Math problems and answers (scores, functions, equations, proofs, fill-in-the-blank questions, multiple-choice questions) are urgently needed in Grade Two. ) * * * Sixty questions. Thank you.

20 10 Subject Competition in Gaozhou City, Guangdong Province

Mathematics Test

Description: The whole volume *** 10 page, 25 questions, total score 120 points, and examination time 120 minutes.

The first volume (multiple choice questions, ***2 pages, out of 30 points. )

First, choose carefully: (This big question * * 10 small question, 3 points for each small question, 30 points for * * *. There are four answers to each question, only one of which is correct. Please fill in the correct answer code in the corresponding blank of volume 2. )

1. The following operations are correct.

A.B. C. D。

2. The average of five mutually unequal natural numbers is 15, and the median is 18, so the largest of these five numbers is

A.35 B.36 C.37？ Cao38

3. If each person wastes 0.23 liters of water every day, the water wasted by 5 million people every day can be expressed by scientific notation as follows.

A.B. C. D。

4. Point A is the point indicated on the number axis. When point A moves three unit lengths along the number axis to point B, the real number represented by point B is

A.3 b. or 0 c.d.0

5. If the algebraic expression is meaningful, the value range of is

A.B. C. D。

6. Xiaoming goes to school by bike from home. He takes a flat road to point A, then goes uphill to point B, and finally goes downhill to school. The relationship between time and distance is shown in figure 1. After school, if he goes back along the same road, and the speed of going up, up and down is the same as that of going to school, what is the latest time he needs to get home from school?

12 minutes

25 minutes, 27 minutes

7. In a square box with a height of 4cm and a bottom length of 18cm, a standard table tennis ball with a diameter of 40mm can be loaded. How many ping-pong balls can you hold at most?

A. 16 B. 18 C.20 D.23

8. As shown in Figure 2, the "Zhao Shuangxian Diagram" is a big square composed of four congruent right-angled triangles with a small square in the middle. Xiao Li randomly throws needles in the big square and its inner area. If the lengths of two right-angled sides of a right-angled triangle are 2 and 1 respectively, then the probability that the needle gets stuck in the small square (shadow) area is

A.B. C. D。

9. As shown in Figure 3, the intersection of the image of the inverse proportional function and the straight line.

Is a and b, the parallel line passing through point A is the Y axis, and the parallel line passing through point B is the axis.

Intersecting at point C, the area of is

A8 b . 6 c . 4d . 2

10. As shown in Figure 4, the middle is a right angle, AB= 12cm. Rotate point B clockwise, so that point C rotates to point D on the AB extension line, then the area of the figure (shaded part) swept by AC edge is () (and the final result retains three significant digits).

a . 1 13 b . 1 12 c . 10 1d . 1 14

Gaozhou 20 10 Subject Competition

Mathematics Test

The second volume (non-multiple choice questions, ***8 pages, out of 90 points. )

Total of title1216171819 202122 23 24 25.

Take the lead

commentator

First, choose carefully: (This big question * * 10 small question, 3 points for each small question, 30 points for * * *. Each question gives four answers, only one of which is correct. Please fill in the corresponding blanks in the table below. )

The title is 1 23455 6789 10.

Answer a question.

Second, fill in patiently (this big question is ***5 small questions, 3 points for each small question, *** 15 points. Please fill in the answer online. )

1 1. as shown in fig. 5(A), a rectangular paper tape is folded along EF to fig. 5(B) and then along BF to fig. 5(C), so the degree in fig. 5(C) is.

12. Decomposition factor =.

13. If the sum of other internal angles of a polygon is 500 after one internal angle is removed, the degree of this angle is.

14. is called a real number, and =

15. As shown in Figure 6, in the right-angled trapezoidal ABCD, when the moving point P starts from point B and moves along the boundary, the maximum area is.

Third, do it seriously: (This big question is ***5 small questions, each with 7 points and * * * 35 points. )

16. Known value

17. If a graph can be divided into several graphs similar to itself, we call it a graph that can be divided similarly. A square is a "figure that can be divided similarly", as shown in Figure 7 (the dotted line in the figure is the dividing line, but there are other dividing methods).

Try to judge whether the three diagrams shown in Figure 8 are "diagrams that can be divided similarly". If so, draw a dividing method in the diagram (draw a dividing line with a dotted line).

