2) \(B=x^2+4x+6=x^2+4x+4+2=\left(x+2\right)^2+2\ge2>0\)

4) \(D=x^2+x+1=x^2+2.\dfrac{1}{2}x+\dfrac{1}{4}+\dfrac{3}{4}=\left(x+\dfrac{1}{2}\right)^2+\dfrac{3}{4}\ge\dfrac{3}{4}>0\)

6) \(F=2x^2+4x+3=2\left(x^2+2x+1\right)+1=2\left(x+1\right)^2+1\ge1>0\)

8) \(H=4x^2+4x+2=4x^2+4x+1+1=\left(2x+1\right)^2+1\ge1>0\)

10) \(L=2x^2+3x+4=2\left(x^2+\dfrac{3}{2}x+2\right)=2\left(x^2+2.\dfrac{3}{4}x+\dfrac{9}{16}+\dfrac{23}{16}\right)=2\left(x+\dfrac{3}{4}\right)^2+\dfrac{23}{8}\ge\dfrac{23}{8}>0\)

76. You look tired now.
______ you _________________ all day?
A. Do / work B. Have / been working C. Are / working D. Did / work
77. Michael_____________ to school by bus this morning.
A. goes B. is going C. went D. will go
78. This is the first time she__________ Hanoi.
A. visits B. is visiting C. was visiting D. has visited
79. When I was a boy, I____________ with my parents.
A. often slept B. sleep C. am sleeping D. have slept
80. My family_________ dinner when my friends came.
A. is having B. has C. was having D. has had

81. When I get my degree, I _______ IELTS for 6 months.
A. study B. have studied C. am studying D. will have been studying
82. When we ____________ TV, the bell rang.
A. watched B. were watching C. will watch D. have watched
83. When she arrived at the airport, her flight ___________ off.
A. took B. have taken C. had taken D. takes
84. We____________ each other before 2010.
A. don’t met B. haven’t met C. wasn’t meeting D. hadn’t met
85. By the time I arrived, they___ for 3 hours.
A. had played B. played C. were playing D. had been playing
86. Mike_____________ video games last year.
A. usually plays B. had played C. played often D. usually played
87. It ___________ for 2 days before the storm came yesterday.
A. had been raining B. rained C. has rained D. was raining
88. They_________ swimming at 3 p.m yesterday afternoon.
A. was going B. had gone C. go D. have been going
89. World Cup ____________ tonight.
A. begin B. will begin C. began D. are beginning
90. This time next year I ______ Ha Long Bay.
A. visit B. have visited C. will be visiting D. will have visiting
91. When I get my degree, I _______ IELTS for 6 months.
A. study B. have studied C. am studying D. will have been studying
92. Suri ____________ dinner with her grandparents at this time tomorrow.
A. has B. is having C. would have D. will be having
93. We__________ TV at 7 p.m tomorrow.
A. will be watching B. were watching C. watch D. watched
94. My brother________ before 2020.
A. graduates B. is graduating C. will have graduated D. will graduated
95. We __ for an hour when it suddenly rained.
A. have run B. had been running C. were running D. ran

96. I _________ up my room before you arrive.
A. shall have cleaned B. shall cleaned C. cleaned D. am cleaning
97. __________ you __________ in this town for 10 years by the end of this year?
A. Will / have been living B. Do / live C. Are / living D. Have / been living
98. Tom_____________ his grandparents yet.
A. haven’t met B. Didn’t met C. won’t meet D. hasn’t met
99. I_________________ Paris next year.
A. am going to visit B. am going to visiting C. visit D. will have visited
100. She_________________ Vietnam by the end of next year.
A. is leaving B. will have left C. leaves D. left

5) \(\left(x+1\right)\left(x+3\right)\left(x+5\right)\left(x+7\right)+15\)

\(=\left[\left(x+1\right)\left(x+7\right)\right]\left[\left(x+3\right)\left(x+5\right)\right]+15\)

\(=\left(x^2+8x+7\right)\left(x^2+8x+15\right)+15\)

Đặt \(x^2+8x+7=t\)

Ta có: \(t\left(t+8\right)+15\)

\(=t^2+8t+15=\left(t+3\right)\left(t+5\right)\)

\(=\left(x^2+8x+7+3\right)\left(x^2+8x+7+5\right)\)

\(=\left(x^2+8x+10\right)\left(x^2+8x+12\right)\)

1) Sửa đề: 

\(x^3+3x^2+3x+1-y^3\) 

\(=\left(x+1\right)^3-y^3\)

\(=\left(x-y+1\right)\left[\left(x+1\right)^2+\left(x+1\right)y+y^2\right]\)

\(=\left(x-y+1\right)\left[x^2+2x+1+xy+y+y^2\right]\)

3) \(x^3-1+5x^2-5+3x-3\)

\(=\left(x-1\right)\left(x^2+x+1\right)+5\left(x^2-1\right)+3\left(x-1\right)\)

\(=\left(x-1\right)\left(x^2+x+1\right)+5\left(x-1\right)\left(x+1\right)+3\left(x-1\right)\)

\(=\left(x-1\right)\left(x^2+x+1+5x+5+3\right)\)

\(=\left(x-1\right)\left(x^2+6x+9\right)=\left(x-1\right)\left(x+3\right)^2\)

4) \(x^4+4=(x^4+4x^2+4)-4x^2\)

\(=\left(x^2+1\right)^2-\left(2x^{ }\right)^2=\left(x^2-2x+1\right)\left(x^2+2x+1\right)\)

