Đề thi thử Đại học năm 2015 môn Toán - Đề số 28

❚❍■ ❚❍Û ✣❸■ ❍➴❈ ◆❿▼ ✷✵✶✺
✯✯✯✯✯✯✯✯✯✯

✣➋ ❙➮ ✷✽
▼ỉ♥✿ ❚♦→♥✳ ❚❤í✐ ❣✐❛♥✿ ✶✽✵ ♣❤ót

❈➙✉ ✶ ✭✷✱✵ ✤✐➸♠✮✳
❛✮ ❱✐➳t ♣❤÷ì♥❣ tr➻♥❤ t✐➳♣ t ợ ỗ t (C) : y = x + 3x + 6x − 1 ❝â ❤➺ sè ❣â❝ ♥❤ä ♥❤➜t✳
❜✮ ❚➻♠ m ✤➸ (C) : y = x − 2(m + 1)x + 2m ❝➢t ✤÷í♥❣ t❤➥♥❣ d : y = −1 t↕✐ ✹ ✤✐➸♠ ♣❤➙♥ ❜✐➺t A✱ B✱ C ✱
3

4

D

2

2

s❛♦ ❝❤♦ AB = BC = CD✳

❈➙✉ ✷ ✭✶✱✵ ✤✐➸♠✮✳
❛✮ ●✐↔✐ ♣❤÷ì♥❣ tr➻♥❤ cos 2x + sin 2x + 1 = √2 sin x + π4 (x ∈ R)✳
❜✮ ❚➼♥❤ ♠æ✤✉♥ ❝õ❛ sè ♣❤ù❝ z = x + yi ❜✐➳t x✱ y ❧➔ ❝→❝ sè t❤ü❝ t❤ä❛ ♠➣♥ x(3 + 5i) + y(1 − 2i)
❈➙✉ ✸ ✭✵✱✺ ✤✐➸♠✮✳ ●✐↔✐ ♣❤÷ì♥❣ tr➻♥❤ log (5x) − log x − 1 = 0 (x ∈ R)✳
❈➙✉ ✹ ✭✶✱✵ ✤✐➸♠✮✳ ❚➻♠ m ✤➸ ❤➺ ♣❤÷ì♥❣ tr➻♥❤ s❛✉ ❝â ♥❣❤✐➺♠

3

2
25

= 45 + 14i✳

5

x3 − 12x − y 3 + 6y 2 − 16 = 0
√
4x2 + 2 4 − x2 − 5 4y − y 2 + m = 0

❈➙✉ ✺ ✭✶✱✵ ✤✐➸♠✮✳ ❚➼♥❤ t➼❝❤ ♣❤➙♥

1
2

I=
0

(x, y ∈ R).

(x − 1)2
❞x.
(2x + 1)4

❈➙✉ ✻ ✭✶✱✵ ✤✐➸♠✮✳ ❚r♦♥❣ ♠➦t ♣❤➥♥❣ ✈ỵ✐ ❤➺ tå❛ ✤ë Oxy✱ ❝❤♦ ❤➻♥❤ t❤❛♥❣ ❝➙♥ ABCD ♥ë✐ t✐➳♣ ✤÷í♥❣ trá♥

(S) : (x − 2)2 + (y − 7)2 = 85✱ ❝↕♥❤ ✤→② AB q✉❛ ✤✐➸♠ M (5; 0)✱ ❤❛✐ ✤÷í♥❣ ❝❤➨♦ t t E
t t ợ ữớ trá♥ (S) t↕✐ A ✈➔ D ❝➢t ♥❤❛✉ t↕✐ F ✱ EF : y = 12✳ ❚➻♠ tå❛ ✤ë ❝→❝ ✤➾♥❤ ❝õ❛ ❤➻♥❤ t❤❛♥❣
ABCD ❜✐➳t A ❝â ❤♦➔♥❤ ✤ë ➙♠✳
√
✶✱✵ ✤✐➸♠ ❍➻♥❤ ❤ë♣ ABCD.A B C D ❝â ✤→② ❧➔ ❤➻♥❤ ❝❤ú ♥❤➟t✱ AB = a✱ AD = a 3✱ ❤➻♥❤ ❝❤✐➳✉

