(People's Education) Mathematics Review Questions for Volume 1 of Junior High School

Excellent exercises for the final review of People's Education No. 7

7. The coordinates after the point P (-5, 3) is translated 3 units along the positive direction of the x-axis and 6 units along the negative direction of the y-axis is _________.

8. If the lengths of the two sides of the triangle are 2cm and 3cm respectively, and the length of the third side is an odd number, then the length of the third side is .

11. If (fill in the blank with "gt;" "lt;")

12. Only one kind of regular polygon is used to cover the ground. Please write such a kind of regular polygon. Polygon____________________

13. It is known that it is a solution of a linear equation of two variables, then __________________

14. If the point is on the axis, then

15 , connect a pair of triangular plates and place them as shown in the figure, then

16. If the solution of the system of equations is, then the solution of the system of equations is.

17. In,

18. A pile of toys is distributed to several children. If each child is divided into 3 pieces, then 3 pieces will remain. If each person is divided into 5 pieces, then each child will have 3 pieces. Everyone is assigned toys, but one child has less than 3 toys, then there are __________ children.

19. Given point A (5, ) and straight line AB parallel to the coordinate axis, the coordinates of the intersection point C of straight line AB and the angle bisectors of the first and third quadrants are ____________________

Test position number

20. As shown in the picture, Xiaoliang starts from point A and goes forward 10m, turns right 150, then goes forward 10m, then turns right 150, and keeps walking like this. He returns for the first time. When we arrived at the starting point A, we walked ___________m.

21. Solving a system of equations (***12 points)

○1 ○2

22. (8 points) What is the value of the algebraic expression? Is it larger than the algebraic value?

23. (8 points) Solve the set of inequalities and express the solution set on the number line

24. (10 points) It is known that the values ??of the algebraic expressions are all 5. At that time, it The value of is 1

(1) Find the values ??of a, b, c

(2).

25. (10 points) Known: The system of equations about (1) is expressed by the algebraic expression of m (2) When m takes what value, in the solution of this system of equations, is greater than 1 and not less than ?

26. (10 points) ○1 Draw the vertices A (-3, -1), B (1, 3),

C ( 2, -2)'s △ABC;

○2 If this triangle is translated so that the coordinates of the corresponding point B' of B are (-1, 0), try to draw the translation

△A'B'C'.

○3The area of ??△A’B’C’ is _______.

y

28. (12 points) There is a right-angled triangle ruler DEF placed on △ABC. As shown in the figure, the two right-angled sides DE and DF of △DEF pass through B respectively. , two points C, in △ABC, ∠A=500

(1) Find ∠ABD ∠ACD

(2) If the right-angled vertex D of the triangle ruler is placed in △ Outside ABC, the two right-angled sides DE and DF still pass through two points B and C. Draw the figure and explore the quantitative relationship between ∠ABD and ∠ACD?

24. As shown in the figure, in △AOB, the coordinates of the two points A and B are (2, 5) and (6, 2) respectively.

① Find the area of ??△AOB ; (5 points)

② If the abscissa of each vertex of △AOB remains unchanged and the ordinate is increased by 3, what is the area of ??the resulting triangle

? (3 points)

(Picture of question 24)

17. (10 points for this question) Solve the following system of equations.

(1) (2)

29. (8 points) (1) First solve the following system of equations:

p>

○1;

○2; Found that the solutions are all,

We know that equations and equations are determined by the solution coefficients. Observe carefully and write a equation with A system of equations with the same solution to the above system of equations:

____________________________

(2) Write the relation ____________________ satisfied by the coefficients of each equation in the above system of equations.

(1) Based on the conclusion obtained in (2), write down the solution to the system of equations through observation____________

(2) Study the following two systems of equations

① ②

Write the rules and solutions of each equation in the system of equations.

(Chifeng City, 2007) "Equation" is a very important mathematical model in real life. Please write a word problem about a system of linear equations of two variables based on your actual life, make the system of linear equations of two variables listed be , and write down the solution process.

(Ziyang City, 2007) After Mr. Chen bought prizes for the sports meeting for the school, he returned to school and handed over the account to Mr. Wang from the Logistics Department and said: "I bought two kinds of books, ***105 copies, and the unit prices are respectively They were 8 yuan and 12 yuan. I received 1,500 yuan before buying the book, and now I still have 418 yuan left." Teacher Wang did the math and said, "You must be wrong."

⑴ Why did Teacher Wang say Was he mistaken? Explain using the knowledge of trial equations;

⑵ Teacher Chen quickly took out the shopping invoice and found that he had made a mistake because he also bought a notebook. However, the unit price of the notebook was blurred and could only be identified. It should be an integer less than 10 yuan. What is the possible unit price of the notebook?

(Zhangzhou City in 2007) (Zigong City in 2007)

(Chenzhou City in 2007) (Jinan City in 2007)

(Qingliu County in 2007 ) (Nanjing City, 2007)

(Zaozhuang, 2007) The known solution is, then the solution is ______________.

(Zhoushan, Zhejiang, 2007) Three students put forward their own ideas on the problem "If the solution of the system of equations is , find the solution of the system of equations." A said: "This problem seems to have insufficient conditions to solve"; B said: "Their coefficients have certain rules, you can try it"; C said: "Can you put both sides of the two equations of the second system of equations? Divide them all by 5 and solve them by substitution." Referring to their discussion, do you think the solution to this problem should be .

