Known: As shown in the figure, BCE and AFE are straight lines, AD∨BC,? 1=? 2,? 3=? 4,
Verification: AB∑CD
Proof: ∫AD∨BC (known)
3=? CAD (two straight lines are parallel with equal internal angles)
∵? 3=? 4 (known)
4=? Equivalent substitution
∵? 1=? 2 (known)
1+? CAF=？ 2+? Equal property
Namely. BAF=？ Computer aided design
4=? Equivalent substitution
? AB∨CD (same angle, two parallel lines)
Test center: determination and properties of parallel lines.
Topic: fill in the blanks by reasoning.
Analysis: According to the judgment and property theorem of parallel lines, the answer can be made.
Answer: Proof: ∫AD∨BC (known)
3=? CAD (two straight lines are parallel with equal internal angles)
∵? 3=? 4 (known)
4=? Equivalent substitution
∵? 1=? 2 (known)
1+? CAF=？ 2+? Equal property
Namely. BAF=？ Computer aided design
4=? Equivalent substitution
? AB∨CD (same angle, two straight lines parallel).
Comments: This topic examines the judgment and property theorem of parallel lines, and understanding the theorem is the key.
V. Answer questions (***3 small questions, ***23 points)
23.(8 points) (20 12? Xiaoming, the second model in Guangling District, went to a brand clothing store to do a social survey. He learned that the store was implemented to stimulate the enthusiasm of sales staff. Total monthly income = basic salary+piece rate bonus? Method, what else? Piece bonus = bonus for selling each piece? How many pieces do you sell a month? , and get the following information:
Shop assistant a and b
Monthly sales (pieces) 200 150
Total monthly income (RMB) 1400 1250
(1) column equation (group), and find the monthly basic salary of the salesperson and the bonus for selling each piece;
(2) The total monthly income of sales personnel shall not be less than 1800 yuan. How many clothes should the salesman sell that month?
Test site: the application of one-dimensional linear inequality; Application of binary linear equations.
Special topic: application problem.
Analysis: (1) Let's assume that the monthly basic salary of a salesperson is B yuan, and every item sold is rewarded with A yuan, because the total monthly income = basic salary+piece rate bonus, and piece rate bonus = bonus for every item sold? Monthly sales, according to the data provided in the table, can be solved by equation.
(2) Suppose that salesperson C wants to sell X pieces of clothing in that month. According to the total monthly income = basic salary+piece rate bonus, the total monthly income of salesperson C is not less than 1.800 yuan, which can be solved as an inequality.
Solution: Solution: (1) Suppose that the monthly basic salary of a salesperson is B yuan, and every product sold will be rewarded with A yuan.
OK,
The solution is a=3 and b=800.
(2) Set the assistant C to sell X pieces of clothes that month.
According to the question, 3x+800? 1800, solution.
Answer: Xiao Bing should sell at least 334 clothes this month.
Comments: The key to understanding the meaning of the question is to list the equality and inequality according to the relationship between the equality and inequality provided by the question.
24.(7 o'clock) In the plane rectangular coordinate system, let the unit length of the coordinate be 1cm, the integer point P starts from the origin O, the speed is 1cm/s, and the point P can only move up or right. Please answer the following questions.
(1) Fill in the form:
P from the departure time of o point, you can get the coordinates of integer points and the number of integer points.
1 sec (0, 1), (1, 0) 2
2 seconds (0,2) (2,0) (1,1) 3
3 seconds (0,3) (3,0) (2, 1) (1, 2) 4
(2) When point P starts from point O 12 seconds, the number of integer points is 13.
(3) When the point P starts from the point O 13 seconds, the integer point (8,5) can be obtained.
(4) When the point P leaves the point O for (m+n) seconds, the integer point can be obtained as (m, n).
Test center: Normal type: coordinates of points.
Analysis: (1) just mark all in the coordinate system;
(2) From (1), we can explore the law and deduce the results;
(3) The map can be moved to the right by 8 units for 8 seconds; Move up 5 units for 5 seconds;
(4) The map can be moved to the right by m units for 8 seconds; It takes 5 seconds to move up n units.
Solution: Solution: (1) Based on the integer point reached at 1 second, move one grid up or right to get the possible integer point at 2 seconds;
Then, based on the integer points obtained in 2 seconds, move one grid up or right to get the integer points that may be obtained in 3 seconds.
The time when P departs from point O, and the possible position of point P (the coordinates of integer points).
1 sec (0, 1) or (1, 0)
2 seconds (0,2), (1, 1), (2,0)
3 seconds (0,3), (1, 2), (2, 1), (3,0)
(2)∵ 1 sec, reaching 2 integer points; At 2 seconds, it reaches 3 integer points; When it reaches 4 integer points in 3 seconds, it should reach 13 integer points in 12 seconds; (3) The abscissa is 8, so it needs to move from the origin to the right along the X axis for 8 seconds, and the ordinate is 5, so it needs to move up for 5 seconds, so it needs 13 seconds. (4) The abscissa is m, which needs to be moved to the right along the X axis from the origin for m seconds, and the ordinate is n, which needs to be moved up for n seconds, so it needs (m+n) seconds.