✈✉æ♥❣ ❣â❝ ❝õ❛ A ❧➯♥ ♠➦t ✤→② ❧➔ ❣✐❛♦ ✤✐➸♠ ❝õ❛ AC ✈➔ BD✱ ♠➦t ♣❤➥♥❣ (CDD C ) t↕♦ ✈ỵ✐ ♠➦t ✤→② ♠ët ❣â❝
600 ✳ ❚➼♥❤ t❤➸ t➼❝❤ ❦❤è✐ ❤ë♣ ABCD.A B C D ✈➔ ❦❤♦↔♥❣ ❝→❝❤ ❣✐ú❛ ❤❛✐ ✤÷í♥❣ t❤➥♥❣ BB ✱ AD✳
x−1
y−1
z−1
✶✱✵ ✤✐➸♠ ❚r♦♥❣ ❦❤ỉ♥❣ ❣✐❛♥ ợ tồ ở Oxyz ữớ t :
=
=
✈➔
2
1
1
❝→❝ ✤✐➸♠ A(1; 2; 0)✱ B(1; 1; 1)✱ C(3; −1; 2)✳

❈➙✉ ✼ ✭

✮✳

❈➙✉ ✽ ✭

✮✳

❛✮ ❚➼♥❤ ❞✐➺♥ t➼❝❤ t❛♠ ❣✐→❝ ABC ✈➔ ✈✐➳t ♣❤÷ì♥❣ tr➻♥❤ ♠➦t ♣❤➥♥❣ (ABC)✳
❜✮ ❚➻♠ ✤✐➸♠ D t❤✉ë❝ ✤÷í♥❣ t❤➥♥❣ ∆ s❛♦ ❝❤♦ t❤➸ t➼❝❤ tù ❞✐➺♥ ABCD ❜➡♥❣ ✷✳
❈➙✉ ✾ ✭✵✱✺ ✤✐➸♠✮✳ ❚r♦♥❣ ❦➻ t✉②➸♥ s✐♥❤ ✈➔♦ tr÷í♥❣ ❆♥ ◆✐♥❤ ♥➠♠ ✷✵✶✼ ❝â ❤❛✐ ❜↕♥ ỳ ổ

t ỹ ỗ ♥❤❛✉✳ ▼é✐ t❤➼ s✐♥❤ ♣❤↔✐ t❤✐ ✸ ♠æ♥ tr➢❝ ♥❣❤✐➺♠ ỵ õ ộ ổ t õ
t ✈➔ ❝→❝ ♠➣ ✤➲ t❤✐ ❝õ❛ ❝→❝ ♠æ♥ ❧➔ ❦❤→❝ ♥❤❛✉✳ ❈→♥ ❜ë ❝♦✐ t❤✐ ♣❤→t ❝→❝ ✤➲ t❤✐ ♠ët ❝→❝❤ ♥❣➝✉ ♥❤✐➯♥ ❝❤♦
❝→❝ t❤➼ s✐♥❤ ❞ü t❤✐✳ ❚➼♥❤ ①→❝ s✉➜t ✤➸ ❤❛✐ ❜↕♥ ♥ú ❍↔✐ ❆♥❤ ✈➔ ❚æ ❚❤✐➺♥ ❝â ♠➣ ✤➲ t❤✐ ❝õ❛ t➜t ❝↔ ❝→❝ ♠æ♥ t❤✐
❧➔ ❦❤→❝ ♥❤❛✉✳

❈➙✉ ✶✵ ✭✶ ✤✐➸♠✮✳ ❈❤♦ a✱ b✱ c ❧➔ ❝→❝ sè t❤ü❝ ❞÷ì♥❣ t❤ä❛ ♠➣♥ a2 + b2 + c2 ≤ 3✳ ❈❤ù♥❣ ♠✐♥❤ r➡♥❣
√
a
b
c
2
√
+√
+√
≥
(a + b + c).
2
c+a
b+c
a+b

◆❣✉②➵♥ ❉÷ ❚❤→✐✱ ❚❚❇❉❑❚ ❈❛♦ ❚❤➢♥❣✱ ✶✶ ✣è♥❣ ✣❛✱ ❚P ❍✉➳✱ ❉✣✿ ✵✾✵✺✾✾✽✸✻✾