Answer: solution: as shown in the figure, ∫a∨b, AM? b，

3=? AMB=90？ And then what? 1=32? ,

2= 180? ﹣90? ﹣32? =58? ,

So the answer is 58? .

Comments: This question mainly examines the nature and application of parallel lines; We should firmly grasp the judgment and nature of parallel lines.

15.a and B are rational numbers. The positions of their corresponding points on the number axis are shown in the figure. Sort A, ﹣a, B and ﹣b in descending order and use? & gt？ The connection is a > b> > b > Answer.

Test center: rational number comparison; Number axis.

Analysis: first, a

Answer: solution: ∵ From the number axis, we can know that a < 0|b|,

? a & lt﹣b

So, the answer is:-a > b > ﹣b>； a.

Comments: This question examines the comparison rule of rational numbers, the application of reciprocal, absolute value and number axis. Note: all positive numbers are greater than 0, all negative numbers are less than 0, and all positive numbers are greater than negative numbers. When comparing two negative numbers, the absolute value is larger, but the number on the number axis is smaller. The number on the right is always greater than the number on the left.

16. As shown in the figure, cut a square piece of paper with a side length of (m+3) into a square with a side length of m, then cut the rest and splice it into a rectangle (no overlap, no seam). If one side of the spliced rectangle is 3 and the other side is 2m+3.

Test site: the geometric background of the complete square formula.

Special topic: geometric problems.

Analysis: Because a square piece of paper with a side length of (m+3) is cut into a square with a side length of m, and the rest is cut into a rectangle (without overlap and gap), the area of the rest can be calculated according to the area formula of the square. One side of the rectangle is 3, and the other side can be calculated by the area formula of the rectangle.

Solution: solution: the rest is based on the meaning of the problem

(m+3)2﹣m2=m2+6m+9﹣m2=6m+9，

One side of the spliced rectangle is 3,

? The length of the other side is (6m+9)? 3=2m+3。

So the answer is 2m+3.

Comments: This question mainly investigates that polynomials are divisible by monomials, and the key to solving the problem is to be familiar with the law of divisibility.

17. It is known that there are two calculators with different purchase prices in a store, both of which sell for 9 1 yuan, of which one earns 30% and the other loses 30%. In this transaction, the store lost 18 yuan.

Test center: the application of one-dimensional linear equation.

Analysis: Set different purchase prices of two calculators, list two linear equations, and get the purchase price. Relative to the selling price, the problem can be solved.

Solution: Solution: Let the purchase price of a calculator with a profit of 30% be X yuan, which is derived from the meaning in the question.

x+30%x=9 1，

Solution: x = 70

Suppose the purchase price of a calculator with a loss of 30% is Y yuan.

y﹣30%y=9 1，

The solution is y =130;

9 1? 2 ~ (130+70) = ~ 18 (yuan),

That is, this store lost money 18 yuan.

So the answer is: 18.

Comments: This topic mainly examines the application of linear equation of one variable, which is the key to correctly clarify the relationship between discount and commodity pricing, purchase price and profit.

18. According to the following procedure, if the initial input value of X is a positive fraction and the final output result is 13, please write a limited value of X 6 or OR.

Test center: Algebra Assessment.

Topic: Chart types.

Analysis: According to the result of 13, the value satisfying the condition X can be obtained from the program block diagram.

Answer: Solution: According to the meaning of the question: 2x+ 1= 13,

Solution: x = 6；;

We can get 2x+ 1=6,

Solution: x =；;

You can get 2x+ 1=,

Solution: x=,

Then the value satisfying the condition x is 6 or alternatively,

So the answer is: 6 or or.

Comments: This topic examines algebraic evaluation, and mastering the algorithm is the key to solve this problem.

Three. Solution: This big question is *** 10, and the score is ***64. Please answer in the designated area of the answer sheet, and write a written explanation, proof process or calculation steps when answering.

19. Calculation:

( 1)23+(﹣ 17)+6+(﹣22);

(2)﹣3+5? 2﹣(﹣2)3? 4.

Test center: mixed operation of rational numbers.

Special topic: calculation problems.

Analysis: (1) After the original formulas are merged, the result can be obtained by addition;

(2) The original formula first calculates the power operation, then calculates the multiplication and division operation, and finally calculates the addition and subtraction operation to get the result.

Solution: (1) Original formula = 23+6-17-22 = 29-39 =-10;

(2) The original formula =-3+ 10+2 = 9.

Comments: This question examines the mixed operation of rational numbers, and mastering the algorithm is the key to solve this question.

20. As shown in the figure, it is known that AB= 16cm, C is a point on AB, AC= 10cm, D is the midpoint of line segment AC, and E is the midpoint of line segment BC. Find the length of line segment DE.

