Find all the solutions of the simultaneous equations (tìm tất cả bộ số (x; y; z) thỏa mãn hệ phương trình)
x + y + xy = 19
y + z + yz = 11
z + x + zx = 14
Find all the integer solutions (x; y) to the inequalities x2 - y < 1 , x2 + y < 4
Cộng từng vế ta có: (x2 - y) + (x2 + y) < 1 + 4
=> 2.x2 < 5 => x2 < 2,5 . vì x nguyên nên x2 = 0 hoặc 1
+) x2 = 0 =>x = 0 và -y < 1 và y < 4 => 4 > y > -1. vì y nguyên nên y = 0; 1;2; ;3
vây (x; y) = (0;0); (0;1); (0;2) ;(0;3)
+) x2 = 1 => x = 1 hoặc -1 và 1- y < 1 ; 1 + y < 4 => y > 0 và y < 3 => 0 < y < 3. vì y nguyên nên y = 1; 2;
vậy (x; y) = (1; 1); (1; 2) (-1;1); (-1; 2)
vậy...
=> x^2 - y + x^2 + y =< 5
=> 2x^2 < 5
=> x^2 <2,5
=> x = { -1;0;1} ( vì x nguyên)
(+) x = -1 => 1 - y < 1 => y > 0
1 + y < 4 => y < 3
=> 0 < y < 3 => y = 1 ;2
có hai cặp ( -1 ; 1 ) ; ( -1 ; 2 )
Tương tự
The charges for the usage of per m3 of water and per kWh of electricity are $1.94 and 26 cents respectively. In May, Mr Kumar used x m3 of water and y kWh of electricity and his bill came to $272.10. In June, his bill came to $202.60 for the usage of (x-5) m3 of water and (3y - 1950) kWh of electricity. Form two equations in x and y and solve these two equations to find the total cost of using (x+8) m3 of water and (2y-725) kWh of electricity.
2. Look at the examples of the past perfect highlighted in the text in exercise 1. Find all the other examples. Complete rule a in the Learn this! box.
(Nhìn vào các ví dụ về quá khứ hoàn thành được đánh dấu trong văn bản ở bài tập 1. Tìm tất cả các ví dụ khác. Hoàn thành quy tắc a trong phần Learn this!)
LEARN THIS! Past perfect (Thì quá khứ hoàn thành)
a. We form the past perfect with (1) _____ or (2) _____ and the past participle.
b. We use the past perfect when we are already talking about past events and we want to talk about an even earlier event.
When I got to the classroom, the lesson had started.
c. We often use the past perfect with after, before or when.
Before I got to the bus station, the bus had already left.
After I’d called Maggie, I watched a film on TV.
LEARN THIS! Past perfect (Thì quá khứ hoàn thành)
a. We form the past perfect with (1) had or (2) hadn’t and the past participle.
(Chúng ta tạo thì quá khứ hoàn thành với had hoặc hadn’t với động từ ở thể quá khứ phân từ.)
b. We use the past perfect when we are already talking about past events and we want to talk about an even earlier event.
(Chúng ta dùng thì quá khứ hoàn thành khi ai đó đang nói về những sự kiện xảy ra trong quá khứ và chúng ta muốn nói đến những sự kiện trước đó nữa.)
When I got to the classroom, the lesson had started.
(Khi mình đến lớp thì bài học đã bắt đầu.)
c. We often use the past perfect with after, before or when.
(Chúng ta thường dùng thì quá khứ hoàn thành với after, before hoặc when.)
Before I got to the bus station, the bus had already left.
(Trước khi mình đến trạm xe buýt, thì xe buýt đã đi mất.)
After I’d called Maggie, I watched a film on TV.
(Sau khi mình gọi cho Maggie, mình xem một bộ phim trên TV.)
had thrown … away; had risen; had increased; had spilled; had kept; had sold; had thrown; had … forgotten; hadn’t saved
Mark the letter A, B, c, or D on your answer sheet to indicate the correct answer to each of the following questions
Whenever problems___________we discuss frankly and find solutions quickly.
A. make up
B. come up
C. put up
D. turn up
Đáp án B
Make up: trang điểm, tạo nên Come up: xảy ra
Put up: cho ở lại một đêm Turn up: đến nơi
Câu này dịch như sau: Bất cứ khi nào có vấn đề xảy ra, chúng tôi thảo luận thắn thẳn và tìm ra giải pháp nhanh chóng.
Supply the correct tense of the verbs in the brackets.
1. Solutions to reduce the air pollution in the city center ______________ by the scientist in
the future. (find)
2. People in my town often ______________ public transports to travel around. (use)
3-4. There ______________ any new debating tournament since we (take) __________ part in one last winter. (not be)
5. At this time tomorrow, our school ______________ the Disneyland on our field trip. (visit)
6. you ever a buffalo? (ride)
7. The children used to a long way to school. (go)
8. They would hate their son texting his friends all day. (see)
9. Do you fancy in the park this Sunday? (skateboard)
10. I’ve just bought a new CD of folk songs. I ______________ to it tonight. (listen)
1. Solutions to reduce the air pollution in the city center ___will be found___________ by the scientist in
the future. (find)
2. People in my town often _____use_________ public transports to travel around. (use)
3-4. There ______hasn't been________ any new debating tournament since we (take) _______took___ part in one last winter. (not be)
5. At this time tomorrow, our school ____will be visiting__________ the Disneyland on our field trip. (visit)
6. Have you ever ridden a buffalo? (ride)
7. The children used to go a long way to school. (go)
8. They would hate to see their son texting his friends all day. (see)
9. Do you fancy skateboarding in the park this Sunday? (skateboard)
10. I’ve just bought a new CD of folk songs. I _________am going to listen_____ to it tonight. (listen)
Mark the letter A, B, C, or D on your answer sheet to indicate the correct answer to each of the following questions.
Question 9: The scientists _______ on this project try to find the solutions to air pollution.
A. working
B. worked
C. are working
D. who working
Đáp án A
Kiến thức rút gọn mệnh đề quan hệ
Rút gọn mệnh đề quan hệ bằng cách bỏ đại từ quan hệ, động từ to be (nếu có), và chuyển động từ về dạng:
- Ving nếu ở thể chủ động
- V.ed nếu ở thể bị động
Tạm dịch: Các nhà khoa học làm việc trong dự án này cố gắng tìm ra giải pháp cho ô nhiễm không khí.
Mark the letter A, B, C, or D to indicate the word(s) CLOSEST in the meaning to the undelined word(s) in each of the following questions.
Whenver problems come up, we discuss them frankly and find solutions quickly.
A. clean
B. encounter
C. arrive
D. happen
Mark the letter A, B, C or D on your answer sheet to indicate the correct answer to each of the following questions.
Sometimes she does not agree ____her husband about child rearing but they soon find the solutions.
A. for
B. on
C. with
D. of
Chọn C
“agree with sb about st”: đồng ý với ai về vấn đề gì
Mark the letter A, B, C or D on your answer sheet to indicate the correct answer to each of the following questions.
Sometimes she does not agree ______her husband about child rearing but they soon find the solutions.
A. with
B. for
C. on
D. of
Chọn A
Cụm từ: Agree with (đồng ý với ai)
Agree about/on (đồng ý về cái gì) =>Loại C
=>Chọn A
Tạm dịch: Đôi khi cô ấy không đồng ý với chồng của mình về việc nuôi con nhưng họ sớm tìm ra các giải pháp.