A: 70
b80
C.90
D. 100
Answer c
The first step of analysis is to examine the basic application problems.
Step two, suppose there are x male teachers and 150-x female teachers. The equation (1-20%) x+(1+15%) (150-x) =150+12, and the solution is x=30. There are 30 male teachers and 30 female teachers 120, and there are more female teachers than male teachers 120-30=90.
Therefore, choose the c option.
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label
Basic application problems of knowledge points
Medium difficulty
Proposer Liang Peijing
2. 1 1 At the end of the year, the inventory quantity of jeans, Martin boots and down jackets was 3: 4: 5, and at the end of 12, the sales ratio of jeans, Martin boots and down jackets was 4: 3: 6. 10 At the end of the year, the inventory of down jackets was more than jeans 10.
A: 90
1 10
C. 130
D. 150
Answer b
The first step of analysis is to examine the basic application problems.
Step 2: Suppose 1 1 has 3x jeans, 4x Martin boots and 5x down jackets in stock at the end of the year. In 65438+February, 4y jeans, 3y Martin boots and 6y down jackets were sold. Column equation: 5x-6y=2(3x-4y)+ 10①, 4x-3y=3(3x-4y)-5②. X= 100，y=55。 Then in June 5438+February, the sales of down jackets in the store were 6% more than jeans. 55-4? 55= 1 10 pieces.
Therefore, choose option B.
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label
Basic application problems of knowledge points
Medium difficulty
Proposer Liang Peijing
Mr Li spent 50,000 yuan on two funds. One year later, Fund A increased by 20% and Fund B increased by 50%. After Mr. Li sold the funds, he made a profit of 1.66 million yuan. If fund A rises by 50% and fund B rises by 20%, how much more will you earn after selling the fund?
900 yuan
1200 yuan
1500 yuan
D. 1800 yuan
Answer d
Analyzing this problem to examine the economic profit belongs to the basic formula category.
In the second step, it is assumed that the investment in fund A is X yuan and that in fund B is (50,000-X) yuan. Can you get x from the meaning of the question? 20%+(50000-x)？ 50% = 16600, x = 28000 yuan. The investment in buying B fund is 50,000-28,000 = 22,000 yuan. So Fund A will go up by 50%, and Fund B will go up by 20%. After selling it, you will make a profit of 28,000? 50%+22000? 20%= 18400 yuan, making more money than before.18400-16600 =1800 yuan.
Therefore, choose the d option.
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label
Economic profit of knowledge points
Medium difficulty
Proposer Liang Peijing
4. It takes 10 days for Team A, 6 days for Team B and 5 days for Team C just to build roads. If Team A and Team B cooperate to build Highway A, Team A will build 240 meters less than Team B after completion. If Team B and Team C cooperate to build Highway B, Team C will build 240 meters more than Team B after completion. Q: Highway A is better than Highway B:
A. less than1500m
B. less than 1500m.
C. Less than1500m
D./kloc-above 0/500m.
Answer b
The first step of analysis is to check the engineering problems.
The second step is to build the same highway, and the total amount of projects is the same, so the work efficiency is inversely proportional to the working time, that is, the work efficiency ratio of the three engineering teams A, B and C is 3: 5: 6. Party A cooperated with Party B to build Highway A, with Party A completing 3 projects and Party B completing 5 projects. Party A completed two projects less than Party B and repaired 240 meters less, so one project 120 meters. So, how long is Highway A (3+5)? 120 = 960m. Similarly, if Party B and Party C cooperate to build Highway B, Party B will complete 5 copies, Party C will complete 6 copies, and Party C will complete 1 copy more than Party B, 240 meters more, so one copy is 240 meters, and the length of Highway B is (5+6)? 240 = 2,640m, and Highway A is 2640-960 = 1.680m less than Highway B. ..
Therefore, choose option B.
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label
Knowledge point engineering problem
Medium difficulty
Proposer Liang Peijing
5. Xiao Li bought 1 barrel of mineral water (assuming the barrel is full of water). The barrel consists of a cone and a cylinder with a radius of 15cm and a height of 37cm. The bottom of the cone and the cylinder are the same, and the height is 9 cm. Xiao Wang has a cylindrical electric kettle with an inner diameter of 20cm at the bottom, and the highest water level when boiling water is 15cm. How many pots of boiling water can Xiao Wang boil at least?
A.4
B.5
C6
D.7
Answer c
The first step is analysis. This question examines geometric problems and belongs to solid geometry.
