. y x \u0253 L\u1eddi gi\u1ea3i. O H\u00ecnh v\u1ebd b\u00ean l\u00e0 \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 b\u1eadc 4 c\u00f3 h\u1ec7 s\u1ed1 a > 0. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 10 (C\u00e2u 21 - M\u0110 101 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2019 - 2020). \u0110\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y c\u00f3 d\u1ea1ng nh\u01b0 \u0111\u01b0\u1eddng cong trong h\u00ecnh b\u00ean? B y = \u2212x3 + 3x2 \u2212 2. A y = x4 \u2212 2x2 \u2212 2. C y = x3 \u2212 3x2 \u2212 2. D y = \u2212x4 + 2x2 \u2212 2. \u0253 L\u1eddi gi\u1ea3i. D\u1ea1ng \u0111\u1ed3 th\u1ecb l\u00e0 \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m b\u1eadc ba y = ax3 + bx2 + cx + d v\u00e0 lim y = \u2212\u221e (nh\u00e1nh ph\u00eda ngo\u00e0i x\u2192+\u221e b\u00ean ph\u1ea3i \u0111i xu\u1ed1ng) n\u00ean h\u1ec7 s\u1ed1 a < 0. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 11 (C\u00e2u 20 - M\u0110 103 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2019 - 2020). \u0110\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y c\u00f3 d\u1ea1ng nh\u01b0 \u0111\u01b0\u1eddng cong trong h\u00ecnh b\u00ean? Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 112 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 A y = x3 \u2212 3x + 1. B y = x4 \u2212 2x2 + 1. y C y = \u2212x4 + 2x2 + 1. D y = \u2212x3 + 3x + 1. x O \u0253 L\u1eddi gi\u1ea3i. \u0110\u01b0\u1eddng cong nh\u01b0 h\u00ecnh v\u1ebd l\u00e0 \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 b\u1eadc ba c\u00f3 d\u1ea1ng y = ax3 + bx2 + cx + d v\u00e0 c\u00f3 h\u1ec7 s\u1ed1 a > 0. N\u00ean nh\u00ecn \u0111\u00e1p \u00e1n ta th\u1ea5y h\u00e0m s\u1ed1 y = x3 \u2212 3x + 1 th\u1ecfa. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 12 (C\u00e2u 6 - M\u0110 101 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2020 - 2021). \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y c\u00f3 d\u1ea1ng nh\u01b0 \u0111\u01b0\u1eddng cong trong h\u00ecnh y b\u00ean? A y = \u22122x4 + 4x2 \u2212 1. B y = \u2212x3 + 3x \u2212 1. O C y = 2x4 \u2212 4x2 \u2212 1. D y = x3 \u2212 3x \u2212 1. x \u0253 L\u1eddi gi\u1ea3i. \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 nh\u1eadn Oy l\u00e0m tr\u1ee5c \u0111\u1ed1i x\u1ee9ng n\u00ean l\u00e0 \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 b\u1eadc 4 tr\u00f9ng ph\u01b0\u01a1ng v\u00e0 lim y = x\u2192+\u221e \u2212\u221e n\u00ean ch\u1ecdn \u201cy = \u22122x4 + 4x2 \u2212 1\u201d. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 13 (C\u00e2u 15 - M\u0110 102 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2020 - 2021). \u0110\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y c\u00f3 d\u1ea1ng nh\u01b0 \u0111\u01b0\u1eddng cong trong h\u00ecnh b\u00ean? y A y = x3 \u2212 3x + 1. B y = \u22122x4 + 4x2 + 1. C y = \u2212x3 + 3x + 1. D y = 2x4 \u2212 4x2 + 1. x O \u0253 L\u1eddi gi\u1ea3i. \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 b\u00ean l\u00e0 c\u1ee7a h\u00e0m s\u1ed1 b\u1eadc 4 v\u00e0 c\u00f3 h\u1ec7 s\u1ed1 c\u1ee7a x4 d\u01b0\u01a1ng. Do \u0111\u00f3, \u0111\u1ed3 th\u1ecb b\u00ean l\u00e0 c\u1ee7a h\u00e0m s\u1ed1 y = 2x4 \u2212 4x2 + 1. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 14 (C\u00e2u 1 - M\u0110 103 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2020 - 2021). Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 113 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 \u0110\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y c\u00f3 d\u1ea1ng nh\u01b0 \u0111\u01b0\u1eddng cong trong h\u00ecnh y Ox b\u00ean? 1 1 . . A y = \u2212x3 \u2212 2x + 2 B y = x3 \u2212 2x + 2 C y = \u2212x4 + 2x2 + 1 D y = x4 + 2x2 + 1 . . 2 2 \u0253 L\u1eddi gi\u1ea3i. T\u1eeb h\u00ecnh d\u00e1ng \u0111\u1ed3 th\u1ecb, ta th\u1ea5y r\u1eb1ng h\u00e0m s\u1ed1 \u0111\u00e3 cho l\u00e0 h\u00e0m b\u1eadc ba v\u00e0 c\u00f3 h\u1ec7 s\u1ed1 a > 0 n\u00ean h\u00e0m s\u1ed1 th\u1ecfa \u0111\u1ec1 l\u00e0 y = x3 \u2212 2x + 1 . 2 Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 15 (C\u00e2u 11 - M\u0110 101 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2020 - 2021). H\u00e0m s\u1ed1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y c\u00f3 \u0111\u1ed3 th\u1ecb nh\u01b0 \u0111\u01b0\u1eddng cong trong h\u00ecnh b\u00ean? y A y= 3x + 1 B y = x2 + 2x. O . x x+2 C y = 2x3 \u2212 x2. D y = x4 \u2212 2x2. \u0253 L\u1eddi gi\u1ea3i. \u0110\u1ed3 th\u1ecb trong h\u00ecnh v\u1ebd l\u00e0 c\u1ee7a h\u00e0m s\u1ed1 c\u00f3 d\u1ea1ng y = ax4 + bx2 + c v\u1edbi a > 0, n\u00ean ch\u1ecdn ph\u01b0\u01a1ng \u00e1n v\u1edbi h\u00e0m s\u1ed1 y = x4 \u2212 2x2. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 16 (C\u00e2u 10 - M\u0110 102 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2020 - 2021). H\u00e0m s\u1ed1 n\u00e0o c\u00f3 \u0111\u1ed3 th\u1ecb nh\u01b0 h\u00ecnh b\u00ean? y 3x \u2212 1 Ox A y= . B y = x2 \u2212 2x. x+2 C y = 2x3 + x2. D y = \u2212x4 + 2x2. \u0253 L\u1eddi gi\u1ea3i. D\u1ef1a v\u00e0o \u0111\u1ed3 th\u1ecb ta th\u1ea5y h\u00e0m s\u1ed1 c\u00f3 3 \u0111i\u1ec3m c\u1ef1c tr\u1ecb n\u00ean ch\u1ec9 c\u00f3 \u0111\u1ed3 th\u1ecb y = \u2212x4 + 2x2 th\u1ecfa m\u00e3n. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 17 (C\u00e2u 27 - M\u0110 103 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2020 - 2021). Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 114 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 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y c\u00f3 \u0111\u1ed3 th\u1ecb nh\u01b0 \u0111\u01b0\u1eddng cong trong h\u00ecnh b\u00ean? y O A y = \u2212x3 + 3x. B y = x4 \u2212 x2. D y = x2 + x. C y = 2x + 1 . x+2 x \u0253 L\u1eddi gi\u1ea3i. \u0110\u1ed3 th\u1ecb \u0111\u00e3 cho l\u00e0 \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 y = ax3 + bx2 + cx + d v\u1edbi a < 0. Suy ra \u0111\u00f3 l\u00e0 \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 y = \u2212x3 + 3x. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 18 (C\u00e2u 22 - M\u0110 104 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2020 - 2021). H\u00e0m s\u1ed1 n\u00e0o sau \u0111\u00e2y c\u00f3 \u0111\u1ed3 th\u1ecb nh\u01b0 \u0111\u01b0\u1eddng cong trong h\u00ecnh b\u00ean? y 2x \u2212 1 Ox A y = x3 \u2212 3x. B y = x4 + x2. C y = . D y = x2 \u2212 x. x+2 \u0253 L\u1eddi gi\u1ea3i. \u0110\u01b0\u1eddng cong b\u00ean l\u00e0 \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 b\u1eadc 3. V\u1eady h\u00e0m s\u1ed1 c\u00f3 \u0111\u1ed3 th\u1ecb b\u00ean l\u00e0 y = x3 \u2212 3x. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 19 (C\u00e2u 3 - M\u0110 102 - BGD&\u0110T - N\u0103m 2021 - 2022). H\u00e0m s\u1ed1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean nh\u01b0 sau? x \u2212\u221e \u22121 1 +\u221e f (x) +0\u22120+ 2 +\u221e f (x) \u2212\u221e \u22122 A y = \u2212x3 + 3x. B y = x3 \u2212 3x. C y = \u2212x4 + 2x2. D y = x4 \u2212 2x2. \u0253 L\u1eddi gi\u1ea3i. T\u1eeb \u0111\u1ed3 th\u1ecb ta c\u00f3 \u0111\u00e2y l\u00e0 \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 b\u1eadc 3 v\u1edbi h\u1ec7 s\u1ed1 a > 0. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 20 (C\u00e2u 17 - M\u0110 102 - BGD&\u0110T - N\u0103m 2021 - 2022). Cho h\u00e0m s\u1ed1 f (x) = ax4 + bx2 + c c\u00f3 \u0111\u1ed3 th\u1ecb l\u00e0 \u0111\u01b0\u1eddng cong trong y 3 h\u00ecnh v\u1ebd b\u00ean S\u1ed1 nghi\u1ec7m th\u1ef1c c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh f (x) = 1 l\u00e0 2 A 4. B 3. C 2. D 1. O 1 x \u22121 Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 115 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 \u0253 L\u1eddi gi\u1ea3i. S\u1ed1 nghi\u1ec7m th\u1ef1c c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh f (x) = 1 b\u1eb1ng v\u1edbi s\u1ed1 giao \u0111i\u1ec3m c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng (d) : y = 1 v\u00e0 \u0111\u1ed3 th\u1ecb (C) c\u1ee7a h\u00e0m s\u1ed1 y = f (x). D\u1ef1a v\u00e0o h\u00ecnh v\u1ebd, ta th\u1ea5y (d) v\u00e0 (C) c\u1eaft nhau t\u1ea1i hai \u0111i\u1ec3m ph\u00e2n bi\u1ec7t n\u00ean ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00e3 cho c\u00f3 hai nghi\u1ec7m th\u1ef1c ph\u00e2n bi\u1ec7t. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 21 (C\u00e2u 29 - M\u0110 104 - BGD&\u0110T - N\u0103m 2018 - 2019). Cho h\u00e0m s\u1ed1 f (x) c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean nh\u01b0 sau: x \u2212\u221e \u22121 2 +\u221e f (x) +0\u22120+ 2 +\u221e f (x) \u2212\u221e \u22122 S\u1ed1 nghi\u1ec7m th\u1ef1c c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh 2f (x) + 3 = 0 l\u00e0 A 3. B 1. C 2. D 0. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 2f (x) + 3 = 0 \u21d4 f (x) = \u22123. 2 x \u2212\u221e \u22121 2 +\u221e f (x) +0\u22120+ 2 +\u221e f (x) \u22122 y = \u2212 3 \u2212\u221e 2 Nh\u00ecn b\u1ea3ng bi\u1ebfn thi\u00ean ta th\u1ea5y ph\u01b0\u01a1ng tr\u00ecnh n\u00e0y c\u00f3 ba nghi\u1ec7m Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 22 (C\u00e2u 17 - \u0110TK - BGD&\u0110T - l\u1ea7n 2 - N\u0103m 2019 - 2020). Cho h\u00e0m s\u1ed1 b\u1eadc b\u1ed1n y = f (x) c\u00f3 \u0111\u1ed3 th\u1ecb trong h\u00ecnh b\u00ean. S\u1ed1 nghi\u1ec7m y c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh f (x) = \u22121 l\u00e0 1 \u22122 A 3. B 1. C 1. D 4. O 2 x \u22123 \u0253 L\u1eddi gi\u1ea3i. S\u1ed1 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh f (x) = \u22121 l\u00e0 s\u1ed1 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. D\u1ef1a v\u00e0o \u0111\u1ed3 th\u1ecb ta th\u1ea5y \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = f (x) c\u1eaft \u0111\u01b0\u1eddng th\u1eb3ng x = \u22121 t\u1ea1i b\u1ed1n \u0111i\u1ec3m ph\u00e2n bi\u1ec7t. Ch\u1ecdn \u0111\u00e1p \u00e1n D Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 116 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 \u0104 C\u00e2u 23 (C\u00e2u 11 - 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 trong h\u00ecnh y 3 b\u00ean. S\u1ed1 nghi\u1ec7m th\u1ef1c c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh f (x) = 1 l\u00e0 A 0. B 3. C 1. D 2. \u22121 x O1 \u22121 \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 \u0111\u01b0\u1eddng th\u1eb3ng y = 1 c\u1eaft \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = f (x) t\u1ea1i 3 \u0111i\u1ec3m ph\u00e2n bi\u1ec7t n\u00ean ph\u01b0\u01a1ng tr\u00ecnh f (x) = 1 c\u00f3 3 nghi\u1ec7m ph\u00e2n bi\u1ec7t. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 24 (C\u00e2u 4 - M\u0110 104 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2019 - 2020). Cho \u0111\u1ed3 th\u1ecb 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 3 b\u00ean. S\u1ed1 nghi\u1ec7m th\u1ef1c c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh f (x) = 2 l\u00e0 A 0. B 3. C 1. D 2. 1 \u22121 O x \u22121 \u0253 L\u1eddi gi\u1ea3i. \u0110\u01b0\u1eddng th\u1eb3ng y = 2 c\u1eaft \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = f (x) t\u1ea1i 3 \u0111i\u1ec3m ph\u00e2n bi\u1ec7t n\u00ean y ph\u01b0\u01a1ng tr\u00ecnh f (x) = 2 c\u00f3 3 nghi\u1ec7m th\u1ef1c. 3 y=2 1 \u22121 O x \u22121 Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 25 (C\u00e2u 17 - M\u0110 102 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2019 - 2020). Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 117 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 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 h\u00ecnh b\u00ean. y S\u1ed1 nghi\u1ec7m th\u1ef1c c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh f (x) = \u22123 l\u00e0 \u22121 2 O A 4. B 1. C 3. D 2. \u22121 1 x \u22122 \u0253 L\u1eddi gi\u1ea3i. y S\u1ed1 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh f (x) = \u22123 b\u1eb1ng s\u1ed1 giao \u0111i\u1ec3m c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m \u22121 1 2 s\u1ed1 y = f (x) v\u00e0 \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = \u22123 . O x \u22121 2 D\u1ef1a v\u00e0o \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = f (x), ta c\u00f3 s\u1ed1 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh \u2212 3 f (x) = \u22123 b\u1eb1ng 4. 2 \u22122 2 Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 26 (C\u00e2u 25 - M\u0110 102 - BGD&\u0110T - \u0110\u1ee3t 4 - 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 h\u00ecnh b\u00ean. S\u1ed1 y1 \u22121 O 1 x 1 nghi\u1ec7m th\u1ef1c c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh f (x) = l\u00e0 2 A 4. B 2. C 3. D 1. \u0253 L\u1eddi gi\u1ea3i. y y = 1 1 1 2 D\u1ef1a v\u00e0o s\u1ef1 t\u01b0\u01a1ng giao c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = f (x) v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng y = , suy \u22121 O 1 2 1 ra ph\u01b0\u01a1ng tr\u00ecnh f (x) = c\u00f3 4 nghi\u1ec7m ph\u00e2n bi\u1ec7t. 2 x Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 27 (C\u00e2u 28 - M\u0110 104 - 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 0 2 +\u221e \u2212\u221e f (x) \u22120+0\u2212 +\u221e 3 f (x) \u22121 S\u1ed1 giao \u0111i\u1ec3m c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111\u00e3 cho v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng y = 1 l\u00e0 Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 118 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 A 2. B 1. C 3. D 0. Ta v\u1ebd \u0111\u01b0\u1eddng th\u1eb3ng y = 1. \u0253 L\u1eddi gi\u1ea3i. 0 x \u2212\u221e 2 +\u221e f (x) +\u221e \u22120+ 0\u2212 \u2212\u221e y3= 1 f (x) \u22121 \u0110\u01b0\u1eddng th\u1eb3ng y = 1 c\u1eaft \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 t\u1ea1i 3 giao \u0111i\u1ec3m. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 28 (C\u00e2u 2 - \u0110TN - BGD&\u0110T - N\u0103m 2016 - 2017). \u0110\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 y = x4 \u2212 2x2 + 2 v\u00e0 \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 y = \u2212x2 + 4 c\u00f3 t\u1ea5t c\u1ea3 bao nhi\u00eau \u0111i\u1ec3m chung? A 0. B 4. C 1. D 2. \u0253 L\u1eddi gi\u1ea3i. S\u1ed1 giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u1ed3 th\u1ecb ch\u00ednh b\u1eb1ng s\u1ed1 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh ho\u00e0nh \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1. \u221a Ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh ho\u00e0nh \u0111\u1ed9 giao \u0111i\u1ec3m: x4 \u2212 2x2 + 2 = \u2212x2 + 4 \u21d4 x4 \u2212 x2 \u2212 2 = 0 \u21d4 \u00f1x = 2 \u221a. x=\u2212 2 V\u1eady hai \u0111\u1ed3 th\u1ecb c\u00f3 t\u1ea5t c\u1ea3 2 giao \u0111i\u1ec3m. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 29 (C\u00e2u 1 - \u0110TK - BGD&\u0110T - N\u0103m 2016 - 2017). Cho h\u00e0m s\u1ed1 y = x3 \u2212 3x c\u00f3 \u0111\u1ed3 th\u1ecb (C). T\u00ecm s\u1ed1 giao \u0111i\u1ec3m c\u1ee7a (C) v\u00e0 tr\u1ee5c ho\u00e0nh. A 2. B 3. C 1. D 0. \u0253 L\u1eddi gi\u1ea3i. \uf8eex = 0 \u221a X\u00e9t ph\u01b0\u01a1ng tr\u00ecnh ho\u00e0nh \u0111\u1ed9 giao \u0111i\u1ec3m x3 \u2212 3x = 0 \u21d4 x(x2 \u2212 3) = 0 \u21d4 \uf8efx = 3 . \uf8f0\u221a x=\u2212 3 V\u1eady c\u00f3 ba giao \u0111i\u1ec3m. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 30 (C\u00e2u 26 - M\u0110 101 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2019 - 2020). S\u1ed1 giao \u0111i\u1ec3m c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = x3 + 3x2 v\u00e0 \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = 3x2 + 3x l\u00e0 A 3. B 1. C 2. D 0. \u0253 L\u1eddi gi\u1ea3i. Ph\u01b0\u01a1ng tr\u00ecnh ho\u00e0nh \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = x3 + 3x2 v\u00e0 \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = 3x2 + 3x l\u00e0 x3 + 3x2 = 3x2 + 3x \u21d4 x3 \u2212 3x = 0 \u21d4 \u00f1x = 0 \u221a x = \u00b1 3. V\u1eady s\u1ed1 giao \u0111i\u1ec3m c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = x3 + 3x2 v\u00e0 \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = 3x2 + 3x l\u00e0 3. Ch\u1ecdn \u0111\u00e1p \u00e1n A Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 119 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 31 (C\u00e2u 7 - M\u0110 101 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2020 - 2021). \u0110\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 y = \u2212x4 + 4x2 \u2212 3 c\u1eaft tr\u1ee5c tung t\u1ea1i \u0111i\u1ec3m c\u00f3 tung \u0111\u1ed9 b\u1eb1ng A 0. B 3. C 1. D \u22123. \u0253 L\u1eddi gi\u1ea3i. G\u1ecdi M (xM ; yM ) l\u00e0 giao \u0111i\u1ec3m c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = \u2212x4 + 4x2 \u2212 3 v\u00e0 tr\u1ee5c Oy. Ta c\u00f3 xM = 0 \u21d2 yM = \u22123. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 32 (C\u00e2u 18 - M\u0110 102 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2020 - 2021). \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = \u2212x4 \u2212 2x2 + 3 c\u1eaft tr\u1ee5c tung t\u1ea1i \u0111i\u1ec3m c\u00f3 tung \u0111\u1ed9 b\u1eb1ng A 1. B 0. C 2. D 3. \u0253 L\u1eddi gi\u1ea3i. Thay x = 0 v\u00e0o y = \u2212x4 \u2212 2x2 + 3, ta \u0111\u01b0\u1ee3c y = 3. V\u1eady \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111\u00e3 cho c\u1eaft tr\u1ee5c tung t\u1ea1i \u0111i\u1ec3m c\u00f3 tung \u0111\u1ed9 b\u1eb1ng 3. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 33 (C\u00e2u 16 - M\u0110 103 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2020 - 2021). \u0110\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 y = \u2212x3 + 2x2 \u2212 1 c\u1eaft tr\u1ee5c tung t\u1ea1i \u0111i\u1ec3m c\u00f3 tung \u0111\u1ed9 b\u1eb1ng A 3. B 1. C \u22121. D 0. \u0253 L\u1eddi gi\u1ea3i. V\u1edbi x = 0 \u21d2 y = \u22121. V\u1eady \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = \u2212x3 + 2x2 \u2212 1 c\u1eaft tr\u1ee5c tung t\u1ea1i \u0111i\u1ec3m c\u00f3 tung \u0111\u1ed9 b\u1eb1ng \u22121. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 34 (C\u00e2u 26 - M\u0110 104 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2020 - 2021). \u0110\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 y = \u22122x3 + 3x2 \u2212 5 c\u1eaft tr\u1ee5c tung t\u1ea1i \u0111i\u1ec3m c\u00f3 tung \u0111\u1ed9 b\u1eb1ng A \u22125. B 0. C \u22121. D 2. \u0253 L\u1eddi gi\u1ea3i. G\u1ecdi M (0; y) l\u00e0 giao \u0111i\u1ec3m c\u1ee7a \u0111\u1ed3 th\u1ecb v\u00e0 tr\u1ee5c tung. Thay x = 0 v\u00e0 h\u00e0m s\u1ed1 ta \u0111\u01b0\u1ee3c y = \u22125. V\u1eady \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u1eaft tr\u1ee5c tung t\u1ea1i \u0111i\u1ec3m c\u00f3 tung \u0111\u1ed9 b\u1eb1ng \u22125. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 35 (C\u00e2u 26 - M\u0110 101 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2020 - 2021). \u0110i\u1ec3m n\u00e0o d\u01b0\u1edbi \u0111\u00e2y thu\u1ed9c \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = x3 \u2212 x + 2? A \u0110i\u1ec3m M (1; 1). B \u0110i\u1ec3m P (1; 2). C \u0110i\u1ec3m Q(1; 3). D \u0110i\u1ec3m N (1; 0). \u0253 L\u1eddi gi\u1ea3i. Thay ho\u00e0nh \u0111\u1ed9 x = 1 v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh c\u1ee7a h\u00e0m s\u1ed1 ta \u0111\u01b0\u1ee3c y = 13 \u2212 1 + 2 = 2. V\u1eady \u0111i\u1ec3m P (1; 2) thu\u1ed9c \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 36 (C\u00e2u 13 - M\u0110 104 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2020 - 2021). \u0110i\u1ec3m n\u00e0o d\u01b0\u1edbi \u0111\u00e2y thu\u1ed9c \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 y = x3 + x \u2212 1? A Q(1; 3). B M (1; 2). C N (1; 1). D P (1; 0). Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 120 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 \u0253 L\u1eddi gi\u1ea3i. Thay x = 1 v\u00e0o bi\u1ec3u th\u1ee9c h\u00e0m s\u1ed1 ta \u0111\u01b0\u1ee3c y = 1. V\u1eady \u0111i\u1ec3m N (1; 1) l\u00e0 \u0111i\u1ec3m c\u1ea7n t\u00ecm. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 37 (C\u00e2u 5 - M\u0110 101 - BGD&\u0110T - N\u0103m 2016 - 2017). \u0110\u01b0\u1eddng cong \u1edf h\u00ecnh b\u00ean l\u00e0 \u0111\u1ed3 th\u1ecb c\u1ee7a m\u1ed9t trong b\u1ed1n h\u00e0m s\u1ed1 d\u01b0\u1edbi \u0111\u00e2y. y O H\u00e0m s\u1ed1 \u0111\u00f3 l\u00e0 h\u00e0m s\u1ed1 n\u00e0o? B y = x4 \u2212 x2 \u2212 1. x A y = \u2212x3 + x2 \u2212 1. C y = x3 \u2212 x2 \u2212 1. D y = \u2212x4 + x2 \u2212 1. \u0253 L\u1eddi gi\u1ea3i. \u0110\u01b0\u1eddng cong c\u00f3 h\u00ecnh d\u1ea1ng l\u00e0 \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 d\u1ea1ng y = ax4 + bx2 + c v\u1edbi h\u1ec7 s\u1ed1 a > 0. Suy ra n\u00f3 l\u00e0 \u0111\u1ed3 th\u1ecb l\u00e0 c\u1ee7a h\u00e0m s\u1ed1 y = x4 \u2212 x2 \u2212 1. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 38 (C\u00e2u 24 - M\u0110 104 - BGD&\u0110T - N\u0103m 2016 - 2017). Cho h\u00e0m s\u1ed1 y = \u2212x4 + 2x2 c\u00f3 \u0111\u1ed3 th\u1ecb nh\u01b0 h\u00ecnh b\u00ean. T\u00ecm t\u1ea5t c\u1ea3 c\u00e1c gi\u00e1 tr\u1ecb th\u1ef1c c\u1ee7a tham s\u1ed1 m \u0111\u1ec3 y ph\u01b0\u01a1ng tr\u00ecnh \u2212x4 + 2x2 = m c\u00f3 b\u1ed1n nghi\u1ec7m th\u1ef1c ph\u00e2n bi\u1ec7t. 1 A m > 0. B 0 \u2264 m \u2264 1. C 0 < m < 1. D m < 1. \u22121 O 1x \u0253 L\u1eddi gi\u1ea3i. D\u1ef1a v\u00e0o \u0111\u1ed3 th\u1ecb, ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 b\u1ed1n nghi\u1ec7m th\u1ef1c ph\u00e2n bi\u1ec7t khi 0 < m < 1. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 39 (C\u00e2u 11 - \u0110TK - BGD&\u0110T - N\u0103m 2017 - 2018). \u0110\u01b0\u1eddng cong h\u00ecnh b\u00ean l\u00e0 \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y? y A y = \u2212x4 + 2x2 + 2. B y = x4 \u2212 2x2 + 2. C y = x3 \u2212 3x2 + 2. D y = \u2212x3 + 3x2 + 2. Ox \u0253 L\u1eddi gi\u1ea3i. \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111\u00e3 cho l\u00e0 \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 tr\u00f9ng ph\u01b0\u01a1ng y = ax4 + bx2 + c c\u00f3 h\u1ec7 s\u1ed1 a < 0. Trong c\u00e1c h\u00e0m s\u1ed1 \u0111\u00e3 cho ch\u1ec9 c\u00f3 h\u00e0m s\u1ed1 y = \u2212x4 + 2x2 + 2 th\u1ecfa m\u00e3n. Ch\u1ecdn \u0111\u00e1p \u00e1n A Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 121 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 y O \u0104 C\u00e2u 40 (C\u00e2u 11 - \u0110TN - BGD&\u0110T - N\u0103m 2016 - 2017). Cho h\u00e0m s\u1ed1 y = ax3 + bx2 + cx + d c\u00f3 \u0111\u1ed3 th\u1ecb nh\u01b0 h\u00ecnh v\u1ebd b\u00ean. M\u1ec7nh \u0111\u1ec1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y \u0111\u00fang ? A a < 0, b > 0, c > 0, d < 0. B a < 0, b < 0, c > 0, d < 0. C a < 0, b < 0, c < 0, d > 0. D a < 0, b > 0, c < 0, d < 0. x \u0253 L\u1eddi gi\u1ea3i. D\u1ef1a v\u00e0o \u0111\u1ed3 th\u1ecb suy ra h\u1ec7 s\u1ed1 a < 0. Ta c\u00f3 y = 3ax2 + 2bx + c c\u00f3 2 nghi\u1ec7m x1, x2 tr\u00e1i d\u1ea5u (do hai \u0111i\u1ec3m c\u1ef1c tr\u1ecb c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 n\u1eb1m hai ph\u00eda v\u1edbi tr\u1ee5c Oy ) n\u00ean 3ac < 0 \u21d2 c > 0 . Ta c\u00f3: y = 6ax + 2b = 0 \u21d4 x = \u2212b . 3a Ta th\u1ea5y \u0111i\u1ec3m u\u1ed1n l\u00e0 trung \u0111i\u1ec3m c\u1ee7a \u0111o\u1ea1n th\u1eb3ng n\u1ed1i hai \u0111i\u1ec3m c\u1ef1c tr\u1ecb n\u1eb1m b\u00ean ph\u1ea3i tr\u1ee5c tung. Do \u0111\u00f3 x = \u2212b < 0 \u21d2 b < 0 . 3a M\u1eb7t kh\u00e1c \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u1eaft tr\u1ee5c tung t\u1ea1i \u0111i\u1ec3m M (0; d) \u21d2 d < 0 . Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 41 (C\u00e2u 23 - \u0110TK - BGD&\u0110T - N\u0103m 2016 - 2017). \u0110\u01b0\u1eddng cong trong h\u00ecnh v\u1ebd b\u00ean l\u00e0 \u0111\u1ed3 th\u1ecb c\u1ee7a m\u1ed9t h\u00e0m s\u1ed1 trong 4 y h\u00e0m s\u1ed1 \u0111\u01b0\u1ee3c li\u1ec7t k\u00ea \u1edf 4 ph\u01b0\u01a1ng \u00e1n A, B, C, D d\u01b0\u1edbi \u0111\u00e2y. H\u1ecfi \u0111\u00f3 l\u00e0 2 O h\u00e0m s\u1ed1 n\u00e0o? 2x \u2212 1 \u22121 2x + 3 y= . A y= . B x+1 x+1 2x \u2212 2 2x + 1 C y = x\u22121 . D y = x\u22121 . x \u0253 L\u1eddi gi\u1ea3i. 2x + 3 2x \u2212 2 D\u1ef1a v\u00e0o \u0111\u1ed3 th\u1ecb ta th\u1ea5y x = 0 th\u00ec y < 0 n\u00ean lo\u1ea1i hai h\u00e0m s\u1ed1 y = x + 1 v\u00e0 y = x \u2212 1 kh\u00f4ng th\u1ecfa m\u00e3n. 2x + 1 x\u22121 \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u00f3 ti\u1ec7m c\u1eadn \u0111\u1ee9ng l\u00e0 x = \u22121 v\u00e0 ti\u1ec7m c\u1eadn ngang l\u00e0 y =2 n\u00ean h\u00e0m s\u1ed1 y = kh\u00f4ng th\u1ecfa m\u00e3n. 2x \u2212 1 V\u1eady, trong 4 h\u00e0m s\u1ed1 \u0111\u00e3 cho, ch\u1ec9 c\u00f3 h\u00e0m s\u1ed1 y = x+1 th\u1ecfa m\u00e3n. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 42 (C\u00e2u 8 - M\u0110 102 - BGD&\u0110T - N\u0103m 2017 - 2018). Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 122 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 \u0110\u01b0\u1eddng cong trong h\u00ecnh v\u1ebd b\u00ean l\u00e0 \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y? y O A y = x4 \u2212 2x2 \u2212 1. B y = \u2212x4 + 2x2 \u2212 1. C y = x3 \u2212 x2 \u2212 1. D y = \u2212x3 + x2 \u2212 1. x \u0253 L\u1eddi gi\u1ea3i. D\u1ef1a v\u00e0o h\u00ecnh d\u00e1ng \u0111\u1ed3 th\u1ecb ta suy ra h\u00e0m s\u1ed1 l\u00e0 h\u00e0m tr\u00f9ng ph\u01b0\u01a1ng y = ax4 + bx2 + c c\u00f3 \u201c\u0110u\u00f4i th\u0103ng thi\u00ean\u201d n\u00ean a > 0. C\u1eaft tr\u1ee5c tung t\u1ea1i \u0111i\u1ec3m n\u1eb1m ph\u00eda d\u01b0\u1edbi tr\u1ee5c ho\u00e0nh n\u00ean c < 0. C\u00f3 3 c\u1ef1c tr\u1ecb n\u00ean a \u00b7 b < 0 \u21d2 b < 0. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 43 (C\u00e2u 4 - M\u0110 104 - BGD&\u0110T - N\u0103m 2017 - 2018). \u0110\u01b0\u1eddng cong trong h\u00ecnh v\u1ebd b\u00ean l\u00e0 \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y? y A y = x3 \u2212 3x2 \u2212 2. B y = x4 \u2212 x2 \u2212 2. O C y = \u2212x4 + x2 \u2212 2. D y = \u2212x3 + 3x2 \u2212 2. x \u0253 L\u1eddi gi\u1ea3i. Quan s\u00e1t h\u00ecnh v\u1ebd ta th\u1ea5y \u0111\u1ed3 th\u1ecb l\u00e0 c\u1ee7a h\u00e0m b\u1eadc ba v\u00e0 c\u00f3 h\u1ec7 s\u1ed1 a < 0. Suy ra \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111\u00e3 cho l\u00e0 c\u1ee7a h\u00e0m y = \u2212x3 + 3x2 \u2212 2. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 44 (C\u00e2u 10 - M\u0110 102 - BGD&\u0110T - N\u0103m 2018 - 2019). \u0110\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y c\u00f3 d\u1ea1ng nh\u01b0 \u0111\u01b0\u1eddng cong trong y h\u00ecnh v\u1ebd b\u00ean B y = \u2212x3 + 3x + 1. A y = \u2212x4 + 2x2 + 1. C y = x3 \u2212 3x + 1. D y = x4 \u2212 2x2 + 1. Ox \u0253 L\u1eddi gi\u1ea3i. Trong b\u1ed1n h\u00e0m s\u1ed1 \u0111\u00e3 cho th\u00ec ch\u1ec9 c\u00f3 h\u00e0m s\u1ed1 y = \u2212x3 + 3x + 1 (h\u00e0m s\u1ed1 \u0111a th\u1ee9c b\u1eadc ba v\u1edbi h\u1ec7 s\u1ed1 a < 0 ) c\u00f3 d\u1ea1ng \u0111\u1ed3 th\u1ecb nh\u01b0 \u0111\u01b0\u1eddng cong trong h\u00ecnh. Ch\u1ecdn \u0111\u00e1p \u00e1n B Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 123 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 45 (C\u00e2u 9 - \u0110TK - BGD&\u0110T - l\u1ea7n 1 - N\u0103m 2019 - 2020). \u0110\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 n\u00e0o sau \u0111\u00e2y c\u00f3 d\u1ea1ng nh\u01b0 h\u00ecnh cong trong h\u00ecnh y O b\u00ean? B y = x4 \u2212 2x2. A y = \u2212x4 + 2x2. C y = x3 \u2212 3x2. D y = \u2212x3 + 3x2. x \u0253 L\u1eddi gi\u1ea3i. D\u1ef1a v\u00e0o h\u00ecnh d\u1ea1ng c\u1ee7a \u0111\u1ed3 th\u1ecb \u0111\u00e3 cho trong h\u00ecnh v\u1ebd, ta th\u1ea5y \u0111\u00f3 l\u00e0 h\u00ecnh d\u1ea1ng \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 y = ax4 + bx2 + c (a = 0) v\u1edbi h\u1ec7 s\u1ed1 a < 0. Trong b\u1ed1n h\u00e0m s\u1ed1 \u0111\u00e3 cho ch\u1ec9 c\u00f3 h\u00e0m s\u1ed1 y = \u2212x4 + 2x2 th\u1ecfa m\u00e3n. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 46 (C\u00e2u 14 - \u0110TK - BGD&\u0110T - l\u1ea7n 2 - N\u0103m 2019 - 2020). \u0110\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y c\u00f3 d\u1ea1ng nh\u01b0 \u0111\u01b0\u1eddng cong trong h\u00ecnh y b\u00ean? B y = \u2212x3 + 3x. A y = x3 \u2212 3x. C y = x4 \u2212 2x2. D y = \u2212x4 + 2x2. Ox \u0253 L\u1eddi gi\u1ea3i. Nh\u00ecn v\u00e0o \u0111\u1ed3 th\u1ecb c\u00f3 d\u1ea1ng h\u00e0m s\u1ed1 b\u1eadc ba \u0111i qua g\u1ed1c to\u1ea1 \u0111\u1ed9 c\u00f3 h\u1ec7 s\u1ed1 a > 0 n\u00ean lo\u1ea1i c\u00e1c ph\u01b0\u01a1ng \u00e1n y = \u2212x3 + 3x, y = x4 \u2212 2x2 v\u00e0 y = \u2212x4 + 2x2. V\u1eady ch\u1ec9 c\u00f3 \u0111\u00e1p \u00e1n y = x3 \u2212 3x \u0111\u00fang. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 47 (C\u00e2u 45 - M\u0110 101 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2019 - 2020). Cho h\u00e0m s\u1ed1 y = ax3 + bx2 + cx + d (a, b, c, d \u2208 R) c\u00f3 \u0111\u1ed3 th\u1ecb l\u00e0 \u0111\u01b0\u1eddng y cong trong h\u00ecnh b\u00ean. C\u00f3 bao nhi\u00eau s\u1ed1 d\u01b0\u01a1ng trong c\u00e1c s\u1ed1 a, b, c, d? A 4. B 1. C 2. D 3. Ox \u0253 L\u1eddi gi\u1ea3i. T\u1eeb \u0111\u1ed3 th\u1ecb ta th\u1ea5y a < 0 v\u00e0 khi x = 0 th\u00ec \u0111\u1ed3 th\u1ecb c\u1eaft tr\u1ee5c tung t\u1ea1i \u0111i\u1ec3m c\u00f3 tung \u0111\u1ed9 d\u01b0\u01a1ng n\u00ean d > 0. Ta c\u00f3 y = 3ax2 + 2bx + c. \uf8f1 \u22122b > 0 \u00ae\u2212b< \u00aeb c<0 c Do hai \u0111i\u1ec3m c\u1ef1c tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1 \u0111\u1ec1u d\u01b0\u01a1ng n\u00ean suy ra \uf8f4 \u21d2 0 \u21d2 > 0 \uf8f2 3a < 0. \uf8f4 3a >0 \uf8f3 c V\u1eady b,d > 0. Ch\u1ecdn \u0111\u00e1p \u00e1n C Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 124 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 \u0104 C\u00e2u 48 (C\u00e2u 19 - M\u0110 103 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2019 - 2020). \u0110\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y c\u00f3 d\u1ea1ng nh\u01b0 \u0111\u01b0\u1eddng cong nh\u01b0 h\u00ecnh y b\u00ean B y = x3 \u2212 3x2. A y = \u2212x4 + 2x2. C y = x4 \u2212 2x2. D y = \u2212x3 + 3x2. x \u0253 L\u1eddi gi\u1ea3i. Quan s\u00e1t \u0111\u1ed3 th\u1ecb th\u1ecb ta th\u1ea5y \u0111\u00e2y l\u00e0 \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m tr\u00f9ng ph\u01b0\u01a1ng c\u00f3 a > 0 Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 49 (C\u00e2u 48 - M\u0110 104 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2019 - 2020). Cho h\u00e0m s\u1ed1 y = ax3 + bx2 + cx + d (a, b, c,) c\u00f3 \u0111\u1ed3 th\u1ecb l\u00e0 \u0111\u01b0\u1eddng cong y trong h\u00ecnh b\u00ean. C\u00f3 bao nhi\u00eau s\u1ed1 d\u01b0\u01a1ng trong c\u00e1c s\u1ed1 a, b, c, d? A 4. B 2. C 1. D 3. Ox \u0253 L\u1eddi gi\u1ea3i. \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u1eaft tr\u1ee5c tung t\u1ea1i \u0111i\u1ec3m c\u00f3 tung \u0111\u1ed9 d\u01b0\u01a1ng \u21d2 d > 0. lim y < 0 \u21d2 a < 0. x\u2192+\u221e Ta c\u00f3: y = 3ax2 + 2bx + c. \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u00f3 2 \u0111i\u1ec3m c\u1ef1c tr\u1ecb n\u1eb1m v\u1ec1 b\u00ean tr\u00e1i tr\u1ee5c tung n\u00ean ph\u01b0\u01a1ng tr\u00ecnh y = 0 c\u00f3 2 nghi\u1ec7m ph\u00e2n bi\u1ec7t x1 < x2 < 0. \uf8f1 2b \uf8f4\uf8f2x1 + x2 =\u2212 < 0 3a . Khi \u0111\u00f3 theo Viet ta c\u00f3: T\u1eeb \u0111\u00f3 suy ra b < 0 v\u00e0 c < 0. c \uf8f4\uf8f3x1.x2 = 3a > 0 V\u1eady trong c\u00e1c s\u1ed1 a, b, c, d c\u00f3 1 s\u1ed1 d\u01b0\u01a1ng. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 50 (C\u00e2u 45 - M\u0110 101 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2019 - 2020). Cho h\u00e0m s\u1ed1 f (x) = ax3 + bx2 + cx + d (a, b, c, d \u2208 R) c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean nh\u01b0 sau x \u2212\u221e 0 4 +\u221e f (x) +0\u22120+ 3 +\u221e f (x) \u2212\u221e \u22125 C\u00f3 bao nhi\u00eau s\u1ed1 d\u01b0\u01a1ng trong c\u00e1c s\u1ed1 a, b, c, d? A 2. B 3. C 1. D 4. Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t \u0253 L\u1eddi gi\u1ea3i. S\u0110T: 0905.193.688 125","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 (x) = 3ax2 + 2bx + c. D\u1ef1a v\u00e0o b\u1ea3ng bi\u1ebfn thi\u00ean ta th\u1ea5y f (x) = 0 c\u00f3 2 nghi\u1ec7m x = 0 v\u00e0 x = 4 \u21d2 f (x) = 3ax(x \u2212 4) = 3ax2 \u2212 12ax \u21d2 f (x) = ax3 \u2212 6ax2 + d. C\u00e1c \u0111i\u1ec3m A(0; 3) v\u00e0 B(4; \u22125) thu\u1ed9c \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 n\u00ean \u00aed = 3 \uf8f11 \u21d4 \uf8f2a = 4 \u21d2 f (x) = 1 x3 \u2212 3 x2 + 3. \u2212 32a + d = \u22125 \uf8f3d = 3 42 Trong c\u00e1c s\u1ed1 a, b, c, d c\u00f3 2 s\u1ed1 d\u01b0\u01a1ng l\u00e0 a = 1 v\u00e0 d = 3. 4 Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 51 (C\u00e2u 4 - M\u0110 102 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2019 - 2020). \u0110\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y c\u00f3 d\u1ea1ng nh\u01b0 \u0111\u01b0\u1eddng cong trong h\u00ecnh b\u00ean? y A y = \u2212x4 + 2x2 \u2212 1. B y = x4 \u2212 2x2 \u2212 1. C y = x3 \u2212 3x2 \u2212 1. D y = \u2212x3 + 3x2 \u2212 1. O x \u0253 L\u1eddi gi\u1ea3i. Nh\u00ecn v\u00e0o h\u00ecnh d\u00e1ng \u0111\u1ed3 th\u1ecb ta th\u1ea5y r\u1eb1ng \u0111\u00e2y l\u00e0 \u0111\u1ed3 th\u1ecb m\u1ed9t h\u00e0m s\u1ed1 b\u1eadc ba c\u00f3 h\u1ec7 s\u1ed1 a \u00e2m. Trong 4 ph\u01b0\u01a1ng \u00e1n l\u1ef1a ch\u1ecdn, ch\u1ec9 c\u00f3 h\u00e0m s\u1ed1 tho\u1ea3 m\u00e3n l\u00e0 y = \u2212x3 + 3x2 \u2212 1. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 52 (C\u00e2u 18 - M\u0110 102 - BGD&\u0110T - \u0110\u1ee3t 4 - N\u0103m 2019 - 2020). \u0110\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y c\u00f3 d\u1ea1ng nh\u01b0 \u0111\u01b0\u1eddng cong trong h\u00ecnh y Ox b\u00ean? B y = \u2212x3 \u2212 3x. A y = x4 + 2x2. C y = x3 \u2212 3x. D y = \u2212x4 + 2x2. \u0253 L\u1eddi gi\u1ea3i. Ta th\u1ea5y \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u00f3 d\u1ea1ng h\u00e0m b\u1eadc ba n\u00ean lo\u1ea1i y = x4 + 2x2 v\u00e0 y = \u2212x4 + 2x2. L\u1ea1i c\u00f3 lim y = +\u221e n\u00ean h\u1ec7 s\u1ed1 a > 0 do \u0111\u00f3 lo\u1ea1i y = \u2212x3 \u2212 3x. x\u2192+\u221e V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 y = x3 \u2212 3x. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 53 (C\u00e2u 33 - M\u0110 102 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2020 - 2021). Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 126 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 Bi\u1ebft h\u00e0m s\u1ed1 y = x+a (a l\u00e0 c\u00e1c s\u1ed1 th\u1ef1c cho tr\u01b0\u1edbc, a = 1) c\u00f3 \u0111\u1ed3 th\u1ecb y x+1 nh\u01b0 trong h\u00ecnh b\u00ean. M\u1ec7nh \u0111\u1ec1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y \u0111\u00fang? A y < 0, \u2200x \u2208 R. B y > 0, \u2200x = \u22121. C y < 0, \u2200x = \u22121. D y > 0, \u2200x \u2208 R. O x \u0253 L\u1eddi gi\u1ea3i. H\u00e0m s\u1ed1 c\u00f3 t\u1eadp x\u00e1c \u0111\u1ecbnh D = R \\\\ {\u22121}. T\u1eeb \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 ta th\u1ea5y \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u00f3 ti\u1ec7m c\u1eadn \u0111\u1ee9ng. Do \u0111\u00f3 \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 nh\u1eadn \u0111\u01b0\u1eddng th\u1eb3ng x = \u22121 l\u00e0m ti\u1ec7m c\u1eadn \u0111\u1ee9ng. D\u1ef1a v\u00e0o \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 ta c\u0169ng suy ra h\u00e0m s\u1ed1 ngh\u1ecbch bi\u1ebfn tr\u00ean kho\u1ea3ng (\u2212\u221e; \u22121) v\u00e0 (\u22121; +\u221e). V\u1eady y < 0, \u2200x = \u22121. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 54 (C\u00e2u 38 - M\u0110 103 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2020 - 2021). Bi\u1ebft h\u00e0m s\u1ed1 y = x+a (a l\u00e0 s\u1ed1 th\u1ef1c cho tr\u01b0\u1edbc, a = \u22121) c\u00f3 \u0111\u1ed3 y x\u22121 th\u1ecb nh\u01b0 trong h\u00ecnh b\u00ean. M\u1ec7nh \u0111\u1ec1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y \u0111\u00fang? A y > 0, \u2200x = 1. B y > 0, \u2200x \u2208 R. C y < 0, \u2200x \u2208 R. D y < 0, \u2200x = 1. Ox \u0253 L\u1eddi gi\u1ea3i. H\u00e0m s\u1ed1 x\u00e1c \u0111\u1ecbnh khi v\u00e0 ch\u1ec9 x = 1. T\u1eeb \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 suy ra lim x + a = \u2212\u221e, x\u21921+ x \u2212 1 k\u00e9o theo a + 1 < 0. =\u2212 a+1 V\u1eady y (x \u2212 1)2 > 0 v\u1edbi m\u1ecdi x = 1. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 55 (C\u00e2u 2 - M\u0110 104 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2020 - 2021). \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y c\u00f3 d\u1ea1ng nh\u01b0 \u0111\u01b0\u1eddng cong trong h\u00ecnh y O b\u00ean? B y = x4 + 4x2 + 1. A y = x3 \u2212 3x + 1. C y = \u2212x3 + 3x + 1. D y = \u2212x4 + 2x2 + 1. x Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 127 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 \u0253 L\u1eddi gi\u1ea3i. D\u1ef1a v\u00e0o \u0111\u1ed3 th\u1ecb ta th\u1ea5y \u0111\u00e2y l\u00e0 h\u00e0m s\u1ed1 b\u1eadc 3 c\u00f3 h\u1ec7 s\u1ed1 a < 0 n\u00ean \u0111\u1ed3 th\u1ecb n\u00e0y l\u00e0 \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 y = \u2212x3 + 3x + 1. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 56 (C\u00e2u 33 - M\u0110 104 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2020 - 2021). Bi\u1ebft h\u00e0m s\u1ed1 y = x+a (a l\u00e0 s\u1ed1 th\u1ef1c cho tr\u01b0\u1edbc, a = \u22121) c\u00f3 y x\u22121 \u0111\u1ed3 th\u1ecb nh\u01b0 trong h\u00ecnh b\u00ean. M\u1ec7nh \u0111\u1ec1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y \u0111\u00fang? A y < 0, \u2200x \u2208 R. B y < 0, \u2200x = 1. C y > 0, \u2200x \u2208 R. D y > 0, \u2200x = 1. MDD-109 x O \u0253 L\u1eddi gi\u1ea3i. T\u1eadp x\u00e1c \u0111\u1ecbnh c\u1ee7a h\u00e0m s\u1ed1 l\u00e0 D = R \\\\ {1} v\u00e0 y \u22121 \u2212 a = 0, \u2200x = 1. = (x \u2212 1)2 T\u1eeb \u0111\u1ed3 th\u1ecb, ta th\u1ea5y h\u00e0m s\u1ed1 ngh\u1ecbch bi\u1ebfn tr\u00ean t\u1eebng kho\u1ea3ng x\u00e1c \u0111\u1ecbnh. T\u1eeb \u0111\u00f3 suy ra y = \u22121 \u2212 a < 0, \u2200x = 1. (x \u2212 1)2 Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 57 (C\u00e2u 13 - M\u0110 101 - BGD&\u0110T - N\u0103m 2021 - 2022). H\u00e0m s\u1ed1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean nh\u01b0 sau? x \u2212\u221e \u22121 1 +\u221e f (x) +0\u22120+ f (x) 2 +\u221e \u2212\u221e \u22122 A y = x4 \u2212 2x2. B y = \u2212x3 + 3x. C y = \u2212x4 + 2x2. D y = x3 \u2212 3x. \u0253 L\u1eddi gi\u1ea3i. T\u1eeb b\u1ea3ng bi\u1ebfn thi\u00ean ta c\u00f3 lim y = \u2212\u221e n\u00ean lo\u1ea1i y = x4 \u2212 2x2 v\u00e0 y = \u2212x3 + 3x. x\u2192+\u221e C\u00f3 lim y = +\u221e n\u00ean lo\u1ea1i y = \u2212x4 + 2x2. Ch\u1ecdn y = x3 \u2212 3x. x\u2192+\u221e Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 58 (C\u00e2u 1 - M\u0110 103 - BGD&\u0110T - N\u0103m 2021 - 2022). H\u00e0m s\u1ed1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean nh\u01b0 sau: Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 128 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 \u22121 1 +\u221e y \u22120+0\u2212 +\u221e 2 y \u22122 \u2212\u221e A y = x3 \u2212 3x. B y = \u2212x3 + 3x. C y = x2 \u2212 2x. D y = \u2212x2 + 2x. \u0253 L\u1eddi gi\u1ea3i. D\u1ef1a v\u00e0o b\u1ea3ng bi\u1ebfn thi\u00ean ta nh\u1eadn th\u1ea5y: \u0110\u00e2y l\u00e0 h\u00e0m s\u1ed1 d\u1ea1ng y = ax3 + bx2 + cx + d, (a = 0). C\u00f3 lim y = \u2212\u221e suy ra a < 0. x\u2192+\u221e V\u1eady h\u00e0m s\u1ed1 th\u1ecfa m\u00e3n l\u00e0 y = \u2212x3 + 3x. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 59 (C\u00e2u 8 - M\u0110 104 - BGD&\u0110T - N\u0103m 2021 - 2022). H\u00e0m s\u1ed1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean nh\u01b0 sau? x \u2212\u221e \u22121 1 +\u221e y \u22120+0\u2212 +\u221e 2 y \u22122 \u2212\u221e A y = x3 \u2212 3x. B y = x2 \u2212 2x. C y = \u2212x3 + 3x. D y = \u2212x2 + 2x. \u0253 L\u1eddi gi\u1ea3i. D\u1ef1a v\u00e0o b\u1ea3ng bi\u1ebfn thi\u00ean tr\u00ean, ta nh\u1eadn th\u1ea5y \u0111\u00e2y l\u00e0 h\u00e0m s\u1ed1 b\u1eadc ba c\u00f3 d\u1ea1ng y = ax3 + bx2 + cx + d v\u1edbi a = 0. M\u00e0 lim ax3 + bx2 + cx + d = \u2212\u221e \u21d2 a < 0. x\u2192+\u221e Do \u0111\u00f3 c\u00f3 duy nh\u1ea5t h\u00e0m s\u1ed1 y = \u2212x3 + 3x tho\u1ea3 m\u00e3n. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 60 (C\u00e2u 5 - \u0110TN - BGD&\u0110T - N\u0103m 2016 - 2017). Cho h\u00e0m s\u1ed1 y = f (x) x\u00e1c \u0111\u1ecbnh tr\u00ean R \\\\ {0}, li\u00ean t\u1ee5c tr\u00ean m\u1ed7i kho\u1ea3ng x\u00e1c \u0111\u1ecbnh v\u00e0 c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean nh\u01b0 sau. x \u2212\u221e 0 1 +\u221e y\u2212 +0\u2212 +\u221e 2 y \u22121 \u2212\u221e \u2212\u221e T\u00ecm t\u1eadp h\u1ee3p t\u1ea5t c\u1ea3 c\u00e1c gi\u00e1 tr\u1ecb c\u1ee7a tham s\u1ed1 th\u1ef1c m sao cho ph\u01b0\u01a1ng tr\u00ecnh f (x) = m c\u00f3 ba nghi\u1ec7m Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 129 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 th\u1ef1c ph\u00e2n bi\u1ec7t. B (\u22121; 2). C (\u22121; 2]. D (\u2212\u221e; 2]. A [\u22121; 2]. \u0253 L\u1eddi gi\u1ea3i. D\u1ef1a v\u00e0o b\u1ea3ng bi\u1ebfn thi\u00ean \u0111\u00e3 cho, ph\u01b0\u01a1ng tr\u00ecnh f (x) = m c\u00f3 ba nghi\u1ec7m ph\u00e2n bi\u1ec7t khi v\u00e0 ch\u1ec9 khi\u22121 < m < 2 hay m \u2208 (\u22121; 2) v\u00ec l\u00fac \u0111\u00f3, \u0111\u01b0\u1eddng th\u1eb3ng y = m c\u1eaft \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = f (x) t\u1ea1i ba \u0111i\u1ec3m ph\u00e2n bi\u1ec7t. