❙Ð ●❉ ❱⑨ ✣❚ ◗❯❷◆● ❚❘➚ ❑➐ ❚❍■ ❚❍Û ❚❍P❚ ◗❯➮❈ ●■❆ ▲❺◆ ✶ ◆❿▼ ✷✵✶✾ ▼➷◆ ❚❖⑩◆ ❚❘×❮◆● ❚❍P❚ ❈❍❯❨➊◆ ▲➊ ◗❯Þ ✣➷◆ ❚❤í✐ ❣✐❛♥ ❧➔♠ ❜➔✐ ✾✵ ♣❤ót✱ ❦❤ỉ♥❣ ❦➸ t❤í✐ ❣✐❛♥ ❣✐❛♦ ✤➲ ✭ ✣➲ t❤✐ ❝â ✻ tr❛♥❣ ✮ ▼➣ ✤➲ t❤✐ ✶✵✶ ❈➙✉ ✶✳ ❑❤è✐ ❝❤â♣ S.ABCD ❝â ✤→② ABCD ❧➔ ❤➻♥❤ ✈✉æ♥❣ ❝↕♥❤ 3a✱ SA = a, SA ⊥ (ABCD)✳ ❚➼♥❤ t❤➸ t➼❝❤ ❦❤è✐ ❝❤â♣ S.ABCD✳ ❆✳ 6a3✳ ❇✳ 9a3✳ ❈✳ 3a3✳ ❉✳ a3 ✳ ❈➙✉ ✷✳ ❈❤♦ ❤➔♠ sè ❜➟❝ ❜❛ y = f (x) õ ỗ t ữ ữợ ú y tr ỹ t✐➸✉ ❝õ❛ ❤➔♠ sè ❜➡♥❣ −1✳ ❇✳ ✣✐➸♠ ❝ü❝ t✐➸✉ ❝õ❛ ❤➔♠ sè ❧➔ −1✳ ❈✳ ✣✐➸♠ ❝ü❝ ✤↕✐ ❝õ❛ ❤➔♠ sè ❧➔ 3✳ O x ❉✳ ●✐→ trà ❝ü❝ ✤↕✐ ❝õ❛ ❤➔♠ sè ❧➔ 0✳ −1 ❈➙✉ ✸✳ ❈❤♦ sè ♣❤ù❝ z = (1 − 2i)2✳ ❚➼♥❤ ♠æ ✤✉♥ ❝õ❛ sè ♣❤ù❝ z1 ✳ ❆✳ 15 ✳ ❇✳ √5✳ ❉✳ √15 ✳ ❈✳ 251 ✳ ❈➙✉ ✹✳ ❚➻♠ ♥❣❤✐➺♠ ❝õ❛ ♣❤÷ì♥❣ tr➻♥❤ log3(x − 2) = 2✳ ❆✳ x = 11✳ ❇✳ x = 8✳ ❈✳ x = 9✳ ❉✳ x = 10✳ ❈➙✉ ✺✳ ❚➼♥❤ ❞✐➺♥ t➼❝❤ ❝õ❛ ♠➦t ❝➛✉ ❝â ❜→♥ ❦➼♥❤ ❜➡♥❣ 3✳ ❆✳ 9π✳ ❇✳ 18π✳ ❈✳ 12π✳ ❉✳ 36π✳ ❈➙✉ ✻✳ ❍➔♠ số y = x3 + 3x2 ỗ tr➯♥ t➟♣ ❤đ♣ ♥➔♦ tr♦♥❣ ❝→❝ t➟♣ ❤đ♣ ✤÷đ❝ ❝❤♦ ữợ (2; +) (0; 2) (; 0) ∪ (2; +∞)✳ ❉✳ (−∞; 0)✳ ❈➙✉ ✼✳ ❚➼♥❤ t➼❝❤ ♣❤➙♥ I = x−1 dx x ✳ ❆✳ I = + ln 2✳ ❇✳ I = 74 ✳ ❈✳ I = ln 2✳ ❉✳ I = − ln 2✳ ❈➙✉ ✽✳ ❑❤è✐ ♥â♥ (N ) ❝â ❜→♥ ❦➼♥❤ ✤→② ❜➡♥❣ ✈➔ ❞✐➺♥ t➼❝❤ ①✉♥❣ q✉❛♥❤ ❜➡♥❣ 15π✳ ❚➼♥❤ t❤➸ t➼❝❤ ❦❤è✐ ♥â♥ (N )✳ ❆✳ 12π✳ ❇✳ 16π✳ ❈➙✉ ✾✳ ❈❤♦ ❜✐➸✉ t❤ù❝ P = ❆✳ P = 18 ✳ 3 ❇✳ P = ❈✳ 45π✳ 3 3 ✳ ❉✳ 36π✳ ✳ ▼➺♥❤ ✤➲ ♥➔♦ tr♦♥❣ ❝→❝ ♠➺♥❤ ✤➲ s❛✉ ❧➔ ✤ó♥❣❄ ❈✳ P = ✳ ❉✳ P = 18 ✳ ❚r❛♥❣ ✶✴✻ ▼➣ ✤➲ ✶✵✶ − i) ❈➙✉ ✶✵✳ ❈❤♦ sè ♣❤ù❝ z = (2 −33i)(4 ✳ ❚➻♠ tå❛ ✤ë ✤✐➸♠ ❜✐➸✉ ❞✐➵♥ ❝õ❛ sè ♣❤ù❝ z tr➯♥ + 2i ♠➦t ♣❤➥♥❣ Oxy✳ ❆✳ (1; 4)✳ ❇✳ (1; −4)✳ ❈✳ (−1; −4)✳ ❉✳ (−1; 4)✳ ❈➙✉ ✶✶✳ ❚r♦♥❣ ❦❤ỉ♥❣ ❣✐❛♥ ✈ỵ✐ ❤➺ tå❛ ✤ë Oxyz✱ ❝❤♦ ♠➦t ♣❤➥♥❣ (P )✿ 2x − 2y + z + 2017 = 0✱ ✈➨❝✲tì ♥➔♦ tr♦♥❣ ❝→❝ ✈➨❝✲tì ữủ ữợ ởt tỡ t (P )❄ ❆✳ ★✔n = (4; −4; 2)✳ ❇✳ ★✔n = (1; −2; 2)✳ ❈✳ ★✔n = (1; −1; 4)✳ ❉✳ ★✔n = (−2; 2; 1)✳ ❈➙✉ ✶✷✳ ❈❤♦ ❦❤è✐ ❧➟♣ ♣❤÷ì♥❣ ABCD.A B C D ❝â ✤ë ❞➔✐ ❝↕♥❤ ❧➔ 3❝♠✳ ❚➼♥❤ t❤➸ t➼❝❤ ❝õ❛ ❦❤è✐ tù ❞✐➺♥ ACB D ✳ ❆✳ 18√2❝♠3✳ ❇✳ 3❝♠3✳ ❈✳ 9❝♠3✳ ❉✳ 18❝♠3✳ ❈➙✉ ✶✸✳ ❚r♦♥❣ ♠➦t ♣❤➥♥❣ tå❛ ✤ë Oxy✱ t➟♣ ❤ñ♣ ❝→❝ ✤✐➸♠ ❜✐➸✉ ❞✐➵♥ ❝→❝ sè ♣❤ù❝ z t❤ä❛ ♠➣♥ |z − + 2i| = |z + + 2i| ❧➔ ✤÷í♥❣ t❤➥♥❣ ❝â ♣❤÷ì♥❣ tr➻♥❤ ❆✳ x + 2y = 0✳ ❇✳ x − 2y = 0✳ ❈✳ x − 2y + = 0✳ ❉✳ x + 2y + = 0✳ ❈➙✉ ✶✹✳ ❚➼♥❤ t❤➸ t➼❝❤ ❦❤è✐ trö ❝â ❜→♥ ❦➼♥❤ R = 3, ❝❤✐➲✉ ❝❛♦ h = ❆✳ V = 90π✳ ❇✳ V = 45π✳ ❈✳ V = 15π✳ ❉✳ V = 45✳ số ữớ t ỗ t ❤➔♠ sè y = xx2 −+3xx −+22 ✳ ❆✳ 2✳ ❇✳ 3✳ ❈✳ 1✳ ❉✳ 0✳ ❈➙✉ ✶✻✳ ❚➻♠ ♥❣✉②➯♥ ❤➔♠ ❝õ❛ ❤➔♠ sè f (x)= −1 2x tr➯♥ −∞; 12 ✳ ❆✳ 12 ln(1 − 2x) + C ✳ ❇✳ ln |2x − 1| + C ✳ ❈✳ 12 ln |2x − 1| + C ✳ ❉✳ − 12 ln |2x − 1| + C ✳ ❈➙✉ ✶✼✳ ❚r♦♥❣ ❦❤ỉ♥❣ ❣✐❛♥ ✈ỵ✐ ❤➺ tå❛ ✤ë Oxyz✱ ❝❤♦ ♠➦t ♣❤➥♥❣ (P ) : 2x − 2y + z + = 0✳ ❚➼♥❤ ❦❤♦↔♥❣ ❝→❝❤ d tø ✤✐➸♠ M (1; 2; 1) ✤➳♥ ♠➦t ♣❤➥♥❣ (P )✳ ❆✳ d = 1✳ ❇✳ d = 13 ✳ ❈✳ d = 3✳ ❉✳ d = 4✳ ❈➙✉ ✶✽✳ ❈❤♦ ❤➻♥❤ ❝❤â♣ S.ABC ❝â t❤➸ t➼❝❤ ❜➡♥❣ 1✳ ❚r➯♥ ❝↕♥❤ BC ❧➜② ✤✐➸♠ E s❛♦ ❝❤♦ BE = 2EC ✳ ❚➼♥❤ t❤➸ t➼❝❤ V ❝õ❛ ❦❤è✐ tù ❞✐➺♥ SAEB ✳ ❆✳ V = 13 ✳ ❇✳ V = 23 ✳ ❈✳ V = 43 ✳ ❉✳ V = 16 ✳ ❈➙✉ ✶✾✳ ❚➼♥❤ ✤↕♦ ❤➔♠ ❝õ❛ ❤➔♠ sè y = log9 x2 + ✳ ln ln x ❆✳ y = 2x ✳ ❇✳ y = ✳ ❈✳ y = ✳ ❉✳ y = ✳ x +1 x +1 (x + 1) ln (x + 1) ln ❈➙✉ ✷✵✳ ●å✐ z1✱ z2 ❧➔ ❤❛✐ ♥❣❤✐➺♠ ♣❤ù❝ ❝õ❛ ♣❤÷ì♥❣ tr➻♥❤ z2 − 4z + = 0✳ ❚➼♥❤ w = 1 + + i(z1 z2 + z2 z1 ) z1 z2 w = 20 + i ✳ ❆✳ ✳ ❇✳ w = 45 + 20i✳ ❈✳ w = − 45 + 20i✳ ❉✳ w = + 20i✳ ❈➙✉ ✷✶✳ ❚➼♥❤ tê♥❣ t➜t ❝↔ ❝→❝ ♥❣❤✐➺♠ ❝õ❛ ♣❤÷ì♥❣ tr➻♥❤ 12 log2(x + 3) = log2 x + + x2 − √ x−4+2 x+3 ❆✳ S = 2✳ ✳ ❇✳ S = 1✳ ❈✳ S = −1✳ ❉✳ S = − √2✳ ❚r❛♥❣ ✷✴✻ ▼➣ ✤➲ ✶✵✶ ❈➙✉ ✷✷✳ ❚r♦♥❣ ❦❤æ♥❣ ❣✐❛♥ Oxyz✱ ❝❤♦ ♠➦t ❝➛✉ (S) : x2 + y2 + z2 − 8x + 10y − 6z + 49 = 0✳ ❚➼♥❤ ❜→♥ ❦➼♥❤ R ❝õ❛ ♠➦t ❝➛✉ (S)✳ ❆✳ R = √151✳ ❇✳ R = √99✳ ❈✳ R = 1✳ ❉✳ R = 7✳ ❈➙✉ ✷✸✳ ❇✐➳t r➡♥❣ ❤➔♠ sè F (x) = mx3 + (3m + n)x2 − 4x + ❧➔ ♠ët ♥❣✉②➯♥ ❤➔♠ ❝õ❛ ❤➔♠ sè f (x) = 3x2 + 10x − 4✳ ❚➼♥❤ mn✳ ❆✳ mn = 1✳ ❇✳ mn = 3✳ ❈✳ mn = 2✳ ❉✳ mn = 0✳ ❈➙✉ ✷✹✳ ❚➼❝❤ ♣❤➙♥ I = (x − 1)2 dx = a − ln b x2 + ✱ tr♦♥❣ ✤â a; b ❧➔ ❝→❝ sè ♥❣✉②➯♥✳ ❚➼♥❤ ❣✐→ trà ❝õ❛ ❜✐➸✉ t❤ù❝ a + b✳ ❆✳ 0✳ ❇✳ −1✳ ❈✳ 3✳ ❉✳ 1✳ ❈➙✉ ✷✺✳ ❑❤è✐ ❝❤â♣ t❛♠ ❣✐→❝ ✤➲✉ ❝â ♥❤✐➲✉ ♥❤➜t ❜❛♦ ♥❤✐➯✉ ♠➦t ♣❤➥♥❣ ✤è✐ ①ù♥❣❄ ❆✳ 6✳ ❇✳ 9✳ ❈✳ 3✳ ❉✳ 4✳ ❈➙✉ ✷✻✳ ❚➻♠ t➜t ❝↔ ❝→❝ ❣✐→ trà t❤ü❝ ❝õ❛ t❤❛♠ sè m ✤➸ ❤➔♠ sè y = x +x 2+−1 m ♥❣❤à❝❤ ❜✐➳♥ tr➯♥ ♠é✐ ❦❤♦↔♥❣ ①→❝ ✤à♥❤ ❝õ❛ ♥â✳ ❆✳ m ≤ −3✳ ❇✳ m < −3✳ ❈✳ m < 1✳ ❉✳ m ≤ 1✳ ❈➙✉ ✷✼✳ (D) ợ ữớ y = x4 ✱ y = 0✱ x = 1✱ x = 4✳ ❚➼♥❤ t❤➸ t➼❝❤ ✈➟t t❤➸ trá♥ ①♦❛② t↕♦ t❤➔♥❤ ❦❤✐ q✉❛② ❤➻♥❤ (D) q✉❛♥❤ trö❝ Ox✳ 21 15π 15 ❆✳ 16 ✳ ❇✳ 21π ✳ ❈✳ ✳ ❉✳ ✳ 16 16 ❈➙✉ ✷✽✳ ❈❤♦ sè ♣❤ù❝ z t❤ä❛ |z − + 2i| = 3✳ ❇✐➳t r➡♥❣ t➟♣ ❤ñ♣ ❝→❝ ✤✐➸♠ ❜✐➵✉ ❞✐➵♥ ❝õ❛ sè ♣❤ù❝ w = 2z + i tr➯♥ ♠➦t ♣❤➥♥❣ (Oxy) ❧➔ ♠ët ✤÷í♥❣ trá♥✳ ❚➻♠ t➙♠ ❝õ❛ ✤÷í♥❣ trá♥ ✤â✳ ❆✳ I(0; 1)✳ ❇✳ I(1; 0)✳ ❈✳ I(1; 1)✳ ❉✳ I(2; −3)✳ ❈➙✉ ✷✾✳ ❈❤♦ x, y > t❤ä❛ ♠➣♥ x + y = 23 ✈➔ ❜✐➸✉ t❤ù❝ P = x4 + 4y1 ✤↕t ❣✐→ trà ♥❤ä ♥❤➜t✳ ❚➼♥❤ x2 + y2✳ 2313 25 ❆✳ 153 ✳ ❇✳ ✳ ❈✳ ✳ ❉✳ ✳ 100 1156 16 ❈➙✉ ✸✵✳ ❈❤♦ sè t❤ü❝ a > 0, a = 1✳ ●✐→ trà log√a √a2 ❜➡♥❣ ❆✳ 1✳ ❇✳ 