Step 2: The barrel bottom radius 15cm, the height is 37cm, the barrel volume of the bucket is, the cone bottom radius 15cm, the height is 9cm, and the cone volume of the bucket is, so the volume of water in the mineral water bucket is =+=. It is required to boil water at least, and only as much water as possible at a time. If the inner diameter of the electric kettle is 20cm and the radius is 10cm, boil the water at most once. Wang Can Jr. burned at least six pots.
Therefore, choose the c option.
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label
Knowledge point geometry problem
Medium difficulty
Proposer Liang Peijing
6. During the Spring Festival, a community organized four activities for the elderly: writing Spring Festival couplets, dancing lions, dancing yangko and making lanterns. Old people can choose projects to participate in activities at will. It is known that there are five elderly people in this community participating in exactly the same project, so there are at least () elderly people in this community.
A.47
b52
C.6 1
Cao 72
Answer c
The first step is analysis. This topic examines the most unfavorable structure and arrangement.
The second step is that the topic is known. Five old people in the community reported the project. First, all the registration methods of the old people are calculated: only one activity is reported; Sign up for two projects; Sign up for three projects; Sign up for four projects; The most unfavorable factor for each project construction is 4 people, and finally 1 is added, so there are at least 6 1 elderly people.
Therefore, choose the c option.
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label
The quantitative relationship of knowledge points-the most unfavorable structure-the most unfavorable arrangement and combination
difficulty
Propose human history
7. There are 90% students in the Physics College of a university who register for postgraduate entrance examination and civil service examination, and the number of people who choose postgraduate entrance examination is only 8 times that of those who only take postgraduate entrance examination. Students who have not signed up for any exams only take the civil service exam ().
A.
B.
C.
D. 1 time
Answer d
The first step of analysis, this question examines the issue of inclusion and exclusion.
Step 2, as shown in the figure below:
The number of students assigned to/kloc-0 who only register for the civil service examination is 8, and the number of students who register for both examinations is the same as that who only take the postgraduate examination, with 4 students respectively. So there are 9 students who signed up for the exam, accounting for 90% of the total. Those who did not register for any exams accounted for 10% of the total number, which was 1. The number of people who did not sign up for any exam was 1 times that of those who only took the civil service exam.
Therefore, choose D in this question.
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label
Quantitative relationship of knowledge points-including problems-two sets of inclusion and exclusion
Medium difficulty
Propose human history
8. The calendar of Sun Xiao is shown below. Every morning, he tore off the calendar of the previous day. One afternoon, Sun Xiao added up the Arabic numerals on the recently torn 65,438+00 pages of the calendar, and the total was 235. The calendar of that day is displayed as () day.
A.3 1
b30
C.29
Cao 28
Answer d
The first step of analysis, this question examines the issue of order.
Second, if the dates near 10 should be arithmetic progression with a tolerance of 1, according to the summation formula, the sum of the consecutive items of 10 should be five times the sum of the middle two items, and the middle two items are consecutive numbers, which should be 23 and 24, so the date of the last day is the 28th.
Therefore, choose D in this question.
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label
Quantitative Relationship of Knowledge Points-Sequence Problem-arithmetic progression
Medium difficulty
Propose human history
9. During the Spring Festival, the community organized lion dance activities, and the speed of the lion dance team was 30? Move in the direction. It is known that 30 meters away from the lion dance team is the best viewing distance. Sun Xiao is 60 meters east of the starting point of the lion dance team, so Sun Xiao can watch the lion dance performance from the best position.
0 minutes
5 minutes
C. 10 score
D. 15 minutes
Answer a
The first step of analysis, this question examines the trip problem.
Step 2, according to the meaning of the question, establish a coordinate system. The schematic diagram of the lion dance team moving from point A to 30 northeast is as follows:
Do OB? OA, to calculate the time for Sun Xiao to watch the performance, we must first find out when the connection between the lion dance team and Sun Xiao is perpendicular to the direction of lion dance, that is, OB? OA, OB distance. Known AB = 60m, press 30? The ratio of each side of the corresponding right triangle is ob = 30m, and the viewing range of the lion dance team is 30m. It can be seen that the best viewing distance of the lion dance team just passed by the grandson, and it didn't last long, so the best viewing time was 0min.
Therefore, choose a in this question.
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label
Quantitative relationship of knowledge points-mathematical operation-travel problem
Medium difficulty
Propose human history
10. On New Year's Eve, Sun Xiao, his wife and daughter, a family of three, wrapped jiaozi together, and the three of them used dumpling wrappers of different colors to distinguish their jiaozi. Finally, it was found that 73 of them were not Sun Xiao's, 72 were his wife's and 765,438+0 were his daughter's, so Sun Xiao bought () jiaozi.