Test center: the distance between two points.

Analysis: the length of CB can be obtained according to the sum and difference of line segments, the length of DC and ce can be obtained according to the nature of the midpoint of line segments, and the answer can be obtained according to the sum and difference of line segments.

Solution: Solution: It is obtained from AB= 16cm and AC= 10cm.

CB=AB﹣AC= 16﹣ 10=6cm，

From point D is the midpoint of line segment AC and point E is the midpoint of line segment BC, it is concluded that

DC= AC=？ 10=5cm，CE= CB=？ 6=3cm，

From the sum and difference of line segments, we get

DE=DC+CE=5+3=8cm。

Comments: This question examines the distance between two points, using the sum and difference of line segments and the nature of the midpoint of line segments.

2 1. Three algebraic expressions m2- 1, m2+2m+ 1, m2+m, please select any two algebraic expressions to simplify, and then find the value of the expression of times when m=2.

Test site: addition and subtraction of algebraic expressions? Simplify the assessment.

Special topic: opening up.

Analysis: select m2 ~ 1, m2+2m+ 1, subtract and merge without brackets to get the simplest result, and substitute the value of m into the calculation to get the value.

Solution: According to the meaning of the question, (m2-10)-(m2+2m+1) = m2-1-m2-2m-65438.

When m=2, the original formula =-4-2 =-6.

Comments: This topic examines the addition, subtraction, simplification and evaluation of algebraic expressions. Mastering the algorithm skillfully is the key to solve this problem.

22. Simplify first and then evaluate:, where x=2 and y =- 1.

Test site: addition and subtraction of algebraic expressions? Simplify the assessment.

Special topic: calculation problems.

Analysis: the original formula is combined without brackets to get the simplest result, and the value can be obtained by substituting the values of x and y into the calculation.

Solution: The original formula = x-2x+y2-x+y2 =-3x+y2,

When x=2 and y =- 1, the original formula =-6+ 1 =-5.

Comments: This topic examines the addition, subtraction, simplification and evaluation of algebraic expressions. Mastering the algorithm skillfully is the key to solve this problem.

23. Solve the equation:

( 1)4x+3(2x﹣3)= 12﹣2(x+4)；

(2) + =2﹣ .

Test center: Solve a linear equation.

Special topic: calculation problems.

Analysis: The (1) equation is removed from brackets, shifted and merged, and the x coefficient is changed to 1, and the solution can be obtained;

(2) The equation can be solved by removing the denominator, brackets, shifting terms and merging, and converting the y coefficient into 1.

Solution: solution: (1) without brackets: 4x+6x-9 =12-2x-8,

Transfer and merger: 8x= 13,

Solution: x =；;

(2) Denominator: 4(5y+4)+3(y﹣ 1)=24﹣(5y﹣5),

Without brackets: 20y+16+3y-3 = 24-5y+5,

28y= 16，

Solution: y=

Comments: This question examines and understands the linear equation of one variable, and its steps are: removing the denominator, brackets, merging moving terms, converting unknown coefficients into 1, and solving.

24. Give a class of students some books to read. If three books are given to each student, the remaining 20 books will be left. If everyone is divided into four books, there are still 25 books missing. According to the above information, please put forward a problem to be solved by one-dimensional linear equation and write out the solution process.

A: The question you designed is how many students are there in this class? Solution: There are X students, who can get the same total number of albums:

3x+20=4x﹣25，

Solution: x=45.

There are 45 students in this class.

Test center: the application of one-dimensional linear equation.

Analysis: There can be x students. According to the equal number of books, each student is assigned 3 books, and the remaining 20 books are assigned 4 books. If there are 25 books missing, you can list the equations to solve.

A: A: The question you designed is: How many students are there in this class?

There are x students, and according to the same number of books, you can get:

3x+20=4x﹣25，

Solution: x=45.

There are 45 students in this class.

Comments: This question examines the application of one-dimensional linear equation, and it is the key to solve the problem to get the equation according to the number of books expressed by the number of classes.

25. As shown in the figure, the straight line AB intersects with CD at point O, OE? CD, yes? AB，？ Freedom =65? .

Q: (1)? Degree of AOC;

(2)? The degree of BOE.

Test sites: diagonal and adjacent complementary corners; vertical line

Analysis: (1) According to OF? AB, do you understand? So BOF is a right angle? BOD=90？ ﹣? DOF, and then get it with the vertex angle? AOC=？ BOD

(2) by OE? Did you get the CD? DOE=90？ And then what? BOE=90？ ﹣? Bode.

Answer: Solution: (1)∵? AB，

BOF=90？ ,

BOD=90？ ﹣? Degree of Freedom =90? ﹣65? =25? ,

AOC=？ BOD=25？ ;

(2)∵OE？ CD，

DOE=90？ ,

BOE=90？ ﹣? BOD=90？ ﹣25? =65? .

