2。 People of different nationalities live in every house.
3。 Everyone drinks different drinks, smokes different brands of cigarettes and keeps different pets.
The question is: Who raises fish?
Tip:
1, the British live in a red house.
2. Swedes have dogs.
3. Danes drink tea.
The green house is on the left of the white house.
5. The owner of the green house drinks coffee.
6. People who smoke Pall Mall cigarettes keep birds.
7. The owner of the yellow house smokes Dunhill cigarettes.
People who live in the middle house drink milk.
9. The Norwegian lives in the first room.
10. People who smoke mixed cigarettes live next door to the cat owner.
1 1. Horse owners live next door to smokers on Dunhill Road.
12. People who smoke blue masters drink beer.
13, Germans smoke prince cigarettes.
14. The Norwegian lives next door to the blue house.
15. People who smoke mixed cigarettes have a neighbor who drinks water.
First, calculate the circumference of the earth, that is
Then surround the earth with a belt with a circumference of+1 m. There must be a gap after the circle is formed.
How big is this gap? Can ants go through it?
1.
The quotient of (1)69708÷92 is () digits, and the highest digit is () digits. (2) 4800 ÷1200 = () ÷12 (3) In the division with remainder, the dividend is = and the number that can be filled in D is () or (). (5) The maximum number that can be filled in the following () is 0.24× () < 250147× () < 850 35× () < 235 283× () <1590 (6).
2. choose. (Fill in the serial number of the correct answer in brackets)
The quotient of (1)25 divided by () is three digits.
A. three digits. B. No more than the smallest four digits. C. four or five digits. D. not sure.
(2)□067÷48, if the quotient is two digits, □ can be filled in ().
A. 1、2、3 B. 1、2、3、4 C.5、6、7、8、9
(3) The largest six digits is () times the largest three digits.
a . 2b 100 c . 100 1
(4) Because101× 99+22 =10021,so □□□□ =□… □
a . 1002 1 22 10 1 99 b . 1002 1 22 99 1 c . 1002 1 99 10 1 22
(5) The quotient of the number A divided by the number B is 20. If the number A is doubled and the number B is multiplied by 2, then the quotient is ().
A.20 B.80 C.5
Step 3 judge. (Mark "√" for the right and "×" for the wrong)
(1) 7272 ÷ 72 =11(2) 57 Except for the five digits with the highest digit of 3, the quotient must be three digits. () (3) Divider digits-Divider digits = quotient digits. () (4) Unit price is required. Finding the total amount of work is an applied problem. ()
Calculate.
(1) Numbers are written directly.
42÷ 14 77÷ 1 1 138÷69 720÷80 0÷4278 460÷20
16×8 19 19÷ 19 140÷35 27÷3×4 15×6 200÷40
(2) Longitudinal calculation.
9624÷24 6780÷60 1096÷78 8480÷53 2300÷25 6732÷68 1750÷35 4007÷28 462÷42
(3) Calculation of parting.
93 150÷23×25 240 16÷(3792÷48) (5040- 1320)÷6 4200÷70÷ 15
5. Formula calculation.
How many are there in (1) 1564? (2) How many times is1792 64?
(3) 4 1 times a number is 86 1. What's this number? (4) The dividend is 13660, and the divisor is 29. What is the quotient? What is the remainder?
6. Application questions.
(1) A 5,600-meter-long canal was built in 8 days in a township. How many meters are built on average every day?
(2) The school planted 60 trees last year, and this year it planted 35 trees three times more than last year. How many trees have been planted in two years?
(3) A TV set assembly team plans to assemble 750 TV sets in 25 days, but actually assembles 10 TV sets every day. How many TV sets are actually assembled every day?
(4) An orchard needs to transport 9,000 Jin of apples, of which 6,000 Jin has already been transported, and the rest are packed in 30 Jin in each basket. How many baskets can the rest hold?
(5) The road construction team originally planned to complete the10000m road in 25 days, but actually completed the task five days ahead of schedule. How many meters of roads are actually built every day?
(6) Along the 48-kilometer-long highway, 8600 poplars and 6040 willows were planted. How many trees are planted per kilometer on average?
1. Multiple choice questions (7 points for each question, ***56 points) Only one of the following four conclusions is correct. Please fill in the English letters of the correct answer in the brackets after the question.