2. A shopping mall purchases a piece of clothing at RMB 1 per piece. If it sells it at RMB 10,000 per piece, it will sell an average of 15 pieces per day and make a profit of RMB 22,500 in 30 days. In order to recover funds as quickly as possible, the mall decided to sell each piece at a 20% price reduction. As a result, it sold an average of 10 more pieces per day than before the price reduction. In this way, it still made a profit of 22,500 yuan in 30 days. The value of the experiment (profit per piece of clothing = per piece The selling price of a piece of clothing - the purchasing price of each piece of clothing)

1. (Baotou, 2007) A factory plans to recruit 120 workers of two types of work, A and B. It is known that there are two types of workers, A and B. The monthly wages of workers of different types of work are 800 yuan and 1,000 yuan respectively.

(1) If the monthly salary paid by the factory is 110,000 yuan, then how many workers will be recruited for the two types of work A and B?

(2) If the requirement for type B is The number of workers in job category A is not less than twice the number of workers in job category A. How many workers in job category A can be recruited to minimize the monthly wages paid?

27． Xiaojie went to the school cafeteria to buy food. He saw that there were the same number of people queuing in front of windows A and B (set as person a, a>8), so he stood behind the queue in window A. After 2 minutes, he found window A 4 people bought food and left the team every minute, 6 people bought food and left the team in window B every minute, and 5 people were added to the queue in window B every minute.

(1) At this time, if small If Jay continues to queue at window A, what is the time it takes for him to arrive at the window (expressed by an algebraic expression containing a)?

(2) At this time, if Xiaojie quickly moves from the queue in window A to the queue in window B and queues up again, and the time it takes to reach window B is longer than the time it takes to continue queuing in window A to reach window A. Time is short, find the value range of a (without considering other factors).

43. (2007 Chongqing) A town in our city organized 20 vehicles to ship three kinds of navel oranges A, B and C** *100 tons are sold overseas. According to the plan, 20 cars have to be shipped. Each car can only carry the same kind of navel oranges and must be full. Based on the information provided in the table below, analyze the following questions:

Navel orange varieties A B C

Carrying capacity per vehicle (tons) 6 5 4

Earnings per ton of navel oranges (100 yuan) 12 16 10

(1) Suppose the number of vehicles transporting navel oranges of type A is , and the number of vehicles transporting navel oranges of type B is , use an algebraic expression containing x to express y; (2) If each shipment is The number of vehicles planting navel oranges is no less than 4. So what are the arrangements for the vehicles? And write down each arrangement plan; (3) To maximize the profit from this sale, which arrangement plan should be adopted? And find the value of maximum profit.

33. Suzhou is located on the coast of Taihu Lake and has rich aquaculture resources. Aquaculture farmer Uncle Li is preparing to carry out mixed farming of hairy crabs and river shrimps. He learned the following information:

①The annual rent per mu of water surface is 500 yuan, and the water surface must be rented according to an integer mu;

②Each mu of water surface can be mixed with 4 kilograms of crab seedlings and 20 kilograms of shrimp seedlings at the beginning of the year;

③The price of crab seedlings per kilogram is 75 yuan, and its feeding cost is 525 yuan, and you can get a profit of 1,400 yuan that year;

④The price of shrimp seedlings per kilogram is 15 yuan, and its feeding cost is 85 yuan Yuan, you can get a profit of 160 Yuan that year;

(1) If you rent an acre of water surface, the annual rent will be __________ Yuan;

(2) The cost of aquaculture Including the annual rent of the water surface, seed costs and feeding costs, find the annual profit of mixed crab and shrimp farming per mu of water surface (profit = income - cost);

(3) Uncle Li currently has 25,000 yuan in capital, and he is ready to Then ask the bank for a loan of no more than 25,000 yuan for mixed crab and shrimp farming. It is known that the annual interest rate of bank loans is 8. How many acres of water surface should Uncle Li rent and how much yuan should he borrow from the bank to make the annual profit exceed 35,000 yuan?

18. (10 points for this question) Solve the inequalities (sets) and represent their solution sets on the number line.

(1); (2).

1. As shown in the figure, AD is the midline of △ABC, and BE is the midline of △ABD. (8)

(1) ∠ABE=15°, ∠BAD=40°, find the degree of ∠BED;

(2) In △BED, make the side of BD High;

(3) If the area of ??△ABC is 40 and BD=5, what is the distance from point E to side BC?

19. (Full score for this question is 6 points) Solving a system of linear equations in three variables

20. (8 points for this question) A linear equation of two variables is known.

(1) Please write down any three sets of solutions to this equation;

(2) If this is a set of equations Solution, we define it as the coordinates of a certain point. Please write the coordinates of the three points according to the three sets of solutions you wrote in (1), and describe these three points in the plane rectangular coordinate system;

(3) Observing the positions of these three points, what did you find?

23. (10 points for this question) There is a sequence of numbers, , ,..., , which satisfies the formula. It is known that .

(1) The value of the sum;

(2) If , , find the value.

24. (Question 12) It is known that a garment factory currently purchases ***122 meters of fabrics of type A and type B from a textile factory, spending 4180 yuan. It is known that type A of fabric costs 30 yuan per meter, and type B of fabric costs 40 yuan per meter. Yuan.

(1) How many meters of fabric A and B should be purchased?

(2) It is now planned to use these two kinds of fabrics to produce 80 sets of fashion models A and B. It is known to make a set of fashion models A and B. The required two kinds of fabrics A and B are as follows:

Armor B

Type A (meter) 0.6 1.1

Type B (meter) 0.9 0.4

① Assume that the number of fashion items produced in Type A is x sets, and find the value range of The sales price of model B of fashion is 90 yuan. When the garment factory produces and sells this batch of fashion, how many sets of each of the two models of fashion will be produced, the total profit will be the largest? What is the maximum profit?