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 61 (C\u00e2u 17 - \u0110TK - BGD&\u0110T - N\u0103m 2017 - 2018). Cho h\u00e0m s\u1ed1 y = f (x) c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean nh\u01b0 h\u00ecnh x \u2212\u221e \u22121 3 +\u221e v\u1ebd. S\u1ed1 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh f (x)\u22122 = 0 l\u00e0 A 0. B 3. C 1. D 2. y +0\u22120+ y 4 +\u221e \u2212\u221e \u22122 \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 f (x) \u2212 2 = 0 \u21d4 f (x) = 2. V\u00ec \u22122 < 2 < 4 n\u00ean t\u1eeb b\u1ea3ng bi\u1ebfn thi\u00ean suy ra ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 3 nghi\u1ec7m ph\u00e2n bi\u1ec7t. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 62 (C\u00e2u 16 - M\u0110 102 - BGD&\u0110T - N\u0103m 2017 - 2018). Cho h\u00e0m s\u1ed1 f (x) = ax4 + bx2 + c (a, b, c \u2208 R). \u0110\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 y = f (x) y nh\u01b0 h\u00ecnh v\u1ebd b\u00ean. S\u1ed1 nghi\u1ec7m th\u1ef1c c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh 4f (x) \u2212 3 = 0 l\u00e0 1 A 4. B 3. C 2. D 0. \u22121 O 1x \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 4f (x) \u2212 3 = 0 \u21d4 f (x) = 3 y . 4 1 S\u1ed1 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 s\u1ed1 giao \u0111i\u1ec3m c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = f (x) O 3 y = 3 v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng y = . 4 4 D\u1ef1a v\u00e0o \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = f (x), suy ra s\u1ed1 nghi\u1ec7m ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 4. \u22121 1x Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 63 (C\u00e2u 24 - M\u0110 104 - BGD&\u0110T - N\u0103m 2017 - 2018). Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 130 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 y = f (x) li\u00ean t\u1ee5c tr\u00ean \u0111o\u1ea1n [\u22122; 4] v\u00e0 c\u00f3 \u0111\u1ed3 th\u1ecb nh\u01b0 h\u00ecnh v\u1ebd y b\u00ean. S\u1ed1 nghi\u1ec7m th\u1ef1c c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh 3f (x) \u2212 5 = 0 tr\u00ean \u0111o\u1ea1n [\u22122; 4] 6 l\u00e0 2 A 0. B 3. C 2. D 1. 1 2 4x \u22122 O \u22123 \u0253 L\u1eddi gi\u1ea3i. 5 y Ph\u01b0\u01a1ng tr\u00ecnh f (x) = . 6 3 S\u1ed1 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh n\u00e0y l\u00e0 s\u1ed1 giao \u0111i\u1ec3m c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = f (x) v\u00e0 2 1 5 \u22122 \u0111\u01b0\u1eddng th\u1eb3ng y = . Quan s\u00e1t h\u00ecnh b\u00ean ta th\u1ea5y c\u00f3 3 giao \u0111i\u1ec3m do \u0111\u00f3 ph\u01b0\u01a1ng O 3 tr\u00ecnh \u0111\u00e3 cho c\u00f3 ba nghi\u1ec7m. 2 4x Ch\u1ecdn \u0111\u00e1p \u00e1n B \u22123 \u0104 C\u00e2u 64 (C\u00e2u 21 - \u0110MH - BGD&\u0110T - N\u0103m 2018 - 2019). +\u221e Cho h\u00e0m s\u1ed1 y = f (x) c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean nh\u01b0 sau + x \u2212\u221e \u22122 0 2 +\u221e y \u22120+0\u22120 D 1. +\u221e 1 y \u22122 \u22122 S\u1ed1 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh 2f (x) + 3 = 0 l\u00e0 A 4. B 3. C 2. \u0253 L\u1eddi gi\u1ea3i. 2f (x) + 3 = 0 \u21d4 f (x) = \u22123 . 2 S\u1ed1 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 s\u1ed1 giao \u0111i\u1ec3m c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = f (x) v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng y = \u22123 . 2 M\u00e0 \u22122 < \u22123 < 1 n\u00ean s\u1ed1 nghi\u1ec7m th\u1ef1c c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh 2f (x) + 3 = 0 l\u00e0 4. 2 Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 65 (C\u00e2u 16 - M\u0110 101 - BGD&\u0110T - N\u0103m 2018 - 2019). Cho h\u00e0m s\u1ed1 f (x) c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean nh\u01b0 sau: Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 131 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 \u22122 0 2 +\u221e f (x) +0\u22120+0\u2212 33 f (x) \u22121 \u2212\u221e \u2212\u221e S\u1ed1 nghi\u1ec7m th\u1ef1c c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh 2f (x) \u2212 3 = 0 l\u00e0 A 2. B 1. C 4. D 3. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 2f (x) \u2212 3 = 0 \u21d4 f (x) = 3 . 2 3 S\u1ed1 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh b\u1eb1ng s\u1ed1 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 D\u1ef1a v\u00e0o b\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a f (x) ta c\u00f3 s\u1ed1 giao \u0111i\u1ec3m c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = f (x) v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng 3 y = l\u00e0 4. Do \u0111\u00f3 ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00e3 cho c\u00f3 4 nghi\u1ec7m. 2 Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 66 (C\u00e2u 23 - \u0110TK - BGD&\u0110T - l\u1ea7n 1 - 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 2 3 +\u221e y +0\u22120+ 1 +\u221e y \u2212\u221e 0 S\u1ed1 nghi\u1ec7m th\u1ef1c c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh 3f (x) \u2212 2 = 0l\u00e0 A 2. B 0. C 3. D 1. \u0253 L\u1eddi gi\u1ea3i. Ph\u01b0\u01a1ng tr\u00ecnh 3f (x) \u2212 2 = 0 \u21d4 f (x) = 2 . 3 2 Nh\u1eadn x\u00e9t: S\u1ed1 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh ch\u00ednh l\u00e0 s\u1ed1 giao \u0111i\u1ec3m c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng y = v\u00e0 \u0111\u1ed3 th\u1ecb h\u00e0m 3 s\u1ed1 y = f (x). 2 D\u1ef1a v\u00e0o b\u1ea3ng bi\u1ebfn thi\u00ean ta th\u1ea5y \u0111\u01b0\u1eddng th\u1eb3ng y = c\u1eaft \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = f (x) t\u1ea1i 3 \u0111i\u1ec3m ph\u00e2n bi\u1ec7t 3 2 n\u00ean ph\u01b0\u01a1ng tr\u00ecnh f (x) = c\u00f3 3 nghi\u1ec7m. 3 V\u1eady ph\u01b0\u01a1ng tr\u00ecnh 3f (x) \u2212 2 = 0 c\u00f3 3 nghi\u1ec7m th\u1ef1c ph\u00e2n bi\u1ec7t. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 67 (C\u00e2u 30 - \u0110TK - BGD&\u0110T - l\u1ea7n 2 - N\u0103m 2019 - 2020). S\u1ed1 giao \u0111i\u1ec3m c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = x3 \u2212 3x + 1 v\u00e0 tr\u1ee5c ho\u00e0nh l\u00e0 A 3. B 0. C 2. D 1. Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t \u0253 L\u1eddi gi\u1ea3i. S\u0110T: 0905.193.688 132","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\u00e9t y = x3 \u2212 3x + 1 c\u00f3 y = 3x2 \u2212 3 = 3(x2 \u2212 1). T\u1ea1i y = 0 \u21d4 x = \u00b11. Ta c\u00f3 c\u00e1c gi\u1edbi h\u1ea1n lim = \u2212\u221e v\u00e0 lim = +\u221e. x\u2192\u2212\u221e x\u2192+\u221e B\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a h\u00e0m s\u1ed1. x \u2212\u221e \u22121 1 +\u221e y +0\u22120+ 3 +\u221e \u22121 y \u2212\u221e T\u1eeb b\u1ea3ng bi\u1ebfn thi\u00ean, ta th\u1ea5y h\u00e0m s\u1ed1 y = x3 \u2212 3x + 1 c\u1eaft tr\u1ee5c ho\u00e0nh t\u1ea1i ba \u0111i\u1ec3m ph\u00e2n bi\u1ec7t. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 68 (C\u00e2u 16 - 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 nh\u01b0 h\u00ecnh v\u1ebd b\u00ean. y 2 S\u1ed1 nghi\u1ec7m th\u1ef1c c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh f (x) = \u22121 l\u00e0 1 A 3. B 1. C 0. D 2. \u22121 0 x \u22122 \u0253 L\u1eddi gi\u1ea3i. S\u1ed1 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh f (x) = \u22121 b\u1eb1ng s\u1ed1 giao \u0111i\u1ec3m c\u1ee7a \u0111\u01b0\u1eddng cong f (x) v\u1edbi \u0111\u01b0\u1eddng th\u1eb3ng y = \u22121. y 2 1 x \u22121 0 \u22122 Nh\u00ecn v\u00e0o h\u00ecnh ta th\u1ea5y c\u00f3 3 giao \u0111i\u1ec3m n\u00ean c\u00f3 3 nghi\u1ec7m. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 69 (C\u00e2u 33 - M\u0110 102 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2019 - 2020). S\u1ed1 giao \u0111i\u1ec3m c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = x3 \u2212 x2 v\u00e0 \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = \u2212x2 + 5x l\u00e0 A 2. B 3. C 1. D 0. \u0253 L\u1eddi gi\u1ea3i. Ph\u01b0\u01a1ng tr\u00ecnh ho\u00e0nh \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u1ed3 th\u1ecb l\u00e0 x3 \u2212 x2 = \u2212x2 + 5x \u21d4 x3 \u2212 5x = 0 \u21d4 \u00f1x = 0 \u221a x = \u00b1 5. Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 133 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\u1eady s\u1ed1 giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u1ed3 th\u1ecb l\u00e0 3. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 70 (C\u00e2u 15 - M\u0110 103 - 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 b\u00ean. S\u1ed1 y 2 nghi\u1ec7m th\u1ef1c c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh f (x) = 1 l\u00e0 \u22121 A 1. B 0. C 2. D 3. 1 x \u22122 \u0253 L\u1eddi gi\u1ea3i. X\u00e9t ph\u01b0\u01a1ng tr\u00ecnh ho\u00e0nh \u0111\u1ed9 giao \u0111i\u1ec3m f (x) = 1 y y=1 T\u1eeb \u0111\u1ed3 th\u1ecb ta v\u1ebd th\u00eam \u0111\u01b0\u1eddng th\u1eb3ng y = 1 ta c\u00f3 h\u00ecnh v\u1ebd b\u00ean. 2 x V\u00ec \u0111\u01b0\u1eddng th\u1eb3ng y = 1 c\u1eaft \u0111\u1ed3 th\u1ecb t\u1ea1i ba \u0111i\u1ec3m ph\u00e2n bi\u1ec7t n\u00ean ph\u01b0\u01a1ng tr\u00ecnh f (x) = 1 c\u00f3 ba nghi\u1ec7m ph\u00e2n bi\u1ec7t \u22121 1 \u22122 Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 71 (C\u00e2u 25 - M\u0110 103 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2019 - 2020). Cho h\u00e0m s\u1ed1 b\u1eadc b\u1ed1n c\u00f3 \u0111\u1ed3 th\u1ecb l\u00e0 \u0111\u01b0\u1eddng cong trong h\u00ecnh b\u00ean. S\u1ed1 y 2 1 nghi\u1ec7m th\u1ef1c c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh f (x) = l\u00e0 2 A 2. B 4. C 1. D 3. 1 x \u22121 O 1 \u0253 L\u1eddi gi\u1ea3i. y 2 1 K\u1ebb \u0111\u01b0\u1eddng th\u1eb3ng y = . 1 1 \u22121 O y= 2 1 2 x D\u1ef1a v\u00e0o \u0111\u1ed3 th\u1ecb ta th\u1ea5y \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 f (x) v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng y = 2 c\u00f3 2 giao \u0111i\u1ec3m. 1 V\u1eady ph\u01b0\u01a1ng tr\u00ecnh f (x) = c\u00f3 2 nghi\u1ec7m th\u1ef1c. 2 1 Ch\u1ecdn \u0111\u00e1p \u00e1n A 134 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 \u0104 C\u00e2u 72 (C\u00e2u 27 - M\u0110 103 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2019 - 2020). S\u1ed1 giao \u0111i\u1ec3m c\u1ee7a y = \u2212x3 + 3x v\u1edbi tr\u1ee5c ho\u00e0nh l\u00e0 A 2. B 0. C 3. D 1. \u0253 L\u1eddi gi\u1ea3i. Ph\u01b0\u01a1ng tr\u00ecnh ho\u00e0nh \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a \u0111\u1ed3 th\u1ecb (C) : y = \u2212x3 + 3x v\u00e0 tr\u1ee5c Ox l\u00e0 \uf8eex = 0 \u221a \u2212x3 + 3x = 0 \u21d4 \uf8efx = 3 \uf8f0\u221a x = \u2212 3. Ph\u01b0\u01a1ng tr\u00ecnh ho\u00e0nh \u0111\u1ed9 giao \u0111i\u1ec3m c\u00f3 3 nghi\u1ec7m ph\u00e2n bi\u1ec7t suy ra (C) v\u00e0 Ox c\u00f3 3 \u0111i\u1ec3m chung. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 73 (C\u00e2u 15 - M\u0110 101 - BGD&\u0110T - N\u0103m 2021 - 2022). Cho h\u00e0m s\u1ed1 f (x) = ax4 + bx2 + c c\u00f3 \u0111\u1ed3 th\u1ecb l\u00e0 \u0111\u01b0\u1eddng cong trong h\u00ecnh y 3 b\u00ean. S\u1ed1 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh f (x) = 1 l\u00e0 A 1. B 2. C 4. D 3. \u22121 O 1 x \u0253 L\u1eddi gi\u1ea3i. y 3 K\u1ebb \u0111\u01b0\u1eddng th\u1eb3ng y = 1 c\u1eaft \u0111\u1ed3 th\u1ecb y = f (x) t\u1ea1i 2 \u0111i\u1ec3m ph\u00e2n bi\u1ec7t n\u00ean ph\u01b0\u01a1ng tr\u00ecnh f (x) = 1 c\u00f3 2 nghi\u1ec7m ph\u00e2n bi\u1ec7t. y=1 \u22121 O 1 x Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 74 (C\u00e2u 8 - M\u0110 103 - 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 0 2 +\u221e \u2212\u221e y \u22120+0\u2212 +\u221e 3 y \u22121 S\u1ed1 giao \u0111i\u1ec3m c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111\u00e3 cho v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng y = 1 l\u00e0 A 1. B 0. C 2. D 3. \u0253 L\u1eddi gi\u1ea3i. D\u1ef1a v\u00e0o b\u1ea3ng bi\u1ebfn thi\u00ean ta th\u1ea5y \u0111\u01b0\u1eddng th\u1eb3ng y = 1 c\u1eaft \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 t\u1ea1i 3 \u0111i\u1ec3m. Ch\u1ecdn \u0111\u00e1p \u00e1n D Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 135 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 75 (C\u00e2u 29 - M\u0110 103 - BGD&\u0110T - N\u0103m 2021 - 2022). Cho h\u00e0m s\u1ed1 f (x) = ax4 + bx2 + c c\u00f3 \u0111\u1ed3 th\u1ecb l\u00e0 \u0111\u01b0\u1eddng cong trong h\u00ecnh y b\u00ean. C\u00f3 bao nhi\u00eau gi\u00e1 tr\u1ecb nguy\u00ean thu\u1ed9c \u0111o\u1ea1n [\u22122; 5] c\u1ee7a tham s\u1ed1 m \u22121 1 O \u22121 \u0111\u1ec3 ph\u01b0\u01a1ng tr\u00ecnh f (x) = m c\u00f3 \u0111\u00fang 2 nghi\u1ec7m th\u1ef1c ph\u00e2n bi\u1ec7t? \u22122 A 1. B 6. C 7. D 5. x \u0253 L\u1eddi gi\u1ea3i. S\u1ed1 nghi\u1ec7m ph\u01b0\u01a1ng tr\u00ecnh f (x) = m l\u00e0 s\u1ed1 giao \u0111i\u1ec3m c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = f (x) v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng y = m. \u00f1m = \u22122 Suy ra ph\u01b0\u01a1ng tr\u00ecnh f (x) = m c\u00f3 \u0111\u00fang hai nghi\u1ec7m th\u1ef1c ph\u00e2n bi\u1ec7t \u21d4 m > \u22121. Do m \u2208 Z \u21d2 m \u2208 {\u22122; 0; 1; 2; 3; 4; 5}. V\u1eady c\u00f3 7 gi\u00e1 tr\u1ecb m th\u1ecfa m\u00e3n y\u00eau c\u1ea7u b\u00e0i to\u00e1n. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 76 (C\u00e2u 36 - M\u0110 104 - BGD&\u0110T - N\u0103m 2021 - 2022). Cho h\u00e0m s\u1ed1 f (x) = ax4 + bx2 + c c\u00f3 \u0111\u1ed3 th\u1ecb l\u00e0 \u0111\u01b0\u1eddng cong trong h\u00ecnh y b\u00ean. C\u00f3 bao nhi\u00eau gi\u00e1 tr\u1ecb nguy\u00ean thu\u1ed9c \u0111o\u1ea1n [\u22122; 5] c\u1ee7a tham s\u1ed1 m \u0111\u1ec3 ph\u01b0\u01a1ng tr\u00ecnh f (x) = m c\u00f3 \u0111\u00fang 2 nghi\u1ec7m th\u1ef1c ph\u00e2n bi\u1ec7t? A 7. B 6. C 5. D 1. \u22121 O 1 \u22121 x \u22122 \u0253 L\u1eddi gi\u1ea3i. \u00aem = \u22122 Ta c\u00f3 y\u00eau c\u1ea7u b\u00e0i to\u00e1n t\u01b0\u01a1ng \u0111\u01b0\u01a1ng v\u1edbi m > \u22121. Do m \u2208 [\u22122; 5] v\u00e0 m nguy\u00ean n\u00ean c\u00f3 7 gi\u00e1 tr\u1ecb m c\u1ea7n t\u00ecm l\u00e0 \u22122, 0, 1, 2, 3, 4, 5. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 77 (C\u00e2u 7 - \u0110MH - BGD&\u0110T - N\u0103m 2016 - 2017). Bi\u1ebft r\u1eb1ng \u0111\u01b0\u1eddng th\u1eb3ng y = \u22122x + 2 c\u1eaft \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = x3 + x + 2 t\u1ea1i \u0111i\u1ec3m duy nh\u1ea5t; k\u00ed hi\u1ec7u (x\u25e6; y\u25e6) l\u00e0 t\u1ecda \u0111\u1ed9 c\u1ee7a \u0111i\u1ec3m \u0111\u00f3. T\u00ecm y\u25e6. A y\u25e6 = 4. B y\u25e6 = 0. C y\u25e6 = 2. D y\u25e6 = \u22121. \u0253 L\u1eddi gi\u1ea3i. Ph\u01b0\u01a1ng tr\u00ecnh ho\u00e0nh \u0111\u1ed9 giao \u0111i\u1ec3m x3 + x + 2 = \u22122x + 2 \u21d4 x3 + 3x = 0 \u21d4 x = 0, Suy ra y(0) = 2. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 78 (C\u00e2u 22 - M\u0110 103 - BGD&\u0110T - N\u0103m 2017 - 2018). Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 136 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 y = f (x) li\u00ean t\u1ee5c tr\u00ean [\u22122; 2] v\u00e0 c\u00f3 \u0111\u1ed3 th\u1ecb nh\u01b0 h\u00ecnh v\u1ebd y 3 b\u00ean. S\u1ed1 nghi\u1ec7m th\u1ef1c c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh 3f (x) \u2212 4 = 0 tr\u00ean \u0111o\u1ea1n [\u22122; 2] l\u00e0 A 3. B 1. C 2. D 4. \u22122 O 1 \u22121 2x \u22121 \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 3f (x) \u2212 4 = 0 \u21d4 f (x) = 4 . 3 4 D\u1ef1a v\u00e0o \u0111\u1ed3 th\u1ecb, ta th\u1ea5y \u0111\u01b0\u1eddng th\u1eb3ng y = c\u1eaft y = f (x) t\u1ea1i 3 \u0111i\u1ec3m ph\u00e2n bi\u1ec7t n\u00ean ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00e3 3 cho c\u00f3 3 nghi\u1ec7m ph\u00e2n bi\u1ec7t. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 79 (C\u00e2u 23 - M\u0110 102 - BGD&\u0110T - N\u0103m 2018 - 2019). Cho h\u00e0m s\u1ed1 f (x) c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean nh\u01b0 sau x \u2212\u221e \u22122 0 2 +\u221e f (x) \u22120+0\u22120+ +\u221e 2 +\u221e f (x) \u22121 \u22121 S\u1ed1 nghi\u1ec7m th\u1ef1c c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh 3f (x) \u2212 5 = 0 l\u00e0 A 2. B 3. C 4. D 0. \u0253 L\u1eddi gi\u1ea3i. X\u00e9t ph\u01b0\u01a1ng tr\u00ecnh 3f (x) \u2212 5 = 0 \u21d4 f (x) = 5 . 3 S\u1ed1 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh b\u1eb1ng s\u1ed1 giao \u0111i\u1ec3m c\u1ee7a \u0111\u1ed3 th\u1ecb (C) c\u1ee7a h\u00e0m s\u1ed1 y = f (x) v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng 5 d: y = . 3 D\u1ef1a v\u00e0o b\u1ea3ng bi\u1ebfn thi\u00ean ta th\u1ea5y \u0111\u01b0\u1eddng th\u1eb3ng d c\u1eaft \u0111\u1ed3 th\u1ecb (C) t\u1ea1i b\u1ed1n \u0111i\u1ec3m ph\u00e2n bi\u1ec7t n\u00ean ph\u01b0\u01a1ng tr\u00ecnh 3f (x) \u2212 5 = 0 c\u00f3 b\u1ed1n nghi\u1ec7m ph\u00e2n bi\u1ec7t. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 80 (C\u00e2u 38 - M\u0110 103 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2019 - 2020). S\u1ed1 giao \u0111i\u00eam c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = x3 + x2 v\u00e0 \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = x2 + 5x. A 3. B 0. C 1. D 2. \u0253 L\u1eddi gi\u1ea3i. Ph\u01b0\u01a1ng tr\u00ecnh ho\u00e0nh \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a y = x3 + x2 v\u00e0 y = x2 + 5x l\u00e0 \u00ef x = 0\u221a x = \u00b1 5. x3 + x2 = x2 + 5x \u21d4 x3 \u2212 5x = 0 \u21d4 V\u1eady \u0111\u1ed3 th\u1ecb y = x3 + x2 v\u00e0 \u0111\u1ed3 th\u1ecb y = x2 + 5x c\u00f3 3 giao \u0111i\u1ec3m. Ch\u1ecdn \u0111\u00e1p \u00e1n A Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 137 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 81 (C\u00e2u 37 - M\u0110 104 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2019 - 2020). S\u1ed1 giao \u0111i\u1ec3m c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = x3 \u2212 x2 v\u00e0 \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = \u2212x2 + 3x l\u00e0 A 1. B 0. C 2. D 3. \u0253 L\u1eddi gi\u1ea3i. S\u1ed1 giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u1ed3 th\u1ecb l\u00e0 s\u1ed1 nghi\u1ec7m th\u1ef1c ph\u00e2n bi\u1ec7t c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh ho\u00e0nh \u0111\u1ed9 giao \u0111i\u1ec3m sau: \u00ef x = 0\u221a x = \u00b1 3. x3 \u2212 x2 = \u2212x2 + 3x \u21d4 x3 \u2212 3x = 0 \u21d4 x x2 \u2212 3 = 0 \u21d4 V\u1eady s\u1ed1 giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111\u00e3 cho l\u00e0 3. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 82 (C\u00e2u 1 - M\u0110 101 - BGD&\u0110T - \u0110\u1ee3t 2 - 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 h\u00ecnh b\u00ean. S\u1ed1 y \u22121 O 1 nghi\u1ec7m th\u1ef1c c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh f (x) = \u22121 l\u00e0 x 2 \u22121 A 3. B 4. C 2. D 1. \u22122 \u0253 L\u1eddi gi\u1ea3i. S\u1ed1 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh f (x) = \u22121 ch\u00ednh l\u00e0 s\u1ed1 giao \u0111i\u1ec3m c\u1ee7a \u0111\u1ed3 th\u1ecb v\u00e0 y 2 \u22121 O 1 \u0111\u01b0\u1eddng th\u1eb3ng d : y = \u22121 song song v\u1edbi tr\u1ee5c Ox. 2 x Nh\u00ecn v\u00e0o \u0111\u1ed3 th\u1ecb ta th\u1ea5y \u0111\u01b0\u1eddng th\u1eb3ng d c\u1eaft \u0111\u1ed3 th\u1ecb t\u1ea1i hai \u0111i\u1ec3m ph\u00e2n bi\u1ec7t n\u00ean \u22121 y = \u2212 1 ph\u01b0\u01a1ng tr\u00ecnh f (x) = \u22121 c\u00f3 hai nghi\u1ec7m ph\u00e2n bi\u1ec7t. 2 2 \u22122 Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 83 (C\u00e2u 26 - M\u0110 101 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2019 - 2020). S\u1ed1 giao \u0111i\u1ec3m c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = \u2212x3 + 6x v\u1edbi tr\u1ee5c ho\u00e0nh l\u00e0 A 2. B 3. C 1. D 0. \u0253 L\u1eddi gi\u1ea3i. Ph\u01b0\u01a1ng tr\u00ecnh ho\u00e0nh \u0111\u1ed9 giao \u0111i\u1ec3m l\u00e0 \u2212x3 + 6x = 0 \u21d4 \u00f1x = 0 \u221a x = \u00b1 6. Suy ra c\u00f3 3 giao \u0111i\u1ec3m. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 84 (C\u00e2u 35 - M\u0110 102 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2019 - 2020). S\u1ed1 giao \u0111i\u1ec3m c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = \u2212x3 + 7x v\u1edbi tr\u1ee5c ho\u00e0nh l\u00e0 A 0. B 3. C 2. D 1. Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t \u0253 L\u1eddi gi\u1ea3i. S\u0110T: 0905.193.688 138","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 ho\u00e0nh \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = \u2212x3 + 7x v\u1edbi tr\u1ee5c ho\u00e0nh l\u00e0 \u2212x3 + 7x = 0. Ta c\u00f3 \uf8eex = 0 \u221a \u2212x3 + 7x = 0 \u21d4 \uf8efx = 7 \uf8f0\u221a x = \u2212 7. Ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 3 nghi\u1ec7m n\u00ean s\u1ed1 giao \u0111i\u1ec3m c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = \u2212x3 + 7x v\u00e0 tr\u1ee5c ho\u00e0nh b\u1eb1ng 3. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 85 (C\u00e2u 28 - M\u0110 102 - BGD&\u0110T - \u0110\u1ee3t 4 - N\u0103m 2019 - 2020). S\u1ed1 giao \u0111i\u1ec3m c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = \u2212x3 + 5x v\u1edbi tr\u1ee5c ho\u00e0nh l\u00e0 A 3. B 2. C 0. D 1. \u0253 L\u1eddi gi\u1ea3i. X\u00e9t ph\u01b0\u01a1ng tr\u00ecnh ho\u00e0nh \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = \u2212x3 + 5x v\u00e0 tr\u1ee5c Ox \u2212x3 + 5x = 0 \u21d4 x x2 \u2212 5 = 0 \u21d4 \u00f1x = 0 \u221a x = \u00b1 5. Ph\u01b0\u01a1ng tr\u00ecnh ho\u00e0nh \u0111\u1ed9 c\u00f3 3 nghi\u1ec7m ph\u00e2n bi\u1ec7t n\u00ean \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 v\u00e0 tr\u1ee5c ho\u00e0nh c\u1eaft nhau t\u1ea1i 3 \u0111i\u1ec3m ph\u00e2n bi\u1ec7t. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 86 (C\u00e2u 15 - \u0110TK - BGD&\u0110T - N\u0103m 2016 - 2017). Cho h\u00e0m s\u1ed1 f (x) = x ln x. M\u1ed9t trong b\u1ed1n \u0111\u1ed3 th\u1ecb cho trong b\u1ed1n ph\u01b0\u01a1ng \u00e1n A, B, C, D d\u01b0\u1edbi \u0111\u00e2y l\u00e0 \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 y = f (x). T\u00ecm \u0111\u1ed3 th\u1ecb \u0111\u00f3. yy 1 x O1 x . B . O1 A y y O1 x 1 x C . . O D \u0253 L\u1eddi gi\u1ea3i. Ch\u00fang ta c\u00f3 y = f (x) = ln x + 1 n\u00ean y y = ln x + 1 l\u00e0 h\u00e0m s\u1ed1 x\u00e1c \u0111\u1ecbnh tr\u00ean (0; +\u221e). y(1) = ln 1 + 1 = 1, t\u1ee9c l\u00e0 \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111i qua \u0111i\u1ec3m (1; 1). T\u1eeb \u0111\u00f3 suy ra, trong b\u1ed1n \u0111\u1ed3 th\u1ecb \u0111\u00e3 cho \u1edf c\u00e1c ph\u01b0\u01a1ng \u00e1n A, B, C, D ch\u1ec9 c\u00f3 \u0111\u1ed3 th\u1ecb O1 x h\u00ecnh b\u00ean l\u00e0 th\u1ecfa m\u00e3n c\u00e1c t\u00ednh ch\u1ea5t tr\u00ean c\u1ee7a h\u00e0m s\u1ed1 y = f (x). Ch\u1ecdn \u0111\u00e1p \u00e1n C Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 139 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 87 (C\u00e2u 28 - M\u0110 101 - BGD&\u0110T - N\u0103m 2016 - 2017). \u0110\u01b0\u1eddng cong \u1edf h\u00ecnh b\u00ean l\u00e0 \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 y = ax + b v\u1edbi a, b, c, d l\u00e0 c\u00e1c y cx + d O 1 s\u1ed1 th\u1ef1c. M\u1ec7nh \u0111\u1ec1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y \u0111\u00fang? A y > 0, \u2200x \u2208 R. B y < 0, \u2200x \u2208 R. C y > 0, \u2200x = 1. D y < 0, \u2200x = 1. x \u0253 L\u1eddi gi\u1ea3i. T\u1eeb \u0111\u1ed3 th\u1ecb \u21d2 h\u00e0m s\u1ed1 ngh\u1ecbch bi\u1ebfn tr\u00ean t\u1eebng kho\u1ea3ng x\u00e1c \u0111\u1ecbnh. M\u1eb7t kh\u00e1c h\u00e0m s\u1ed1 kh\u00f4ng x\u00e1c \u0111\u1ecbnh t\u1ea1i x = 1 \u21d2 y < 0, \u2200x = 1. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 88 (C\u00e2u 5 - M\u0110 102 - BGD&\u0110T - N\u0103m 2016 - 2017). \u0110\u01b0\u1eddng cong \u1edf h\u00ecnh b\u00ean l\u00e0 \u0111\u1ed3 th\u1ecb c\u1ee7a m\u1ed9t trong b\u1ed1n h\u00e0m s\u1ed1 d\u01b0\u1edbi \u0111\u00e2y. y H\u00e0m s\u1ed1 \u0111\u00f3 l\u00e0 h\u00e0m s\u1ed1 n\u00e0o? B y = \u2212x4 + 2x2 + 1. A y = x4 \u2212 2x2 + 1. C y = \u2212x3 + 3x2 + 1. D y = x3 \u2212 3x2 + 3. O x \u0253 L\u1eddi gi\u1ea3i. \u0110\u00e2y l\u00e0 \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 c\u00f3 d\u1ea1ng y = ax3 + bx2 + cx + d, h\u01a1n n\u1eefa ta th\u1ea5y khi x \u2192 +\u221e th\u00ec y \u2192 +\u221e do \u0111\u00f3 a > 0. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 89 (C\u00e2u 16 - M\u0110 104 - BGD&\u0110T - N\u0103m 2016 - 2017). x\u22122 \u0110\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 y = c\u00f3 bao nhi\u00eau ti\u1ec7m c\u1eadn? x2 \u2212 4 A 0. B 3. C 1. D 2. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 y = x\u22122 = 1 . Do \u0111\u00f3, \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 n\u00e0y c\u00f3 m\u1ed9t \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn \u0111\u1ee9ng x = \u22122 v\u00e0 x2 \u2212 4 x + 2 m\u1ed9t \u0111\u01b0\u1eddng ti\u1ec7m c\u1eadn ngang y = 0. Ch\u1ecdn \u0111\u00e1p \u00e1n D \u0104 C\u00e2u 90 (C\u00e2u 32 - \u0110TK - BGD&\u0110T - N\u0103m 2016 - 2017). Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 140 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 = (x \u2212 2)(x2 \u2212 1) c\u00f3 \u0111\u1ed3 th\u1ecb nh\u01b0 h\u00ecnh v\u1ebd b\u00ean. H\u00ecnh n\u00e0o d\u01b0\u1edbi \u0111\u00e2y y O l\u00e0 \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 y = |x \u2212 2|(x2 \u2212 1)? y x y O x O x A . B . y y O x O x C . D . \u0253 L\u1eddi gi\u1ea3i. H\u00e0m s\u1ed1 y = (x \u2212 2)(x2 \u2212 1) c\u00f3 \u0111\u1ed3 th\u1ecb (C) Ta c\u00f3 y = |x \u2212 2| (x2 \u2212 1) = \u00ae(x \u2212 2) x2 \u2212 1 1 khi x 2 \u2212 (x \u2212 2) x2 \u2212 khi x < 2 C\u00e1ch v\u1ebd \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = |x \u2212 2| (x2 \u2212 1) nh\u01b0 sau: \u2022 Gi\u1eef nguy\u00ean \u0111\u1ed3 th\u1ecb (C) \u1ee9ng v\u1edbi x 2. \u2022 L\u1ea5y \u0111\u1ed1i x\u1ee9ng \u0111\u1ed3 th\u1ecb (C) \u1ee9ng v\u1edbi x < 2 qua tr\u1ee5c Ox. B\u1ecf \u0111\u1ed3 th\u1ecb (C) \u1ee9ng v\u1edbi x < 2. H\u1ee3p 2 ph\u1ea7n \u0111\u1ed3 th\u1ecb tr\u00ean l\u00e0 \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = |x \u2212 2| (x2 \u2212 1). Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 91 (C\u00e2u 46 - M\u0110 102 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2019 - 2020). Cho h\u00e0m s\u1ed1 y = ax3 + bx2 + cx + d, (a, b, c, d \u2208 R) c\u00f3 \u0111\u1ed3 th\u1ecb l\u00e0 y \u0111\u01b0\u1eddng cong trong h\u00ecnh v\u1ebd. C\u00f3 bao nhi\u00eau s\u1ed1 d\u01b0\u01a1ng trong c\u00e1c s\u1ed1 a, b, c, d? A 4. B 3. C 1. D 2. O x \u0253 L\u1eddi gi\u1ea3i. H\u00ecnh d\u1ea1ng \u0111\u1ed3 th\u1ecb cho th\u1ea5y a < 0. \u0110\u1ed3 th\u1ecb c\u1eaft tr\u1ee5c tung t\u1ea1i m\u1ed9t \u0111i\u1ec3m n\u1eb1m ph\u00eda d\u01b0\u1edbi tr\u1ee5c ho\u00e0nh n\u00ean d < 0. \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u00f3 hai \u0111i\u1ec3m c\u1ef1c tr\u1ecb n\u1eb1m b\u00ean ph\u1ea3i tr\u1ee5c tung n\u00ean h\u00e0m s\u1ed1 \u0111\u00e3 cho c\u00f3 hai \u0111i\u1ec3m c\u1ef1c tr\u1ecb c\u00f9ng d\u01b0\u01a1ng, khi \u0111\u00f3 y = 3ax2 + 2bx + c c\u00f3 hai nghi\u1ec7m ph\u00e2n bi\u1ec7t c\u00f9ng d\u01b0\u01a1ng \uf8f1 + x2 = \u2212b > 0 m\u00e0 \uf8f2x1 c 3a \uf8f3x1x2 = 3a > 0 a < 0 n\u00ean c < 0, b > 0. V\u1eady trong c\u00e1c s\u1ed1 a, b, c, d c\u00f3 1 s\u1ed1 d\u01b0\u01a1ng. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 92 (C\u00e2u 46 - M\u0110 103 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2019 - 2020). Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 141 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 Cho h\u00e0m s\u1ed1 y = ax3 + bx2 + cx + d c\u00f3 \u0111\u1ed3 th\u1ecb l\u00e0 \u0111\u01b0\u1eddng cong trong y Ox h\u00ecnh b\u00ean. C\u00f3 bao nhi\u00eau s\u1ed1 d\u01b0\u01a1ng trong c\u00e1c a, b, c, d? A 4. B 2. C 1. D 3. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 y = 3ax2 + 2bx + c . D\u1ef1a v\u00e0o \u0111\u1ed3 th\u1ecb ta th\u1ea5y a < 0. H\u00e0m s\u1ed1 c\u00f3 2 c\u1ef1c tr\u1ecb \u00e2m n\u00ean \uf8f4\uf8f1\u2206y > 0 \uf8f1b2 \u2212 9ac > 0 \uf8f2 \uf8f4 0 S<0 \u21d0 \uf8f4 2b < \u21d2 \u00aeb < 0 \uf8f4 c < 0. \uf8f4\uf8f3P > 0 \uf8f2\u2212 3a \uf8f4 c >0 \uf8f4 \uf8f4 \uf8f3 3a \u0110\u1ed3 th\u1ecb c\u1eaft tr\u1ee5c Oy t\u1ea1i \u0111i\u1ec3m (0; d) n\u00ean d > 0. V\u1eady c\u00f3 \u0111\u00fang m\u1ed9t s\u1ed1 d\u01b0\u01a1ng trong c\u00e1c s\u1ed1 a, b, c, d. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 93 (C\u00e2u 48 - M\u0110 102 - BGD&\u0110T - \u0110\u1ee3t 4 - N\u0103m 2019 - 2020). Cho h\u00e0m s\u1ed1 y = ax3 + bx2 + cx + d (a, b, c, d \u2208 R) c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean nh\u01b0 sau: x \u2212\u221e 0 4 +\u221e y +0\u22120+ \u22121 +\u221e y \u2212\u221e \u22125 C\u00f3 bao nhi\u00eau s\u1ed1 d\u01b0\u01a1ng trong c\u00e1c s\u1ed1 a, b, c, d? A 4. B 2. C 3. D 1. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 y = ax3 + bx2 + cx + d \u21d2 y = 3ax2 + 2bx + c. T\u1eeb b\u1ea3ng bi\u1ebfn thi\u00ean ta th\u1ea5y: lim f (x) = +\u221e \u21d2 a > 0. x\u2192+\u221e y(0) = \u22121 \u21d4 d = \u22121 < 0. Ph\u01b0\u01a1ng tr\u00ecnh y = 0 c\u00f3 hai nghi\u1ec7m x1 = 0, x2 = 4, theo \u0111\u1ecbnh l\u00ed Vi-et ta c\u00f3 \u22122b \u22122b b x1 + x2 = \u21d4 =4>0 \u21d2 < 0 \u21d2 b < 0. x1x2 = c 3a 3a a \u21d4 c = 0 \u21d4 c = 0. 3a 3a V\u1eady trong c\u00e1c s\u1ed1 a, b, c, d ch\u1ec9 c\u00f3 a l\u00e0 s\u1ed1 d\u01b0\u01a1ng. Ch\u1ecdn \u0111\u00e1p \u00e1n D Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 142 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 \u0104 C\u00e2u 94 (C\u00e2u 43 - M\u0110 103 - BGD&\u0110T - \u0110\u1ee3t 2 - N\u0103m 2019 - 2020). Cho h\u00e0m s\u1ed1 f (x) = ax3 + bx2 + cx + d (a, b, c, d \u2208 R) c\u00f3 b\u1ea3ng bi\u1ebfn thi\u00ean nh\u01b0 sau x \u2212\u221e \u22122 0 +\u221e f (x) +0\u22120+ 1 +\u221e f (x) \u2212\u221e \u22121 C\u00f3 bao nhi\u00eau s\u1ed1 d\u01b0\u01a1ng trong c\u00e1c s\u1ed1 a, b, c, d? A 3. B 4. C 2. D 1. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 f (x) = 3ax2 + 2bx + c. T\u1eeb b\u1ea3ng bi\u1ebfn thi\u00ean ta suy ra lim f (x) = +\u221e \u21d2 a > 0. x\u2192+\u221e f (0) = \u22121 \u21d4 d = \u22121 < 0. H\u00e0m s\u1ed1 \u0111\u1ea1t c\u1ef1c tr\u1ecb t\u1ea1i x = 0 v\u00e0 x = \u22122 \u21d2 \u00aef (0) = 0 \u00aec = 0 \u00aec = 0 \u21d4 \u21d4 f (\u22122) = 0 12a \u2212 4b = 0 b = 3a > 0. V\u1eady c\u00f3 2 s\u1ed1 d\u01b0\u01a1ng l\u00e0 a v\u00e0 b. Ch\u1ecdn \u0111\u00e1p \u00e1n C \u0104 C\u00e2u 95 (C\u00e2u 45 - \u0110TK - BGD&\u0110T - l\u1ea7n 1 - 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 \u22121 0 1 +\u221e +\u221e f (x) \u22120+0\u22120+ +\u221e \u22121 f (x) \u22122 \u22122 S\u1ed1 nghi\u1ec7m thu\u1ed9c \u0111o\u1ea1n [\u2212\u03c0 ; 2\u03c0] c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh 2f (sin x) + 3 = 0 l\u00e0 A 4. B 6. C 3. D 8. \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 2f (sin x) + 3 = 0 \u21d4 f (sin x) = \u22123 . 