1.a, b and c are positive integers, a >；; B, and it is equal to ()
A.b. or C. 1
2. In the four digits consisting of numbers 2, 4, 5 and 7, each number only appears once. Arrange all four digits from small to large, and the four digits of ranking 13 are ().
AD 4527-5247
3. 1989 China's GDP (gross national product) was only equivalent to 53.5% of that of Britain at that time, and now it is equivalent to 8 1% of that of Britain. If Britain's current GDP is m times that of 1989, then China's current GDP is about 1989 ().
A. 1.5 times B. 1.5m times C.27.5 times D.m times.
4. If x is an integer, the value of the fraction is an integer, and the value of x is ().
A.3 B.4 C.6 D.8
5. It is known that a is an integer and the root of the equation about x is a prime number, and it is satisfied, then a is equal to ().
A.2 B.2 or 5 c
6. As shown in the figure, Rt△ABC, ∠ C = 90 and ∠ A = 30 are known. Take a point P on the straight line BC or AC to make △PAB an isosceles triangle, then the qualified point P is ().
A.2 B.4 C.6 D.8
7. Three cubes with side lengths of 3, 5 and 8 are bonded together. Among these solids bonded together in various ways, the surface area of the one with the smallest surface area is ().
From 570 to 502 A.D.
8. In quadrilateral ABCD, diagonal AC bisects ∠BAD, AB > AD, and the following conclusion is correct ().
A.AB-AD>CB-CD B.AB-AD=CB-CD
The relationship between C.a b-AD < CB-CD d. a b-AD and c b-CD is uncertain.
Fill in the blanks (7 points for each small question, 84 points for * * *)
9. The minimum value of a polynomial is _ _ _ _.
10. If known, the value of is equal to _ _ _ _ _.
1 1. The picture shows a computer motherboard with right angles at each corner. The data is shown in the figure, and the unit is mm, so the perimeter of the motherboard is _ _ _ _ mm 。
12. A school built a rectangular water tank without a cover. Now the inner wall and bottom of the tank are ground with a circular grinding wheel with radius r, so the area that the grinding wheel can't grind is _ _.
13. There are two acute angles and one obtuse angle in α, β and γ, and their values are given. When calculating the numerical value, three students worked out three different results, 23, 24 and 25 respectively, and one of them was indeed the correct answer, so α+β+γ = _ _ _ _.
14. Let a be a constant, and the remainder obtained by dividing by polynomial is, then A = _ _ _.
15. In △ABC, the straight line where Gao BD and CE are located intersects at point O. If △ ABC is not a right triangle and ∠ A = 60, ∠ BOC = _ _ _ degrees.
16. Xiao Wang's school held a grade exam, chose several courses, and then tried another course. Wang Kao got 98 points, and Wang's average score was higher than the original 1 point. Later, he took an extra course, and Wang Kao got 70 points. At this time, Wang's average score dropped by 1 minute compared with the initial average score, so Wang * * * took _ _ courses (including two extra exams), and the final average score was _ _.
17. As we all know, the range of is _ _ _ _ _ _.
18. There is a reciprocal key on the calculator, which can find the reciprocal of the input non-zero number (note: sometimes it is necessary to press the or key first to realize this function, which will not be explained below). For example, if you enter 2 and press the key, you will get 0.5. Now enter a number on the calculator, and then press the key in the following order: The result on the display screen is -0.75, so the original number entered is _ _ _ _ _.
19. There are three different types of batteries, A, B and C, and the prices are different. If you have a sum of money, you can buy 4 A, 18 B,16 C; Or type a 2, type b 15, type c 24; Or A 6 type, B 12 type, C 20 type. If all this money is used to buy C-type batteries, you can buy _ _ _ _.
20. As shown in the figure, in the known pentagonal ABCDE, ∠ ABC = ∠ AED = 90, AB = CD = AE = BC+DE = 2, then the area of pentagonal ABCDE is _ _.
First, multiple-choice questions:
1.-,-,-,-The order of these four numbers from small to large is ().
(1)-< -& lt； -& lt； -(B)-& lt； -& lt； -& lt； -
(C)-& lt； -& lt； -& lt； -(D)-& lt； -& lt； -& lt； -
2. The three sides of a triangle are A, B and C (A, B and C are all prime numbers), and A+B+C = 16, then the shape of the triangle is ().
