This paper is divided into two parts: multiple-choice questions and non-multiple-choice questions. Three big questions and 25 small questions, 4 pages in total, full score 150. Examination time 120 minutes.

Precautions:

1. Before answering the questions, candidates must fill in the answer sheet on 1, 3 and 5 with a black pen or signature pen.

Your candidate number and name; Fill in the room number and seat number of the examination room, and then mark the corresponding two numbers with 2B pencil.

The number has been blacked out.

2. After choosing the answer for each multiple-choice question, black the answer label corresponding to the same question on the answer sheet with 2B pencil; If you need to change,

Wipe it clean with an eraser, and then select other answer labels; You can't answer on the test paper.

3. Non-multiple choice questions must be answered with a pen or signature pen, and the handwriting is black. For topics involving painting, use 2B pencil. A.

The case must be written in the corresponding position in the designated area of each topic on the answer sheet; If you need to change, cross out the original answer first, but

Then write a new answer; Don't change the answer beyond the specified area. Pencils, ballpoint pens and alterations are not allowed.

Liquid. Answers that do not answer according to the above requirements are invalid.

Candidates must keep the answer sheet clean and tidy, and return this paper and the answer sheet together after the exam.

The first part of the multiple-choice questions (***30 points)

A, multiple-choice questions (this topic is entitled *** 10 small questions, 3 points for each small question, 30 points for each small question. Only one of the four options given in each small question meets the requirements of the topic. )

1. If the temperature of a city is -2℃ ~ 6℃ on a certain day, the temperature difference of that day is ().

(A)8℃ (B)6℃ (C)4℃ (D)-2℃

2. As shown in figure 1, ab//cd, if ∠ 2 = 135, the degree of ∠l is ().

30 (B)45 (C)60 (D)75

3. If the algebraic expression is meaningful in the real number range, the value range of x is ().

(A)x & gt； 0 (b) x ≥ 0 (c) x ≥ 0 (d) x ≥ 0 and X≠ 1

4. Figure 2 is three views of an object, so the shape of this object is ().

(a) cone (b) cylinder

(3) triangular pyramid (4) triangular prism

5. The two roots of a quadratic equation are () respectively.

(A)Xl= 1，x2=3 (B)Xl= 1，x2=-3

(C)X 1=- 1，X2=3 (D)XI=- 1，X2=-3

Math Test Paper Page 1 (***4)

6. The vertex coordinate of parabola Y=X2- 1 is ().

(a)(0. 1)(b)(0. 1)(c)( 1.0)(d)( 1.0)

7. The lengths of the four groups of line segments are known as follows. With each group of line segments as sides, a triangle can be composed of ().

(A) 1，2，3 (B)2，5，8 (C)3，4，5 (D)4，5， 10

8. In the figure below, the straight line y=x- 1 is ().

9. The side development diagram of a cylinder is a rectangle with adjacent side lengths of 10 and 16 respectively, so the radius of the bottom circle of the cylinder is ().

10. As shown in Figure 3-①, divide a square board into 36 congruent small squares with dotted lines, and then press one of them.

Cut the solid line into seven small pieces of wood with different shapes and put them together into a puzzle. Use this puzzle to make Figure 3-2.

Pattern, the shaded area in Figure 3-② is () of the whole pattern area.

The second part is not a multiple-choice question (* *120)

2. Fill in the blanks (this big question is ***6 small questions, each with 3 points, *** 18 points. )

1 1. Calculation: ≤ =

12. Calculation:

13. If the image of the inverse proportional function passes through the point (1, a 1), then the value of k is.

14. It is known that A= and B= (n is a positive integer). When n≤5, there exists a < B；; Please use a calculator to calculate when.

When n≥6, several values of A and B, thus it is concluded that when n≥6, the relationship between A and B is

15. In the sunshine at a certain moment, the shadow length of Amy with a height of 160cm is 80cm, and the shadow length of the flagpole beside her is10 m.

The height of flagpole is 100 meter.

Page 2 of the test paper (***4)

16. As shown in Figure 4, dig out a circular cardboard with a diameter of a+b, with diameters of A and B respectively.

Two circles, the remaining cardboard area is

Third, answer the question (this big question is ***9 small questions, *** 102 points. The answer should be written,

Proof process or calculus step)

17. (The full mark of this small question is 9) Solve the inequality group.

19. (The full mark of this little question is lO)

There are 54 students in Class 6, Senior One, a middle school in Guangzhou. After investigation, 40 of them have different degrees of myopia.

The frequency distribution of myopia in different age groups is as follows:

The first onset age of myopia is 2 ~ 5 years old, 5 ~ 8 years old, 8 years old ~1year old, 1 1 year old ~1year old, 17 years old.

Author: Ikechi CC 2006-6-30 2 1:58 Reply to this speech

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Math papers and answers! ! ! ! ! !

Frequency (number of people) 3 4 13 a 6

(Note: 2-5 years old in the table means 2 years old but under 5 years old, and others are similar.)

(1) Find the value of a and complete the following frequency distribution histogram;

(2) What conclusion can be drawn from the histogram of the last study (write only one conclusion)? What do you think this conclusion reflects about education and society?

20. (Full score for this small question 10)

As shown in fig. 6, turntable A is divided into three sectors with equal areas, and turntable B is divided.

Divide into two equal parts. Xiao Xia and Xiaoqiu use them to make decisions and win.

The game of whether or not. The rule is to turn to disk A once in summer and B once in autumn.

Game (when the pointer is on the boundary line, it is considered invalid and rotated again).

(1) Xiao Xia said: "If the sum of the numbers in the area pointed by two pointers is 6 or 7,

Then I won; Otherwise, you win. " According to the rules designed by Xiao Xia, please write down the possibility of winning.

