1, calculation:

Answer: 7/8

2、 =_______________________.

Answer:

Original formula =

=2×

=

3. There is a cuboid, all of which are10cm long, 8cm wide and 4cm high. How to make a cuboid with the largest surface area?

4. Can you find the laws of the following equations? Write more groups like this.

Can you find the trick to solve this problem?

6. If a× = b× = c× (A, B and C are not 0), can A, B and C be arranged from small to large?

7. Compare the size of sum.

8, calculation, if □ +□ +□ = ○, ○+△ = △ +△, then (□ +□) ÷△ =.

9. If A is a non-zero-sum natural number, who is the big than \ or \? Why?

10, A× = B× = C ÷ = D ÷ (A ≠ 0) is known. Put A, B, C and D in the order from small to large.

1 1, among the five natural numbers, the smallest natural number is equal to the sum of these five numbers. What are these five numbers?

12, the sum of numerator and denominator of a fraction is 3985, and the fractional value is, what is the original fraction?

13, a bottle of salt water 600g, in which the weight ratio of salt to water is 1: 24. (1) If 6 grams of salt is added, what is the weight ratio of salt to water? (2) If the weight ratio of salt to water is 1: 30, how many grams of water should be added?

/kloc-the ratio of boys to girls in class 0/4 and class 6 (2) is 6: 5. After transferring two girls, there are still 42 students in the class. What is the ratio of boys to girls now?

15. Among the following four formulas, _ _ _ _ has the largest number.

( 1) (2)(3)(4)

16, Xiaoming and Xiaohua weigh the same. What is the weight ratio between Xiaoming and Xiaohua?

17, a math extracurricular interest group, was occupied by boys last semester. After adding 2 1 girls this semester, boys only occupied it. How many girls are there in this group?

18, a basket of oranges weighs 34 kg. After eating, the basket weighs 28 kilograms. How many kilograms of oranges are there in this basket?

19. Cut the 5-meter-long iron wire into 6 sections on average, each section is 5 meters, and 2 sections are _ _ _ _ _ meters.

20. a and b are natural numbers not equal to 0, and b× < b, b× > b, then a is _ _ _ _.

2 1、 、 、 、 、_____、_____。

22. Two ropes with the same length. A cut off, B cut rice. Which of the remaining two ropes is longer? Why?

23. The area of a square piece of paper is square decimeter. If you fold it in half and then fold it in half, what is the area at this time?

24. When the grain stored in warehouse A is transferred to warehouse B, the grain stored in the two warehouses is equal, so what is the raw grain stored in warehouse B?

25. The product of two fractions is, and the sum is 2. What are these two scores?

26. The cold winter has arrived. In order to meet the customers' demand, Friendship Shopping Mall bought 72 new coats, which are going to be sold in 240 yuan. As a result, the weather suddenly turned warmer after they sold it. In order not to overstock the goods, the mall decided to sell the rest at the original price. How much can these coats sell in Friendship Shopping Mall?

27. There are a bunch of apples *** 100. Those who ate all the apples on the first day ate the remaining apples on the next eight days. After eating like this for nine days, how many are left?

Second, the application problem:

1. Xiaoming and his mother bought a present for grandma. The assistant aunt packed it in a rectangular box with a length of 45 cm, a width of 20 cm and a height of 10 cm, and wrapped it with a rope. How many centimeters of colored rope does it take to find the knot?

2. A cuboid with a regular principal shape at the bottom, with a bottom circumference of 24 cm, a height of 15 cm, and a surface area of how many square centimeters?

The sum of the sides of a cuboid is 28 decimeters. Given that the bottom is a square with a side length of 2 decimeters, what is the height of the cuboid?

4. Three cubes with a side length of 2 cm are spliced into a cuboid. How many square centimeters is the surface area of the cuboid reduced compared with the original cuboid?

5. How many square centimeters has the surface area of a rectangular steel with a length of 1 m and a width of 14 cm been reduced after sawing the largest cube from one end of the steel?

6. Make a cuboid or cube with 8 cubes 2 cm long (all used up). In order to minimize the sum of side lengths, it should be spelled as _ _ _ _ _ _, and its side length is _ _. In order to make the side length as long as possible, it should be spelled as _ _ _ _ _ _, the sum of its side lengths is _ _ _ _ _ _, and the surface area is _ _ _ _ _ _.

7. The surface area of a small cube is18cm2, so what is the surface area of a big cube composed of 1000 identical small cubes?

There is a cuboid on the desktop. No matter which direction you look, how many faces can you see at most?

9. A cuboid with a length of 9 cm, a width of 6 cm and a height of 3 cm can be cut into three cuboids with equal volume. How many square centimeters can the surface area be increased?

10, find the surface area of the figure below.

1 1. If a cuboid is cut into two equal cubes, the surface area will increase by 160 square centimeters. What is the original surface area of this cuboid?

12. There is a rectangular stone with a length of 30 cm, a width of 18 cm and a height of 15 cm. When processing, eight vertices are cut into small cubes with side length of 1 cm. What is the current surface area?

13. Divide a cuboid into a cube with a surface area of 150 cm2 and a cuboid with a surface area of 1 10 cm2. What are the length, width and height of the original cuboid?

14. If the height of a cuboid is reduced by 2 cm, it becomes a cube with a surface area of 150 cm2. Find the surface area of the original cuboid.

15, three cubes with sides of 3 cm, 5 cm and 8 cm are bonded together to get a new cube. What is the surface area of the cube with the smallest surface area among all bonding methods?

16. The side length of the cube is 4 cm. Dig a small cube with a length of 2 cm from the center of its front, back, left, right, upper and lower sides. What is the surface area of the excavated cube?

17, use a small cube block with the length of 1 cm to make a larger cube. At least? _ _ _ _ block.