(a) right triangle (b) isosceles triangle (c) equilateral triangle (d) right triangle or isosceles triangle
3. If 25x = 2000 and 80y = 2000 are known, it is equal to ().
(A)2 (B) 1 (C) (D)
4. let A+B+C = 0, ABC > 0, and the value is ().
(a)-3 (b) 1 (c) 3 or-1 (d)-3 or 1
5. let real numbers a, b and c satisfy a.
(A) (B)|b| (C)c-a (D)―c―a
6. If all three sides of an isosceles triangle are integers and the perimeter is 10, then the length of the base is ().
(a) All even numbers (B)2 or 4 or 6 or 8 (C)2 or 4 or 6 (D)2 or 4.
7. The number of nonnegative integer solutions of the ternary equation x+y+z = 1999 is ().
(A)2000 1999(B) 19992000(C)200 1000(D)200 1999。
8. As shown in figure 1, in trapezoidal ABCD, AB//CD, and cd = 3ab, EF//CD, EF divides trapezoidal ABCD into two parts with equal areas, and AE :ED is equal to ().
Article 2 (2) (3) (iv)
9. As shown in Figure 2, one vertex of a right triangle with side lengths of 3cm, 4cm and 5cm coincides with the vertex B of the square, and the other two vertices are on the two sides AD and DC of the square, so the area of the square is ().
(A) cm2 (B) cm2
Square centimeter
10. It is known that p+q+r = 9, which is equal to ().
9 (B) 10 (C)8 (D)7
2. Fill in the blanks:
1 1. Simplified: =.
12. Assuming that the polynomial 2x2+3xy-2y2-x+8y-6 can be decomposed into the form of (x+2y+m) (2x-y+n), then
The value of is.
13.△ ABC, AB & gtAC, AD and AE are the median line of BC and the bisector of ∠A respectively, so the relationship between AD and AE is AD AE. (fill in ">", "<" or "=")
14. As shown in Figure 3, in the acute angle △ABC, AD and CE are the heights of BC and AB respectively. If the acute angle between AD and CE is 58, the size of ∠ BAC+∠ BCA is.
15. Let A2-B2 = 1+ and B2-C2 = 1-, then the value of A4+B4+C4-A2 B2-B2C2-C2A2 is equal to.
16. Given that x is a real number and x2+= 3, the value of x3+ is.
17. It is known that n is a positive integer. If it is a reduced fraction, then the value of this fraction is equal to.
18. As shown in Figure 4, in △ABC, AC = 2, BC = 4, ∠ ACB = 60. Fold △ABC to make point B and point C coincide, and the crease is de, then the area of △AEC is.
19. It is known that non-negative real numbers A, B and C satisfy the conditions: 3a+2b+c = 4, 2a+b+3c = 5. Let the maximum value of s = 5a+4b+7c be m and the minimum value be n, then n-m is equal to.
20. Let A, B, C and D be positive integers, A7 = B6, C3 = D2, C-A = 17, then D-B is equal to.
Three. Answer the question:
2 1. It is known that real numbers A and B satisfy the condition | A-B | =
22. As shown in Figure 5, in the square ABCD, AB =, points E and F are on BC and CD respectively, and ∠ BAE = 30, ∠ DAF = 15, find the area of △AEF.
23. Put five balls numbered 1, 2, 3, 4 and 5 into five boxes numbered 1, 2, 3, 4 and 5, and there is only one ball in each box.
= 1 * GB3 ① A * * *, how many different ways are there?
= 2 * GB3 ② If the ball with the number 1 happens to be placed in the box of 1, how many different ways can * * * be placed?
= 3 * GB3 ③ If at least one ball is put in a box with the same number (that is, put in the same number), how many different ways are there?
Reference answer
First, multiple-choice questions:
The title is 1 23455 6789 10.
Answer A B B B D D C C D A
2. Fill in the blanks:
The title is112131415.
Answer 1-
& gt 122 5
Title16171819 20
Answer 2
-2 60 1
Three. Answer the question:
2 1.∵| a-b | = & lt； 1,
∴ a and B have the same number, a≠0, b≠0,
∴a-b- 1 =(a-b)- 1 & lt； 0,
∴( - ) =( - )[ 1-(a-b)]=。
= 1 * GB3 ① if both a and b are positive numbers, they are determined by the following formula.