18. As shown in Figure 9, the elevation of the top of the mountain A measured at the foot of the mountain C is 1000m measured at the foot of the mountain D. Find the mountain height AB (the root sign can be reserved in the calculation result).

19. A factory wants to recruit 150 two types of workers. The monthly wages of two types of workers are 800 yuan and 1000 yuan respectively. At present, the number of workers in Class B is required to be not less than twice that of Class A. When asked how many people are recruited for each of the two types of jobs, can the total monthly salary be the least? What is the total minimum wage?

20. In order to formulate a new physical fitness test standard for senior high school students, 50 female students were randomly selected from a school in our city for a one-minute sit-up test. The test results are shown in the following table, and the histogram of frequency distribution is drawn.

Please complete the figures and tables given;

(2) Please use statistical knowledge according to the information provided in the chart, try to determine a more reasonable passing standard, and explain your reasons. (Score according to the reasonableness of passing the standard).

6 12 15 18 20 25 27 30 32 36

Number of people1171052222

Fourth, calm down and think carefully: (This big question is ***5 small questions, each with 8 points and * * * 40 points)

2 1. According to the relationship between polynomial multiplication and factorization, it can be concluded that the coefficients of the two linear binomials on the right are related, the product of the upper and lower angles on the left is the coefficient of the quadratic term on the left of the original formula, the product of the two numbers on the right is the constant term on the left of the original formula, and the sum of the cross products is the coefficient of the linear term on the left of the original formula. This method of decomposing quadratic trinomial is called "cross multiplication". Please observe carefully, analyze and understand, and answer the following questions.

(1) Fill in the blanks:

① Decomposition factor:.

② factorize the left factor to solve the equation: () () =0,

, 。

(2) Solve the equation.

22. Two judgments are given below:

(1) has two triangles, and the median lines of both sides and the third side are congruent;

(2) Of the six elements of a triangle, two triangles with five equal elements are congruent.

Is the above judgment correct? If correct, please give the proof process; If not, please explain why.

23. Organize activities to climb Bijia Mountain on weekends in Grade 3 1 class. Considering the physical differences between boys and girls, they are divided into two teams. The two teams started from the foot of the mountain at the same time and went down the mountain along the same road. It is known that the time ratio between men and women teams is 2: 3. (1) Write the speed ratio of men's and women's teams directly;

(2) When the men's team reached the top of the mountain, the women's team was halfway up the mountain, and there was still 600 meters from the top of the mountain. Find the distance from the foot of the mountain to the top of the mountain;

(3) On the basis of the content mentioned in question (2) (except the last question), the women's team will continue to climb the mountain from A, and the men's team will take a rest after reaching the top of the mountain, and then go down the mountain from the original road and meet the women's team at B on the mountainside. Please ask the corresponding questions according to the above situation and then give the answers (requirements: ① No other conditions can be attached to the questions; (2) The problem must be solved by using all the known conditions provided by the above scenario).

24.d is the circumscribed circle made by a moving point on the side of BC (except points B and C), and point E is on the bad arc.

(1) When AD is high and AE passes through the center of the circle (as shown in figure 10). Prove: (2) When AD is not perpendicular to BC and AE is not beyond the center of the circle, what additional conditions are needed to make the conclusion in (1) hold? Please explain your reasons.

25. Known quadratic function.

(1) When the image of this function has two intersections with the axis, the range of required values;

(2) When it is a positive integer, let the image and axis of this function intersect at point A and point B, and find the length of line segment AB;

(3) If we take 1, 2…, 20 10 in turn, the 20 10 line segment cut by the intersection of the image and the axis of the function is A 1B 1, A2010b20/kloc.

Gaozhou 20 10 Subject Competition

Answer math questions

First, choose carefully: (This big question * * 10 small question, 3 points for each small question, 30 points for * * *. Each question gives four answers, only one of which is correct. Please fill in the corresponding blanks in the table below. )

The title is 1 23455 6789 10.

Answer C C C B D B C C A A

Second, fill in patiently (this big question is ***5 small questions, 3 points for each small question, *** 15 points. Please fill in the answer online. )

1 1. 12. 13. 14. 15. 12

Third, do it seriously: (This big question is ***5 small questions, each with 7 points and * * * 35 points. )

16. Solution: 1.

= ... 2 points.

= ... 3 o'clock ... 3 o'clock ... 3 o'clock ...