23 ✳ ❈✳ 49 ✳ ❉✳ 94 ✳ 3 ❈➙✉ ✸✶✳ ●å✐ M (a; b) tr ỗ t số y = x −x s❛♦ ❝❤♦ ❦❤♦↔♥❣ ❝→❝❤ tø M ✤➳♥ ✤÷í♥❣ t❤➥♥❣ d : y = 2x + ♥❤ä ♥❤➜t✳ ❚➼♥❤ (4a + 5)2 + (2b − 7)2✳ ❆✳ 2✳ ❇✳ 0✳ ❈✳ 18✳ ❉✳ 162✳ ❈➙✉ ✸✷✳ ❚r♦♥❣ ❦❤æ♥❣ ❣✐❛♥ Oxyz✱ ❝❤♦ ♠➦t ♣❤➥♥❣ (P ) : x − y + = ✈➔ ❤❛✐ ✤✐➸♠ A(1; 2; 3), B(1; 0; 1)✳ ✣✐➸♠ C(a; b; −2) ∈ (P ) s❛♦ ❝❤♦ t❛♠ ❣✐→❝ ABC ❝â ❞✐➺♥ t➼❝❤ ♥❤ä ♥❤➜t✳ ❚➼♥❤ a + b✳ ❆✳ 2✳ ❇✳ 0✳ ❈✳ 1✳ ❉✳ −3✳ ❚r❛♥❣ ✸✴✻ ▼➣ ✤➲ (D) ữủ ợ ❜ð✐ ❤❛✐ ✤÷í♥❣ y = 2(x2 − 1); y = − x2✳ ❚➼♥❤ t❤➸ t➼❝❤ ❦❤è✐ trá♥ ①♦❛② t↕♦ t❤➔♥❤ ❞♦ (D) q✉❛② q✉❛♥❤ trö❝ Ox✳ 64π 64 32π ❆✳ 32 ✳ ❇✳ ✳ ❈✳ ✳ ❉✳ ✳ 15 15 15 15 ❈➙✉ ✸✹✳ ❈❤♦ ❤➔♠ sè f (x) ❝â ✤↕♦ ❤➔♠ f (x) = (x − 1)(x2 − 3)(x4 − 1) ✈ỵ✐ ♠å✐ x t❤✉ë❝ R✳ ❙♦ s→♥❤ f (−2), f (0), f (2)✱ t❛ ✤÷đ❝ ❆✳ f (−2) < f (2) < f (0)✳ ❇✳ f (−2) < f (0) < f (2)✳ ❈✳ f (2) < f (0) < f (−2)✳ ❉✳ f (0) < f (−2) < f (2)✳ ❈➙✉ ✸✺✳ ❈❤♦ ❤❛✐ sè ♣❤ù❝ z, w t❤ä❛ ♠➣♥ |z − 3√2| = √2, |w − 4√2i| = 2√2✳ ❇✐➳t r➡♥❣ |z − w| ✤↕t ❣✐→ trà ♥❤ä ♥❤➜t ❦❤✐ z = zo, w = wo✳ ❚➼♥❤ |3zo − wo|✳ ❆✳ 6√2✳ ❇✳ 2√2✳ ❈✳ 4√2✳ ❉✳ 1✳ ❈➙✉ ✸✻✳ ❚r♦♥❣ ❦❤æ♥❣ ❣✐❛♥ Oxyz✱ ❝❤♦ ♠➦t ♣❤➥♥❣ (P ) : x + y + z − = ✈➔ ❜❛ ✤✐➸♠ ✤✐➸♠ ★✥✥✥✥✥✔ ★✥✥✥✥✥✥✔ ★✥✥✥✥✥✔ A(3; 1; 1), B(7; 3; 9) ✈➔ C(2; 2; 2)✳ ✣✐➸♠ M (a; b; c) tr➯♥ (P ) s❛♦ ❝❤♦ |M A + 2M B + 3M C| ✤↕t ❣✐→ trà ♥❤ä ♥❤➜t✳ ❚➼♥❤ 2a − 15b + c✳ ❆✳ 8✳ ❇✳ 1✳ ❈✳ 3✳ ❉✳ 6✳ ❈➙✉ ✸✼✳ ❈❤♦ ❤➻♥❤√ ❝❤â♣ S.ABCD ❝â ✤→② ABCD ❧➔ ❤➻♥❤ ✈✉æ♥❣✱ t➙♠ O✱ ❝↕♥❤ a ✈➔ SO ⊥ (ABCD), SA = 2a 2✳ ●å✐ M, N ❧➛♥ ❧÷đt ❧➔ tr✉♥❣ ✤✐➸♠ ❝õ❛ SA, BC ✳ ❚➼♥❤ ❣â❝ ❣✐ú❛ ✤÷í♥❣ t❤➥♥❣ M N ✈➔ ♠➦t ♣❤➥♥❣ (ABCD)✳ ❆✳ π3 ✳ ❇✳ π4 ✳ ❈✳ arctan 2✳ ❉✳ π6 ✳ ❈➙✉ ✸✽✳ ❚➼♥❤ sè ❣✐→ trà ♥❣✉②➯♥ ❝õ❛ t❤❛♠ sè m tr➯♥ ❦❤♦↔♥❣ (−2019; 2019) ✤➸ ❤➔♠ sè y = x4 − 2mx2 3m + ỗ tr (1; 2) ❆✳ 2✳ ❇✳ 2020✳ ❈✳ 1✳ ❉✳ 2019✳ ❈➙✉ ✸✾✳ ❚➼♥❤ tê♥❣ t➜t ❝↔ ❝→❝ ❣✐→ trà ❝õ❛ t❤❛♠ sè m tỗ t t ởt số ự z tọ ỗ tớ |z| = m |z 4m + 3mi| = m2✳ ❆✳ 10✳ ❇✳ 9✳ ❈✳ 4✳ ❉✳ 6✳ ❈➙✉ ✹✵✳ ▼ët ❝❤✐➳❝ ✈á♥❣ ✤❡♦ t❛② ỗ t ố ọ õ ❝➢t ❝❤✐➳❝ ✈á♥❣ ✤â t❤➔♥❤ ✷ ♣❤➛♥ ♠➔ sè ❤↕t ð ♠é✐ ♣❤➛♥ ✤➲✉ ❧➔ sè ❧➫ ❄ ❆✳ 5✳ ❇✳ 180✳ ❈✳ 10✳ ❉✳ 90✳ ❈➙✉ ✹✶✳ ❈❤♦ ❤➔♠ số f (x) õ f (x) ỗ t❤à ❝õ❛ ❤➔♠ sè y = f (x) ♥❤÷ ❤➻♥❤ ✈➩ ❜➯♥✳ ❚➼♥❤ sè ✤✐➸♠ ❝ü❝ trà ❝õ❛ √ √ ❤➔♠ sè y = f (x2) tr➯♥ ❦❤♦↔♥❣ (− 5; 5)✳ ❆✳ 2✳ ❇✳ 5✳ ❈✳ 4✳ ❉✳ 3✳ ② y = f (x) ① ❚r❛♥❣ ✹✴✻ ▼➣ ✤➲ ✶✵✶ ❈➙✉ ✹✷✳√ ❈❤♦ ❤➻♥❤ ❝❤â♣ S.ABCD ❝â SA ⊥ (ABCD)✱ ✤→② ABCD ❧➔ ❤➻♥❤ ❝❤ú ♥❤➟t ✈ỵ✐ √ ✈➔ BC = a 2✳ ❚➼♥❤ ❦❤♦↔♥❣ ❝→❝❤ ❣✐ú❛ SD ✈➔ BC ✳ ✳ ❇✳ a√3✳ ❈✳ 3a4 ✳ AC = a√ a ❆✳ ❈➙✉ ✹✸✳ ❉✳ 2a3 ✳ ◆❣÷í✐ t❛ ❧➔♠ t↕ t➟♣ ❝ì t❛② ữ ợ ố trử ❜➡♥❣ ♥❤❛✉ ✈➔ t❛② ❝➛♠ ❝ơ♥❣ ❧➔ ❦❤è✐ trư✳ ❇✐➳t ❤❛✐ ✤➛✉ ❧➔ ❤❛✐ ❦❤è✐ trư ✤÷í♥❣ ❦➼♥❤ ✤→② ❜➡♥❣ ✶✷✱ ❝❤✐➲✉ ❝❛♦ ❜➡♥❣ ✻✱ ❝❤✐➲✉ ❞➔✐ t↕ ❜➡♥❣ ✸✵ ✈➔ ❜→♥ ❦➼♥❤ t❛② ❝➛♠ ❜➡♥❣ ✷✳ ❍➣② t➼♥❤ t❤➸ t➼❝❤ ✈➟t ❧✐➺✉ ❧➔♠ ♥➯♥ t↕ t❛② ✤â✳ ❆✳ 108π✳ ❇✳ 504π✳ ❈✳ 6480π✳ ❉✳ 502π✳ ❈➙✉ ✹✹✳ ❙➠♠ ❧è♣ ①❡ ỉ tỉ ❦❤✐ ❜ì♠ ❝➠♥❣ ✤➦t ♥➡♠ tr➯♥ ♠➦t ♣❤➥♥❣ ♥➡♠ ♥❣❛♥❣ ❝â ❤➻♥❤ ❝❤✐➳✉ ❜➡♥❣ ♥❤÷ ❤➻♥❤ ✈➩ ợ ữớ trỏ ọ R1 = 20cm ữớ trỏ ợ R2 = 30cm t t ❦❤✐ ❝➢t ❜ð✐ ♠➦t ♣❤➥♥❣ ✤✐ q✉❛ trư❝✱ ✈✉ỉ♥❣ ❣â❝ ợ t ữớ trỏ ọ q✉❛ ✤ë ❞➔② ❝õ❛ ✈ä s➠♠✳ ❚➼♥❤ t❤➸ t➼❝❤ ❦❤æ♥❣ ❦❤➼ ✤÷đ❝ ❝❤ù❛ ❜➯♥ tr♦♥❣ s➠♠✳ ❆✳ 1400πcm3✳ ❇✳ 1250πcm3✳ ❈✳ 2500πcm3✳ ❉✳ 600πcm3✳ ❈➙✉ ✹✺✳ ❈❤♦ ❤➔♠ sè f (x) ①→❝ ✤à♥❤ tr➯♥ R✱ ❝â ✤↕♦ ❤➔♠ f (x) = (x + 1)3 (x − 2)5 (x + 3)3✳ ❙è ✤✐➸♠ ❝ü❝ trà ❝õ❛ ❤➔♠ sè f (|x|) ❧➔ ❆✳ 3✳ ❇✳ 1✳ ❈✳ 2✳ ❉✳ 5✳ ❈➙✉ ✹✻✳ ❈❤♦ F (x) ❧➔ ♠ët ♥❣✉②➯♥ ❤➔♠ ❝õ❛ ❤➔♠ sè f (x) = cos12 x ✳ ❇✐➳t F π4 + kπ = k ✈ỵ✐ ♠å✐ k ∈ Z✳ ❚➼♥❤ F (0) + F (π) + F (2π) + + F (10π)✳ ❆✳ 45✳ ❇✳ 0✳ ❈✳ 55✳ ❉✳ 44✳ ởt ữớ ỷ số t 100 tr ỗ ✈➔♦ ♥❣➙♥ ❤➔♥❣ ✈ỵ✐ ❧➣✐ s✉➜t 0, 5%/t❤→♥❣ ✈➔ ỉ♥❣ t rút ộ t ởt tr ỗ tø s❛✉ ♥❣➔② ❣û✐ ♠ët t❤→♥❣ ❝❤♦ ✤➳♥ ❦❤✐ ❤➳t t✐➲♥ ✭t❤→♥❣ ❝✉è✐ ❝ò♥❣ ❝â t❤➸ ❦❤ỉ♥❣ ❝á♥ ✤õ ♠ët tr ỗ ọ ổ t rút t t s ♥❤✐➯✉ t❤→♥❣❄ ❆✳ 100✳ ❇✳ 140✳ ❈✳ 138✳ ❉✳ 139✳ ❈➙✉ ✹✽✳ ❈❤♦ ❤➻♥❤ ❝❤â♣ S.ABCD ❝â ✤→② ❧➔ ❤➻♥❤ ❜➻♥❤ ❤➔♥❤ ✈➔ ❝â t❤➸ t➼❝❤ ❜➡♥❣ 48✳ ❚r➯♥ ❝↕♥❤ SB, SD ❧➜② ✤✐➸♠ ❝→❝ M, N s❛♦ ❝❤♦ SM = M B, SD = 3SN ✳ ▼➦t ♣❤➥♥❣ (AM N ) ❝➢t SC t↕✐ P ✳ ❚➼♥❤ t❤➸ t➼❝❤ V ❝õ❛ ❦❤è✐ tù ❞✐➺♥ SM N P ✳ ❆✳ V = 13 ✳ ❇✳ V = 12 ✳ ❈✳ V = 2✳ ❉✳ V = 1✳ ; 2019π ❈➙✉ ✹✾✳ ❚➼♥❤ sè ♥❣❤✐➺♠ ❝õ❛ ♣❤÷ì♥❣ tr➻♥❤ cotx = 2x tr♦♥❣ ❦❤♦↔♥❣ 11π 12 ❆✳ 2019✳ ❇✳ 2018✳ ❈✳ 1✳ ❉✳ 2020✳ ❚r❛♥❣ ✺✴✻ ▼➣ ✤➲ ✶✵✶ ❈➙✉ ✺✵✳ ❈❤♦ ❤➔♠ sè f (x) ❝â ✤↕♦ ❤➔♠ ❧✐➯♥ tö❝ tr➯♥ R ✈➔ t❤ä❛ ♠➣♥ ✱ f (x) dx = f (1) = ✳ ❚➼♥❤ t➼❝❤ ♣❤➙♥ I = f (x) tan2 x + f (x) tan x dx cot ❆✳ − ln(cos 1)✳ ❇✳ 0✳ ✳ ❈✳ −1✳ ❉✳ − cot 1✳ ✲ ✲ ✲ ✲ ✲ ✲ ✲ ✲ ✲ ✲ ❍➌❚✲ ✲ ✲ ✲ ✲ ✲ ✲ ✲ ✲ ✲ ❚r❛♥❣ ✻✴✻ ▼➣ ✤➲ ✶✵✶ ❙Ð ●❉ ❱⑨ ✣❚ ◗❯❷◆● ❚❘➚ ❑➐ ❚❍■ ❚❍Û ❚❍P❚ ◗❯➮❈ ●■❆ ▲❺◆ ✶ ◆❿▼ ì P ị ❣✐❛♥ ❧➔♠ ❜➔✐ ✾✵ ♣❤ót✱ ❦❤ỉ♥❣ ❦➸ t❤í✐ ❣✐❛♥ ❣✐❛♦ ✤➲ ✭ ✣➲ t❤✐ ❝â ✻ tr❛♥❣ ✮ ▼➣ ✤➲ t❤✐ ✶✵✷ − i) ❈➙✉ ✶✳ ❈❤♦ sè ♣❤ù❝ z = (2 −33i)(4 ✳ ❚➻♠ tå❛ ✤ë ✤✐➸♠ ❜✐➸✉ ❞✐➵♥ ❝õ❛ sè ♣❤ù❝ z tr➯♥ + 2i ♠➦t ♣❤➥♥❣ Oxy✳ ❆✳ (1; 4)✳ ❇✳ (−1; −4)✳ ❈✳ (−1; 4)✳ ❉✳ (1; −4)✳ ❈➙✉ ✷✳ ❚➼♥❤ sè ✤÷í♥❣ t✐➺♠ ❝➟♥ ỗ t số y = xx2 +3xx +22 ✳ ❆✳ 3✳ ❇✳ 1✳ ❈✳ 0✳ ❉✳ 2✳ ❈➙✉ ✸✳ ❈❤♦ ❜✐➸✉ t❤ù❝ P = 3 3 ✳ ▼➺♥❤ ✤➲ ♥➔♦ tr♦♥❣ ❝→❝ ♠➺♥❤ ✤➲ s❛✉ ❧➔ ✤ó♥❣❄ ❆✳ P = ✳ ❇✳ P = ✳ ❈✳ P = ✳ ❉✳ P = 23 ✳ ❈➙✉ ✹✳ ❍➔♠ sè y = −x3 + 3x2 ỗ tr t ủ tr ❝→❝ t➟♣ ❤đ♣ ✤÷đ❝ ❝❤♦ 2 18 18 ữợ ❆✳ (2; +∞)✳ ❇✳ (−∞; 0)✳ ❈✳ (−∞; 0) ∪ (2; +∞)✳ ❉✳ (0; 2)✳ ❈➙✉ ✺✳ ❚➻♠ ♥❣✉②➯♥ ❤➔♠ ❝õ❛ ❤➔♠ sè f (x) = −1 2x tr➯♥ −∞; 12 ✳ ❆✳ ln |2x − 1| + C ✳ ❇✳ − 12 ln |2x − 1| + C ✳ ❈✳ 12 ln |2x − 1| + C ✳ ❉✳ 12 ln(1 − 2x) + C ✳ ❈➙✉ ✻✳ ❑❤è✐ ♥â♥ (N ) ❝â ❜→♥ ❦➼♥❤ ✤→② ❜➡♥❣ ✈➔ ❞✐➺♥ t➼❝❤ ①✉♥❣ q✉❛♥❤ ❜➡♥❣ 15π✳ ❚➼♥❤ t❤➸ t➼❝❤ ❦❤è✐ ♥â♥ (N )✳ ❆✳ 36π✳ ❇✳ 12π✳ ❈✳ 45π✳ ❈➙✉ ✼✳ ❚➼♥❤ ❞✐➺♥ t➼❝❤ ❝õ❛ ♠➦t ❝➛✉ ❝â ❜→♥ ❦➼♥❤ ❜➡♥❣ 3✳ ❆✳ 36π✳ ❇✳ 9π✳ ❈✳ 12π✳ ❈➙✉ ✽✳ ❈❤♦ sè ♣❤ù❝ z = (1 − 2i)2✳ ❚➼♥❤ ♠æ ✤✉♥ ❝õ❛ sè ♣❤ù❝ z1 ✳ ❆✳ 251 ✳ ❇✳ √1 ✳ ❈✳ √5✳ ❉✳ 16π✳ ❉✳ 18π✳ ❉✳ 15 ✳ ❈➙✉ ✾✳ ❚➼♥❤ t❤➸ t➼❝❤ ❦❤è✐ trö ❝â ❜→♥ ❦➼♥❤ R = 3, ❝❤✐➲✉ ❝❛♦ h = ❆✳ V = 15π✳ ❇✳ V = 45π✳ ❈✳ V = 90π✳ ❉✳ V = 45✳ ❈➙✉ ✶✵✳ ❚r♦♥❣ ❦❤ỉ♥❣ ❣✐❛♥ ✈ỵ✐ ❤➺ tå❛ ✤ë Oxyz✱ ❝❤♦ ♠➦t ♣❤➥♥❣ (P )✿ 2x − 2y + z + 2017 = tỡ tr tỡ ữủ ữợ ❧➔ ♠ët ✈➨❝✲tì ♣❤→♣ t✉②➳♥ ❝õ❛ (P )❄ ❆✳ ★✔n = (−2; 2; 1)✳ ❇✳ ★✔n = (4; −4; 2)✳ ❈✳ ★✔n = (1; −1; 4)✳ ❉✳ ★✔n = (1; −2; 2)✳ ❈➙✉ ✶✶✳ ❚➻♠ ♥❣❤✐➺♠ ❝õ❛ ♣❤÷ì♥❣ tr➻♥❤ log3(x − 2) = 2✳ ❆✳ x = 10✳ ❇✳ x = 8✳ ❈✳ x = 9✳ ❉✳ x = 11✳ ❚r❛♥❣ ✶✴✻ ▼➣ ✤➲ ✶✵✷ ❈➙✉ ✶✷✳ ❚➼♥❤ t➼❝❤ ♣❤➙♥ I = x−1 dx x ✳ ❆✳ I = − ln 2✳ ❇✳ I = + ln 2✳ ❈✳ I = 74 ✳ ❉✳ I = ln 2✳ ❈➙✉ ✶✸✳ ❈❤♦ ❤➔♠ sè ❜➟❝ ❜❛ y = f (x) õ ỗ t ữ ữợ ú ỹ t ❝õ❛ ❤➔♠ sè ❧➔ −1✳ ❇✳ ●✐→ trà ❝ü❝ t✐➸✉ ❝õ❛ ❤➔♠ sè ❜➡♥❣ −1✳ ❈✳ ●✐→ trà ❝ü❝ ✤↕✐ ❝õ❛ ❤➔♠ sè ❧➔ 0✳ ❉✳ ✣✐➸♠ ❝ü❝ ✤↕✐ ❝õ❛ ❤➔♠ sè ❧➔ 3✳ y O x −1 ❈➙✉ ✶✹✳ ❑❤è✐ ❝❤â♣ S.ABCD ❝â ✤→② ABCD ❧➔ ❤➻♥❤ ✈✉æ♥❣ ❝↕♥❤ 3a✱ SA = a, SA ⊥ (ABCD)✳ ❚➼♥❤ t❤➸ t➼❝❤ ❦❤è✐ ❝❤â♣ S.ABCD✳ ❆✳ 6a3✳ ❇✳ 9a3✳ ❈✳ 3a3✳ ❉✳ a3 ✳ ❈➙✉ ✶✺✳ ❈❤♦ ❦❤è✐ ❧➟♣ ♣❤÷ì♥❣ ABCD.A B C D ❝â ✤ë ❞➔✐ ❝↕♥❤ ❧➔ 3❝♠✳ ❚➼♥❤ t❤➸ t➼❝❤ ❝õ❛ ❦❤è✐ tù ❞✐➺♥ ACB D ✳ ❆✳ 3❝♠3✳ ❇✳ 9❝♠3✳ ❈✳ 18❝♠3✳ ❉✳ 18√2❝♠3✳ ❈➙✉ ✶✻✳ ❚r♦♥❣ ♠➦t ♣❤➥♥❣ tå❛ ✤ë Oxy✱ t➟♣ ❤ñ♣ ❝→❝ ✤✐➸♠ ❜✐➸✉ ❞✐➵♥ ❝→❝ sè ♣❤ù❝ z t❤ä❛ ♠➣♥ |z − + 2i| = |z + + 2i| ❧➔ ✤÷í♥❣ t❤➥♥❣ ❝â ♣❤÷ì♥❣ tr➻♥❤ ❆✳ x + 2y = 0✳ ❇✳ x − 2y + = 0✳ ❈✳ x − 2y = 0✳ ❉✳ x + 2y + = 0✳ ❈➙✉ ✶✼✳ ❚r♦♥❣ ❦❤ỉ♥❣ ❣✐❛♥ ✈ỵ✐ ❤➺ tå❛ ✤ë Oxyz✱ ❝❤♦ ♠➦t ♣❤➥♥❣ (P ) : 2x − 2y + z + = 0✳ ❚➼♥❤ ❦❤♦↔♥❣ ❝→❝❤ d tø ✤✐➸♠ M (1; 2; 1) ✤➳♥ ♠➦t ♣❤➥♥❣ (P )✳ ❆✳ d = 31 ✳ ❇✳ d = 3✳ ❈✳ d = 4✳ ❉✳ d = 1✳ ❈➙✉ ✶✽✳ ❇✐➳t r➡♥❣ ❤➔♠ sè F (x) = mx3 + (3m + n)x2 − 4x + ❧➔ ♠ët ♥❣✉②➯♥ ❤➔♠ ❝õ❛ ❤➔♠ sè f (x) = 3x2 + 10x − 4✳ ❚➼♥❤ mn✳ ❆✳ mn = 3✳ ❇✳ mn = 2✳ ❈✳ mn = 1✳ ❉✳ mn = 0✳ ❈➙✉ ✶✾✳ ●å✐ (D) ❤➻♥❤ ♣❤➥♥❣ ❣✐ỵ✐ ❤↕♥ ❜ð✐ ❝→❝ ✤÷í♥❣ y = x4 ✱ y = 0✱ x = 1✱ x = 4✳ ❚➼♥❤ t❤➸ t➼❝❤ ✈➟t t❤➸ trá♥ ①♦❛② t↕♦ t❤➔♥❤ ❦❤✐ q✉❛② ❤➻♥❤ (D) q✉❛♥❤ trö❝ Ox✳ 21π 21 15π ❆✳ 15 ✳ ❇✳ ✳ ❈✳ ✳ ❉✳ ✳ 16 16 16 ❈➙✉ ✷✵✳ ❚➼♥❤ tê♥❣ t➜t ❝↔ ❝→❝ ♥❣❤✐➺♠ ❝õ❛ ♣❤÷ì♥❣ tr➻♥❤ 21 log2(x + 3) = log2 x + + x2 − √ x−4+2 x+3 ✳ ❆✳ S = 2✳ ❇✳ S = 1✳ ❈✳ S = − √2✳ ❉✳ S = −1✳ ❈➙✉ ✷✶✳ ❚➻♠ t➜t ❝↔ ❝→❝ ❣✐→ trà t❤ü❝ ❝õ❛ t❤❛♠ sè m ✤➸ ❤➔♠ sè y = x +x 2+−1 m ♥❣❤à❝❤ ❜✐➳♥ tr➯♥ ♠é✐ ❦❤♦↔♥❣ ①→❝ ✤à♥❤ ❝õ❛ ♥â✳ ❆✳ m ≤ −3✳ ❇✳ m < −3✳ ❈✳ m ≤ 1✳ ❉✳ m < 1✳ ❚r❛♥❣ ✷✴✻ ▼➣ ✤➲ ✶✵✷ ❈➙✉ ✷✷✳ ❑❤è✐ ❝❤â♣ t❛♠ ❣✐→❝ ✤➲✉ ❝â ♥❤✐➲✉ ♥❤➜t ❜❛♦ ♥❤✐➯✉ ♠➦t ♣❤➥♥❣ ✤è✐ ①ù♥❣❄ ❆✳ 3✳ ❇✳ 6✳ ❈✳ 9✳ ❉✳ 4✳ ❈➙✉ ✷✸✳ ❈❤♦ sè t❤ü❝ a > 0, a = 1✳ ●✐→ trà log√a √a2 ❜➡♥❣ ❆✳ 1✳ ❇✳ 23 ✳ ❈✳ 49 ✳ ❉✳ 94 ✳ 3 ❈➙✉ ✷✹✳ ❚➼❝❤ ♣❤➙♥ I = (x − 1)2 dx = a − ln b x2 + ✱ tr♦♥❣ ✤â a; b ❧➔ ❝→❝ sè ♥❣✉②➯♥✳ ❚➼♥❤ ❣✐→ trà ❝õ❛ ❜✐➸✉ t❤ù❝ a + b✳ ❆✳ 0✳ ❇✳ 1✳ ❈✳ 3✳ ❉✳ −1✳ ❈➙✉ ✷✺✳ ❚➼♥❤ ✤↕♦ ❤➔♠ ❝õ❛ ❤➔♠ sè y = log9 x2 + ✳ ln x ln ❆✳ y = (x2 +11) ln ✳ ❇✳ y = 2x ✳ ❈✳ y = ✳ ❉✳ y = ✳ x +1 (x + 1) ln x +1 ❈➙✉ ✷✻✳ ●å✐ z1✱ z2 ❧➔ ❤❛✐ ♥❣❤✐➺♠ ♣❤ù❝ ❝õ❛ ♣❤÷ì♥❣ tr➻♥❤ z2 − 4z + = 0✳ ❚➼♥❤ w = ✳ 1 + + i(z1 z2 + z2 z1 ) z1 z2 w = 20 + i ✳ ❇✳ w = − 45 + 20i✳ ❈✳ w = 45 + 20i✳ ❉✳ w = + 20i✳ ❆✳ ❈➙✉ ✷✼✳ ❈❤♦ ❤➻♥❤ ❝❤â♣ S.ABC ❝â t❤➸ t➼❝❤ ❜➡♥❣ 1✳ ❚r➯♥ ❝↕♥❤ BC ❧➜② ✤✐➸♠ E s❛♦ ❝❤♦ ✳ ❚➼♥❤ t❤➸ t➼❝❤ V ❝õ❛ ❦❤è✐ tù ❞✐➺♥ SAEB ✳ ❆✳ ✳ ❇✳ V = 31 ✳ ❈✳ V = 43 ✳ ❉✳ V = 23 ✳ ❈➙✉ ✷✽✳ ❈❤♦ sè ♣❤ù❝ z t❤ä❛ |z − + 2i| = 3✳ ❇✐➳t r➡♥❣ t➟♣ ❤ñ♣ ❝→❝ ✤✐➸♠ ❜✐➵✉ ❞✐➵♥ ❝õ❛ sè ♣❤ù❝ w = 2z + i tr➯♥ ♠➦t ♣❤➥♥❣ (Oxy) ❧➔ ♠ët ✤÷í♥❣ trá♥✳ ❚➻♠ t➙♠ ❝õ❛ ✤÷í♥❣ trá♥ ✤â✳ ❆✳ I(2; −3)✳ ❇✳ I(0; 1)✳ ❈✳ I(1; 0)✳ ❉✳ I(1; 1)✳ ❈➙✉ ✷✾✳ ❈❤♦ x, y > t❤ä❛ ♠➣♥ x + y = 32 ✈➔ ❜✐➸✉ t❤ù❝ P = x4 + 4y1 ✤↕t ❣✐→ trà ♥❤ä ♥❤➜t✳ ❚➼♥❤ x2 + y2✳ 2313 153 ❆✳ 25 ✳ ❇✳ ✳ ❈✳ ✳ ❉✳ ✳ 16 1156 100 ❈➙✉ ✸✵✳ ❚r♦♥❣ ❦❤æ♥❣ ❣✐❛♥ Oxyz✱ ❝❤♦ ♠➦t ❝➛✉ (S) : x2 + y2 + z2 − 8x + 10y − 6z + 49 = 0✳ ❚➼♥❤ ❜→♥ ❦➼♥❤ R ❝õ❛ ♠➦t ❝➛✉ (S)✳ ❆✳ R = 7✳ ❇✳ R = 1✳ ❈✳ R = √99✳ ❉✳ R = √151✳ ❈➙✉ ✸✶✳ ❈❤♦ ❤➻♥❤√ ❝❤â♣ S.ABCD ❝â ✤→② ABCD ❧➔ ❤➻♥❤ ✈✉æ♥❣✱ t➙♠ O✱ ❝↕♥❤ a ✈➔ SO ⊥ (ABCD), SA = 2a 2✳ ●å✐ M, N ❧➛♥ ❧÷đt ❧➔ tr✉♥❣ ✤✐➸♠ ❝õ❛ SA, BC ✳ ❚➼♥❤ ❣â❝ ❣✐ú❛ ✤÷í♥❣ t❤➥♥❣ M N ✈➔ ♠➦t ♣❤➥♥❣ (ABCD)✳ ❆✳ π4 ✳ ❇✳ arctan 2✳ ❈✳ π3 ✳ ❉✳ π6 ✳ BE = 2EC V = ❈➙✉ ✸✷✳ ❈❤♦ F (x) ❧➔ ♠ët ♥❣✉②➯♥ ❤➔♠ ❝õ❛ ❤➔♠ sè f (x) = cos12 x ✳ ❇✐➳t F ♠å✐ k ∈ Z✳ ❚➼♥❤ F (0) + F (π) + F (2π) + + F (10π)✳ ❆✳ 55✳ ❇✳ 45✳ ❈✳ 44✳ π + kπ = k ✈ỵ✐ ❉✳ 0✳ ❚r❛♥❣ ✸✴✻ ▼➣ ✤➲ ✶✵✷ ❈➙✉ ✸✸✳ ❚➼♥❤ sè ❣✐→ trà ♥❣✉②➯♥ ❝õ❛ t❤❛♠ sè m tr➯♥ ❦❤♦↔♥❣ (2019; 2019) số ỗ tr (1; 2)✳ ❆✳ 1✳ ❇✳ 2020✳ ❈✳ 2019✳ ❉✳ 2✳ ❈➙✉ ởt ỏ t ỗ t ố ♥❤❛✉✳ ❍ä✐ ❝â ❜❛♦ ♥❤✐➯✉ ❝→❝❤ ❝➢t ❝❤✐➳❝ ✈á♥❣ ✤â t❤➔♥❤ ✷ ♣❤➛♥ ♠➔ sè ❤↕t ð ♠é✐ ♣❤➛♥ ✤➲✉ ❧➔ sè ❧➫ ❄ ❆✳ 5✳ ❇✳ 90✳ ❈✳ 10✳ ❉✳ 180✳ ❈➙✉ ✸✺✳ ❚➼♥❤ sè ♥❣❤✐➺♠ ❝õ❛ ♣❤÷ì♥❣ tr➻♥❤ cotx = 2x tr♦♥❣ ❦❤♦↔♥❣ 11π ; 2019π 12 ❆✳ 2018✳ ❇✳ 1✳ ❈✳ 2020✳ ❉✳ 2019✳ ❈➙✉ ✸✻✳ ❈❤♦ (D) ữủ ợ ữớ y = 2(x2 − 1); y = − x2✳ ❚➼♥❤ t❤➸ t➼❝❤ ❦❤è✐ trá♥ ①♦❛② t↕♦ t❤➔♥❤ ❞♦ (D) q✉❛② q✉❛♥❤ trö❝ Ox✳ 32 32π 64 ❆✳ 64π ✳ ❇✳ ✳ ❈✳ ✳ ❉✳ ✳ 15 15 15 15 ❈➙✉ ✸✼✳ ❚➼♥❤ tê♥❣ t➜t ❝↔ ❝→❝ ❣✐→ trà ❝õ❛ t❤❛♠ số m tỗ t t ởt số ự z tọ ỗ tớ |z| = m |z − 4m + 3mi| = m2✳ ❆✳ 6✳ ❇✳ 9✳ ❈✳ 4✳ ❉✳ 10✳ y = x4 − 2mx2 − 3m + ❈➙✉ ✸✽✳ ◆❣÷í✐ t❛ ❧➔♠ t↕ t➟♣ ỡ t ữ ợ ❦❤è✐ trư ❜➡♥❣ ♥❤❛✉ ✈➔ t❛② ❝➛♠ ❝ơ♥❣ ❧➔ ❦❤è✐ trư✳ ❇✐➳t ❤❛✐ ✤➛✉ ❧➔ ❤❛✐ ❦❤è✐ trư ✤÷í♥❣ ❦➼♥❤ ✤→② ❜➡♥❣ ✶✷✱ ❝❤✐➲✉ ❝❛♦ ❜➡♥❣ ✻✱ ❝❤✐➲✉ ❞➔✐ t↕ ❜➡♥❣ ✸✵ ✈➔ ❜→♥ ❦➼♥❤ t❛② ❝➛♠ ❜➡♥❣ ✷✳ ❍➣② t➼♥❤ t❤➸ t➼❝❤ ✈➟t ❧✐➺✉ ❧➔♠ ♥➯♥ t↕ t❛② ✤â✳ ❆✳ 6480π✳ ❇✳ 502π✳ ❈✳ 108π✳ ❉✳ 504π✳ ❈➙✉ ✸✾✳ ❚r♦♥❣ ❦❤æ♥❣ ❣✐❛♥ Oxyz✱ ❝❤♦ ♠➦t ♣❤➥♥❣ (P ) : x + y + z − = ✈➔ ❜❛ ✤✐➸♠ ✤✐➸♠ ★✥✥✥✥✥✔ ★✥✥✥✥✥✥✔ ★✥✥✥✥✥✔ ✈➔ C(2; 2; 2)✳ ✣✐➸♠ M (a; b; c) tr➯♥ (P ) s❛♦ ❝❤♦ |M A + 2M B + 3M C| ✤↕t ❣✐→ trà ♥❤ä ♥❤➜t✳ ❚➼♥❤ 2a − 15b + c✳ ❆✳ 1✳ ❇✳ 6✳ ❈✳ 3✳ ❉✳ 8✳ ❈➙✉ ✹✵✳ ❈❤♦ ❤❛✐ sè ♣❤ù❝ z, w t❤ä❛ ♠➣♥ |z − 3√2| = √2, |w − 4√2i| = 2√2✳ ❇✐➳t r➡♥❣ |z − w| ✤↕t ❣✐→ trà ♥❤ä ♥❤➜t ❦❤✐ z = zo, w = wo✳ ❚➼♥❤ |3zo − wo|✳ ❆✳ 6√2✳ ❇✳ 1✳ ❈✳ 4√2✳ ❉✳ 2√2✳ ❈➙✉ ✹✶✳ ▼ët ♥❣÷í✐ ỷ số t 100 tr ỗ ợ ❧➣✐ s✉➜t 0, 5%/t❤→♥❣ ✈➔ ỉ♥❣ t❛ rót ✤➲✉ ✤➦♥ ộ t ởt tr ỗ tứ s ỷ ♠ët t❤→♥❣ ❝❤♦ ✤➳♥ ❦❤✐ ❤➳t t✐➲♥ ✭t❤→♥❣ ❝✉è✐ ❝ò♥❣ õ t ổ ỏ ởt tr ỗ ọ ổ t❛ rót ❤➳t t✐➲♥ s❛✉ ❜❛♦ ♥❤✐➯✉ t❤→♥❣❄ ❆✳ 139✳ ❇✳ 140✳ ❈✳ 100✳ ❉✳ 138✳ ❈➙✉ ✹✷✳ ●å✐ M (a; b) tr ỗ t số y = x −x s❛♦ ❝❤♦ ❦❤♦↔♥❣ ❝→❝❤ tø M ✤➳♥ ✤÷í♥❣ t❤➥♥❣ d : y = 2x + ♥❤ä ♥❤➜t✳ ❚➼♥❤ (4a + 5)2 + (2b − 7)2✳ A(3; 1; 1), B(7; 3; 9) ❚r❛♥❣ ✹✴✻ ▼➣ ✤➲ ✶✵✷ ❆✳ 90✳ ❇✳ 10✳ ❈✳ 180✳ ❉✳ 5✳ ❈➙✉ ✹✽✳ ❚➼♥❤ sè ❣✐→ trà ♥❣✉②➯♥ ❝õ❛ t❤❛♠ sè m tr (2019; 2019) số ỗ tr➯♥ ❦❤♦↔♥❣ (1; 2)✳ ❆✳ 2019✳ ❇✳ 1✳ ❈✳ 2✳ ❉✳ 2020✳ ❈➙✉ ✹✾✳ ❚➼♥❤ sè ♥❣❤✐➺♠ ❝õ❛ ♣❤÷ì♥❣ tr➻♥❤ cotx = 2x tr♦♥❣ ❦❤♦↔♥❣ 11π ; 2019π 12 ❆✳ 2019✳ ❇✳ 1✳ ❈✳ 2020✳ ❉✳ 2018✳ ❈➙✉ ✺✵✳ ❈❤♦ ❤➔♠ sè f (x) ❝â ✤↕♦ ❤➔♠ f (x) = (x − 1)(x2 − 3)(x4 − 1) ✈ỵ✐ ♠å✐ x t❤✉ë❝ R✳ ❙♦ s→♥❤ f (−2), f (0), f (2)✱ t❛ ✤÷đ❝ ❆✳ f (2) < f (0) < f (−2)✳ ❇✳ f (−2) < f (0) < f (2)✳ ❈✳ f (0) < f (−2) < f (2)✳ ❉✳ f (−2) < f (2) < f (0)✳ ✲ ✲ ✲ ✲ ✲ ✲ ✲ ✲ ✲ ✲ ❍➌❚✲ ✲ ✲ ✲ ✲ ✲ ✲ ✲ ✲ ✲ y = x4 − 2mx2 − 3m + ❚r❛♥❣ ✻✴✻ ▼➣ ✤➲ ✶✵✻ ❙Ð ●❉ ❱⑨ ✣❚ ◗❯❷◆● ❚❘➚ ❑➐ ❚❍■ ❚❍Û ❚❍P❚ ◗❯➮❈ ●■❆ ▲❺◆ ✶ ◆❿▼ ✷✵✶✾ ▼➷◆ ❚❖⑩◆ ì P ị ✾✵ ♣❤ót✱ ❦❤ỉ♥❣ ❦➸ t❤í✐ ❣✐❛♥ ❣✐❛♦ ✤➲ ✭ ✣➲ t❤✐ ❝â ✻ tr❛♥❣ ✮ ▼➣ ✤➲ t❤✐ ✶✵✼ ❈➙✉ ✶✳ ❈❤♦ ❦❤è✐ ❧➟♣ ♣❤÷ì♥❣ ABCD.A B C D ❝â ✤ë ❞➔✐ ❝↕♥❤ ❧➔ 3❝♠✳ ❚➼♥❤ t❤➸ t➼❝❤ ❝õ❛ ❦❤è✐ tù ❞✐➺♥ ACB D ✳ ❆✳ 18√2❝♠3✳ ❇✳ 18❝♠3✳ ❈✳ 3❝♠3✳ ❉✳ 9❝♠3✳ ❈➙✉ ✷✳ ❚➼♥❤ t❤➸ t➼❝❤ ❦❤è✐ trö ❝â ❜→♥ ❦➼♥❤ R = 3, ❝❤✐➲✉ ❝❛♦ h = ❆✳ V = 15π✳ ❇✳ V = 90π✳ ❈✳ V = 45π✳ ❉✳ V = 45✳ ❈➙✉ ✸✳ ❚r♦♥❣ ❦❤ỉ♥❣ ❣✐❛♥ ✈ỵ✐ ❤➺ tå❛ ✤ë Oxyz✱ ❝❤♦ ♠➦t ♣❤➥♥❣ (P ) : 2x − 2y + z + = 0✳ ❚➼♥❤ ❦❤♦↔♥❣ ❝→❝❤ d tø ✤✐➸♠ M (1; 2; 1) ✤➳♥ ♠➦t ♣❤➥♥❣ (P )✳ ❆✳ d = 1✳ ❇✳ d = 13 ✳ ❈✳ d = 3✳ ❉✳ d = 4✳ ❈➙✉ ✹✳ ❍➔♠ sè y = x3 + 3x2 ỗ tr t ủ tr t ủ ữủ ữợ (2; +∞)✳ ❇✳ (0; 2)✳ ❈✳ (−∞; 0)✳ ❉✳ (−∞; 0) ∪ (2; +∞)✳ − i) ❈➙✉ ✺✳ ❈❤♦ sè ♣❤ù❝ z = (2 −33i)(4 ✳ ❚➻♠ tå❛ ✤ë ✤✐➸♠ ❜✐➸✉ ❞✐➵♥ ❝õ❛ sè ♣❤ù❝ z tr➯♥ + 2i ♠➦t ♣❤➥♥❣ Oxy✳ ❆✳ (1; 4)✳ ❇✳ (1; −4)✳ ❈✳ (−1; −4)✳ ❉✳ (−1; 4)✳ ❈➙✉ ✻✳ ❚➼♥❤ t➼❝❤ ♣❤➙♥ I = x−1 dx x ✳ ❈✳ I = + ln 2✳ ❉✳ I = ln 2✳ ❆✳ I = − ln 2✳ ❇✳ I = 74 ✳ ❈➙✉ ✼✳ ❚r♦♥❣ ❦❤ỉ♥❣ ❣✐❛♥ ✈ỵ✐ ❤➺ tå❛ ✤ë Oxyz✱ ❝❤♦ ♠➦t ♣❤➥♥❣ (P )✿ 2x − 2y + z + 2017 = 0✱ ✈➨❝✲tì ♥➔♦ tr♦♥❣ ❝→❝ tỡ ữủ ữợ ởt tỡ t ❝õ❛ (P )❄ ❆✳ ★✔n = (1; −2; 2)✳ ❇✳ ★✔n = (4; −4; 2)✳ ❈✳ ★✔n = (1; −1; 4)✳ ❉✳ ★✔n = (−2; 2; 1)✳ ❈➙✉ ✽✳ số ữớ t ỗ t số y = xx2 −+3xx −+22 ✳ ❆✳ 3✳ ❇✳ 1✳ ❈✳ 2✳ ❉✳ 0✳ ❈➙✉ ✾✳ ❈❤♦ sè ♣❤ù❝ z = (1 − 2i)2✳ ❚➼♥❤ ♠æ ✤✉♥ ❝õ❛ sè ♣❤ù❝ z1 ✳ ❆✳ 15 ✳ ❇✳ √1 ✳ ❈✳ 251 ✳ ❉✳ √5✳ ❈➙✉ ✶✵✳ ❈❤♦ ❜✐➸✉ t❤ù❝ P = ❆✳ P = 18 ✳ ❇✳ P = 3 3 18 ✳ ✳ ▼➺♥❤ ✤➲ ♥➔♦ tr♦♥❣ ❝→❝ ♠➺♥❤ ✤➲ s❛✉ ❧➔ ✤ó♥❣❄ ❈✳ P = ✳ ❉✳ P = ✳ ❚r❛♥❣ ✶✴✻ ▼➣ ✤➲ ✶✵✼ ❈➙✉ ✶✶✳ ❚➻♠ ♥❣❤✐➺♠ ❝õ❛ ♣❤÷ì♥❣ tr➻♥❤ log3(x − 2) = 2✳ ❆✳ x = 11✳ ❇✳ x = 8✳ ❈✳ x = 10✳ ❉✳ x = 9✳ ❈➙✉ ✶✷✳ ❑❤è✐ ❝❤â♣ S.ABCD ❝â ✤→② ABCD ❧➔ ❤➻♥❤ ✈✉æ♥❣ ❝↕♥❤ 3a✱ SA = a, SA ⊥ (ABCD)✳ ❚➼♥❤ t❤➸ t➼❝❤ ❦❤è✐ ❝❤â♣ S.ABCD✳ ❆✳ 3a3✳ ❇✳ 9a3✳ ❈✳ 6a3✳ ❉✳ a3 ✳ ❈➙✉ ✶✸✳ ❑❤è✐ ♥â♥ (N ) ❝â ❜→♥ ❦➼♥❤ ✤→② ❜➡♥❣ ✈➔ ❞✐➺♥ t➼❝❤ ①✉♥❣ q✉❛♥❤ ❜➡♥❣ 15π✳ ❚➼♥❤ t❤➸ t➼❝❤ ❦❤è✐ ♥â♥ (N )✳ ❆✳ 36π✳ ❇✳ 12π✳ ❈✳ 16π✳ ❉✳ 45π✳ ❈➙✉ ✶✹✳ ❚➻♠ ♥❣✉②➯♥ ❤➔♠ ❝õ❛ ❤➔♠ sè f (x) = −1 2x tr➯♥ −∞; 12 ✳ ❆✳ − 21 ln |2x − 1| + C ✳ ❇✳ 21 ln |2x − 1| + C ✳ ❈✳ ln |2x − 1| + C ✳ ❉✳ 21 ln(1 − 2x) + C ✳ ❈➙✉ ✶✺✳ ❈❤♦ ❤➔♠ số y = f (x) õ ỗ t ữ ữợ ú y ❆✳ ✣✐➸♠ ❝ü❝ t✐➸✉ ❝õ❛ ❤➔♠ sè ❧➔ −1✳ ❇✳ ●✐→ trà ❝ü❝ ✤↕✐ ❝õ❛ ❤➔♠ sè ❧➔ 0✳ ❈✳ ✣✐➸♠ ❝ü❝ ✤↕✐ ❝õ❛ ❤➔♠ sè ❧➔ 