8. If two sides of a triangle are 2cm and 3cm respectively, and the length of the third side is odd, then the length of the third side is.
1 1, if (use ">" "< fill in the blanks)
12. Use only one regular polygon to cover the ground. Please write such a regular polygon _ _ _ _ _ _ _ _ _ _ _
13, known as the solution of a binary linear equation, then _ _ _ _ _ _ _ _ _
14, if the point is on the axis, then
15, put a pair of triangles as shown in the figure, and then
16. If the solution of the equation is, then the solution of the equation is.
17, medium,
18, a pile of toys for several children. If each child is divided into three pieces, the remaining three pieces will be left. If each child is divided into five pieces, each child will be given toys. However, if a child has less than three toys, then * * * has _ _ _ _ _ _ _.
19, given point A(5,), and the straight line AB is parallel to the coordinate axis, then the coordinate of the intersection point C of the straight line AB and the bisector of the first and third quadrants is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
Test position number
20. As shown in the figure, Liang Xiao starts from point A 10m, turns right 150, goes on 100 m, turns right 150, and so on. When he first returned to the starting point A, he left _ _ _ _ _ _ _ _.
2 1, solve the equation (*** 12 points)
○ 1 ○2
22.(8 points) Why is the value of algebraic expression greater than that of algebraic expression?
23.(8 points) Solve the inequality group and express the solution set on the number axis.
24.( 10) The value of the known algebraic expression is 5, and when used, its value is 1.
(1) find a, b, c, b, c.
(2) duty.
25.( 10) The known equation group (1) is expressed by the algebraic expression of m (2). When m is taken, the solution of this equation group is greater than 1 and not less than?
26.( 10 point) ○ 1 The vertices drawn in the plane rectangular coordinate system are A (-3,-1) and B (1, 3).
ABC of △C(2, -2)
○2 If the triangle translation makes the coordinate of the corresponding point B' of B (-1, 0), try to draw the translation.
△A'B'C '
○ The area of 3 △ a 'b 'c' is _ _ _ _ _ _.
y
28.( 12 points) There is a right-angle triangular ruler DEF placed on △ABC, as shown in the figure, the two right-angle siDEs de and DF of △DEF pass through point B and point C respectively, and in △ABC, ∠A=500.
(1) Find ∠ABD+∠ACD
(2) If the right-angle vertex D of the triangle ruler is placed outside △ABC, and the two right-angle sides de and DF still pass through points B and C, draw a diagram to explore the quantitative relationship between ∠ABD and ∠ACD.
24. As shown in the figure, in △AOB, the coordinates of point A and point B are (2,5) and (6,2) respectively.
① Find the area of △AOB; (5 points)
(2) If the abscissa of each vertex of the original δ△AOB remains unchanged and the ordinate increases by 3, a triangle is obtained.
What is the area? (3 points)
(Figure 24)
17. (This is called 10) Solve the following equation.
( 1) (2)
29.(8 points) (1) Solve the following equation first:
○ 1 ;
○2 ; Find all the solutions,
We know that equations and equations are determined by their solution coefficients. After careful observation, write the same equations as the above equations:
__________________________
(2) Write the relationship _ _ _ _ _ _ _ that the coefficients of the above equations satisfy.
(1) Write the solution of equation _ _ _ _ _ _ _ _ according to the conclusion obtained in (2).
(2) Study the following two equations.
① ②
Write the laws and solutions of each equation in the equation.
(Chifeng City, 2007) "Equation" is a very important mathematical model in real life. Please write an application problem of binary linear equations according to your real life, zero the listed binary linear equations and write out the solution process.
(Ziyang, 2007) After Mr. Chen bought the prizes for the sports meeting for the school, he returned to the school and settled the bill for Mr. Wang from the logistics department, saying, "I bought two books, *** 105, and the unit prices were 8 yuan and 12 respectively. I received 1500 before I bought the book, and now I still have 4 18. "
(1) Why did Miss Wang say that she had made a mistake? Explain with the knowledge of equations;
[2] Teacher Chen quickly took out the shopping invoice and found that it was really a mistake, because he also bought a notebook. However, the unit price of the notebook is blurred, and only integers less than 10 yuan can be identified. What is the possible unit price of this notebook?
(Zhangzhou City in 2007) (Zigong City in 2007)
(Chenzhou City in 2007) (Jinan City in 2007)
(Qingliu County 2007) (Nanjing 2007)
(Zaozhuang, 2007) If the known solution is, the solution is _ _ _ _ _ _ _ _ _.
(Zhoushan, Zhejiang, 2007) Three students put forward their own ideas on the question "If the solution of the equations is 0, find the solution of the equations". A said: "This problem seems to be not enough to solve"; B said: "Their coefficients have certain rules, you can try"; C said, "Can you divide the two sides of the second equation group by 5 and substitute it for the solution?" Referring to their discussion, do you think the solution to this problem should be.
2. A shopping mall buys a kind of clothing at the price of RMB per piece. If you sell at the price of RMB per piece, you will sell 15 pieces every day on average, and make a profit of 22,500 yuan in 30 days. In order to recover the funds as soon as possible, the mall decided to reduce the price of each item by 20%. As a result, we sold 10 more pieces every day than before the price reduction, so we can still make a profit of 22,500 yuan in 30 days. Try to find the value (profit per garment = selling price per garment-buying price per garment).
