Precautions:
1. The full mark of this volume is 130, and the examination time is 120 minutes.
2. In the volume, all questions should give accurate results except approximate results.
1. Fill in carefully (this big question * * has 12 small questions, 15 blank, each blank is 2 points, and ***30 points. Please fill in the results directly on the question line. As long as you understand the concept and calculate it carefully, I believe you will fill it in correctly! )
The reciprocal of 1 The arithmetic square root of is.
2. Decomposition factor:.
3. Let two real roots of a quadratic equation of one variable be added, then.
According to the information released by the National Examination Center, the number of candidates taking the national college entrance examination this year has reached 10,100000, which can be expressed as a person by scientific notation.
5. The range of independent variables in the function is,
The range of independent variables in the function is.
6. The sales of a shopping mall in May this year was 2 million yuan, which was 400,000 yuan less than that in May last year, so the sales in May last year were 1 10,000 yuan.
7. If the image of the inverse proportional function passes through a point, the value of is.
8. The sum of the internal angles of an octagon is degrees.
9. As shown in the figure, if it is known, then.
10. As shown in the figure, the chord length of is and the radius length is.
1 1. Write a random event in life:
12. As shown in figure 1, it is a square decorative tile with black and white colors and a side length of, and four tiles can be spliced into the pattern shown in figure 2. It is known that the cost of black and white parts of the tile shown in figure 1 is RMB/and RMB/respectively, so the cost of black and white materials used to make such tiles is RMB (the result is accurate.
Figure 1 Figure 2
Second, choose carefully (this big topic * * *, a total of 7 small questions, 3 points for each small question, ***2 1 point. Only one of the four options given in each question is correct. Please fill in the letter code before the correct option in the brackets after the question. As long as you master the concept and think carefully, I believe you will definitely choose the right one! )
13. The result of simplifying the score is ()
A.B. C. D。
14. The following is the same quadratic radical ()
A.B. C. D。
15. Among the following four patterns, the one with rotational symmetry is ().
A.B. C. D。
16. The solution of the unary quadratic equation is ()
A.，b，
C.，d，
17. The radius of the cone bottom is, the length of the bus is, then its side area is ().
A.B. C. D。
18. As shown in the figure, it is a geometry composed of a cylinder and a cuboid, and the lower bottom surface of the cylinder is close to the upper bottom surface of the cuboid, so the top view of this geometry is ().
exceed
19. Any positive integer can be decomposed into: (is a positive integer and). If the absolute value of the difference between these two factors is the smallest among all these factorizations, we call it the optimal factorization, and stipulate that, for example, 18 can be decomposed into three kinds, namely, and then there are. Give the following statement: (1) (2); (3) ; (4) If it is a complete square number, then the correct statement is ()
A.B. C. D。
Third, seriously answer (this big question * * * has 8 small questions, with a score of ***60. The answer needs to write the necessary text description, calculation steps or proof process. As long as you think positively and calculate carefully, you will definitely get it right! )
20. (This question ***2 is a minor issue, with the score of (1) being 4, the score of (2) being 6, and the full score being 10).
(1) calculation:;
(2) Solve the inequality group and write all its integer solutions.
2 1. (The full score for this short question is 7)
As shown in the figure, it is known that the quadrilateral is a diamond and the point is the midpoint of the edge.
22. (The full score for this short question is 6)
As shown in the figure, it is diameter, tangency, intersection, connection, and if so, find the degree.
23. (The full score for this short question is 8)
As shown in the figure, A and B hit the target in a shooting competition (the circle that hits the center of the target is 10 ring, and each number in the target represents the number of rings obtained by hitting the ring where the number is located), and each shot is six times.
(1) Please count their shooting scores by tabulation;
(2) Please compare their shooting with the statistical knowledge you have learned.
24. (The full score for this short question is 6)
A shopping mall is engaged in lottery promotion: the shopping mall puts three identical balls in an opaque box with the words "10 yuan", "20 yuan" and "30 yuan" written on them. It is stipulated that customers can touch out a ball in this box for every 100 yuan they spend in this mall on that day (every time customers touch out a ball to have a look, the mall will send corresponding prizes according to the amount marked on the ball touched by customers. At present, a customer spent 235 yuan at a time in the mall. According to the regulations, the customer can win the prize twice, and ask the customer the probability that the sum of the two winning product prices exceeds 40 yuan.
