1, a: 1/6

2. _ _ _ _ _ A: 4/900

3. The perimeter ratio of two circles is 4: 1, so the area ratio of these two circles is _ _ _ _ _.

A: 16: 1

4. The side length of the cube changed from 5 cm to 8 cm, and the surface area increased by _ _ _ _ square cm.

A: 234

A train traveled 360 kilometers in the first three hours, then increased the speed by 10% and traveled for two hours, so the train traveled _ _ _ _ _ kilometers.

A: 624

6. As we all know, the bottom area of a cylinder is equal to the side area. If the height of this cylinder is 5cm, its volume is _ _ _ _ cubic centimeter (take 3. 14).

A: 1570

7. The teacher wants to give three children 20 identical apples, and requires each child to get at least three apples. So * * * has _ _ _ distribution methods?

A: 78

8. As shown on the right, take the two right-angled sides of the right-angled triangle ABC as the radius.

Make two semicircles, and it is known that the sum of the lengths of these two semicircles is 37.68 cm.

Then the maximum area of triangle ABC is _ _ _ _ square centimeter (take 3. 14).

Answer: Hint: According to condition 3. 14*(AB+AC)/2=37.68.

So AB+AC=24

So the maximum area of triangle ABC is 12* 12/2=72 square centimeters.

9. There are two bottles of brine. The concentration of brine in bottle A is three times that of bottle B. After mixing 100g of brine in bottle A with 300g of brine in bottle B, new brine with the concentration of 15% is obtained, so the concentration of brine in bottle A is _ _ _ _ _.

Answer: Note: The weight ratio of Party A and Party B is 1: 3, so the concentration difference ratio is 3: 1.

Assuming that the concentration of B is x%, then A is 3x%.

3x- 15 = 3( 15-x)x = 10

So the concentration of a bottle of salt water is 30%

Second, solve the problem.

1、

A: x= 1

Last year, the total output value of a factory exceeded the total expenditure by 500,000 yuan. This year has increased by 10% compared with last year, and the total expenditure has been saved by 20%. If the total output value this year is 6.5438+0 million yuan more than the total expenditure, what are the total output value and total expenditure last year?

A: If the total expenditure last year was X million yuan, then the total output value was (X+500) million yuan.

1. 1(x+50)- 100 = 0.8x

The solution is x= 150.

So the total expenditure last year was 6.5438+0.5 million yuan, and the total output value was 2 million yuan.

3. There are _ _ _ _ four digits that meet the following conditions: their digits are all odd; Its digits are different from each other; Every number of it can be divisible by itself.

Answer: It is easy to know that if you choose four out of five odd numbers, there must be three or nine.

That is to say, in any case, this four-digit number must be a multiple of 3, that is, the sum of these four different odd numbers is a multiple of 3.

1+3+5+7+9=25

To leave four multiples that add up to three, you can only remove 1 or 7.

However, if 1 is removed, the sum of numbers is 24, which cannot be divisible by 9, so only 7 can be removed, leaving four odd numbers of 1, 3, 5 and 9.

Obviously, as long as you put five in one place, there are six different arrangements in the first three places.

Therefore, there are six four-digit numbers that meet the requirements.

As shown in the figure, ABCD is a simulated runway with a side length of 6 meters. Toy car a runs clockwise from a at a speed of 5 cm per second, and toy car b runs counterclockwise from the midpoint of CD. As a result, the second encounter between the two cars happened at point B. How many centimeters does car B travel per second?

Answer: There are two situations: ① A is slow and B is fast, so the first meeting point will be on AB side. It can be seen that by the second head-on encounter, A walked AB, which is 6 meters, while B walked 9 meters, which is 33 meters. At the same time, the distance ratio is 6: 33 = 2: 1 1, so the speed of b is 5× = 27.5cm.

② B is slower than A, and will meet at a certain point between C and B for the first time, so by the time of the second meeting, A walked 30 meters, while B walked 9 meters, 30: 9 = 10: 3, which is the speed ratio, so the speed of B is 5× =1.5cm.