2. It takes 20 days for Team A to build a canal, and 30 days for Team B to build it alone. If two teams cooperate, the work efficiency will be reduced because of the influence of each other's construction. The working efficiency of team A is four fifths of the original, while that of team B is only nine tenths of the original. Now it is planned to complete the canal in 16 days, and it is required that the two teams cooperate for as few days as possible. So how many days will the two teams cooperate?
It takes 4 hours for Party A and Party B to do a job, and 5 hours for Party B and Party C to do a job. Now, please ask Party A and Party C to work together for 2 hours, and the remaining Party B needs to work for 6 hours. How many hours does it take to finish the work alone?
A number, MINUS 20% of it and plus 5, is still 3 less than the original. So, this number is _ _ _ _ _ _ _ _.
2. The number A is less than the number B 16%, and the number B is 20% larger than the number C. Among the three numbers A, B and C, the smallest number is _ _ _ _ _ _ _ _ _.
3. At 6: 10 on the clock, the obtuse angle formed by the minute hand and the hour hand is _ _ _ _ _ _ _ _ _.
4. A true score, if multiplied by 3, the numerator is smaller than the denominator 16, if divided, the denominator is smaller than the numerator by 2, and this true score is _ _ _ _ _ _ _ _.
5. The weight of 1 1 plum is equal to the weight of two apples and 1 peach, and the weight of two plums and1apple is equal to the weight of1peach, so the weight of a peach is equal to the weight of _ _ _ _ _ _ _ _.
6. The sum of number A and number B is 16, and number A is _ _ _ _ _ _ _.
7. Among the paintings exhibited in the "June 1st" art exhibition, 14 is not in grade 6, 17 is not in grade 5, and 2 1 is exhibited in grade 5 and 6. Therefore, the paintings exhibited in other grades are _ _ _ _ _ _ _.
8.100g 15% saline water, put 8g of salt. In order to make the concentration of the solution reach 20%, then you have to add _ _ _ _ _ _ _ g of water.
9. The two factories A and B produce the same number of products. The quantity of genuine products in Factory A is three times that of defective products in Factory B, and the quantity of genuine products in Factory B is four times that of defective products in Factory A.. Then, the ratio of the number of genuine products produced by factory A and factory B is _ _ _ _ _ _ _.
2. Application questions: (9 points for each question, formula calculation is required, only the number of answers is given, but not given)
1. The quotient of dividing two numbers is 22, the remainder is 8, and the sum of dividend, divisor, quotient and remainder is 866. Q: How much is the dividend?
There were 407 contestants in the Singer's Grand Prix in February and June 1 Day. The number of female singers who did not win the prize accounted for the total number of female singers, 16 male singers did not win the prize, but the number of male singers who won the prize was the same. Q: How many male singers are there?
3.A goes from place A to place B, and B and C go from place B to place A. Three people start at the same time. A first meets B on the way, and then meets C in 15 minutes. A walks 70 meters per minute, B walks 60 meters per minute and C walks 50 meters per minute. Q: What is the distance between A and B?
4. A batch of military support materials can be transported in three days if they are transported by eight big trucks, and 75% of the total materials can be transported in eight days if they are transported by five small trucks. How many days can three big trucks and four small trucks carry?
5. The number of boys in three groups is the same. The number of boys in the first group is equal to the number of girls in the second group, and the number of boys in the third group is the sum of the three groups of boys. What percentage of boys are in the three groups?
6. When the two water inlet pipes A and B are opened at the same time, 40% of the pool can be filled in 4 hours, then the pipe A is opened for 5 hours respectively, and then the pipe B is opened for 7.4 hours respectively, before the pool can be filled. Q: If pipe B is opened separately, how long will it take to fill the pool?
First, fill in the blanks. 18%
1. A cylinder has () faces. () The areas of two faces are equal, and its sides can be expanded into (). The length and width are () and () respectively.
2. The radius of the bottom surface of the cylinder is 3cm and the height is 5cm. Its bottom area is () cm2, lateral area is () cm2, and its surface area is () cm2. Its volume is ().
3. The diameter of the cone bottom is 20 decimeters, the height is 9 decimeters, and the volume is () cubic decimeters.
4. The distance between Party A and Party B is 20km, and the distance drawn on the map is10cm. The scale of this map is ().