∴ A-b=, A2-Ab= B, and the solution is B =,
∴( - ) = = ( 1- )
=- ? =-
=- .
= 2 * GB3 ② If both A and B are negative numbers, it is determined by the following formula.
∴ A-b=-, A2-Ab=-B, and B =,
∴( - ) = = ( 1+ )
= =
= .
To sum up, when a and b are both positive numbers, the result of the original formula is-; When a and b are both negative numbers, the result of the original formula is
22. Rotate the△ △ADF 90 clockwise around point A to the position of△ △ABG.
∴ AG=AF，∠GAB=∠FAD= 15，
∠GAE= 15 +30 =45，
∠EAF=90 -(30 + 15 ) =45，
∴∠ gae =∠ FAE，AE = AE，
∴△AEF≌△AEG，∴EF=EG，
∠AEF=∠AEG=60，
In Rt△ABE, ab =, ∠ BAE = 30,
∴∠AEB=60，BE= 1，
At Rt△EFC, FEC = 180-(60+60) = 60,
EC=BC-BE= - 1，EF=2( - 1)，
∴EG=2( - 1)，S△AEG= EG？ AB=3，
∴S△AEF=S△AEG=3-。
23.= 1 * GB3 ① Put the first ball first, there are five different ways, and then put the second ball. At this time, the third, fourth and fifth balls are placed in four different ways, and so on, with 3, 2 and 1 respectively, so that the total number of * * * is 5× 4.
= 2 * GB3 ② Put the ball 1 into the box 1, and place the other four balls at will. They have 4, 3, 2, 1 in turn, so that * * * has 4× 3× 2× 1 = 24 different ways.
= 3 * GB3 ③ (scheme 1)
120 kinds of delivery methods, all the wrong delivery methods are excluded, and the rest is the number of the delivery method with at least one ball in the same number box.
In order to study the calculation method of all misnumbered release species, let A 1 be the release species with only one ball in a box, obviously A 1 = 0, A2 is the release species with only two balls in two boxes and misnumbered, ∴ A2 = 1, and A3 is the release species with only three balls out of three.
Let's study the calculation method of A n+ 1 A A nd consider its relationship with an and an- 1.
If there are n balls misplaced now, the number of categories is n, take any one of them, bring the ball of n+ 1 and the box of n+ 1, put any ball in the previous n boxes (definitely not the ball numbered m) into the box of n+ 1, and put the ball of n+/kloc-. * * * There are different versions.
However, in the operation just now, the case that the ball numbered M was put into the n+ 1 th box was ignored, that is, there was another case where the ball numbered M was put into the n+ 1 th box, the ball numbered N+ 1 th box, and the other balls were n- 1 th box. So it is reasonable to have Na N- 1
To sum up, an+1= nan+nan-1= n (an+an-1).
From A 1=0, A2= 1, A3 = 2 (1+0) = 2, A4 = 3 (2+ 1) = 9, A5 = 4 (9+2) = 44.
Therefore, at least one ball is put into a box with the same number, and the number of release methods is the number of all release methods minus the number of five balls with wrong numbers, that is, 120-44 = 76.
(Solution 2)
There are five ways to choose a ball from five balls. Put it in a box with the same number (for example, put the ball of 1 in the box of 1), and the other four balls are placed at will, with 24 ways of placement, so * * * has 5× 24 = 120 ways of placement.
However, many of these methods are repetitive. For example, the method of putting two balls in boxes with the same number (for example, putting ball 1 and ball 2 in boxes 1 and 2 respectively) is calculated twice, then two balls should be subtracted from the total and put in the same box.
Case number: 120-= 120-60 (species).
Obviously, in this calculation, the method of putting three balls into boxes with the same number (for example, putting ball 1, ball 2 and ball 3 into box 1, box 2 and box 3 respectively) is calculated once less, so = 20 should be added to the previous formula.
Then calculate the situation that four balls and five balls are put in the same number box, subtract the situation that four balls are put in the same number box, and finally add the situation that five balls are put in the same number box.
The whole formula is120-+-=120-60+20-5+1= 76 species.