\(=\left(x-1\right)^2\left(x+1\right)^2\)

51. The Earth ___________ around the Sun.
A. go B. went C. is going D. goes

52. Watch out! The trucks _____.
A. is coming B. come C. will come D. are coming

53. Someone ______ my pocket on the bus.
A. will steal B. stole C. has stolen D. was stealing
54. My father_________________ PS4 all day.
A. has been played B. is playing C. has been playing D. had played
55. The boat was sailing north when a terrible storm_________________ .
A. had broken B. broke C. would break D.was breaking
56. While Susie __ books, her brothers ____TV.
A. was reading / watches B. reads / watches
C. is reading / is watching D. was reading/ were watching
57. Before Celine went out with friends, she_________________ her homework.
A. had finished B. was finishing C. have finished D. finished
58. We_________________ for half an hour before it started raining.
A. have played B. Played C. had been playing D. will play
59. Mr. Bí: “She’s late”.
Mr. Be: “Don’t worry. She _____________” .
A. comes B. is come C. have come D. will come

60. At present next Friday, ____ you______ with us ?
A. Do / join B. Do / joining C. Will / join D. Did / join
61. When you come back, I___ my homework.
A. finish B. am finished C. am finishing D. will have finished
62. By the time you begin to study English, I ____________ IELTS for 6 years.
A. had been studying B. will have been studying C. is studying D. studied
63. Tony_________ swimming at weekend.
A. often goes B. is going often C. go often D. is often going
64. My mother________ at the kitchen now.
A. cooks B. Cooked C. is cooking D. are cooking
65. We are going to visit Da Nang next month. ____ you______ with us?
A. Do/ join B. Do/ joining C. Will/ join D. Did/ join
66. I think she_________________ to school tomorrow.
A. doesn’t comes B. isn’t coming C. won’t come D. haven’t come

67. Children_____________ lunch before.
A. have just finished B. had been finished C. finish D. have been finishing
68. They went home after they_______ all the games in Vincom Center.
A. played B. had played C. have played D. had been playing
69. Mary ____________ English for ten years.
A. studies B. has studied C. is studying D. have studied
70. She _________ very good at playing tennis.
A. is B. are C. am D. were

impression

1) a) \(\sqrt{98}-\sqrt{72}+0,5\sqrt{8}\)

\(=\sqrt{49.2}-\sqrt{36.2}+0,5\sqrt{4.2}\)

\(=7\sqrt{2}-6\sqrt{2}+0,5.2\sqrt{2}\)

\(=7\sqrt{2}-6\sqrt{2}+\sqrt{2}=2\sqrt{2}\)

b) \(\sqrt{9a}-\sqrt{16a}+\sqrt{49}\)

\(=3\sqrt{a}-4\sqrt{a}+7=7-\sqrt{a}\)

2. a) \(2\sqrt{7}=\sqrt{4.7}=\sqrt{28}\)

\(3\sqrt{2}=\sqrt{9.2}=\sqrt{18}\)

Mà \(\sqrt{28}>\sqrt{18}\Rightarrow2\sqrt{7}>3\sqrt{2}\)

b) \(5=2+3=2+\sqrt{9}\)

Vì \(\sqrt{9}>\sqrt{2}\Rightarrow2+\sqrt{9}>2+\sqrt{2}\Rightarrow5>2+\sqrt{2}\)

3. a) \(\sqrt{\dfrac{2}{3}}=\sqrt{\dfrac{6}{9}}=\dfrac{\sqrt{6}}{3}\)

b) \(\dfrac{x}{y}.\sqrt{\dfrac{y}{x}}=\sqrt{\dfrac{x^2}{y^2}.\dfrac{y}{x}}=\sqrt{\dfrac{x}{y}}=\dfrac{\sqrt{xy}}{y}\)

a) \(A=\dfrac{1}{3}\sqrt{27}-\sqrt{12}+\sqrt[]{7+4\sqrt{3}}\)

\(=\dfrac{1}{3}\sqrt{9.3}-\sqrt{4.3}+\sqrt{2^2+2.2.\sqrt{3}+\left(\sqrt{3}\right)^2}\)

\(=\sqrt{3}-2\sqrt{3}+\sqrt{\left(2+\sqrt{3}\right)^2}\)

\(=\sqrt{3}-2\sqrt{3}+2+\sqrt{3}=2\)

ĐK: \(x>0;x\ne1\)

\(B=\left(\dfrac{1}{x-\sqrt{x}}+\dfrac{1}{\sqrt{x}-1}\right):\dfrac{\sqrt{x}}{x-2\sqrt{x}+1}\)

\(=\left(\dfrac{1}{\sqrt{x}\left(\sqrt{x}-1\right)}+\dfrac{\sqrt{x}}{\sqrt{x}\left(\sqrt[]{x}-1\right)}\right):\dfrac{\sqrt{x}}{\left(\sqrt{x}-1\right)^2}\)

\(=\dfrac{\sqrt{x}+1}{\sqrt{x}\left(\sqrt{x}-1\right)}.\dfrac{\left(\sqrt{x}-1\right)^2}{\sqrt{x}}\)

\(=\dfrac{x-1}{x}\)

b) \(B< A\Leftrightarrow\dfrac{x-1}{x}< 2\)

\(\Leftrightarrow x-1< 2x\)

\(\Leftrightarrow x>-1\)

Vậy, B<A<=> x>-1

1. B

2. B

3. D

4. C

5. A