The length of a precision part is 4 mm, and the length drawn on the drawing is 4 cm. The scale of this picture is ().
6. Choose four numbers from 2, 4, 6, 3 and 9 to form the proportional formula ().
7. Just process a cylinder with a volume of 129 cubic centimeter into the largest cone part. The volume of this cone part is () cubic centimeters, and the cut-off volume accounts for () of the cylinder volume.
0 30 60 90120km
8. The () on the scale map indicates the () of the actual distance.
9. Expand the diameter of the cylinder to three times the original height, the bottom area to () times, the side area to () times and the volume to () times.
Second, right or wrong (tick the right one). Wrong "×") 6%
1, and the volume of the cone is equal to 13 of the volume of the cylinder. …………………………………………… ( )
2. The characteristic of broken line statistical chart is that it can not only represent quantity, but also indicate the increase or decrease of quantity. ……( )
3. Only one side of a cylinder can be unfolded into a rectangle. …………………………………………( )
The diameter of a sphere is twice its radius. ………………………………………………( )
The larger the bottom area of a cylinder, the larger its volume. …………………………………………( )
6. The circumference and area of a circle with a radius of 2 decimeters are equal. …………………………………………( )
Third, the calculation problem
1, solution ratio. 9%
X:40 = 2.5:4 1 14:X = 0.4:8 X 3.5 = 40.5
2. Calculate the following questions. 12%
12 ÷ 25 - 23 ×7 10 ( 23 - 34 × 13 )÷ 98 13.8― 79 + 6.2 ― 1 19
4. The following is the output value of the first and second factories of a company from 1999 to 2004: 10%.
Year of output value
(ten thousand yuan)
Branch factory
1999
In 2000,
200 1 year
In 2002
In 2003
In 2004
Branch 300 380 490 550 700 900
The second factory 450 560 620 700 900 1200
Complete the following statistical chart according to the data in the table.
1999-2004 Statistics on the output value of the first and second branch factories of a company.
date month year
Unit: 10,000 yuan for one branch and two branches.
1400
1200
1000
Eight hundred
600
celebrity
200
1999 2000 200 1 2002 2003 2004
5. Calculate the surface area and volume of the following objects. Unit: centimeter. 10%
10 r= 10
20
Sixth, the application problem. 35%
1, the Wangs want to make a cylindrical oil tank. It is known that the diameter of the bottom is 4 decimeters and the height is 5 decimeters. Please help Uncle Wang calculate how many square decimetres of iron sheets are needed at least. What is the volume of this fuel tank? (Ignore the thickness of the iron sheet)
There is a conical wheat pile on the threshing floor. Bottom circumference12.56m and height1.65m.. If each cubic meter of wheat weighs 750 kilograms, how many kilograms is this pile of wheat?
3. The school should make 10 cylindrical ventilation pipes, each section is 120cm long and the bottom radius is 10cm. How many square centimeters of iron sheet should I buy at least? How many square meters?
On the map with the scale of 1: 2500000, the distance from Nanjing to Yangzhou is 3.8 cm. What is the actual distance from Nanjing to Yangzhou?
5. There is a cone-shaped stone with a height of 1.5m and a bottom circumference of 6.28m How many tons does this stone weigh according to the weight of 2.5 tons per cubic meter of stone?
6. School calculation: (1) The distance from the hospital to the shopping mall.
(2) The distance from the school to the children's activity center.
(3) The distance from the school to the hospital.
(4) How far can you ask?
Hospital shopping center
Children's activity center
0 200 400 600 m
Proportion:
7. There is a cylindrical steel with a radius of 4cm at the bottom and a length of 2m. It should be cast into rectangular steel with a cross-sectional area of 4 cm. What is the length of this rectangular steel?
1. If a * b = 5× a- 1/2× b is specified, where a and b are natural numbers,/10 * 6 = _ _ _ _ _ _ _ _
2. A simplest fraction, its numerator is divided by 2, denominator is multiplied by 3, and 3/29 is obtained after simplification. This simplest fraction is _ _ _ _ _ _ _ _.
3. As shown in the figure, at this time, a sector with a central angle of 45, in which the right side of the isosceles triangle is 6 cm and the area of the shaded part is _ _ _ _ _ square cm.