3✳ O x ❉✳ ●✐→ trà ❝ü❝ t✐➸✉ ❝õ❛ ❤➔♠ sè ❜➡♥❣ −1✳ −1 ❈➙✉ ✶✻✳ ❚r♦♥❣ ♠➦t ♣❤➥♥❣ tå❛ ✤ë Oxy✱ t➟♣ ❤ñ♣ ❝→❝ ✤✐➸♠ ❜✐➸✉ ❞✐➵♥ ❝→❝ sè ♣❤ù❝ z t❤ä❛ ♠➣♥ |z − + 2i| = |z + + 2i| ❧➔ ✤÷í♥❣ t❤➥♥❣ ❝â ♣❤÷ì♥❣ tr➻♥❤ ❆✳ x + 2y + = 0✳ ❇✳ x − 2y + = 0✳ ❈✳ x − 2y = 0✳ ❉✳ x + 2y = 0✳ ❈➙✉ ✶✼✳ ❚➼♥❤ ❞✐➺♥ t➼❝❤ ❝õ❛ ♠➦t ❝➛✉ ❝â ❜→♥ ❦➼♥❤ ❜➡♥❣ 3✳ ❆✳ 18π✳ ❇✳ 9π✳ ❈✳ 12π✳ ❉✳ 36π✳ ❈➙✉ ✶✽✳ ❚➼♥❤ tê♥❣ t➜t ❝↔ ❝→❝ ♥❣❤✐➺♠ ❝õ❛ ♣❤÷ì♥❣ tr➻♥❤ 21 log2(x + 3) = log2 x + + x2 − √ x − + x + 3✳ ❆✳ S = 1✳ ❇✳ S = − √2✳ ❈✳ S = −1✳ ❉✳ S = 2✳ ❈➙✉ ✶✾✳ ❈❤♦ sè ♣❤ù❝ z t❤ä❛ |z − + 2i| = 3✳ ❇✐➳t r➡♥❣ t➟♣ ❤ñ♣ ❝→❝ ✤✐➸♠ ❜✐➵✉ ❞✐➵♥ ❝õ❛ sè ♣❤ù❝ w = 2z + i tr➯♥ ♠➦t ♣❤➥♥❣ (Oxy) ❧➔ ♠ët ✤÷í♥❣ trá♥✳ ❚➻♠ t➙♠ ❝õ❛ ✤÷í♥❣ trá♥ ✤â✳ ❆✳ I(1; 0)✳ ❇✳ I(0; 1)✳ ❈✳ I(1; 1)✳ ❉✳ I(2; −3)✳ ❈➙✉ ✷✵✳ ❑❤è✐ ❝❤â♣ t❛♠ ❣✐→❝ ✤➲✉ ❝â ♥❤✐➲✉ ♥❤➜t ❜❛♦ ♥❤✐➯✉ ♠➦t ♣❤➥♥❣ ✤è✐ ①ù♥❣❄ ❆✳ 4✳ ❇✳ 3✳ ❈✳ 6✳ ❉✳ 9✳ ❈➙✉ ✷✶✳ ❚r♦♥❣ ❦❤æ♥❣ ❣✐❛♥ Oxyz✱ ❝❤♦ ♠➦t ❝➛✉ (S) : x2 + y2 + z2 − 8x + 10y − 6z + 49 = 0✳ ❚➼♥❤ ❜→♥ ❦➼♥❤ R ❝õ❛ ♠➦t ❝➛✉ (S)✳ ❈✳ R = 7✳ ❉✳ R = √151✳ ❆✳ R = 1✳ ❇✳ R = √99✳ ❚r❛♥❣ ✷✴✻ ▼➣ ✤➲ ✶✵✼ ❈➙✉ ✷✷✳ ❈❤♦ sè t❤ü❝ a > 0, a = 1✳ ●✐→ trà log√a √a2 ❜➡♥❣ ❆✳ 94 ✳ ❇✳ 32 ✳ ❈✳ 49 ✳ ❉✳ 1✳ ❈➙✉ ✷✸✳ ❈❤♦ ❤➻♥❤ ❝❤â♣ S.ABC ❝â t❤➸ t➼❝❤ ❜➡♥❣ 1✳ ❚r➯♥ ❝↕♥❤ BC ❧➜② ✤✐➸♠ E s❛♦ ❝❤♦ 3 ✳ ❚➼♥❤ t❤➸ t➼❝❤ V ❝õ❛ ❦❤è✐ tù ❞✐➺♥ SAEB ✳ ✳ ❇✳ V = 61 ✳ ❈✳ V = 13 ✳ ❉✳ V = 23 ✳ ❆✳ ❈➙✉ ✷✹✳ ❇✐➳t r➡♥❣ ❤➔♠ sè F (x) = mx3 + (3m + n)x2 − 4x + ❧➔ ♠ët ♥❣✉②➯♥ ❤➔♠ ❝õ❛ ❤➔♠ sè f (x) = 3x2 + 10x − 4✳ ❚➼♥❤ mn✳ ❆✳ mn = 0✳ ❇✳ mn = 3✳ ❈✳ mn = 2✳ ❉✳ mn = 1✳ ❈➙✉ ✷✺✳ ❈❤♦ x, y > t❤ä❛ ♠➣♥ x + y = 23 ✈➔ ❜✐➸✉ t❤ù❝ P = x4 + 4y1 ✤↕t ❣✐→ trà ♥❤ä ♥❤➜t✳ ❚➼♥❤ x2 + y2✳ 2313 153 ❆✳ 25 ✳ ❇✳ ✳ ❈✳ ✳ ❉✳ ✳ 16 1156 100 ❈➙✉ ✷✻✳ (D) ợ ữớ y = x4 ✱ y = 0✱ x = 1✱ x = 4✳ ❚➼♥❤ t❤➸ t➼❝❤ ✈➟t t❤➸ trá♥ ①♦❛② t↕♦ t❤➔♥❤ ❦❤✐ q✉❛② ❤➻♥❤ (D) q✉❛♥❤ trö❝ Ox✳ 15π 15 21 ✳ ❇✳ ✳ ❈✳ ✳ ❉✳ ✳ ❆✳ 21π 16 16 16 ❈➙✉ ✷✼✳ ❚➼♥❤ ✤↕♦ ❤➔♠ ❝õ❛ ❤➔♠ sè y = log9 x2 + ✳ ln ❆✳ y = x22ln+31 ✳ ❇✳ y = (x2 +x1) ln ✳ ❈✳ y = (x2 +11) ln ✳ ❉✳ y = 2x ✳ x +1 BE = 2EC V = ❈➙✉ ✷✽✳ ❚➼❝❤ ♣❤➙♥ I = (x − 1)2 dx = a − ln b x2 + ✱ tr♦♥❣ ✤â a; b ❧➔ ❝→❝ sè ♥❣✉②➯♥✳ ❚➼♥❤ ❣✐→ trà ❝õ❛ ❜✐➸✉ t❤ù❝ a + b✳ ❆✳ −1✳ ❇✳ 0✳ ❈✳ 3✳ ❉✳ 1✳ ❈➙✉ ✷✾✳ ●å✐ z1✱ z2 ❧➔ ❤❛✐ ♥❣❤✐➺♠ ♣❤ù❝ ❝õ❛ ♣❤÷ì♥❣ tr➻♥❤ z2 − 4z + = 0✳ ❚➼♥❤ w 1 + + i(z1 z2 + z2 z1 )✳ z1 z2 ❆✳ w = + 20i✳ ❇✳ w = 20 + 45 i✳ ❈✳ w = 45 + 20i✳ ❉✳ w = − 45 + 20i✳ = ❈➙✉ ✸✵✳ ❚➻♠ t➜t ❝↔ ❝→❝ ❣✐→ trà t❤ü❝ ❝õ❛ t❤❛♠ sè m ✤➸ ❤➔♠ sè y = x +x 2+−1 m ♥❣❤à❝❤ ❜✐➳♥ tr➯♥ ♠é✐ ❦❤♦↔♥❣ ①→❝ ✤à♥❤ ❝õ❛ ♥â✳ ❆✳ m ≤ −3✳ ❇✳ m < 1✳ ❈✳ m ≤ 1✳ ❉✳ m < −3✳ ❈➙✉ ✸✶✳ ❚r♦♥❣ ❦❤æ♥❣ ❣✐❛♥ Oxyz✱ ❝❤♦ ♠➦t ♣❤➥♥❣ (P ) : x − y + = ✈➔ ❤❛✐ ✤✐➸♠ A(1; 2; 3), B(1; 0; 1)✳ ✣✐➸♠ C(a; b; −2) ∈ (P ) s❛♦ ❝❤♦ t❛♠ ❣✐→❝ ABC ❝â ❞✐➺♥ t➼❝❤ ♥❤ä ♥❤➜t✳ ❚➼♥❤ a + b✳ ❆✳ 0✳ ❇✳ 1✳ ❈✳ −3✳ ❉✳ 2✳ ❚r❛♥❣ ✸✴✻ ▼➣ ✤➲ ✶✵✼ ❈➙✉ ✸✷✳ ◆❣÷í✐ t❛ ❧➔♠ t↕ t ỡ t ữ ợ ❤❛✐ ❦❤è✐ trư ❜➡♥❣ ♥❤❛✉ ✈➔ t❛② ❝➛♠ ❝ơ♥❣ ❧➔ ❦❤è✐ trư✳ ❇✐➳t ❤❛✐ ✤➛✉ ❧➔ ❤❛✐ ❦❤è✐ trư ✤÷í♥❣ ❦➼♥❤ ✤→② ❜➡♥❣ ✶✷✱ ❝❤✐➲✉ ❝❛♦ ❜➡♥❣ ✻✱ ❝❤✐➲✉ ❞➔✐ t↕ ❜➡♥❣ ✸✵ ✈➔ ❜→♥ ❦➼♥❤ t❛② ❝➛♠ ❜➡♥❣ ✷✳ ❍➣② t➼♥❤ t❤➸ t➼❝❤ ✈➟t ❧✐➺✉ ❧➔♠ ♥➯♥ t↕ t❛② ✤â✳ ❆✳ 504π✳ ❇✳ 6480π✳ ❈✳ 108π✳ ❉✳ 502π✳ ❈➙✉ (D) ữủ ợ ✤÷í♥❣ y = 2(x2 − 1); y = − x2✳ ❚➼♥❤ t❤➸ t➼❝❤ ❦❤è✐ trá♥ ①♦❛② t↕♦ t❤➔♥❤ ❞♦ (D) q✉❛② q✉❛♥❤ trö❝ Ox✳ 32 64π 32π ❆✳ 64 ✳ ❇✳ ✳ ❈✳ ✳ ❉✳ ✳ 15 15 15 15 ❈➙✉ ✸✹✳ ❈❤♦ ❤➔♠ sè f (x) ❝â ✤↕♦ ❤➔♠ f (x) = (x − 1)(x2 − 3)(x4 − 1) ✈ỵ✐ ♠å✐ x t❤✉ë❝ R✳ ❙♦ s→♥❤ f (−2), f (0), f (2)✱ t❛ ✤÷đ❝ ❆✳ f (−2) < f (0) < f (2)✳ ❇✳ f (2) < f (0) < f (−2)✳ ❈✳ f (−2) < f (2) < f (0)✳ ❉✳ f (0) < f (−2) < f (2)✳ ❈➙✉ ✸✺✳ ❈❤♦ ❤➔♠ sè f (x) ❝â f (x) ỗ t số y = f (x) ♥❤÷ ❤➻♥❤ ✈➩ ❜➯♥✳ ❚➼♥❤ sè ✤✐➸♠ ❝ü❝ trà ❝õ❛ √ √ ❤➔♠ sè y = f (x2) tr➯♥ ❦❤♦↔♥❣ (− 5; 5)✳ ❆✳ 2✳ ❇✳ 3✳ ❈✳ 4✳ ❉✳ 5✳ ② y = f (x) ① ❈➙✉ ✸✻✳ ▼ët ♥❣÷í✐ ❣û✐ sè t 100 tr ỗ ợ st 0, 5%/t❤→♥❣ ✈➔ ỉ♥❣ t❛ rót ✤➲✉ ✤➦♥ ♠é✐ t❤→♥❣ ởt tr ỗ tứ s ỷ ởt t ❝❤♦ ✤➳♥ ❦❤✐ ❤➳t t✐➲♥ ✭t❤→♥❣ ❝✉è✐ ❝ò♥❣ ❝â t❤➸ ổ ỏ ởt tr ỗ ọ ổ t rút ❤➳t t✐➲♥ s❛✉ ❜❛♦ ♥❤✐➯✉ t❤→♥❣❄ ❆✳ 140✳ ❇✳ 138✳ ❈✳ 100✳ ❉✳ 139✳ ❈➙✉ ✸✼✳ ❈❤♦ ❤➻♥❤ ❝❤â♣ S.ABCD ❝â ✤→② ❧➔ ❤➻♥❤ ❜➻♥❤ ❤➔♥❤ ✈➔ ❝â t❤➸ t➼❝❤ ❜➡♥❣ 48✳ ❚r➯♥ ❝↕♥❤ SB, SD ❧➜② ✤✐➸♠ ❝→❝ M, N s❛♦ ❝❤♦ SM = M B, SD = 3SN ✳ ▼➦t ♣❤➥♥❣ (AM N ) ❝➢t SC t↕✐ P ✳ ❚➼♥❤ t❤➸ t➼❝❤ V ❝õ❛ ❦❤è✐ tù ❞✐➺♥ SM N P ✳ ❆✳ V = 1✳ ❇✳ V = 12 ✳ ❈✳ V = 13 ✳ ❉✳ V = 2✳ ❚r❛♥❣ ✹✴✻ ▼➣ ✤➲ ✶✵✼ ❈➙✉ ✸✽✳ ❙➠♠ ❧è♣ ①❡ ỉ tỉ ❦❤✐ ❜ì♠ ❝➠♥❣ ✤➦t ♥➡♠ tr➯♥ ♠➦t ♣❤➥♥❣ ♥➡♠ ♥❣❛♥❣ ❝â ❤➻♥❤ ❝❤✐➳✉ ❜➡♥❣ ♥❤÷ ❤➻♥❤ ✈➩ ợ ữớ trỏ ọ R1 = 20cm ữớ trỏ ợ R2 = 30cm t t ❦❤✐ ❝➢t ❜ð✐ ♠➦t ♣❤➥♥❣ ✤✐ q✉❛ trư❝✱ ✈✉ỉ♥❣ ❣â❝ ợ t ữớ trỏ ọ q✉❛ ✤ë ❞➔② ❝õ❛ ✈ä s➠♠✳ ❚➼♥❤ t❤➸ t➼❝❤ ❦❤æ♥❣ ❦❤➼ ✤÷đ❝ ❝❤ù❛ ❜➯♥ tr♦♥❣ s➠♠✳ ❆✳ 2500πcm3✳ ❇✳ 1400πcm3✳ ❈✳ 600πcm3✳ ❉✳ 1250πcm3✳ ❈➙✉ ✸✾✳ ❚➼♥❤ sè ♥❣❤✐➺♠ ❝õ❛ ♣❤÷ì♥❣ tr➻♥❤ cotx = 2x tr♦♥❣ ❦❤♦↔♥❣ 11π ; 2019π 12 ❆✳ 2018✳ ❇✳ 1✳ ❈✳ 2020✳ ❉✳ 2019✳ ❈➙✉ M (a; b) tr ỗ t ❝õ❛ ❤➔♠ sè y = x −x s❛♦ ❝❤♦ ❦❤♦↔♥❣ ❝→❝❤ tø M ✤➳♥ ✤÷í♥❣ t❤➥♥❣ d : y = 2x + ♥❤ä ♥❤➜t✳ ❚➼♥❤ (4a + 5)2 + (2b − 7)2✳ ❆✳ 