18. The areas of three adjacent faces of a cuboid are 10 cm2, 15 cm2 and 6 cm2 respectively. How many cubic centimeters is the volume of this cuboid?

19, a cuboid, if two adjacent faces are squares, is this cuboid a cube?

20. How many cubes with a length of 6 cm, a width of 4 cm and a height of 5 cm can a rectangular box hold at most?

2 1, a cube with a surface area of 48 square centimeters, cut into two identical cuboids, how many square centimeters does the surface area increase?

22. A cuboid package is 50 meters long, 30 meters wide and 5 meters high. Q: How many cuboid containers of 8 cubic meters can hold at most?

23. A cube with a side length of 2 cm is still a cube after the volume is increased by 208 cubic centimeters. How many centimeters has the side length of this cube increased?

24. Make a rectangular carton with four identical rectangles and three identical square cardboard. Its surface area is 266 square decimeters. The length, width and height of a cuboid are integer decimeters, and the bigger the carton, the better. What is the volume of this carton?

25. Two cars, A and B, are driving in opposite directions from east to west at the same time. Car A travels 56 kilometers per hour and car B travels 48 kilometers per hour. The two cars meet at a distance of 32 kilometers from the midpoint. How many kilometers are there between things?

Summary of key middle school entrance examination II

Fill in the blanks

1, a piece of ice loses half its weight every hour, and after five hours, it weighs kilograms, so the initial weight of this piece of ice is _ _ _ _ _ _ kilograms.

2, large and small bottles of water ***9.7 liters, large bottles of water 0.3 liters, then the ratio of large bottles and small bottles of water is 3: 2, the original ratio of two bottles of water is _ _ _ _ _.

3. If the numerator of a fraction is multiplied and the denominator is divided by 100, the fraction is _ _ _ _ _.

There are two baskets of apples, A and B. The first basket has 30 kilograms. If you pour from the second basket to the first basket, the two baskets of apples are equally heavy, and the second basket of apples has _ _ _ _ _ kg.

5、( ) :25= = ; 8×[2+(□×7)]⊙= 8 is known. Then□ = _ _ _ _ _ _.

6. It is known that =+,A and B are two different natural numbers, so the minimum sum of A and B is _ _ _ _ _.

7. For the existing 5, 5, 5, 1, please use addition, subtraction, multiplication, division and brackets to calculate _ _ _ _ _ _ of Formula 24; If you use 7, 7, 3, 3, how to make it up? _________。

8. There is a square with a side length of 1 decimeter. First, Party A crossed out the square area, and then Party B crossed out the remaining area. Then A crosses out the remaining area, B crosses out the remaining area, ... and so on, and so on, which is crossed out three times respectively, leaving a square with _ _ _ _ _ _ _ _ square decimeter.

9. Xiaoming has 95 red and blue colored balls. There are as many red balls as there are blue balls, and the difference between the two balls is _ _ _ _.

1 1, the price of a commodity is reduced after the price increase, and the current price is _ _ _ of the original price. If it is greater than a, then b is less than a. ..

12. In the subtraction formula, the sum of the minuend, the subtraction and the difference is 50, the difference is less than the subtraction, and the subtraction is _ _.

1 1, two students, A and B, 5: 4. If A gives B 22.5 points, their score ratio is 5: 7. It turns out that B got _ _ _ _.

13. It is known that A and B are two natural numbers, and A equals B; If A minus 3 and B plus 3 are equal, then the sum of A and B is _ _ _ _ _ _; When water becomes ice, its volume increases, but when it becomes water, its volume decreases.

Second, the calculation problem.

( 1)、 × 140- 1÷ (2)、 (3)、 (4.3×2.375÷ × )×

(4) Divide the product of 25 by the quotient of 0.375. What is the result?

Third, the application problem.

1. The weight ratio of rice stored in granary A and granary B is 8: 7. If rice is shipped from warehouse A and 8 tons are shipped from warehouse B, then warehouse B stores more rice than warehouse A 17 tons ... Q: How many tons of rice are there in warehouse A?

The speed ratio of car A and car B is 4: 3. The two cars leave from A and B at the same time, and the directions are opposite. 10 minutes later. Then go in the same direction (B is in front, A is behind), and A catches up with B in a few minutes?

Three good friends, A, B and C, went to climb the mountain. At lunch, Party C found that his bread was lost, so both Party A and Party B gave him the same amount of bread. It is known that Party A takes out his own bread and Party B takes out his own. What is the ratio of bread brought by Party A and Party B?

4. build a road. The ratio of repaired length to unrepaired length is 1: 5, and then 490 meters. The ratio of repaired length to unrepaired length is exactly 3. What is the total length of this road?

5. The school red scarf hydrological station measures the depth of the river and inserts a pole into the river. The pole was stuck in the mud and exposed to the water. When the water level rises 12 cm, the water depth is just the benchmark. What is the initial depth of this river?

6. Use rice for a piece of cloth, use the rest for the second time, and use 6 meters for the second time. How long is this cloth?

、

7. The school bought three kinds of books, among which story books accounted for 40 less than science books and literature books 160. How many books are there in these three books?

8. Let A=, B=, C=, D=, E=, then what is the result of (B-A)÷(C÷D÷E)?

9. A = 333133335b = 22223/2227 is known. Who is older, A or B? Why?

10, the number of people who take part in the Chinese contest is the number of people who take part in the math contest, and the number of Chinese winners is the number of math winners. And the number of people who didn't win in the two competitions is 320, so what is the total number of people who participated in the two competitions?

1 1. Students in grade five and six of a primary school donated books to poor mountainous areas, while in grade five they donated 154. The sixth grade donated five books less than the fifth grade. Q: How many books were donated in the sixth grade?