4. There are only two questions in a math exam. As a result, the whole class 10 people are all right, the first question has 25 people right, and the second question has 18 people wrong, so the people who are wrong in both questions are _ _ _ _ _ _.
5. It takes 14 days to complete a project, 7 days for Team B and 6 days for Team C. Now Team B and Team C have worked together for three days, and Team A will need _ _ _ _ _ _ days to complete the task.
6. Among the integers from1to 2000, there are _ _ _ _ _ _ _ numbers that are multiples of 3, but not multiples of 5.
7. A string of beads is made of 8 red and 2 black in turn into a circle ***40 capsules. A cricket jumps from the second black bead, and every time it jumps over six beads, it falls on the next one, and it must jump at least _ _ _ _ _ _ times before it falls on the black bead again.
8. The natural number n has many factors. Sum these factors in pairs to get a new set of numbers, the smallest of which is 4, the largest is 196, and n has _ _ _ _ _ _ _ factors.
9. There are two ants A and B on the two vertices of a square wooden frame ABCD with a side length of 1 m, crawling counterclockwise along the wooden frame, as shown in the figure. 10 seconds later, the distance between Party A and Party B is the same. After 30 seconds, the distance between A and B is the same again. It takes _ _ _ _ _ _ seconds for an ant to crawl along the wooden frame and _ _ _ _ _ _ seconds for a B ant to crawl along the wooden frame.
10. A car travels from place A to place B at a speed of 750 meters per minute and is expected to arrive in 50 minutes. But the car broke down after driving for 3/5 miles. It took five minutes to repair it. If we still need to get to B within the scheduled time, how many meters per minute must the car be faster than before?
1 1. xinxin business service company charges 3% service fee for customers to sell goods and 2% service fee for customers to shop. Today, a customer entrusted the company to sell some self-produced goods and buy new equipment. Knowing that the company deducted the customer service fee of 264 yuan, the customer just broke even. What is the cost (price) of buying new equipment?
12. Party A and Party B can complete a project within 8 days. A it takes one person 12 days. Now that two people have worked together for a few days, the rest of the project will be completed by B alone, so the time ratio of the first two paragraphs of B is 1:3. How many days is the actual duration of this project?
1. A number divided by 5 is 3, divided by 6 is 4, and divided by 7 is 5. This natural number is at least _ _ _ _ _ _ _.
2. Reading 80 pages a day can't be finished in 4 days, and there are more than 5 days; Read 90 pages a day, you can't finish it in 3 days, and there are still more than 4 days; If you read n pages every day, it only takes n(n is a natural number) days to finish reading. The number of pages in this book is _ _ _ _ _ _.
3. Party A and Party B play games and arbitrarily specify 9 consecutive integers. A fills these integers in the first row of boxes as shown in the figure in any order, and then B fills these 9 numbers in the second row of boxes in any order. Finally, multiply all the differences of two numbers in the same column (***9), and stipulate that if the product is even, A wins; If the product is odd, b wins. Then _ _ _ _ _ wins. (Fill in "A" or "B")
4. Attach a rectangle with the length of16m, the length and width of which are equal to _ _ _ _ _ _ respectively, and its area is the largest, with the largest square centimeter of _ _ _ _ _ _ _.
5. There are four natural numbers, each of which is not divisible by the other three numbers, but the product of any two of them can be divisible by the other two numbers. The sum of these four numbers is at least equal to _ _ _ _ _ _.
6. As shown in the figure, in the quadrilateral ABCD, ∠ B = 90, AB = 4, BC = 3, CD = 13, DA = 12. The area of the quadrilateral ABCD is equal to _ _ _ _ _.
7. 124 students play cards in groups of four, the winner stays to continue the game, and the other three are eliminated. In this way, * * * needs to play _ _ _ _ to decide the champion.
8. There are several piles of Go, each pile has the same number of pieces, and albinos account for 36%. Xiao Ming took half of the first pile (all black spots), and Xiao Guang mixed the rest of Weiqi together, and found that Bai Zi just accounted for 40%. You know there used to be _ _ _ _ piles of chess pieces.