18✳ ❇✳ 0✳ ❈✳ 162✳ ❉✳ 2✳ ❈➙✉ ✹✶✳ ❈❤♦ ❤❛✐ sè ♣❤ù❝ z, w t❤ä❛ ♠➣♥ |z − 3√2| = √2, |w − 4√2i| = 2√2✳ ❇✐➳t r➡♥❣ |z − w| ✤↕t ❣✐→ trà ♥❤ä ♥❤➜t ❦❤✐ z = zo, w = wo✳ ❚➼♥❤ |3zo − wo|✳ ❇✳ 6√2✳ ❈✳ 1✳ ❆✳ 4√2✳ ❉✳ 22 ởt ỏ t ỗ ❤↕t ❣✐è♥❣ ♥❤❛✉✳ ❍ä✐ ❝â ❜❛♦ ♥❤✐➯✉ ❝→❝❤ ❝➢t ❝❤✐➳❝ ✈á♥❣ ✤â t❤➔♥❤ ✷ ♣❤➛♥ ♠➔ sè ❤↕t ð ♠é✐ ♣❤➛♥ ✤➲✉ ❧➔ sè ❧➫ ❄ ❆✳ 90✳ ❇✳ 10✳ ❈✳ 180✳ ❉✳ 5✳ ❈➙✉ ✹✸✳ ❚➼♥❤ sè ❣✐→ trà ♥❣✉②➯♥ ❝õ❛ t❤❛♠ sè m tr➯♥ ❦❤♦↔♥❣ (−2019; 2019) ✤➸ ❤➔♠ sè y = x4 − 2mx2 − 3m + ỗ tr (1; 2) 2019✳ ❆✳ 2020✳ ❉✳ 2✳ ❈➙✉ ✹✹✳ ❈❤♦ ❤➻♥❤√ ❝❤â♣ S.ABCD ❝â ✤→② ABCD ❧➔ ❤➻♥❤ ✈✉æ♥❣✱ t➙♠ O✱ ❝↕♥❤ a ✈➔ SO ⊥ ✳ ●å✐ M, N ❧➛♥ ❧÷đt ❧➔ tr✉♥❣ ✤✐➸♠ ❝õ❛ SA, BC ✳ ❚➼♥❤ ❣â❝ ❣✐ú❛ ✤÷í♥❣ t❤➥♥❣ M N ✈➔ ♠➦t ♣❤➥♥❣ (ABCD)✳ ❆✳ π4 ✳ ❇✳ arctan 2✳ ❈✳ π6 ✳ ❉✳ π3 ✳ (ABCD), SA = 2a ❈➙✉ ✹✺✳√ ❈❤♦ ❤➻♥❤ ❝❤â♣ S.ABCD ❝â SA ⊥ (ABCD)✱ ✤→② ABCD ❧➔ ❤➻♥❤ ❝❤ú ♥❤➟t ✈ỵ✐ √ ✈➔ BC = a 2✳ ❚➼♥❤ ❦❤♦↔♥❣ ❝→❝❤ ❣✐ú❛ SD ✈➔ BC ✳ ❆✳ ✳ ❇✳ 2a3 ✳ ❈✳ a√3✳ AC = a 3a ❉✳ tọ ỗ tớ |z| = m |z 4m + 3mi| = m2✳ ❆✳ 6✳ ❇✳ 4✳ ❈✳ 9✳ ❉✳ 10✳ √ a ✳ ❈➙✉ ✹✻✳ ❚➼♥❤ tê♥❣ t➜t ❝↔ ❝→❝ ❣✐→ trà ❝õ❛ t❤❛♠ sè m tỗ t t ởt số ự z ❚r❛♥❣ ✺✴✻ ▼➣ ✤➲ ✶✵✼ ❈➙✉ ✹✼✳ ❈❤♦ ❤➔♠ sè f (x) ❝â ✤↕♦ ❤➔♠ ❧✐➯♥ tö❝ tr➯♥ R ✈➔ t❤ä❛ ♠➣♥ ✱ f (x) dx = f (1) = ✳ ❚➼♥❤ t➼❝❤ ♣❤➙♥ I = f (x) tan2 x + f (x) tan x dx cot ✳ ❆✳ − cot 1✳ ❇✳ 0✳ ❈✳ − ln(cos 1)✳ ❉✳ −1✳ ❈➙✉ ✹✽✳ ❚r♦♥❣ ❦❤æ♥❣ ❣✐❛♥ Oxyz✱ ❝❤♦ ♠➦t ♣❤➥♥❣ (P ) : x + y + z − = ✈➔ ❜❛ ✤✐➸♠ ✤✐➸♠ ★✥✥✥✥✥✔ ★✥✥✥✥✥✥✔ ★✥✥✥✥✥✔ ✈➔ C(2; 2; 2)✳ ✣✐➸♠ M (a; b; c) tr➯♥ (P ) s❛♦ ❝❤♦ |M A + 2M B + 3M C| ✤↕t ❣✐→ trà ♥❤ä ♥❤➜t✳ ❚➼♥❤ 2a − 15b + c✳ ❆✳ 8✳ ❇✳ 1✳ ❈✳ 6✳ ❉✳ 3✳ ❈➙✉ ✹✾✳ ❈❤♦ F (x) ❧➔ ♠ët ♥❣✉②➯♥ ❤➔♠ ❝õ❛ ❤➔♠ sè f (x) = cos12 x ✳ ❇✐➳t F π4 + kπ = k ✈ỵ✐ ♠å✐ k ∈ Z✳ ❚➼♥❤ F (0) + F (π) + F (2π) + + F (10π)✳ ❆✳ 55✳ ❇✳ 44✳ ❈✳ 45✳ ❉✳ 0✳ ❈➙✉ ✺✵✳ ❈❤♦ ❤➔♠ sè f (x) ①→❝ ✤à♥❤ tr➯♥ R✱ ❝â ✤↕♦ ❤➔♠ f (x) = (x + 1)3 (x − 2)5 (x + 3)3✳ ❙è ✤✐➸♠ ❝ü❝ trà ❝õ❛ ❤➔♠ sè f (|x|) ❧➔ ❆✳ 5✳ ❇✳ 1✳ ❈✳ 3✳ ❉✳ 2✳ ✲ ✲ ✲ ✲ ✲ ✲ ✲ ✲ ✲ ✲ ❍➌❚✲ ✲ ✲ ✲ ✲ ✲ ✲ ✲ ✲ ✲ A(3; 1; 1), B(7; 3; 9) ❚r❛♥❣ ✻✴✻ ▼➣ ✤➲ ✶✵✼ ❙Ð ●❉ ❱⑨ ✣❚ ◗❯❷◆● ❚❘➚ ❑➐ ❚❍■ ❚❍Û ❚❍P❚ ◗❯➮❈ ●■❆ ▲❺◆ ✶ ◆❿▼ ✷✵✶✾ ì P ị ❧➔♠ ❜➔✐ ✾✵ ♣❤ót✱ ❦❤ỉ♥❣ ❦➸ t❤í✐ ❣✐❛♥ ❣✐❛♦ ✤➲ ✭ ✣➲ t❤✐ ❝â ✻ tr❛♥❣ ✮ ▼➣ ✤➲ t❤✐ ✶✵✽ ❈➙✉ ✶✳ ❈❤♦ ❤➔♠ sè ❜➟❝ ❜❛ y = f (x) õ ỗ t ữ ữợ ú y ỹ ❤➔♠ sè ❧➔ 3✳ ❇✳ ●✐→ trà ❝ü❝ t✐➸✉ ❝õ❛ ❤➔♠ sè ❜➡♥❣ −1✳ ❈✳ ●✐→ trà ❝ü❝ ✤↕✐ ❝õ❛ ❤➔♠ sè ❧➔ 0✳ O x ❉✳ ✣✐➸♠ ❝ü❝ t✐➸✉ ❝õ❛ ❤➔♠ sè ❧➔ −1✳ −1 ❈➙✉ ✷✳ ❚➼♥❤ ❞✐➺♥ t➼❝❤ ❝õ❛ ♠➦t ❝➛✉ ❝â ❜→♥ ❦➼♥❤ ❜➡♥❣ 3✳ ❆✳ 9π✳ ❇✳ 36π✳ ❈✳ 12π✳ ❉✳ 18π✳ ❈➙✉ ✸✳ ❚➻♠ ♥❣❤✐➺♠ ❝õ❛ ♣❤÷ì♥❣ tr➻♥❤ log3(x − 2) = 2✳ ❆✳ x = 8✳ ❇✳ x = 9✳ ❈✳ x = 10✳ ❉✳ x = 11✳ ❈➙✉ ✹✳ số ữớ t ỗ t số y = xx2 −+3xx −+22 ✳ ❆✳ 0✳ ❇✳ 1✳ ❈✳ 3✳ ❉✳ 2✳ ❈➙✉ ✺✳ ❈❤♦ ❦❤è✐ ❧➟♣ ♣❤÷ì♥❣ ABCD.A B C D ❝â ✤ë ❞➔✐ ❝↕♥❤ ❧➔ 3❝♠✳ ❚➼♥❤ t❤➸ t➼❝❤ ❝õ❛ ❦❤è✐ tù ❞✐➺♥ ACB D ✳ ❆✳ 18❝♠3✳ ❇✳ 18√2❝♠3✳ ❈✳ 9❝♠3✳ ❉✳ 3❝♠3✳ ❈➙✉ ✻✳ ❚r♦♥❣ ♠➦t ♣❤➥♥❣ tå❛ ✤ë Oxy✱ t➟♣ ❤ñ♣ ❝→❝ ✤✐➸♠ ❜✐➸✉ ❞✐➵♥ ❝→❝ sè ♣❤ù❝ z t❤ä❛ ♠➣♥ |z − + 2i| = |z + + 2i| ❧➔ ✤÷í♥❣ t❤➥♥❣ ❝â ♣❤÷ì♥❣ tr➻♥❤ ❆✳ x − 2y + = 0✳ ❇✳ x − 2y = 0✳ ❈✳ x + 2y + = 0✳ ❉✳ x + 2y = 0✳ − i) ❈➙✉ ✼✳ ❈❤♦ sè ♣❤ù❝ z = (2 −33i)(4 ✳ ❚➻♠ tå❛ ✤ë ✤✐➸♠ ❜✐➸✉ ❞✐➵♥ ❝õ❛ sè ♣❤ù❝ z tr➯♥ + 2i ♠➦t ♣❤➥♥❣ Oxy✳ ❆✳ (1; −4)✳ ❇✳ (−1; −4)✳ ❈✳ (1; 4)✳ ❉✳ (−1; 4)✳ ❈➙✉ ✽✳ ❑❤è✐ ❝❤â♣ S.ABCD ❝â ✤→② ABCD ❧➔ ❤➻♥❤ ✈✉æ♥❣ ❝↕♥❤ 3a✱ SA = a, SA ⊥ (ABCD)✳ ❚➼♥❤ t❤➸ t➼❝❤ ❦❤è✐ ❝❤â♣ S.ABCD ✳ a ❆✳ 3a3✳ ❇✳ ✳ ❈✳ 9a3✳ ❉✳ 6a3✳ ❈➙✉ ✾✳ ❚➻♠ ♥❣✉②➯♥ ❤➔♠ ❝õ❛ ❤➔♠ sè f (x) = −1 2x tr➯♥ −∞; 12 ✳ ❆✳ ln |2x − 1| + C ✳ ❇✳ 12 ln(1 − 2x) + C ✳ ❈✳ 12 ln |2x − 1| + C ✳ ❉✳ − 12 ln |2x − 1| + C ✳ ❈➙✉ ✶✵✳ ❚➼♥❤ t➼❝❤ ♣❤➙♥ I = x−1 dx x ✳ ❚r❛♥❣ ✶✴✻ ▼➣ ✤➲ ✶✵✽ ❆✳ I = ln 2✳ ❇✳ I = − ln 2✳ ❈✳ I = + ln 2✳ ❉✳ I = 74 ✳ ❈➙✉ ✶✶✳ ❚r♦♥❣ ❦❤æ♥❣ ❣✐❛♥ ✈ỵ✐ ❤➺ tå❛ ✤ë Oxyz✱ ❝❤♦ ♠➦t ♣❤➥♥❣ (P ) : 2x − 2y + z + = 0✳ ❚➼♥❤ ❦❤♦↔♥❣ ❝→❝❤ d tø ✤✐➸♠ M (1; 2; 1) ✤➳♥ ♠➦t ♣❤➥♥❣ (P )✳ ❇✳ d = 4✳ ❈✳ d = 1✳ ❉✳ d = 3✳ ❆✳ d = 31 ✳ ❈➙✉ ✶✷✳ ❑❤è✐ ♥â♥ (N ) ❝â ❜→♥ ❦➼♥❤ ✤→② ❜➡♥❣ ✈➔ ❞✐➺♥ t➼❝❤ ①✉♥❣ q✉❛♥❤ ❜➡♥❣ 15π✳ ❚➼♥❤ t❤➸ t➼❝❤ ❦❤è✐ ♥â♥ (N )✳ ❆✳ 36π✳ ❇✳ 12π✳ ❈✳ 16π✳ ❉✳ 45π✳ ❈➙✉ ✶✸✳ ❈❤♦ sè ♣❤ù❝ z = (1 − 2i)2✳ ❚➼♥❤ ♠æ ✤✉♥ ❝õ❛ sè ♣❤ù❝ z1 ✳ ❆✳ √1 ✳ ❇✳ 251 ✳ ❈✳ √5✳ ❉✳ 15 ✳ ❈➙✉ ✶✹✳ ❍➔♠ số y = x3 + 3x2 ỗ tr➯♥ t➟♣ ❤đ♣ ♥➔♦ tr♦♥❣ ❝→❝ t➟♣ ❤đ♣ ✤÷đ❝ ❝❤♦ ữợ (0; 2) (2; +) ❈❤♦ ❜✐➸✉ t❤ù❝ P = 3 ❈✳ (−∞; 0)✳ 3 ❉✳ (−∞; 0) ∪ (2; +∞)✳ ✳ ▼➺♥❤ ✤➲ ♥➔♦ tr♦♥❣ ❝→❝ ♠➺♥❤ ✤➲ s❛✉ ❧➔ ✤ó♥❣❄ ❆✳ P = ✳ ❈✳ P = ✳ ❉✳ P = ✳ ✳ ❇✳ P = ❈➙✉ ✶✻✳ ❚➼♥❤ t❤➸ t➼❝❤ ❦❤è✐ trö ❝â ❜→♥ ❦➼♥❤ R = 3, ❝❤✐➲✉ ❝❛♦ h = ❆✳ V = 90π✳ ❇✳ V = 45✳ ❈✳ V = 45π✳ ❉✳ V = 15π✳ ❈➙✉ ✶✼✳ ❚r♦♥❣ ❦❤ỉ♥❣ ❣✐❛♥ ✈ỵ✐ ❤➺ tå❛ ✤ë Oxyz✱ ❝❤♦ ♠➦t ♣❤➥♥❣ (P )✿ 2x − 2y + z + 2017 = 0✱ 18 2 18 tỡ tr tỡ ữủ ữợ ✤➙② ❧➔ ♠ët ✈➨❝✲tì ♣❤→♣ t✉②➳♥ ❝õ❛ (P )❄ ❆✳ ★✔n = (4; −4; 2)✳ ❇✳ ★✔n = (−2; 2; 1)✳ ❈✳ ★✔n = (1; −1; 4)✳ ❉✳ ★✔n = (1; −2; 2)✳ ❈➙✉ ✶✽✳ ❈❤♦ ❤➻♥❤ ❝❤â♣ S.ABC ❝â t❤➸ t➼❝❤ ❜➡♥❣ 1✳ ❚r➯♥ ❝↕♥❤ BC ❧➜② ✤✐➸♠ E s❛♦ ❝❤♦ BE = 2EC ✳ ❚➼♥❤ t❤➸ t➼❝❤ V ❝õ❛ ❦❤è✐ tù ❞✐➺♥ SAEB ✳ ❆✳ V = 31 ✳ ❇✳ V = 23 ✳ ❈✳ V = 16 ✳ ❉✳ V = 43 ✳ ❈➙✉ ✶✾✳ ❚➼♥❤ tê♥❣ t➜t ❝↔ ❝→❝ ♥❣❤✐➺♠ ❝õ❛ ♣❤÷ì♥❣ tr➻♥❤ 12 log2(x + 3) = log2 x + + x2 − √ x−4+2 x+3 ✳ ❆✳ S = −1✳ ❇✳ S = 1✳ ❈✳ S = − √2✳ ❉✳ S = 2✳ ❈➙✉ ✷✵✳ ●å✐ (D) ❤➻♥❤ ♣❤➥♥❣ ❣✐ỵ✐ ❤↕♥ ❜ð✐ ❝→❝ ✤÷í♥❣ y = x4 ✱ y = 0✱ x = 1✱ x = 4✳ ❚➼♥❤ t❤➸ t➼❝❤ ✈➟t t❤➸ trá♥ ①♦❛② t↕♦ t❤➔♥❤ ❦❤✐ q✉❛② ❤➻♥❤ (D) q✉❛♥❤ trö❝ Ox✳ 21 15π 21π ❆✳ 15 ✳ ❇✳ ✳ ❈✳ ✳ ❉✳ ✳ 16 16 16 ❈➙✉ ✷✶✳ ❚r♦♥❣ ❦❤æ♥❣ ❣✐❛♥ Oxyz✱ ❝❤♦ ♠➦t ❝➛✉ (S) : x2 + y2 + z2 − 8x + 10y − 6z + 49 = 0✳ ❚➼♥❤ ❜→♥ ❦➼♥❤ R ❝õ❛ ♠➦t ❝➛✉ (S)✳ ❆✳ R = 7✳ ❇✳ R = √151✳ ❈✳ R = √99✳ ❉✳ R = 1✳ ❚r❛♥❣ ✷✴✻ ▼➣ ✤➲ ✶✵✽ ❈➙✉ ✷✷✳ ❈❤♦ x, y > t❤ä❛ ♠➣♥ x + y = 32 ✈➔ ❜✐➸✉ t❤ù❝ P = x4 + 4y1 ✤↕t ❣✐→ trà ♥❤ä ♥❤➜t✳ ❚➼♥❤ x2 + y2✳ 153 25 ❆✳ 2313 ✳ ❇✳ ✳ ❈✳ ✳ ❉✳ ✳ 1156 100 16 ❈➙✉ ✷✸✳ ❑❤è✐ ❝❤â♣ t❛♠ ❣✐→❝ ✤➲✉ ❝â ♥❤✐➲✉ ♥❤➜t ❜❛♦ ♥❤✐➯✉ ♠➦t ♣❤➥♥❣ ✤è✐ ①ù♥❣❄ ❆✳ 6✳ ❇✳ 4✳ ❈✳ 9✳ ❉✳ 3✳ ❈➙✉ ✷✹✳ ❈❤♦ sè ♣❤ù❝ z t❤ä❛ |z − + 2i| = 3✳ ❇✐➳t r➡♥❣ t➟♣ ❤ñ♣ ❝→❝ ✤✐➸♠ ❜✐➵✉ ❞✐➵♥ ❝õ❛ sè ♣❤ù❝ w = 2z + i tr➯♥ ♠➦t ♣❤➥♥❣ (Oxy) ❧➔ ♠ët ✤÷í♥❣ trá♥✳ ❚➻♠ t➙♠ ❝õ❛ ✤÷í♥❣ trá♥ ✤â✳ ❆✳ I(1; 1)✳ ❇✳ I(2; −3)✳ ❈✳ I(1; 0)✳ ❉✳ I(0; 1)✳ ❈➙✉ ✷✺✳ ❚➻♠ t➜t ❝↔ ❝→❝ ❣✐→ trà t❤ü❝ ❝õ❛ t❤❛♠ sè m ✤➸ ❤➔♠ sè y = x +x 2+−1 m ♥❣❤à❝❤ ❜✐➳♥ tr➯♥ ♠é✐ ❦❤♦↔♥❣ ①→❝ ✤à♥❤ ❝õ❛ ♥â✳ ❆✳ m ≤ −3✳ ❇✳ m < 1✳ ❈✳ m ≤ 1✳ ❉✳ m < −3✳ ❈➙✉ ✷✻✳ ❇✐➳t r➡♥❣ ❤➔♠ sè F (x) = mx3 + (3m + n)x2 − 4x + ❧➔ ♠ët ♥❣✉②➯♥ ❤➔♠ ❝õ❛ ❤➔♠ sè f (x) = 3x2 + 10x − 4✳ ❚➼♥❤ mn✳ ❆✳ mn = 0✳ ❇✳ mn = 1✳ ❈✳ mn = 2✳ ❉✳ mn = 3✳ ❈➙✉ ✷✼✳ ❚➼❝❤ ♣❤➙♥ I = (x − 1)2 dx = a − ln b x2 + ✱ tr♦♥❣ ✤â a; b ❧➔ ❝→❝ sè ♥❣✉②➯♥✳ ❚➼♥❤ ❣✐→ trà ❝õ❛ ❜✐➸✉ t❤ù❝ a + b✳ ❆✳ −1✳ ❇✳ 0✳ ❈✳ 3✳ ❉✳ 1✳ ❈➙✉ ✷✽✳ ●å✐ z1✱ z2 ❧➔ ❤❛✐ ♥❣❤✐➺♠ ♣❤ù❝ ❝õ❛ ♣❤÷ì♥❣ tr➻♥❤ z2 − 4z + = 0✳ ❚➼♥❤ 1 + + i(z1 z2 + z2 z1 )✳ z1 z2 ❆✳ w = − 45 + 20i✳ ❇✳ w = 45 + 20i✳ ❈✳ w = + 20i✳ ❉✳ w = 20 + 45 i✳ ❈➙✉ ✷✾✳ ❈❤♦ sè t❤ü❝ a > 0, a = 1✳ ●✐→ trà log√a √a2 ❜➡♥❣ ❆✳ 1✳ ❇✳ 23 ✳ ❈✳ 49 ✳ ❉✳ 94 ✳ ❈➙✉ ✸✵✳ ❚➼♥❤ ✤↕♦ ❤➔♠ ❝õ❛ ❤➔♠ sè y = log9 x2 + ✳ ln ❆✳ y = x22ln+31 ✳ ❇✳ y = (x2 +x1) ln ✳ ❈✳ y = (x2 +11) ln ✳ ❉✳ y = 2x ✳ x2 + w = 3 ❈➙✉ ✸✶✳ ❈❤♦ ❤➻♥❤ ❝❤â♣ S.ABCD ❝â ✤→② ❧➔ ❤➻♥❤ ❜➻♥❤ ❤➔♥❤ ✈➔ ❝â t❤➸ t➼❝❤ ❜➡♥❣ 48✳ ❚r➯♥ ❝↕♥❤ SB, SD ❧➜② ✤✐➸♠ ❝→❝ M, N s❛♦ ❝❤♦ SM = M B, SD = 3SN ✳ ▼➦t ♣❤➥♥❣ (AM N ) ❝➢t SC t↕✐ P ✳ ❚➼♥❤ t❤➸ t➼❝❤ V ❝õ❛ ❦❤è✐ tù ❞✐➺♥ SM N P ✳ ❆✳ V = 1✳ ❇✳ V = 12 ✳ ❈✳ V = 2✳ ❉✳ V = 13 ✳ ❈➙✉ ✸✷✳ ❚➼♥❤ sè ❣✐→ trà ♥❣✉②➯♥ ❝õ❛ t❤❛♠ sè m tr➯♥ ❦❤♦↔♥❣ (−2019; 2019) ✤➸ ❤➔♠ sè y = x4 − 2mx2 3m + ỗ tr (1; 2) ❆✳ 2020✳ ❇✳ 2✳ ❈✳ 1✳ ❉✳ 2019✳ ❚r❛♥❣ ✸✴✻ ▼➣ ✤➲ ✶✵✽ ❈➙✉ ✸✸✳ ❈❤♦ ❤➻♥❤ ♣❤➥♥❣ (D) ✤÷đ❝ ợ ữớ y = 2(x2 1); y = − x2✳ ❚➼♥❤ t❤➸ t➼❝❤ ❦❤è✐ trá♥ ①♦❛② t↕♦ t❤➔♥❤ ❞♦ (D) q✉❛② q✉❛♥❤ trö❝ Ox✳ 32π 32 64 ❆✳ 64π ✳ ❇✳ ✳ ❈✳ ✳ ❉✳ ✳ 15 15 15 15 ❈➙✉ ✸✹✳ ❈❤♦ ❤➻♥❤√ ❝❤â♣ S.ABCD ❝â ✤→② ABCD ❧➔ ❤➻♥❤ ✈✉æ♥❣✱ t➙♠ O✱ ❝↕♥❤ a ✈➔ SO ⊥ (ABCD), SA = 2a 2✳ ●å✐ M, N ❧➛♥ ❧÷đt ❧➔ tr✉♥❣ ✤✐➸♠ ❝õ❛ SA, BC ✳ ❚➼♥❤ ❣â❝ ❣✐ú❛ ✤÷í♥❣ t❤➥♥❣ M N ✈➔ ♠➦t ♣❤➥♥❣ (ABCD)✳ ❈✳ π3 ✳ ❉✳ π4 ✳ ❆✳ arctan 2✳ ❇✳ π6 ✳ ❈➙✉ ✸✺✳ ▼ët ♥❣÷í✐ ❣û✐ sè t 100 tr ỗ ợ st 0, 5%/t❤→♥❣ ✈➔ ỉ♥❣ t❛ rót ✤➲✉ ✤➦♥ ♠é✐ t❤→♥❣ ởt tr ỗ tứ s ỷ ởt t ❝❤♦ ✤➳♥ ❦❤✐ ❤➳t t✐➲♥ ✭t❤→♥❣ ❝✉è✐ ❝ò♥❣ ❝â t❤➸ ổ ỏ ởt tr ỗ ọ ổ t rút ❤➳t t✐➲♥ s❛✉ ❜❛♦ ♥❤✐➯✉ t❤→♥❣❄ ❆✳ 139✳ ❇✳ 140✳ ❈✳ 138✳ ❉✳ 100✳ ❈➙✉ ✸✻✳ ❈❤♦ ❤➔♠ sè f (x) õ f (x) ỗ t ❤➔♠ sè y = f (x) ♥❤÷ ❤➻♥❤ ✈➩ ❜➯♥✳ ❚➼♥❤ sè ✤✐➸♠ ❝ü❝ trà ❝õ❛ √ √ ❤➔♠ sè y = f (x2) tr➯♥ ❦❤♦↔♥❣ (− 5; 5)✳ ❆✳ 3✳ ❇✳ 4✳ ❈✳ 5✳ ❉✳ 2✳ ② y = f (x) ① ❈➙✉ ✸✼✳ ❚➼♥❤ tê♥❣ t➜t ❝↔ ❝→❝ ❣✐→ trà ❝õ❛ t❤❛♠ sè m ✤➸ tỗ t t ởt số ự z tọ ỗ tớ |z| = m |z 4m + 3mi| = m2✳ ❆✳ 6✳ ❇✳ 9✳ ❈✳ 4✳ ❉✳ 10✳ ❈➙✉ ✸✽✳ ❈❤♦ ❤❛✐ sè ♣❤ù❝ z, w t❤ä❛ ♠➣♥ |z − 3√2| = √2, |w − 4√2i| = 2√2✳ ❇✐➳t r➡♥❣ |z − w| ✤↕t ❣✐→ trà ♥❤ä ♥❤➜t ❦❤✐ z = zo, w = wo✳ ❚➼♥❤ |3zo − wo|✳ ❆✳ 4√2✳ ❇✳ 2√2✳ ❈✳ 6√2✳ ❉✳ 1✳ ❈➙✉ ✸✾✳ ❙➠♠ ❧è♣ ①❡ ỉ tỉ ❦❤✐ ❜ì♠ ❝➠♥❣ ✤➦t ♥➡♠ tr➯♥ ♠➦t ♣❤➥♥❣ ♥➡♠ ♥❣❛♥❣ ❝â ❤➻♥❤ ❝❤✐➳✉ ữ ợ ữớ trỏ ọ R1 = 20cm ữớ trỏ ợ R2 = 30cm ✈➔ ♠➦t ❝➢t ❦❤✐ ❝➢t ❜ð✐ ♠➦t ♣❤➥♥❣ ✤✐ q✉❛ trư❝✱ ✈✉ỉ♥❣ ❣â❝ ✈ỵ✐ ♠➠t ♣❤➥♥❣ ♥➡♠ ♥❣❛♥❣ ❧➔ ❤❛✐ ✤÷í♥❣ trá♥✳ ❇ä q✉❛ ✤ë ❞➔② ❝õ❛ ✈ä s➠♠✳ ❚➼♥❤ t❤➸ t➼❝❤ ❦❤ỉ♥❣ ❦❤➼ ✤÷đ❝ ❝❤ù❛ ❜➯♥ tr♦♥❣ s➠♠✳ ❆✳ 2500πcm3✳ ❇✳ 1250πcm3✳ ❈✳ 1400πcm3✳ ❉✳ 600πcm3✳ ❚r❛♥❣ ✹✴✻ ▼➣ ✤➲ ✶✵✽ ❈➙✉ ✹✵✳ ◆❣÷í✐ t❛ ❧➔♠ t↕ t➟♣ ỡ t ữ ợ ❦❤è✐ trư ❜➡♥❣ ♥❤❛✉ ✈➔ t❛② ❝➛♠ ❝ơ♥❣ ❧➔ ❦❤è✐ trư✳ ❇✐➳t ❤❛✐ ✤➛✉ ❧➔ ❤❛✐ ❦❤è✐ trư ✤÷í♥❣ ❦➼♥❤ ✤→② ❜➡♥❣ ✶✷✱ ❝❤✐➲✉ ❝❛♦ ❜➡♥❣ ✻✱ ❝❤✐➲✉ ❞➔✐ t↕ ❜➡♥❣ ✸✵ ✈➔ ❜→♥ ❦➼♥❤ t❛② ❝➛♠ ❜➡♥❣ ✷✳ ❍➣② t➼♥❤ t❤➸ t➼❝❤ ✈➟t ❧✐➺✉ ❧➔♠ ♥➯♥ t↕ t❛② ✤â✳ ❆✳ 6480π✳ ❇✳ 108π✳ ❈✳ 504π✳ ❉✳ 502π✳ ❈➙✉ ✹✶✳ ❚r♦♥❣ ❦❤æ♥❣ ❣✐❛♥ Oxyz✱ ❝❤♦ ♠➦t ♣❤➥♥❣ (P ) : x + y + z − = ✈➔ ❜❛ ✤✐➸♠ ✤✐➸♠ ★✥✥✥✥✥✔ ★✥✥✥✥✥✥✔ ★✥✥✥✥✥✔ ✈➔ C(2; 2; 2)✳ ✣✐➸♠ M (a; b; c) tr➯♥ (P ) s❛♦ ❝❤♦ |M A + 2M B + 3M C| ✤↕t ❣✐→ trà ♥❤ä ♥❤➜t✳ ❚➼♥❤ 2a − 15b + c✳ ❆✳ 8✳ ❇✳ 6✳ ❈✳ 1✳ ❉✳ 3✳ ❈➙✉ ✹✷✳ ❚r♦♥❣ ❦❤æ♥❣ ❣✐❛♥ Oxyz✱ ❝❤♦ ♠➦t ♣❤➥♥❣ (P ) : x − y + = ✈➔ ❤❛✐ ✤✐➸♠ A(1; 2; 3), B(1; 0; 1)✳ ✣✐➸♠ C(a; b; −2) ∈ (P ) s❛♦ ❝❤♦ t❛♠ ❣✐→❝ ABC ❝â ❞✐➺♥ t➼❝❤ ♥❤ä ♥❤➜t✳ ❚➼♥❤ a + b✳ ❆✳ −3✳ ❇✳ 1✳ ❈✳ 2✳ ❉✳ 0✳ ❈➙✉ ✹✸✳√ ❈❤♦ ❤➻♥❤ ❝❤â♣ S.ABCD ❝â SA ⊥ (ABCD)✱ ✤→② ABCD ❧➔ ❤➻♥❤ ❝❤ú ♥❤➟t ✈ỵ✐ √ AC = a ✈➔ BC = a 2✳ ❚➼♥❤ ❦❤♦↔♥❣ ❝→❝❤ ❣✐ú❛ SD √ ✈➔ BC ✳ √ ❆✳ a 3✳ ❇✳ 2a3 ✳ ❈✳ a ✳ ❉✳ 3a4 ✳ ❈➙✉ ✹✹✳ ▼ët ❝❤✐➳❝ ✈á♥❣ t ỗ t ố ọ õ ♥❤✐➯✉ ❝→❝❤ ❝➢t ❝❤✐➳❝ ✈á♥❣ ✤â t❤➔♥❤ ✷ ♣❤➛♥ ♠➔ sè ❤↕t ð ♠é✐ ♣❤➛♥ ✤➲✉ ❧➔ sè ❧➫ ❄ ❆✳ 180✳ ❇✳ 90✳ ❈✳ 10✳ ❉✳ 5✳ ❈➙✉ ✹✺✳ M (a; b) tr ỗ t ❤➔♠ sè y = x −x s❛♦ ❝❤♦ ❦❤♦↔♥❣ ❝→❝❤ tø M ✤➳♥ ✤÷í♥❣ t❤➥♥❣ d : y = 2x + ♥❤ä ♥❤➜t✳ ❚➼♥❤ (4a + 5)2 + (2b − 7)2✳ ❆✳ 0✳ ❇✳ 162✳ ❈✳ 2✳ ❉✳ 18✳ A(3; 1; 1), B(7; 3; 9) ❈➙✉ ✹✻✳ ❈❤♦ ❤➔♠ sè f (x) ❝â ✤↕♦ ❤➔♠ ❧✐➯♥ tö❝ tr➯♥ R ✈➔ t❤ä❛ ♠➣♥ ✱ f (x) dx = f (1) = ✳ ❚➼♥❤ t➼❝❤ ♣❤➙♥ I = f (x) tan2 x + f (x) tan x dx cot ✳ ❆✳ − ln(cos 1)✳ ❇✳ 0✳ ❈✳ − cot 1✳ ❉✳ −1✳ ❈➙✉ ✹✼✳ ❈❤♦ ❤➔♠ sè f (x) ①→❝ ✤à♥❤ tr➯♥ R✱ ❝â ✤↕♦ ❤➔♠ f (x) = (x + 1)3 (x − 2)5 (x + 3)3✳ ❙è ✤✐➸♠ ❝ü❝ trà ❝õ❛ ❤➔♠ sè f (|x|) ❧➔ ❆✳ 3✳ ❇✳ 2✳ ❈✳ 5✳ ❉✳ 1✳ ❈➙✉ ✹✽✳ ❚➼♥❤ sè ♥❣❤✐➺♠ ❝õ❛ ♣❤÷ì♥❣ tr➻♥❤ cotx = 2x tr♦♥❣ ❦❤♦↔♥❣ 11π ; 2019π 12 ❆✳ 2020✳ ❇✳ 2019✳ ❈✳ 1✳ ❉✳ 2018✳ ❚r❛♥❣ ✺✴✻ ▼➣ ✤➲ ✶✵✽ ❈➙✉ ✹✾✳ ❈❤♦ ❤➔♠ sè f (x) ❝â ✤↕♦ ❤➔♠ f (x) = (x − 1)(x2 − 3)(x4 − 1) ✈ỵ✐ ♠å✐ x t❤✉ë❝ R✳ ❙♦ s→♥❤ f (−2), f (0), f (2)✱ t❛ ✤÷đ❝ ❆✳ f (2) < f (0) < f (−2)✳ ❇✳ f (−2) < f (0) < f (2)✳ ❈✳ f (0) < f (−2) < f (2)✳ ❉✳ f (−2) < f (2) < f (0)✳ ❈➙✉ ✺✵✳ ❈❤♦ F (x) ❧➔ ♠ët ♥❣✉②➯♥ ❤➔♠ ❝õ❛ ❤➔♠ sè f (x) = cos12 x ✳ ❇✐➳t F π4 + kπ ♠å✐ k ∈ Z✳ ❚➼♥❤ F (0) + F (π) + F (2π) + + F (10π)✳ ❆✳ 44✳ ❇✳ 45✳ ❈✳ 55✳ ❉✳ 0✳ ✲ ✲ ✲ ✲ ✲ ✲ ✲ ✲ ✲ ✲ ❍➌❚✲ ✲ ✲ ✲ ✲ ✲ ✲ ✲ ✲ ✲ =k ✈ỵ✐ ❚r❛♥❣ ✻✴✻ ▼➣ ✤➲ ✶✵✽ ✣⑩P ⑩◆ ❇❷◆● ✣⑩P ⑩◆ ❈⑩❈ ▼❶ ✣➋ ▼➣ ✤➲ t❤✐ ✶✵✶ ✶✳ ❈ ✶✵✳ ❈ ✶✾✳ ❈ ✷✽✳ ❉ ✸✼✳ ❆ ✹✻✳ ❉ ✷✳ ❆ ✶✶✳ A ✷✵✳ ❇ ✷✾✳ ❆ ✸✽✳ ❇ ✹✼✳ ❉ ✸✳ ❆ ✶✷✳ ❈ ✷✶✳ ❇ ✸✵✳ ❈ ✸✾✳ ❆ ✹✽✳ ❉ ✹✳ ❆ ✶✸✳ ❇ ✷✷✳ ❈ ✸✶✳ ❈ ✹✵✳ ❆ ✹✾✳ ❇ ✺✳ D ✶✹✳ ❇ ✷✸✳ ❈ ✸✷✳ ❇ ✹✶✳ ❉ ✺✵✳ ❇ ✻✳ ❇ ✶✺✳ A ✷✹✳ ❈ ✸✸✳ ❇ ✹✷✳ ❇ ✼✳ ❉ ✶✻✳ ❉ ✷✺✳ ❆ ✸✹✳ ❈ ✹✸✳ ❇ ✽✳ ❆ ✶✼✳ ❆ ✷✻✳ ❈ ✸✺✳ ❆ ✹✹✳ ❇ ✾✳ ❇ ✶✽✳ ❇ ✷✼✳ ❇ ✸✻✳ ❆ ✹✺✳ ❆ ▼➣ ✤➲ t❤✐ ✶✵✷ ✶✳ ❇ ✶✵✳ B ✶✾✳ ❇ ✷✽✳ ❆ ✸✼✳ ❉ ✹✻✳ ❆ ✷✳ D ✶✶✳ ❉ ✷✵✳ ❇ ✷✾✳ ❉ ✸✽✳ ❉ ✹✼✳ ❈ ✸✳ ❇ ✶✷✳ ❆ ✷✶✳ ❉ ✸✵✳ ❇ ✸✾✳ ❉ ✹✽✳ ❈ ✹✳ ❉ ✶✸✳ ❇ ✷✷✳ ❇ ✸✶✳ ❈ ✹✵✳ ❆ ✹✾✳ ❉ ✺✳ ❇ ✶✹✳ ❈ ✷✸✳ ❈ ✸✷✳ ❈ ✹✶✳ ❆ ✺✵✳ ❇ ✻✳ ❇ ✶✺✳ ❇ ✷✹✳ ❈ ✸✸✳ ❇ ✹✷✳ ❉ ✼✳ A ✶✻✳ ❈ ✷✺✳ ❈ ✸✹✳ ❆ ✹✸✳ ❉ ✽✳ ❉ ✶✼✳ ❉ ✷✻✳ ❈ ✸✺✳ ❆ ✹✹✳ ❈ ✾✳ ❇ ✶✽✳ ❇ ✷✼✳ ❉ ✸✻✳ ❆ ✹✺✳ ❇ ▼➣ ✤➲ t❤✐ ✶✵✸ ✶✳ ❉ ✶✵✳ ❆ ✶✾✳ ❉ ✷✽✳ ❆ ✸✼✳ ❉ ✹✻✳ ❇ ✷✳ D ✶✶✳ ❈ ✷✵✳ ❈ ✷✾✳ ❉ ✸✽✳ ❇ ✹✼✳ ❆ ✸✳ ❆ ✶✷✳ ❈ ✷✶✳ ❇ ✸✵✳ ❉ ✸✾✳ ❉ ✹✽✳ ❉ ✹✳ ❈ ✶✸✳ ❆ ✷✷✳ ❇ ✸✶✳ ❉ ✹✵✳ ❆ ✹✾✳ ❇ ✺✳ ❉ ✶✹✳ B ✷✸✳ ❈ ✸✷✳ ❆ ✹✶✳ ❆ ✺✵✳ ❈ ✻✳ ❇ ✶✺✳ ❈ ✷✹✳ ❆ ✸✸✳ ❈ ✹✷✳ ❈ ✼✳ A ✶✻✳ ❈ ✷✺✳ ❆ ✸✹✳ ❆ ✹✸✳ ❈ ✽✳ ❈ ✶✼✳ ❈ ✷✻✳ ❈ ✸✺✳ ❈ ✹✹✳ ❆ ✾✳ ❆ ✶✽✳ ❈ ✷✼✳ ❇ ✸✻✳ ❆ ✹✺✳ ❇ ▼➣ ✤➲ t❤✐ ✶✵✹ ✶✳ ❆ ✶✵✳ ❇ ✶✾✳ ❉ ✷✽✳ ❆ ✸✼✳ ❆ ✹✻✳ ❇ ✷✳ ❆ ✸✳ ❆ ✹✳ ❉ ✺✳ ❉ ✶✶✳ ❈ ✶✷✳ ❉ ✶✸✳ ❈ ✶✹✳ ❇ ✷✵✳ ❇ ✷✶✳ ❉ ✷✷✳ ❇ ✷✸✳ ❉ ✷✾✳ ❉ ✸✵✳ ❆ ✸✶✳ ❉ ✸✷✳ ❉ ✸✽✳ ❉ ✸✾✳ ❉ ✹✵✳ ❆ ✹✶✳ ❉ ✹✼✳ ❆ ✹✽✳ ❈ ✹✾✳ ❇ ✺✵✳ ❈ ✻✳ ❆ ✶✺✳ B ✷✹✳ ❆ ✸✸✳ ❉ ✹✷✳ ❆ ✶ ✼✳ ❇ ✶✻✳ D ✷✺✳ ❇ ✸✹✳ ❇ ✹✸✳ ❈ ✽✳ ❆ ✶✼✳ ❈ ✷✻✳ ❉ ✸✺✳ ❉ ✹✹✳ ❉ ✾✳ D ✶✽✳ ❈ ✷✼✳ ❆ ✸✻✳ ❆ ✹✺✳ ❉ ▼➣ ✤➲ t❤✐ ✶✵✺ ✶✳ ❆ ✶✵✳ ❇ ✶✾✳ ❉ ✷✽✳ ❇ ✸✼✳ ❆ ✹✻✳ ❉ ✷✳ ❆ ✶✶✳ ❈ ✷✵✳ ❇ ✷✾✳ ❈ ✸✽✳ ❉ ✹✼✳ ❇ ✸✳ ❇ ✶✷✳ ❇ ✷✶✳ ❉ ✸✵✳ ❈ ✸✾✳ ❇ ✹✽✳ ❈ ✹✳ C ✶✸✳ ❈ ✷✷✳ ❆ ✸✶✳ ❈ ✹✵✳ ❈ ✹✾✳ ❉ ✺✳ ❇ ✶✹✳ ❆ ✷✸✳ ❆ ✸✷✳ ❆ ✹✶✳ ❆ ✺✵✳ ❉ ✻✳ ❉ ✶✺✳ D ✷✹✳ ❈ ✸✸✳ ❇ ✹✷✳ ❆ ✼✳ ❆ ✶✻✳ ❆ ✷✺✳ ❇ ✸✹✳ ❆ ✹✸✳ ❆ ✽✳ ❇ ✶✼✳ ❈ ✷✻✳ ❆ ✸✺✳ ❉ ✹✹✳ ❈ ✾✳ D ✶✽✳ ❇ ✷✼✳ ❇ ✸✻✳ ❈ ✹✺✳ ❇ ▼➣ ✤➲ t❤✐ ✶✵✻ ✶✳ ❉ ✶✵✳ ❆ ✶✾✳ ❆ ✷✽✳ ❇ ✸✼✳ ❇ ✹✻✳ ❈ ✷✳ ❉ ✶✶✳ ❉ ✷✵✳ ❉ ✷✾✳ ❆ ✸✽✳ ❈ ✹✼✳ ❉ ✸✳ ❈ ✶✷✳ B ✷✶✳ ❉ ✸✵✳ ❉ ✸✾✳ ❈ ✹✽✳ ❉ ✹✳ ❈ ✶✸✳ ❈ ✷✷✳ ❇ ✸✶✳ ❇ ✹✵✳ ❈ ✹✾✳ ❉ ✺✳ ❆ ✶✹✳ ❉ ✷✸✳ ❇ ✸✷✳ ❆ ✹✶✳ ❇ ✺✵✳ ❆ ✻✳ ❇ ✶✺✳ D ✷✹✳ ❉ ✸✸✳ ❆ ✹✷✳ ❆ ✼✳ ❉ ✶✻✳ D ✷✺✳ ❈ ✸✹✳ ❇ ✹✸✳ ❆ ✽✳ ❆ ✶✼✳ ❈ ✷✻✳ ❇ ✸✺✳ ❈ ✹✹✳ ❆ ✾✳ ❆ ✶✽✳ ❇ ✷✼✳ ❇ ✸✻✳ ❆ ✹✺✳ ❆ ▼➣ ✤➲ t❤✐ ✶✵✼ ✶✳ ❉ ✶✵✳ ❉ ✶✾✳ ❉ ✷✽✳ ❈ ✸✼✳ ❆ ✹✻✳ ❉ ✷✳ ❈ ✶✶✳ ❆ ✷✵✳ ❈ ✷✾✳ ❈ ✸✽✳ ❉ ✹✼✳ ❇ ✸✳ ❆ ✶✷✳ ❆ ✷✶✳ ❆ ✸✵✳ ❇ ✸✾✳ ❆ ✹✽✳ ❆ ✹✳ ❇ ✶✸✳ ❇ ✷✷✳ ❈ ✸✶✳ ❆ ✹✵✳ ❆ ✹✾✳ ❇ ✺✳ ❈ ✶✹✳ ❆ ✷✸✳ ❉ ✸✷✳ ❆ ✹✶✳ ❇ ✺✵✳ ❈ ✻✳ ❆ ✶✺✳ ❉ ✷✹✳ ❈ ✸✸✳ ❈ ✹✷✳ ❉ ✼✳ B ✶✻✳ ❈ ✷✺✳ ❉ ✸✹✳ ❇ ✹✸✳ ❆ ✽✳ C ✶✼✳ D ✷✻✳ ❆ ✸✺✳ ❇ ✹✹✳ ❉ ✾✳ ❆ ✶✽✳ ❆ ✷✼✳ ❇ ✸✻✳ ❉ ✹✺✳ ❈ ▼➣ ✤➲ t❤✐ ✶✵✽ ✶✳ ❇ ✶✵✳ ❇ ✶✾✳ ❇ ✷✽✳ ❇ ✸✼✳ ❉ ✹✻✳ ❇ ✷✳ B ✶✶✳ ❈ ✷✵✳ ❉ ✷✾✳ ❈ ✸✽✳ ❈ ✹✼✳ ❆ ✸✳ ❉ ✶✷✳ ❇ ✷✶✳ ❉ ✸✵✳ ❇ ✸✾✳ ❇ ✹✽✳ ❉ ✹✳ D ✶✸✳ ❉ ✷✷✳ ❇ ✸✶✳ ❆ ✹✵✳ ❈ ✹✾✳ ❆ ✺✳ ❈ ✶✹✳ ❆ ✷✸✳ ❆ ✸✷✳ ❆ ✹✶✳ ❆ ✺✵✳ ❆ ✻✳ ❇ ✶✺✳ ❇ ✷✹✳ ❇ ✸✸✳ ❆ ✹✷✳ ❉ ✷ ✼✳ ❇ ✶✻✳ ❈ ✷✺✳ ❇ ✸✹✳ ❈ ✹✸✳ ❆ ✽✳ ❆ ✶✼✳ A ✷✻✳ ❈ ✸✺✳ ❆ ✹✹✳ ❉ ✾✳ ❉ ✶✽✳ ❇ ✷✼✳ ❈ ✸✻✳ ❆ ✹✺✳ ❉ ... ❦❤è✐ tù ❞✐➺♥ SM N P ✳ ❆✳ V = 13 ✳ ❇✳ V = 12 ✳ ❈✳ V = 2✳ ❉✳ V = 1 ; 2 019 ❈➙✉ ✹✾✳ ❚➼♥❤ sè ♥❣❤✐➺♠ ❝õ❛ ♣❤÷ì♥❣ tr➻♥❤ cotx = 2x tr♦♥❣ ❦❤♦↔♥❣ 11 π 12 ❆✳ 2 019 ❇✳ 2 018 ✳ ❈✳ 1 ❉✳ 2020✳ ❚r❛♥❣ ✺✴✻ ▼➣ ✤➲... tr➻♥❤ cotx = 2x tr♦♥❣ ❦❤♦↔♥❣ 11 π ; 2 019 12 ❆✳ 2020✳ ❇✳ 2 019 ❈✳ 2 018 ✳ ❉✳ 1 ❈➙✉ ✹✹✳ ❚r♦♥❣ ❦❤æ♥❣ ❣✐❛♥ Oxyz✱ ❝❤♦ ♠➦t ♣❤➥♥❣ (P ) : x − y + = ✈➔ ❤❛✐ ✤✐➸♠ A (1; 2; 3), B (1; 0; 1) ✳ ✣✐➸♠ C(a; b; −2) ∈ (P... ❤➻♥❤ (D) q✉❛♥❤ trö❝ Ox✳ 15 21 15π ❆✳ 16 ✳ ❇✳ 21 ✳ ❈✳ ✳ ❉✳ ✳ 16 16 ❈➙✉ ✷✻✳ ●å✐ z1✱ z2 ❧➔ ❤❛✐ ♥❣❤✐➺♠ ♣❤ù❝ ❝õ❛ ♣❤÷ì♥❣ tr➻♥❤ z2 − 4z + = 0✳ ❚➼♥❤ w = 1 + + i(z1 z2 + z2 z1 )✳ z1 z2 ❈✳ w = + 20i✳ ❉✳