Chứng minh biểu thức sau ko phụ thuộc vào x:
\(A=x\left(x^2+x+1\right)-x^2\left(x+1\right)-x+5\)
\(B=x\left(2x+1\right)-x^2\left(x+2\right)+x^3-x+3\)
\(C=4\left(6-x\right)+x^2\left(2+3x\right)-x\left(5x-4\right)+3x^2\left(1-x\right)\)
\(D=5\left(3x^{n+1}-y^{n-1}\right)+3\left(x^{n+1}+5y^{n-1}\right)-5\left(3x^{n+1}+2y^{n-1}\right)\)
Bài 1: Tính giá trị biểu thức:
\(A=5x\left(x-4y\right)-4y\left(y-5x\right)\) với \(x=-\frac{1}{5};y=-\frac{1}{2}\)
\(B=6xy\left(xy-y^2\right)-8x^2\left(x-y^2\right)+5y^2\left(x^2-xy\right)\)
Với x = \(\frac{1}{2}\); y = 2
Bài 2: Chứng minh rằng:
a) \(\left(4x^2-2xy+y^2\right)\left(2x+y\right)=8x^3+y^3\)
b) \(\left(x^2+x+1\right)\left(x^5-x^4+x^3-x+1\right)=x^7+x^5+1\)
Bài 1: Cho tứ giác ABCD biết góc A : B : C : D = 1 : 2 : 3 : 4
a) Tính các góc của tứ giác ABCD
b) Chứng minh: AB // CD
c) Gọi giao điểm của AD cắt BC = E. Tính các góc của ΔCDE
Bài 2: Cho tứ giác ABCD có ∠C = \(80^0\) ; D = \(70^0\) . Các tia phân giác của các góc A và B cắt nhau tại I. Tính AIB.
Bài 3: Cho tứ giác ABCD có AB = BC; CD = DA.
a) Chứng minh rằng BD là đường trung trực của AC
b) Cho biết ∠B = \(100^0\) ; D = \(70^0\) . Tính ∠A và C
Khoanh tròn trước câu trả lời đúng:
1. Tứ giác có nhiều nhất:
A. 4 góc vuông
B. 3 góc vuông
C. 2 góc vuông
D. 1 góc vuông
2. Tứ giác ABCD có B = A + \(10^0\); C = B + \(10^0\) ; D = C + \(10^0\) ; Khẳng định nào dưới đây là đúng:
A. A = \(65^0\)
B. A = \(75^0\)
C. A = \(85^0\)
D. A = \(95^0\)
3. Tứ giác ABCD có C = \(60^0\) ; D = \(80^0\) ; A - B = \(10^0\) ; Tính số đo ∠A.
A. A = \(115^0\)
B. A = \(105^0\)
C. A = \(125^0\)
D. A = \(135^0\)
Use the correct form of the words in the boxes to complete the sentences in each group A-H below. You may use sone of the words more than once. In some cases, more than one word may be correct.
D [ temper, manner, manners] 1. Where did you learn such excellent table __________? 2. The children like him because of his gentle __________. 3. Cliff is so calm that I have never seen him lose his __________. 4. What you’re saying should be done in a professional __________. E [familiar, accustomed, aware] 1. I hope you’re __________ of the dangers involved in rock climbing. 2. Is anyone in this classroom __________ with the word “incubator”? 3. Paul is feeling tired because he’s not __________ to working for so long without a break. F [custom, habit, fashion, trend, routine] 1. Going to work has become a daily __________ for most people. 2. The general __________ for men in the 1970s was to have long hair and sideburns. 3. In many countries it is the __________ to roast turkey for Christmas. 4. Sandra has the bad __________ of biting her nails. 5. Slightly flared trousers are in __________ this year so many people are wearing them. 6. If you go shopping, definitely go to Blare’s. They’ve got all the latest __________. G [ common, ordinary, usual, normal, regular] 1. It is __________ to feel weak when you are ill, even if you’ve just got a __________ cold. 2. __________ exercise means working out for one hour at least twice a week. 3. It was a(n) __________ weekend. We went to the cinema on Saturday evening and for a drive on Saturday morning, as __________. H [eager, keen, enthusiastic, interested, willing] 1. I am __________ to help you with your homework if you make an effort. 2. He’s really __________ on heavy metal music. That’s all he listens to. 3. Please sit down as I’m __________ to start the meeting. 4. Billy is a(n) __________ tennis player, so he plays tennis every afternoon. 5. Sheila is __________ in taking up gardening this spring. 6. We were __________ about going to Ireland for Christmas.
Use the correct form of the words in the boxes to complete the sentences in each group A-H below. You may use some of the words more than once. In some cases, more than one word may be correct.
A [rise, raise, aries, lift]
1. Should the need __________, we’ll order more food for the extra guests.
2. The charity organisation __________ enough money to build a shelter for the refugees.
3. The sun __________ in the East and sets in the West.
4. We __________ at seven every weekend to get ready for school.
5. Can you __________ the table so that I can slide the rug underneath?
B [grow, grow up, bring up, (be) born, become]
1. In the last six months Joe has __________ taller by 15 centimetres.
2. When Brett was __________, he weighed 3.8 kilograms.
3. Most parents have fond memories of the years they were __________ their children.
4. When Jean __________, she wants to __________ a mechanical engineer.
Choose one sentence that has the same meaning as the root one.
Unless he starts saving now, he can’t go on holiday.
A. Start saving now or he can’t go on holiday
B. He can’t go on holiday if he doesn’t start saving now
C. He cannot go on holiday now because he didn’t save enough money.
D. He doesn’t go on holiday so he starts saving from now.