Seek the seventh grade mathematics Olympic Games problem

This rectangular swimming pool is 50 meters long, 30 meters wide and 5 meters high. Put it into a cuboid with a bottom area of 1m2 and a height of 6m. The top of the refrigerator is higher than the water surface, and it is 2 meters deep after being put in. Find the volume of water.

A, fill in the blanks (this big question ***6 small questions, 4 points for each small question, ***24 points)

1. if a>0, b<0, and | b| > A, then _ _ _ _ 0.

2.0.0630 This number is accurate to _ _ _ _ _, with _ _ _ _ significant digits.

3. If one person can make m parts a day (assuming everyone's work efficiency is the same), then X people can make _ _ _ _ parts a day.

4. A three-digit number, where the number on one digit is B, and the number on the hundredth digit is the sum of the number on one digit and the number on the tenth digit, then this three-digit number can be expressed as _ _ _ _ _ _ _ _ _ _ _.

5. If the monomials -3a6bn+2 and 2a2mb4 are similar terms, the value of 5m2n3-(3m+2n) 2 is _ _ _ _ _ _.

6. Now the father is more than six times as old as his son. 10 years later, the father is three times as old as his son. Now the son is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

Second, multiple-choice questions (***6 small questions, 5 points for each small question, ***30 points)

1. It is known that m = 12a2b, n = 8ab2, p =- 14a2b, and the following calculation is correct ().

a . M+N = 20a 3 B3 B . N+P =-6ab C . M-P = 2a2b D . M+P =-2a2b

2. There are a seats in the first row of the auditorium, 1 seat in the back row, and 15 seats in the auditorium * * *, so the total number of seats in this auditorium is ().

a . 15a+ 105 b . 15a+ 136 c . 15a+ 120d . 14a+ 105

There are two trucks driving in the same direction on the same highway. At first, car A was 4km in front of car B, with a speed of 45km and a speed of 60km. Then before the second car catches up with the first car, the distance between the two cars is _ _ _ _ m1minute.

1. A two-digit number, where the ten digits are x and the digits are X- 1. What are the two digits obtained by exchanging ten digits with digits?

2. The little mother took Mi Yuan to the street to buy food. She spent half on meat and the remaining third on vegetables. So how much money does she have left?

1, known set a = {x |1/32 ≤1/2x ≤ 4}, B=[m- 1, 2m+ 1], a ∩ b = φ, try.

2. The known complete works I={x | 2≤x≤30, x∈N}, A={x | x=2n, n∈N*}, B={x | x=3k+ 1, k∈N*}. Find the complement of [(A ∩ B)] ∩ C.

3. The known complete set I={ real number pair (x, y)}, set A={(x, y)| (y-4)/(x-2)=3}, and B={(x, y)| y=3x-2}

It is quite difficult to find the complement of A ∩ B. Let me tell you the answer:

The first question:

From 1/32≤ 1/2x≤4.

116x ≤1≤ 8x (because x must be a positive number, which can be seen at a glance).

That is,1/8 ≤ x.

Since a ∩ b = φ, there must be 2m+ 1 less than 1/8.

Get a solution,

M is less than -7/ 16.

the second question

A is 24681012141618 20 22 24 26 28 30.

B is 4 710131619 22 25 28.

A and b are 4 10 22 28.

The intersection prime of the complement set is the prime set {235711317192329}.

The third question:

The complement set of A is point set (2,4), which is exactly (2,4) on B. That is to say, the answer to this question is point set {(2,4)}.

Go ahead.

1. As shown in Figure 7, two cars A and B respectively travel in opposite directions at the same time, meet at C, continue to travel to B and A respectively, return immediately, and meet again at D, given AC = 30km, AD = 40km, AB= () km, speed of A: speed of B = (): ().

2. In Figure 6, the side lengths of square GFCD and square AEHG are integers, and the sum of their areas is 1 17, where p is a point on AE and q is a point on CD. Then the area of triangle BCH is (); The area of quadrilateral PHQG is ()

Here are the answers ~

1. It is known that the equation 2a(x- 1)=(5-a)x+3b about x has countless solutions, so a = _ _ _ _ _ _ _ _ _

A: 2a(x- 1)=(5-a)x+3b。

2ax-2a=5x-ax+3b

3ax-5x=2a+3b

x(3a-5)=2a+3b

Equation 2a(x- 1)=(5-a)x+3b There are many solutions to x.

So no matter what value X takes, it always holds.

So this equation has nothing to do with X.

So 3a-5 = 0, 2a+3b = 0.

a=5/3，b= - 10/9

2. What is the sum of all possible four-digit numbers composed of natural number 1 ~ 9, and there are no duplicate numbers?

A: First of all, let's look at a * * *, and how many four digits there are.

There are nine possibilities in a thousand, eight possibilities in a hundred, seven possibilities in ten, and six possibilities in an individual.

A * * * has 3024 four digits.

Look at a seat first. Because every number has an equal status, so

One ninth, that is, 336 units are 1, 336 units are 2, 336 units are 3, ... 336 units are 9.

All these bits add up to 336× (1+2+...+9 )×1.

Look at ten more. Because every number has an equal status, so

One ninth, that is, 336 bits are 1, 336 bits are 2, 336 bits are 3, ... 336 bits are 9.

All these bits add up to 336× (1+2+...+9 )×10.

Look at hundreds more. As can be seen from the above analysis, the sum of all hundreds is 336× (1+2+...+9 )×100.

Look at thousands more. As can be seen from the above analysis, the sum of all thousands is 336× (1+2+...+9 )×1000.

So the sum of all four digits is:

336×( 1+2+...+9)× 1+336×( 1+2+...+9)× 10+336×( 1+2+...+9)× 100+336×( 1+2+...+9)× 1000

=336×( 1+2+...+9)×( 1+ 10+ 100+ 1000)

=336×45× 1 1 1 1

= 16798320

A square table consists of a table top and four legs. 1 m3 of wood can be used to make 50 desktops or 300 legs. There are now 5 cubic meters of wood. How many pieces of wood can be used to make a desktop and how many legs can be used to make a square table?

The speed of the ship in still water is 1 hour 24 kilometers, and the current speed is 2 kilometers per hour. It takes six hours for the ship to go back and forth between A and B. How long does it take to sail downstream from A and from B to A respectively? What is the distance between A and B?

Warehouse A stores 200 tons of coal and warehouse B stores 70 tons. If warehouse A transports 15 tons and warehouse B transports 25 tons every day, how many days later will warehouse B store twice as much coal as warehouse A?

There are 27 workers in Workshop A and 0/9 workers in Workshop B, and now there are 20 new workers. In order to make the number of workers in workshop A twice that in workshop B, how should new workers be assigned to two workshops?

1, assuming that X square tables can be made, then

You need to make x desktops and 4x legs.

x *( 1/50)+4x *( 1/300)= 5

The solution is x= 150.

2. Solution: Let the distance between Party A and Party B be X kilometers.

According to the meaning of the question: x/(24+2)+x/(24-2)=6.

The solution is x=7 1.5.

rule ...........

Three questions

After x days of solution, the stored media is twice that of warehouse A.

Then 2*(200- 15x)=70+25x.

The solution is x=6.

Four questions

If x people are assigned to workshop a, 20-x people will be assigned to workshop B.

According to the meaning of the question, 27+x=2*( 19+20-x)

The solution is x= 17.

1. A two-digit number, where the ten digits are x and the digits are X- 1. What is the two-digit number obtained by exchanging ten digits with digits?

2. The little mother took Mi Yuan to the street to buy food. She spent half on meat and the remaining third on vegetables. So how much money does she have left?