1. (Baotou, 2007) A factory plans to recruit two types of workers, A and B 120. It is known that the monthly wages of the two types of workers are 800 yuan and 1000 yuan respectively.
(1) If the monthly salary paid by the factory is 1 10000 yuan, how many workers will be recruited for each of the two jobs?
(2) If the number of Class B workers is required to be not less than twice that of Class A, how many Class A workers can be recruited to set the minimum monthly salary?
27. Xiaojie went to the school cafeteria to buy food. He saw that there were as many people waiting in line in front of window A as in front of window B (assuming A, a > 8), so he stood in line behind window A. After two minutes, he found that there were four people shopping in window A every minute, six people in window B every minute, and five people left the queue behind window B.
(1) At this time, if Xiaojie continues to line up in window A, how long will it take him to reach the window (expressed by algebraic expression with a)?
(2) At this time, if Xiaojie quickly moves from the queue in the A window to the queue behind the queue in the B window, the time to reach the B window is less than the time to continue queuing in the A window to reach the A window, and the value range of A is found (regardless of other factors).
43. (Chongqing, 2007) A town in our city organized 20 vehicles to transport 100 tons of A, B and C navel oranges to other places for sale. According to the plan, 20 cars will be transported, each car can only transport the same navel orange, and it must be full. According to the information provided in the following table, solve the following problems:
Navel orange variety A B C
Capacity of each vehicle (ton) 6 5 4
Get (100 yuan) 12 16 10 per ton of navel orange.
(1) Let the number of vehicles carrying A navel orange be, and the number of vehicles carrying B navel orange be, and express y with an algebraic expression containing X; (2) If there are not less than 4 vehicles loaded with navel oranges, how many vehicles are arranged? And write the layout plan; (3) What arrangements should be taken to maximize the profit of this sale? And find the value of the maximum profit.
33. Suzhou is located on the coast of Taihu Lake and is rich in aquaculture resources. Uncle Li, an aquaculture farmer, is going to polyculture hairy crabs and river shrimps. He learned the following information:
(1) The annual rent per mu of water surface is 500 yuan, and the water surface needs to be rented for the whole mu;
② At the beginning of the year, 4 kg of crab seedlings and 20 kg of shrimp seedlings can be mixed per mu of water surface;
(3) The price per kilogram of crab seedlings is 75 yuan, and its feeding cost is 525 yuan, and the income in that year can be 1.400 yuan;
④ The price per kilogram of shrimp fry is 15 yuan, and its feeding cost is 85 yuan, and the annual income is 160 yuan;
(1) If you rent an acre of water surface, the annual rent * * * is RMB _ _ _ _ _ _ _ _;
(2) The aquaculture cost includes the annual rent on the water surface, the fry and feeding expenses, and the annual profit of mixed culture of crabs and shrimps per mu of water surface (profit = income-cost);
(3) Uncle Li has an existing fund of 25,000 yuan, and plans to borrow no more than 25,000 yuan from the bank for mixed culture of crabs and shrimps. As we all know, the annual interest rate of bank loans is 8%. How many acres of water should Uncle Li rent and how much should he borrow from the bank so that his annual profit can exceed 35,000 yuan?
18. (This question 10 points) Solve the inequality (group) and express its solution set on the number axis.
( 1) ; (2) .
1. As shown in the figure, AD is the center line of △ABC and BE is the center line of △ABD. (8)
(1) ∠ Abe = 15, ∠ bad = 40, find the degree of ∠BED;
(2) in the delta bed, determine the height of BD side;
(3) If the area of △ABC is 40 and BD=5, what is the distance from point E to BC?
19. (The full mark of this question is 6) Solve a system of linear equations with three variables.
20. (8 points in this question) Known binary linear equation.
(1) Please write three groups of solutions of this equation at will;
(2) If we specify a set of solutions of this equation as the coordinates of a certain point, please write the coordinates of three points according to the three sets of solutions you wrote in (1) and draw these three points in the plane rectangular coordinate system;
(3) What do you find by observing the positions of these three points?
23. (this question 10 points) There is such a column number,,,,,, which satisfies the formula and is known.
(1) and value;
(2) If, the value of.
24. (Question 12) It is known that a clothing factory now buys two kinds of fabrics from textile mills *** 122 meters, which costs 4 180 yuan. It is known that 30 yuan per meter for Class A fabrics and 40 yuan per meter for Class B fabrics.
(1) How many meters do I need for fabrics A and B?
(2) It is planned to produce 80 sets of A and B fashions with these two fabrics. It is known that two kinds of fabrics A and B are needed to make a suit of A or B fashion, as shown in the following table:
Cloth fashion Jiayi
One (meter) 0.6 1. 1
Type B (meter) 0.9-0.4
(1) Set X sets for producing a type of fashion, and find the range of X;
(2) If the price of a fashion model is 100 yuan and the price of a fashion model is 90 yuan, how many sets of two fashion models does this clothing factory produce, and the total profit is the largest? What is the maximum profit?