= ... 4 points.

party history

Original formula = ... 5 points.

= ... 6 points.

Seven points

17.

(2 points) (2 points) (3 points)

(Note: Other correct segmentation methods are given points accordingly. )

18. solution: DE BC in e, DF AB in f.

rule

The quadrilateral DEBF is rectangular.

exist

..............................., 3 points.

and

.................................., 4 points.

Five o'clock.

............................... scored six points.

Answer: The height AB of this mountain is 500 () meters and .............................................. is 7 minutes.

19, solution: If Party A hires people, and the monthly salary of the two jobs totals Y yuan, then Party B recruits (150-) people, ... 1 minute.

According to the meaning of the question, get 2 points.

Get 3 points.

..........................., 4 points.

That is, when there are no more than 50 employees in Class A and no less than 100 employees in Class B, the total monthly salary is the least. ..... 5 points

and

................................ scored six points.

Answer: The total salary is the least when there are no more than 50 employees in a job and no less than 100 employees in a job. Minimum total wage140,000 yuan. Seven points

20.( 1) (Note: the first question (1) is 4 points, and the figure and table are 2 points each).

6 12 15 18 20 25 27 30 32 36

No.1171810 52222

(2) A: The test standard should be that most students can achieve it through hard work. The median and mode of this sample are 18, and 82% of the students take 17 times per minute, so it is more appropriate to take 16 to 18 times as the passing standard. (16, 17, 18 are all correct) ......................... scored 7 points.

(Note: This question will be graded as appropriate)

Fourth, calm down and think carefully: (This big question is ***5 small questions, each with 8 points and * * * 40 points)

2 1, ( 1)①, (……………………………………………………………………………………………………………………………………………………………………………………………………………….

(2), ....................................................... 3 points.

(2) Multiply the two sides of the equation and simplify it to get ……5 points.

Suppose that the original equation is, and the solution of this equation is ... 6 points.

that is

To solve these two equations, you get

After testing, they are all roots of the original equation. ...................................................................................................................................................................

(Note: Different methods can be graded accordingly. )

22. Solution: (1) is correct. ..................... 1 point

As shown in the figure, in

They are,

On the midline,

Prove: ............................., two points.

Prove that, respectively, is the midpoint. If you rotate and click 180 clockwise, you can get 3 points.

............................., 4 points.

In the same way, you can get 5 points.

Six points.

(2) incorrect. At 7 o'clock in ..................., if the three sides with the length of 8, 12, 18 and 12,18,27 are obviously similar, the five elements are equal, but not equal. Eight points, eight points, eight points

23. Solution: (1) The speed ratio of men's and women's teams is 3: 2; ......................... 1 min.

(2) Set the distance from the foot of the mountain to the top of the mountain as meters, and score 2 points according to the meaning of the question.

Solution (m)3 points.

After testing, it is the root of the listed equation.

A: The foot of the mountain is 1800 meters away from the top of the mountain; Four points.

(3) Ask "How many meters is B from the top of the mountain?" Or "How many meters does it take for the men's team to get down from B to the foot of the mountain?" Five points.

According to the last question, if the distance from B to the top of the mountain is meters, the speed of the men's team is 3km/h and the speed of the women's team is 2km/h, which means 6 points according to the question.

Solution: (m)7 points.

A:B The distance to the top of the mountain is less than 360 meters. Eight points.

24.( 1) Proof: Connect BE, AE is the diameter, …1.

AD high, ......................... 2 points.

∽ ............................................... 3 points.

..... 4 points

(2) For AB AC=AE AD to be established,

You must add a condition ... 5 points.

There are two kinds of graphics at this time.

As shown in the figure and figure connected with BE,

Can get, push

Abac = AEAD .......................... 7 points.

In the same way as in Figure B, you can get 8 points.

(It is also correct to add the condition as)

25. Answer: (1) The value according to the meaning of the question must satisfy ....................... 1.

The solution is any real number that is not equal to the sum of 0; ................................., two points.

(2) Let the coordinates of A and B be 0, which are two unequal real roots of the equation. .....................................................................................................................................................

The length of AB is.

.................................., 4 points.

If you substitute the formula (1), you will get

Six points.

(3) When 1, 2, …, 20 10 is taken in turn, the length of the cutting line segment is,

Seven points

..........................., eight.