2 D\u1ef1a v\u00e0o b\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a h\u00e0m s\u1ed1 f (x): \uf8eex = a v\u1edbi a < \u22121 Ta c\u00f3: f (x) = \u22123 \u21d4 \uf8ef\uf8efx = b v\u1edbi \u2212 1 < b < 0 \uf8ef 2 \uf8efx = c v\u1edbi 0 < c < 1 \uf8f0 x=d v\u1edbi d > 1 \uf8ee sin x = a v\u1edbi a < \u22121 Do \u0111\u00f3: f (sin x) = \u22123 \u21d4 \uf8ef sin x = b v\u1edbi \u2212 1 < b < 0 \uf8ef . \uf8ef v\u1edbi 0 < c < 1 2 \uf8ef sin x = c v\u1edbi d > 1 \uf8f0 sin x = d Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 143 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 +) C\u00e1c tr\u01b0\u1eddng h\u1ee3p: sin x = a, sin x = d v\u00f4 nghi\u1ec7m do a < \u22121, d > 1. +) Do \u22121 < b < 0 n\u00ean t\u1ed3n t\u1ea1i g\u00f3c \u03b1 v\u1edbi \u2212\u03c0 < \u03b1 < 0 sao cho sin \u03b1 = b. 2 \u00f1x = \u03b1 + k2\u03c0 Khi \u0111\u00f3: sin x = b \u21d4 sin x = sin \u03b1 \u21d4 x = \u03c0 \u2212 \u03b1 + m2\u03c0 (k, m \u2208 Z). Theo \u0111\u1ea7u b\u00e0i, ta l\u1ea5y nghi\u1ec7m x \u2208 [\u2212\u03c0 ; 2\u03c0] n\u00ean \u2212\u03c0 \u2264 \u03b1 + k2\u03c0 \u2264 2\u03c0 ho\u1eb7c \u2212\u03c0 \u2264 \u03c0 \u2212 \u03b1 + m2\u03c0 \u2264 2\u03c0, v\u1edbi \u2212\u03c0 k, m \u2208 Z v\u00e0 2 < \u03b1 < 0. Suy ra k = 0, k = 1; m = \u22121, m = 0. Do \u0111\u00f3, sin x = b c\u00f3 4 nghi\u1ec7m thu\u1ed9c \u0111o\u1ea1n [\u2212\u03c0 ; 2\u03c0]. \u03c0 +) T\u01b0\u01a1ng t\u1ef1, do 0 < c < 1 n\u00ean t\u1ed3n t\u1ea1i g\u00f3c \u03b2 v\u1edbi 0 < \u03b2 < 2 sao cho sin \u03b2 = x3. \u00f1x = \u03b2 + n2\u03c0 Khi \u0111\u00f3: sin x = c \u21d4 sin x = sin \u03b2 \u21d4 x = \u03c0 \u2212 \u03b2 + l2\u03c0 (n, l \u2208 Z). Theo \u0111\u1ea7u b\u00e0i, ta l\u1ea5y nghi\u1ec7m x \u2208 [\u2212\u03c0 ; 2\u03c0] n\u00ean \u2212\u03c0 \u2264 \u03b2 + n2\u03c0 \u2264 2\u03c0 ho\u1eb7c \u2212\u03c0 \u2264 \u03c0 \u2212 \u03b2 + l2\u03c0 \u2264 2\u03c0 v\u1edbi \u03c0 n, l \u2208 Z v\u00e0 0 < \u03b2 < . Suy ra n = 0; l = 0. 2 Do \u0111\u00f3, sin x = c c\u00f3 2 nghi\u1ec7m thu\u1ed9c \u0111o\u1ea1n [\u2212\u03c0 ; 2\u03c0]. V\u1eady, ph\u01b0\u01a1ng tr\u00ecnh 2f (sin x) + 3 = 0 c\u00f3 6 nghi\u1ec7m thu\u1ed9c \u0111o\u1ea1n [\u2212\u03c0 ; 2\u03c0]. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 96 (C\u00e2u 49 - M\u0110 103 - 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 2 +\u221e 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 3f (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 15. B 12. C 14. D 13. \u0253 L\u1eddi gi\u1ea3i. X\u00e9t h\u00e0m s\u1ed1 g(x) = f (x2 \u2212 4x) tr\u00ean kho\u1ea3ng (0; +\u221e). Ta c\u00f3 g (x) = (2x \u2212 4)f (x2 \u2212 4x). Khi \u0111\u00f3 g (x) = 0 \u21d4 \uf8ee2x \u2212 4 = 0 \u21d4 \uf8eex = 2 \u00b1 \u221a = 2 2 \uf8efx2 \u2212 4x = \u22124 \uf8efx = 0 \uf8ef \uf8ef \uf8ef\uf8f0x2 \u2212 4x = \u22122 \uf8ef\uf8f0x x2 \u2212 4x = 0 x = 4. M\u1eb7t kh\u00e1c, \uf8ee \u00aex = 2 \u221a\u221a \u00f1 \u2212 4 < x2 \u2212 4x < \u22122 \uf8ef 2\u2212 2<x<2+ 2 f x2 \u2212 4x > 0 \u21d4 x2 \u2212 4x > 0 \u21d4 \uf8ef <0 \uf8ef \uf8efx \uf8f0 x > 4. L\u1ea1i c\u00f3 g(0) = f (0) = \u22123, g \u00c4 \u00b1 \u221a\u00e4 = f (\u22122) = 2, g(2) = f (\u22124) = \u22122, g(4) = f (0) = \u22123. 2 2 B\u1ea3ng bi\u1ebfn thi\u00ean c\u1ee7a g(x) tr\u00ean kho\u1ea3ng (0; +\u221e) Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 144 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 \u221a\u221a +\u221e 0 2\u2212 2 2 2+ 2 4 2x \u2212 4 \u2212 \u22120+ + + f (x2 \u2212 4x) \u22120+0+0\u22120+ g (x) +0\u22120+0\u22120+ 2 2 +\u221e g(x) \u22123 \u22122 \u22123 Ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00e3 cho t\u01b0\u01a1ng \u0111\u01b0\u01a1ng v\u1edbi f (x2 \u2212 4x) = m S\u1ed1 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh b\u1eb1ng s\u1ed1 giao . m3 \u0111i\u1ec3m c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 g(x) v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng y = . 3 D\u1ef1a v\u00e0o b\u1ea3ng bi\u1ebfn thi\u00ean tr\u00ean, y\u00eau c\u1ea7u b\u00e0i to\u00e1n th\u1ecfa m\u00e3n khi \u22123 < m \u2264 2 \u21d4 \u22129 < m \u2264 6. 3 V\u00ec m \u2208 Z v\u00e0 \u22129 < m \u2264 6 n\u00ean m \u2208 {\u22128; \u22127; . . . ; 5; 6}. V\u1eady c\u00f3 t\u1ea5t c\u1ea3 15 gi\u00e1 tr\u1ecb nguy\u00ean c\u1ee7a m th\u1ecfa m\u00e3n y\u00eau c\u1ea7u b\u00e0i to\u00e1n. Ch\u1ecdn \u0111\u00e1p \u00e1n A \u0104 C\u00e2u 97 (C\u00e2u 41 - M\u0110 102 - 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 trong h\u00ecnh b\u00ean. y S\u1ed1 nghi\u1ec7m th\u1ef1c ph\u00e2n bi\u1ec7t c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh f (f (x)) = 1 l\u00e0 3 A 9. B 7. C 3. D 6. 1 2 \u22121 O1 x \u22121 \u0253 L\u1eddi gi\u1ea3i. y Ta th\u1ea5y \u0111\u01b0\u1eddng th\u1eb3ng y = 1, c\u1eaft \u0111\u1ed3 th\u1ecb (C) : y = f (x) t\u1ea1i ba \u0111i\u1ec3m ph\u00e2n 3 bi\u1ec7t c\u00f3 ho\u00e0nh \u0111\u1ed9 l\u1ea7n l\u01b0\u1ee3t l\u00e0 x = a (a < \u22121), x = 0, x = b (1 < b < 2). 1 y=b \uf8eef (x) = a < \u22121 y=1 \u22121 2 Ta th\u1ea5y, f (f (x)) = 1 \u21d4 \uf8eff (x) = 0 a x \uf8f0 O1 b \u22121 y=a 1 < f (x) = b < 2. (C) : y = f (x) T\u1eeb \u0111\u1ed3 th\u1ecb suy ra f (x) = 0 c\u00f3 ba nghi\u1ec7m ph\u00e2n bi\u1ec7t x1, x2, x3. V\u00ec a < \u22121 suy ra ph\u01b0\u01a1ng tr\u00ecnh f (x) = a c\u00f3 duy nh\u1ea5t m\u1ed9t nghi\u1ec7m x4 kh\u00e1c x1, x2, x3. V\u00ec 1 < b < 2, suy ra ph\u01b0\u01a1ng f (x) = b c\u00f3 ba nghi\u1ec7m ph\u00e2n bi\u1ec7t x5, x6, x7 kh\u00e1c x1, x2, x3, x4. V\u1eady f (f (x)) = 1 c\u00f3 7 nghi\u1ec7m th\u1ef1c ph\u00e2n bi\u1ec7t. Ch\u1ecdn \u0111\u00e1p \u00e1n B Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 145 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 98 (C\u00e2u 41 - M\u0110 103 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2020 - 2021). 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 h\u00ecnh b\u00ean. y 1 S\u1ed1 nghi\u1ec7m th\u1ef1c ph\u00e2n bi\u1ec7t c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh f (f (x)) = 0 l\u00e0 A 4. B 10. C 12. D 8. \u22121 1 O x \u22121 \u0253 L\u1eddi gi\u1ea3i. y=d y \uf8eef (x) = a, a < \u22121 y=c 1 \uf8eff (x) = b, \u2212 1 < b < 0 D\u1ef1a v\u00e0o \u0111\u1ed3 th\u1ecb ta c\u00f3 f (f (x)) = 0 \u21d4 \uf8ef \u22121 1 \uf8ef\uf8f0f (x) = c, 0 < c < 1 y=b O x f (x) = d, d > 1. y=a \u22121 Ph\u01b0\u01a1ng tr\u00ecnh f (x) = a v\u00f4 nghi\u1ec7m (v\u00ec \u0111\u01b0\u1eddng th\u1eb3ng y = a kh\u00f4ng c\u1eaft \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 f (x)). Ph\u01b0\u01a1ng tr\u00ecnh f (x) = b c\u00f3 4 nghi\u1ec7m ph\u00e2n bi\u1ec7t. Ph\u01b0\u01a1ng tr\u00ecnh f (x) = c c\u00f3 4 nghi\u1ec7m ph\u00e2n bi\u1ec7t. Ph\u01b0\u01a1ng tr\u00ecnh f (x) = d c\u00f3 2 nghi\u1ec7m ph\u00e2n bi\u1ec7t. V\u1eady ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00e3 cho c\u00f3 10 nghi\u1ec7m ph\u00e2n bi\u1ec7t. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 99 (C\u00e2u 39 - M\u0110 104 - BGD&\u0110T - \u0110\u1ee3t 1 - N\u0103m 2020 - 2021). Cho h\u00e0m s\u1ed1 b\u1eadc b\u1ed1n y = f (x) c\u00f3 \u0111\u1ed3 th\u1ecb l\u00e0 \u0111\u01b0\u1eddng cong h\u00ecnh b\u00ean. S\u1ed1 y 1 nghi\u1ec7m th\u1ef1c ph\u00e2n bi\u1ec7t c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh f (f (x)) = 0 l\u00e0 O A 12. B 10. C 8. D 4. MDD-109 \u22121 1 x \u22121 \u0253 L\u1eddi gi\u1ea3i. D\u1ef1a v\u00e0o \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = f (x), ph\u01b0\u01a1ng tr\u00ecnh f (x) = 0 c\u00f3 4 nghi\u1ec7m y y=d x = a, x = b, x = c, x = d v\u1edbi a < \u22121 < b < 0 < c < 1 < d. 1 y=c \uf8eef (x) = a, (a < \u22121) a bO d \uf8eff (x) = b, (\u22121 < b < 0) \u22121MDD-109c 1 y = bx Ph\u01b0\u01a1ng tr\u00ecnh f (f (x)) = 0 \u21d4 \uf8ef \u22121 y = a \uf8ef\uf8f0f (x) = c, (0 < c < 1) f (x) = d, (d > 1). D\u1ef1a v\u00e0o \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y = f (x) ta c\u00f3 Ph\u01b0\u01a1ng tr\u00ecnh f (x) = a, (a < \u22121) c\u00f3 2 nghi\u1ec7m ph\u00e2n bi\u1ec7t. Ph\u01b0\u01a1ng tr\u00ecnh f (x) = b, (\u22121 < b < 0) c\u00f3 4 nghi\u1ec7m ph\u00e2n bi\u1ec7t. Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 146 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 Ph\u01b0\u01a1ng tr\u00ecnh f (x) = c, (0 < c < 1) c\u00f3 4 nghi\u1ec7m ph\u00e2n bi\u1ec7t. Ph\u01b0\u01a1ng tr\u00ecnh f (x) = d, (d > 1) v\u00f4 nghi\u1ec7m. V\u1eady ph\u01b0\u01a1ng tr\u00ecnh f (f (x)) = 0 c\u00f3 10 nghi\u1ec7m th\u1ef1c ph\u00e2n bi\u1ec7t. Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 100 (C\u00e2u 8 - \u0110MH - 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 sao cho \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 y = x4 + 2mx2 + 1 c\u00f3 ba \u0111i\u1ec3m c\u1ef1c tr\u1ecb t\u1ea1o th\u00e0nh m\u1ed9t tam gi\u00e1c vu\u00f4ng c\u00e2n. A m = \u2212 \u221a1 . B m = \u22121. C m = \u221a1 . D m = 1. 39 39 \u0253 L\u1eddi gi\u1ea3i. Ta c\u00f3 y = 4x3 + 4mx = 0 \u21d4 \u00f1x = 0 x2 = \u2212m \u0110i\u1ec1u ki\u1ec7n \u0111\u1ec3 h\u00e0m s\u1ed1 c\u00f3 3 c\u1ef1c tr\u1ecb l\u00e0: \u2212m > 0 \u21d4 m < 0. (lo\u1ea1i) Do AB2 = AC2 n\u00ean tam gi\u00e1c ABC lu\u00f4n c\u00e2n t\u1ea1i A. . Do \u0111\u00f3 ABC vu\u00f4ng t\u1ea1i A khi A# B\u00bb \u00b7 A# C\u00bb = 0 \u21d4 m + m4 = 0 \u21d4 \u00f1m = 0 (nh\u1eadn) m = \u22121 Ch\u1ecdn \u0111\u00e1p \u00e1n B \u0104 C\u00e2u 101 (C\u00e2u 35 - \u0110TK - BGD&\u0110T - N\u0103m 2017 - 2018). \u221a C\u00f3 bao nhi\u00eau gi\u00e1 tr\u1ecb nguy\u00ean c\u1ee7a tham s\u1ed1 m \u0111\u1ec3 ph\u01b0\u01a1ng tr\u00ecnh 3 m + 3 3 m + 3 sin x = sin x c\u00f3 nghi\u1ec7m th\u1ef1c. A 5. B 7. C 3. D 2. \u221a \u0253 L\u1eddi gi\u1ea3i. \u0110\u1eb7t t = 3 m + 3 sin x ta c\u00f3 h\u1ec7 Suy ra \u00aet3 = m + 3 sin x sin3 x = m + 3t. t3 \u2212 sin3 x + 3 (t \u2212 sin x) = 0 \u21d4 (t \u2212 sin x) t2 + t sin x + sin2 x + 3 = 0 \u21d4t = sin x \u21d4 sin3 x \u2212 3 sin x = m. X\u00e9t h\u00e0m s\u1ed1 f (u) = u3 \u2212 3u, u \u2208 [\u22121; 1] ta c\u00f3 f (u) = 3u2 \u2212 3, f (u) = 0 \u21d4 u = \u00b11. B\u1ea3ng bi\u1ebfn thi\u00ean x \u22121 1 f0 \u2212 0 2 f \u22122 T\u1eeb \u0111\u00f3, ta suy ra ph\u01b0\u01a1ng tr\u00ecnh sin3 x \u2212 3 sin x = m c\u00f3 nghi\u1ec7m khi v\u00e0 ch\u1ec9 khi \u22122 \u2264 m \u2264 2. Suy ra c\u00f3 5 gi\u00e1 tr\u1ecb nguy\u00ean c\u1ee7a m. Ch\u1ecdn \u0111\u00e1p \u00e1n A Th.S Nguy\u1ec5n Ho\u00e0ng Vi\u1ec7t 147 S\u0110T: 0905.193.688"]