A.30
b35
C.40
Grass 45
Answer b
The first step of analysis is to examine the basic application problems.
Step 2: Among these topics, 73 are not Sun Xiao's, so they should be his wife and daughter, 72 are Sun Xiao and daughter, and 7 1 is Sun Xiao and his wife. .
Therefore, choose B in this question.
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label
Quantitative relationship of knowledge points-mathematical operation-basic application problems
Medium difficulty
Propose human history
1 1. There are eight children who need to have lunch together. There are two tables, a round table can seat five people and a square table can seat four people. How many ways can children sit at the round table?
A. 1200
1344
C.3344
D.6720
Answer b
The first step is analysis. This question examines the arrangement and combination, which belongs to circular arrangement.
Step 2: First, you need to choose five people from eight people to sit on the round table, and then five people make a circular arrangement. * * * has a sitting method, step by step, so * * * has seeds.
Therefore, choose option B.
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label
Knowledge point arrangement and combination
Medium difficulty
Proposer Wang Chenglong
12. As shown in the figure, A-BCD is a regular tetrahedron with a side length of 3, M is a point on the side, MB=2MA, G is the center of gravity of the triangle BCD, and the moving point P is on the side BC, so the minimum value of PM+PG ().
Answer.
B.
C3
d。
Answer b
The first step of analysis is to check the plane geometry.
The second step is to expand the diagram, as shown in the figure. Because G is the center of gravity, BG is the center line and the bisector of a regular triangle. 30 pounds? And then what? MBP is 60 years old? Is it easy to find? MBG is a right angle. If the ratio of the distance from the center of gravity to the vertex to the distance from the center of gravity to the midpoint of the opposite side is 2: 1, BG=. According to Pythagorean theorem, therefore MG=
Therefore, choose option B.
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label
Knowledge point plane geometry
Medium difficulty
Proposer Wang Chenglong
13. A football invitational tournament was held in a city, and * * * 9 teams signed up, including the top 3 teams in the last competition. Now these nine teams are divided into three groups by drawing lots for a single round robin, so the probability that the top three teams in the last game will be divided into the same group is:
A.
B.
C.
D.
Answer b
The first step of analysis, this topic examines probability calculation.
Step 2: The top three teams in the last competition should be in the same group. If the grouping of the first team has been determined, the second team can choose one of the remaining eight positions. At this time, there are two positions in the same group as the first team, and the probability of meeting the conditions is; The third team can choose one of the remaining seven positions, and the position in the same group as the first two teams is only 1, and the probability of meeting the conditions is. Multiplication is used step by step, and the probability is.
Therefore, choose option B.
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label
Probability calculation of knowledge points
Medium difficulty
Proposer Wang Chenglong
14. The Gregorian calendar revised by 1582 is widely adopted all over the world. It stipulates that a leap year is a year in which the number of years can be divisible by 4, but it is not a leap year that can be divisible by 100 but not by 400. According to this regulation, 1582 to 20 14 * * has () leap years.
A. 104
B 105
C. 103
D. 106
Answer b
The first step of analysis is to examine the time problem.
Second, most candidates' initial memory of leap year is that there is a leap year every four years, so there will be (20 14- 1582) in the calculation? 4+ 1= 108, so it is very confusing to have no correct options.
There is no doubt that there is a leap year every four years, but it is clearly stipulated in the title? A leap year is a year in which the number of years is divisible by 4, but a year divisible by 100 but not by 400 is not a leap year? Therefore, the whole 100 years contained in it need to be verified. There are four years: 1600, 1700, 1800 and 1900. After verification, it is found that 1700, 1800 and 1900 are not divisible by 400, so they need to be initialized.
Therefore, choose option B.
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label
Probability calculation of knowledge points
Medium difficulty
Proposer Wang Chenglong
15.A head office consists of three branches, A, B and C. If the output of Company A increases by 10%, the output of the head office will increase by 5%; If the output of Company B increases by 10%, the output of the head office will increase by 2%. If the output of Company C is reduced by 10%, what percentage can the output of the head office be reduced? ()
A.2
B.3
C4
D.5
Answer b
The first step of analysis is to examine the basic application problems.
The second step is to assume that the output values of companies A, B and C are A, B and C respectively, and the demand is x%. Then:
; ; Add the three formulas and eliminate (a+b+c) to get x %=3.
Therefore, choose option B.
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label
Probability calculation of knowledge points
Medium difficulty
Proposer Wang Chenglong