#Junior Middle School Mathematical Olympiad# The introductory word problem is to use language or text to describe relevant facts, reflect a certain quantitative relationship, and solve an unknown quantity of questions. Each word problem includes known conditions and the question being asked. In the past, Chinese word problems usually required descriptions to meet three requirements: non-contradiction, that is, there should be no contradiction between conditions or between conditions and questions; completeness, that is, the conditions must be sufficient to ensure that the numerical value of the unknown quantity can be obtained from the conditions. ; Independence, that is, several known conditions cannot be inferred from each other. Below are the special test questions and answers for junior high school Mathematical Olympiad fraction equation application questions brought to you by None. You are welcome to read them.
1. A certain class of students went to the Martyrs Cemetery 12km away from the school to sweep the tombs. Some students rode bicycles first, and then the rest of the students set off by car. Due to **********, there were no bicycles. The speed of is , then the equation can be formulated as. ********** in the question represents the content of the part stained by ink. According to this situation and the listed equations, its content should be ( )
A. The speed of the car is the speed of the bicycle 3 times, the result is that they arrive at the same time B. The speed of the car is 3 times that of the bicycle, and the students in the back are later than the students in the front C. The speed of the car is 3 times the speed of the bicycle, and the students in the front are later than the students in the back D. The speed of the car is faster than that of the bicycle The speed is more than 3 kilometers per hour, and the results arrive at the same time. Answer: A
2. In order to solve the problem of centralized heating for some citizens in winter, a city needs to lay a 3,000-meter-long pipeline to minimize the impact of construction on traffic. Impact, when carrying out construction "...", assuming that x meters of pipes are actually laid every day, the equation can be obtained. According to this scenario, the missing conditions represented by "..." in the question should be filled in as ( )
A .Laying 10 meters more than the original plan every day, but it was completed 15 days later. B. Laying 10 meters less than the original plan every day, but it was completed 15 days later. C. Laying 10 meters less than the original plan every day, but it was completed 15 days ahead of schedule. D. Every day It was laid 10 meters more than the original plan, and the result was completed 15 days ahead of schedule. Answer: D
3. It takes the same time for a truck to travel 25 kilometers and for a car to travel 35 kilometers. It is known that the car travels 20 kilometers more per hour than the truck. Kilometers, what is the speed of each car? Assume that the speed of the truck is kilometers per hour. The correct equation according to the question is ( ) A. B. C. D. Answer: C
4. When the Municipal Development Zone invited bids for a project, it received two requests from A and B. Based on the bidding documents of the engineering team, the engineering leading group calculated that there are three construction options: ① Team A completes the project alone and it is completed on schedule; ② Team B completes the project alone and it is faster than specified The construction period was extended by 5 days; ③ "...", the remaining work was done by Team B alone, and it was completed on schedule. A student set the specified construction period as x days and listed the equation according to the meaning of the question: , then the "..." part in plan ③ should be ( )
A. Team A worked for 4 days first B. A and B worked together for 4 days C. Team A did the project first D. Team A and B worked together on the project Answer: B
5. A certain workshop has to process 170 parts and improve after processing 90 parts By understanding the operating method, we can process 10 more parts per day and complete the task in 5 days. If we improve the operating method and process x parts per day, the correct equation listed is ( )
A. B. C. D. Answer: A
6. Two cleaning teams, A and B, participated in the "Urban and Rural Cleaning Project" in a community. Team A worked alone for 2 days and completed one third of the project. At this time, team B joined , the two teams worked together for another day and completed the entire project. Then Team B needs to complete the project alone ( )
A. 6 days B. 4 days C. 2 days D. 3 days Answer: C
7. Someone contracts 1125 The task of laying floor tiles per square meter was planned to be completed within a certain time. After working for 3 days as planned, the work efficiency was improved, so that the area of ??floor tiles laid every day was 1.5 times the original plan. As a result, the task was completed 4 days in advance, and the original plan was to complete the task every day. Shop ( )
A. 70 square meters B. 65 square meters C. 75 square meters D. 85 square meters Answer: C
8. Eighth grade students go to a school 10,000 square meters away During a visit to a museum in Mi, some students left first on bicycles. After 20 minutes, the rest of the students set off by car, but they arrived at the same time. It is known that the speed of the car is twice the speed of the cyclist, then the speed of the cyclist is ( )
A. kilometers/hour B. kilometers/hour C. 15 kilometers/hour D .30 kilometers/hour Answer: C