25. (The full score for this short question is 6)
Figure 1 is a regular triangle pattern composed of several small circles, with a circle on the top layer and a * * stacked layer on the bottom layer. After the figure 1 is inverted, it is combined with the original figure 1 to form the shape of Figure 2, so that we can calculate that the number of all circles in the figure 1 is.
Figure 1 Figure 2 Figure 3 Figure 4
If the circle * * * in figure 1 has 12 layers, (1) we fill in a series of continuous positive integers in each circle from top to bottom as shown in figure 3, then the numbers in the bottom and left circles are; (2) We fill in a series of continuous integers in each circle from top to bottom as shown in Figure 4, and find the sum of absolute values of all numbers in all circles in Figure 4.
26. (The full score for this short question is 9)
Xiaoming walks to school at a constant speed from home in the morning. 10 minutes later, Xiao Ming's mother found that Xiao Ming didn't bring her math textbook. She immediately took the textbook and rode her bike to chase Xiao Ming at a constant speed, and she arrived at school at the same time. It is known that Xiao Ming was on his way to school at that time, and when he left, he was kilometers away from home. The image of his function relationship is shown by the dotted line in the figure.
(1) Try to find the functional relationship corresponding to the broken line segment;
(2) Please explain the actual meaning of the line segment in the figure;
(3) Please draw an image of the functional relationship between the distance (kilometers) from home of Xiaoming's mother and the time (minutes) after Xiaoming left in the process of catching up with Xiaoming. (Friendly reminder: Please mark the drawn image with data appropriately. )
27. (The full score for this short question is 8)
Wang wants to make a ladder as shown in figure 1. The ladder has eight parallel steps, and the distance between every two adjacent steps is equal. The lengths of the top step and the bottom step of the ladder are known. When carpenters do these steps, the intercepted boards are longer than the treads, so as to ensure that a 4cm tenon is made at the two outer ends of each step (as shown in Figure 2). In this way, the pedal can be fixed. At present, there are plates with a length of 2. 1m on the market, which can be used to make ladder pedals (the width and thickness of the plates just meet the requirements for making ladder pedals). How many boards does Wang need to buy to make these pedals? Please explain the reason. (regardless of the wear and tear of the saw seam)
Practical exploration (this big topic is ***2 small topic, full score 19. As long as you use your head, practice boldly and explore boldly, you will succeed! )
28. (Full score for this small question 10)
As shown in the figure, a point on the plane starts from this point and moves at a constant speed of 1 unit length along the ray direction. In the process of movement, the side length of the rectangle is diagonal; Passing through this point and perpendicular to the straight line of the ray, starting from this point at the same time, moving in the same direction and speed as this point.
(1) In the process of point movement, try to judge the position relationship with the axis and explain the reasons.
(2) If both the point and the straight line move for seconds, find the area of the overlapping area swept by the rectangle and the straight line at this time (expressed by inclusion algebra).
29. (The full score for this short question is 9)
(1) As we all know, please draw a straight line and divide this triangle into two isosceles triangles. Please choose the alternative diagram given below and draw all the different division methods. Just draw a picture, without explaining the reason, but mark the degrees equal to the two angles in the picture. )
(2) It is known to be the smallest internal angle. A straight line passing through the vertex divides this triangle into two isosceles triangles. Please explore the relationship between and.
[Reference answer]
A, fill it in carefully (this big question * * has 12 small questions, 15 is empty, with 2 points for each space and ***30 points).
1.5,3 2.3.6,4 4.5.
6.7.8. 1080 9. 1 10 10.
1 1. It will rain in our city tomorrow (the answer is not unique) 12.6.37.
Second, choose carefully (this big topic * * *, a total of 7 small questions, 3 points for each small question, ***2 1 point)
13.A 14。 C 15。 D 16。 B 17。 A 18。 C 19。 B
Third, answer carefully (this big question has 8 small questions, ***60 points)
20. Solution: (1) 3 points in the original formula.
.4 points
② Pass, with a score of 0. 2.
To get 0.4 points.
The solution set of the inequality group is 0.5 points.
All its integer solutions are .6 points.
2 1. Proof: In diamonds,. 1 min.
Is the middle point,
.3 points
0.5 points again
.7 points
22. Solution: Tangent to the diameter Yes, 0.2 points.
, .4 points
.6 points
23.( 1) Solution:
Ring number 6 7 8 9 10
Click rate multiplied by 2 2 2
B hits 1 3 2
2 points for the correct list.