So the answer is: (0,2), (1, 1), (2,0); 3,(0,3)、( 1,2)、(2, 1)、(3,0),4; 13; 13; (m+n)。
Comments: This question mainly examines the changing law of integral. The key to solve this problem is to master the given method and get the coordinates of the corresponding possible integer points.
25.(8 points) Celebrate? July 1st? On the birthday of the Party, Yuxin Sub-district Office will issue a batch of publicity materials. Blue Sky Advertising Company's quotation: 20 yuan is charged for each material, and the design fee is 1 1,000 yuan; Fukang quotation: 40 yuan for each material, no design fee.
(1) When is it more cost-effective to choose Blue Sky Company?
(2) Under what circumstances is it economical to choose Fukang Company;
(3) Under what circumstances are the charges of the two companies the same?
Test site: the application of one-dimensional linear inequality; Application of one-dimensional linear equation.
Analysis: If the number of promotional materials produced is X, the charge of advertising company A is 50x+2000, and that of advertising company B is 70x. Using the knowledge of inequality and equation, we can give the answer.
Solution: If the number of promotional materials produced is X, Blue Sky Advertising Company charges (20x+ 1000) yuan, and Fukang Advertising Company charges 40x yuan.
(1) when 20x+ 1000: 40x, that is, X.
A: When the number of promotional materials produced is 50, the fees charged by the two companies are the same.
Comments: This question examines the application of linear equations and linear inequalities. The key to solve this problem is to express the charges of the two companies and solve them with inequalities and equations.
Sixth, additional questions (***2 small questions, choose 1 question, 20 points)
26.( 10) It is known that the sum of all integer solutions of the inequality group about x is-9. Find the range of m 。
Test site: integer solutions of unary linear inequalities.
Special topic: computational problems; Discuss by category.
Analysis: First, determine the solution set of the inequality group, first express it with a formula containing m, then according to the number of integer solutions, we can determine which integer solutions there are, and according to the situation of the solutions, we can get the inequality about m, thus finding the value range of m. 。
Solution: solution: ∫, obtained from ①, x < ﹣,
Inequality has a solution,
? The solution set of the inequality group is-5.
∵ Sum of all integer solutions of inequality group ∵ 9,
? Integer solutions of inequality groups are ﹣4, ﹣3, ﹣2 or ﹣4, ﹣3, ﹣2, ﹣ 1, 0, 1.
When the integer solutions of the inequality group are ﹣4, ﹣3 and ﹣2, there is ﹣ 2 < ﹣? -1, the range of m is 3? m & lt6;
When the integer solution of the inequality group is ﹣4, ﹣3, ﹣2, ﹣ 1, 0, 1, there is 1 < ﹣? 2, the range of m is -6? m & lt﹣3.
Comments: The key to solve this problem is to correctly solve the solution set of inequality groups and determine the value range of m according to integer solutions. To solve the solution set of inequality groups, we should follow the following principles: take the largest with the same size, take the smallest with the same size, find the middle with the smallest, and the big one cannot be solved.
27.( 10 point) As shown in the figure, l 1∑l2, MN intersects with straight line l 1, l2 intersects with straight line l 1, l2 intersects with straight line l 1, L2 intersects with points C and D, and point P is on MN (.
If point P moves between point A and point B, what is the quantitative relationship between,, and? Please explain the reason.
(2) If point P moves out of points A and B, what is the quantitative relationship between,, and? Just need a conclusion.
Test site: the nature of parallel lines.
Analysis: (1) According to the properties of parallel lines, the relationship between them can be found. Point P can be regarded as a parallel line, parallel to AC, and can be found according to the fact that the included angles of two parallel lines are equal;
(2) Classification discussion: ① When point P is on the extension line of point AB, and ② When point P is on the extension line of point BA, the answers are obtained by using the properties of parallel lines when point P is PO∨l 1∨L2 respectively.
Solution: (1) As shown in the figure, if the intersection p is PO∨AC, then PO∨l 1∨L2, as shown in the figure:
? =? DPO，=？ CPO，
? =+;
(2) If point P is on the extension line of BA and the intersection point P is PO∨AC, then PO∨l 1∨L2, as shown in the figure:
then what =+.
(3) If point P is on the extension line of BA and the intersection point P is PO∨AC, then PO∨l 1∨L2, as shown in the figure:
Then =+
Comments: This question examines the nature of parallel lines. The key to solving this question is to master that two parallel lines have the same internal angle, the same angle and the same fat internal angle.