(2) Please design a fair game rule for the game played by Xiao Xia and Xiaoqiu, and use appropriate methods.

(e.g. tree diagram, list) shows its fairness.

Math Paper Page 3 (***4)

2 1. (The full score of this small question is 12)

At present, there are about 1.28 million primary and junior high school students in Guangzhou, among which the number of primary school students is higher than that of junior high school students.

More than twice as many as 654.38+04,000 people (data source: Guangzhou Education Statistics Manual in 2005).

(1) Find the current number of primary school students and junior high school students in Guangzhou;

(2) Suppose that every primary school student needs to pay miscellaneous fees this year, and every junior high school student needs to pay miscellaneous fees 1 000 yuan, and these fees,

How much should the Guangzhou Municipal Government allocate for this purpose?

22. (The full score of this short question is 12)

As shown in Figure 7, the radius ⊙ 0 is 1, which is tangent to the straight line passing through point A (2,0).

⊙0 is at point b, and the y axis is at point C.

(1) Find the length of line segment AB;

(2) Take the straight line AC as the image, and find the analytical expression of the linear function.

23. (The full score of this short question is 12)

Fig. 8 is a schematic diagram of a part of streets in a certain area, in which CE vertically bisects AF,

AB//DC，BC//df。 There are only two direct routes from mile to mile to e station.

For the arriving bus, route 1 is B-D-A-E, and route 2 is

B-C-F-E, please compare the distance between the two routes and give proof.

24. (The full score of this short question is 14)

In ABC, AB=BC, rotate ABC clockwise around point A to get A 1B 1C 1, so that the Cl point falls on.

On the straight line BC (point C 1 does not coincide with point c),

(1) As shown in Figure 9-①, when the angle of C> is 60, write and prove the positional relationship between ABl edge and CB edge.

(2) When c = 60, write the positional relationship between ABl edge and CB edge (without proof);

(3) When c < 60, please use a ruler to draw △AB 1C 1 (keep drawing traces,

Don't write), and then guess whether your conclusions in (1) and (2) are still valid? And explain why.

25. (The full score of this short question is 14)

The parabola Y=x2+mx-2m2 (m ≠ 0) is known.

(1) Verification: there are two different intersections between parabola and X axis;

(2) Take point P(0, n) as the vertical line of the Y axis, and the parabola intersects with point A and point B (point A is to the left of point P), which is

Are there real numbers m and n that make AP=2PB? If it exists, find the conditions that m and n meet; If it doesn't exist,

Please explain the reason.

Academic Examination of Guangzhou Junior High School Graduates in 2006

Answers to mathematical reference questions

First, multiple-choice questions:

The title is 1 23455 6789 10.

The answers are ABBA, ABBA, ABB, CBC, CCD.

Second, fill in the blanks:

1 1.a2 12。 x 13。 - 1

14.a is greater than b15.2016.ab (pai)/2.

Third, answer questions:

17. Solution:

Take its public part and get

∴ The solution set of the original inequality group is

18. Description: Open-ended question, with different conclusions. Only one case is given and proved below.

Solution: Proposition: As shown in the figure, the coincidence point, if, then.

Proof: ∫ (known)

(Equal vertex angle)

(known)

∴△ ≌△

∴

∴

19.( 1), omitted.

(2) The conclusion is not unique, as long as it is reasonable.

20. Solution: (1) All possible outcomes are:

a 1 1 2 3 3

b 45454555

And 5 6 6 7 7 8

As can be seen from the table, Xiao Xia's chances of winning are as follows: Xiaoqiu's chances of winning are:

(2) As shown in the above table, it is easy to know that there are three odd numbers and three even numbers in the possibility of sum; Three prime numbers, three composite numbers.

So the rules of the game can be designed as follows: if the sum is odd, Xiao Xia wins; Even number, Xiaoqiu wins. (The answer is not unique)

2 1. Solution: (1) If the number of junior high school students is 10,000, then the number of primary school students is 10,000.

solve

Junior high school students 1 10,000, and primary school students 900,000.

(2) Yuan,

That is 1 100 million yuan.

22. Solution: (1) link, then △ is a right triangle.

∴

(2)∫ (male * * * Angle)

(Right angles are equal)

∴△ ∽△

∴

∴ The coordinates of the point are

Let the analytical formula of linear function be:, and substitute it into this point to solve it.

∴ The analytical formula of a linear function with a straight line as an image is:

23. (There is more than one method! Solution: The length of these two routes is the same.

Proof: extension of intersection point

∵

∴

∴ , ,

∴

∵

This is the advantage of men.

∴△ ≌△

∴

A quadrilateral is a parallelogram.

∴ ………①

Vertical bisection

∴ , ………②

∴ ………③

The route length is; The route length is:

We can know that the length of the route is equal to the length of the route.

24. Solution: (1)

Prove: According to the characteristics of rotation,

,

∵

∴

∵

∴

∴

∴

(2)

(3) sketch. Established. The reason is similar to the first question.

25. Solution: (1)△

∵

∴△

Parabola and axis have two different intersections.

(2) From the meaning of the problem, it is easy to know the coordinates of the point and satisfy the equation:

, namely

Because the equation has two unequal real roots, δ, that is,

………………….①

According to the root formula, the two roots are:

,

∴

Discuss in two situations:

The first type: the point is to the left of the point and the point is to the right of the point.

∵

∴

∴ ……………….②

∴ ……………………….③

It can be solved by Equation 2.

…………………………..④

The second type: both points are on the left side of the point.

∵

∴

∴ ……………….⑤

∴ ……………………….⑥

It can be solved by formula ⑤.

……….⑦

Comprehensive 1346⑦, we can see that there is a point that meets the conditions. At this time, the conditions should be met:

, or

Some can't be displayed, please go to the resource website to find them.

References:

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