(2) Ring, ring, ring, ring, ring, ring, ring, ring, ring, ring, ring, ring, ring, ring, ring, ring, ring, ring, ring, ring, ring, ring, ring, ring, ring, ring, ring, ring, ring, ring, ring, ring.
The average scores of A and B are the same, but A is more stable than B, with 8 points.
24. Solution: The column tree diagram is as follows:
First prize price 10 20 30.
Second prize price10 203010 203010 20304 points.
Sum of two bonus prices 20 30 40 30 40 50 60
There are nine situations for the results of the two lucky draws, and there are three situations in which the sum of the two prize prices exceeds that of 40 yuan, so the probability of finding is .6 points.
25. Solution: (1) 67. Two points.
(2) There are numbers in all circles in Figure 4.
There are 23 negative numbers, 1 zero, 54 positive numbers and 4 points.
The sum of absolute values of all numbers in all circles in Figure 4.
.6 points
26. Solution: (1) The functional relationship corresponding to the line segment is: () 2 points.
The functional relationship corresponding to the line segment is: .4 points.
(2) The practical significance of the line segment in the figure is that after starting from 12 minutes, Xiao Ming walked along an arc road with a radius of 1 km, taking his home as the center, for 8 minutes and 7 minutes.
(3) The dotted line is shown in the figure. 9 points
27. Option 1: As shown in the figure, the pedals are set at the 2nd, 3rd, 4th, 5th, 6th and 7th gears from top to bottom.
Parallel lines with lengths of,,,, and.
Pay,,, at the point,,,.
The distance between every two steps of pedals is equal,
. , , ,
, , , ,
2 points
Suppose that the length of the boards needed to make these pedals is 0,,,,,,,,,, .5 minutes respectively.
Uncle Wang must buy no less than three boards. Six points.
Say it again,
Uncle Wang needs to buy at least three such boards. 8 points
Solution 2: Take the midpoint as shown in the figure.
Link.
The lengths of the second, third, fourth, fifth, sixth and seventh steps from top to bottom are as follows
,,,,, and then by the trapezoid midline theorem
Get 0.2 points
.3 points
If you want to do it,,, What is the length of boards required for these pedals?
,,, Then.
Uncle Wang must not buy less than three boards.
4 points
The created parallel lines intersect with,, and respectively at,,, and points.
The distance between every two steps of pedals is equal,
. , , ,
, , , ,
6 points
. And,,,
, .
Uncle Wang needs to buy at least three such boards. 8 points
Solution 3: If the ninth step is made under the ladder, follow it.
The distance between the first steps of the ladder is equal to the distance between two adjacent steps of the ladder.
From (as shown in the figure), set the length of the ninth step pedal as cm, and then from the trapezoidal median.
The properties of the line can be obtained by the length of the fifth step pedal.
The length of the pedal in the seventh step is obtained from the meaning of the question, and the length of the pedal in the eighth step is obtained by solving this equation.
2 points
From this, we can get cm,,,,.
For example, the lengths of boards to be cut off for making,,,, and these pedals are,,,,,,, and .5 minutes respectively.
(The following solution 1)
Four, practice and exploration (this big topic ***2 small questions, full score 19)
28. Solution: (1) axis. 1 fraction
Reason: average,, .2 points.
Let it intersect at one point, intersect at one point, and the diagonal lines of the rectangle are equally divided, then,
If the crossing point is taken as the axis, then,,, axis. Three points
(2) If the point intersects with the ray, the straight line perpendicular to the ray intersects with the point, and the straight line perpendicular to the ray intersects with the point, then.
, , , , .
4 points
(1) when, that is, .6 points.
(2) when, when, let a straight line through, through, and then,,,
.8 points
(3) when, when,
................................ 10.
29. Solution: (1) As shown in the figure (* * There are two different segmentation methods, each with 1 point and ***2 points).
(2) Let the straight lines passing through this point intersect in the middle,
① If the vertex angle is as shown in Figure 1, then,
, .
There can only be at this time, that is,
, that is. Four points.
(2) if it is the bottom corner, there are two situations.
The first case: As shown in Figure 2, when, then,
China people.
1. from, get, have at this time, that is, 0.5 points.
2. From, from, this time, that is.
6 points
3. From, from, at this time, that is, any acute angle less than 0.7 points.
In the second case, as shown in Figure 3, when,,, there can only be,
Therefore, this is the smallest angle contradiction with the topic.
When it is the bottom corner, it does not hold. Nine points