Comments: This topic examines the nature of equal vertex angle, the definition of verticality and the calculation of angle. This is a basic problem and relatively simple. Accurate map recognition is the key to solve the problem.

26. As shown in the picture, you know? A=？ f，？ C=？ Are D, BD and CE parallel? And explain why.

Test center: determination and properties of parallel lines.

Analysis: by? A=？ F can determine AC∑DF, which can be obtained? ABD=？ D=？ C, BD∑CE can be determined.

Answer: Solution: Parallel. The reason for this is the following：

∵? A=？ f，

? AC∑DF，

ABD=？ D, then what? C=？ D

ABD=？ c，

? BD∨CE。

Comments: This question mainly examines the judgment and nature of parallel lines. Mastering the judgment and nature of parallel lines is the key to solve the problem, that is, ① two straight lines are parallel? The isosceles angles are equal, and ② two straight lines are parallel? Internal dislocation angles are equal; ③ Two straight lines are parallel and complementary.

27. Experiment and inquiry:

We know that the decimal form is 0. On the contrary, the decimal of infinite loop is 0. It is written in the form of fractions. Generally speaking, any infinite circulating decimal can be written in fractional form. We take the decimal 0 of an infinite loop. Let's take an example to discuss: set 0. =x, starting from 0. =0.777? It can be seen that 10x-x= 7. -0.= 7, that is, 10x-x = 7. Solve the equation and get x =. So, you get 0. Now please discuss the following questions:

(1) Please write the infinite decimal 0. As a fraction, that is, 0. =;

(2) Please write the infinite decimal 0. Decimal form, that is, 0. =;

(3) Can you judge 0 by the above solution? = 1? State your reasons.

Test center: the application of one-dimensional linear equation.

Analysis: (1) Set 0. =x starts at 0 according to the meaning of the question. =0.444? It can be seen that the value of 10x-x can be further calculated;

(2) Set 0. =x starts at 0 according to the meaning of the question. =0.7575? It can be seen that the value of100x-x-x can be further calculated;

(3) Set 0. =x starts at 0 according to the meaning of the question. =0.999? It can be seen that the value of 10x-x can be further calculated.

Solution: Solution: (1) Set 0. =x, starting from 0. =0.444? It can be seen that 10x-x = 4. -0.= 4,

That is, 10x-x = 4.

Solve the equation and get x=.

So, you get 0. =.

So the answer is:

(2) Set 0. =x, starting from 0. =0.7575? It can be seen that 100x-x = 75. -0.= 75,

That is 100 x-x = 75.

Solve the equation and get x=.

So, you get 0. =.

So the answer is:

(3) Set 0. =x, starting from 0. =0.999? It can be seen that 10x-x = 9. -0.= 9,

That is, 10x-x = 9.

Solve the equation to get x= 1.

So, 0. = 1.

Comments: This question mainly examines the application of linear equation of one variable, and the key to solve this question is to find out the law, that is, to convert infinite decimal into integer form through equation form.

28. Known? AOB=20？ ,? AOE= 100？ , OB split equally? AOC, OD split equally? AOE。

(1) Q? Degree of chemical oxygen demand;

(2) If O is the observation center, OA is due east, and the direction angle of ray OD is 40? ;

(3) What if? OA and OE on both sides of AOE are 5? , 3 per second? At the same time, rotate counterclockwise around point O. When OA returns to its original position, OA and OE stop moving. After a few seconds, AOE=42? .

Test center: calculation of angle; Direction angle; Definition of angular bisector.

Analysis: (1) According to the figure? EOB=80？ ; And then find out from the definition of angular bisector? Degree of chemical oxygen demand;

(2) According to the representation method of the direction angle, the answer is obtained;

(3) let x seconds pass. AOE=42？ Then list the equations and answer according to the meaning of the question.

Answer: Solution: (1)∵? AOB=20？ ,? AOE= 100？ ,

EOB=？ AOE﹣？ AOB=80？ .

Divide it equally with÷?ob? AOC, OD split equally? AOE，

AOC=2？ AOB=40？ ,? AOD=？ AOE=50？ ,

COD=？ AOD﹣？ AOC=50？ ﹣40? = 10? ;

(2) By (1),? AOD=50？ ,

Ray OD is 50 north by east? That is to say, the ray OD is 40 north by east? ;

So the answer is: 40 east of due north? ;

(3) let x seconds pass. AOE=42？ rule

3x﹣5x+ 100？ =42? ,

The solution is x=29.

That is to say, after 29 seconds, AOE=42? .

Comments: This topic examines the direction angle, using the nature of the angle bisector, the sum and difference of angles, and the expression of the direction angle.