9. Six faces of four identical dice are written with 1, 2, 3, 4, 5 and 6 respectively. They are stacked together (as shown in the figure) to form a cuboid. The antonym of 1 is _ _ _ _ _, the antonym of 3 is _ _ _ _ _ _, and the antonym of 5 is _ _ _ _ _ _ _ _.
10. Workers in groups A, B and C, 4 in group A and 5 in group B; Group B needs four people to do the work, and Group C needs seven people to complete it. A project needs a group 13 people and a group 12 people to complete within 3 days. How many days will it take if it is done by 10 people in Group C?
1 1.A and B start from A and B respectively, heading in opposite directions. At the time of departure, the speed ratio of A and B is 5:4. After meeting, the speed of A decreases by 20% and the speed of B increases by 20%. Then when A arrives at B, B is still 10 km away from A, so how many kilometers are A and B apart?
12. Party A and Party B make the same parts, and each person can make one part every 3 minutes. A takes a break of 2 minutes for every 2 parts produced, and B takes a break of 1 minute for every 3 parts produced ... Now they have to finish the task of manufacturing 202 parts together. How many minutes will it take at least?
1. The teacher wrote down 13 natural number on the blackboard and asked Xiao Wang to calculate the average (keep two decimal places). The answer calculated by Xiao Wang is 12.43. The teacher said that the last figure was wrong and all the other figures were right. The correct answer should be _ _ _ _ _.
Two fifths of Lao Wang's weight is equal to two thirds of Xiao Li's weight. 3/7 of Lao Wang's weight is lighter than 3/4 of Xiao Li's weight 1.5 kg, so Lao Wang's weight _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ kg.
3. In one exam, 17 students got 100 in math, 100 in Chinese, 100 in both subjects and 100 in at least one of the two subjects. There are _ _ _ _ _ _ _ _ people in Class 45 who failed in both subjects 100.
4. A fruit shop bought six baskets of fruits with bananas and oranges weighing 8, 9, 16, 20, 22 and 27 kg respectively, and only sold one basket of oranges that day. In the remaining five baskets, bananas weigh twice as much as oranges. I asked if the basket bought by the fruit shop that day was a banana.
5. As shown in the figure, there are six points A 1, A2, A3, A4, A5 and A6 around the boundary of the semicircle, where A 1, A2 and A3 are on the diameter of the semicircle, and these six points can form _ _ _ _ _ _ _.
6. There are 100 students going to the park 33 kilometers away from the school. The walking speed of the students is 5 kilometers per hour. There is only one car that can take 25 people in the school, and the speed is 55 kilometers per hour. In order to get to the park in the shortest time, we decided to combine walking and cycling, so the shortest time is _ _ _ _ _ _ _.
7. There are 48 books distributed to two groups of children. It is known that the second group has five more people than the first group. If all the books are distributed to the first group, each person has four books and the rest; There are five books for each person, and there are not enough books. If all of them are given to the second group, there will be three books for each person, and there will be a surplus. There are four books for each person, but there are not enough books. There are _ _ _ _ _ _ people in the second group.
8. As shown in the figure, it is known that squares and triangles partially overlap, and the area of triangle B is 7 square centimeters larger than that of triangle A, so x = _ _ _ _ _ _ _ _ centimeters.
9. One morning at school, there are four classes: math, Chinese, foreign languages and physical education. Mathematics can only be ranked in Class One or Two, Chinese can only be ranked in Class Two or Three, and foreign languages must be ranked ahead of physical education. There are _ _ _ _ _ kinds of timetables that meet the above requirements.
10. Two students, A and B, started from school and walked in the same direction in a stadium. The first group walked at a speed of 4 kilometers per hour half the time and 5 kilometers per hour in the other half. B first walked half at a speed of 4 kilometers per hour, and the other half walked half at a speed of 5 kilometers per hour, so the first one to arrive at the stadium was _ _ _ _ _ _ _.
1 1. There are four classes in Grade Five, and each class has two monitor. Every time there is a monitor meeting, each class participates in a monitor. The first meeting is A, B, C and D; E, B, F and D attended the second meeting; Attending the third meeting were A, E, B and G; H did not attend three meetings. Who are the two monitor of each class?
12. 1984 A person's age is exactly equal to the sum of the figures of his birth year, so this person is1984 _ _ _ _ _ _ _ _.