Math test
Note: 1. This test paper is ***5 pages, full mark 120, and the test time is 120 minutes. Candidates should fill in all the answers in the corresponding position on the answer sheet. It is useless to write them down on this paper. After the exam, please return the test paper and the answer sheet together. Calculators are not allowed to be used during the exam.
2. Before answering questions, candidates must fill in their names and test card numbers on the test paper, and fill in candidates' information on the answer sheet.
3. Drawing must use 2B pencil, and please describe it clearly in black and bold.
A, multiple-choice questions (this big question * * * has 8 small questions, each with 2 points, *** 16 points. Of the four options given in each question, only one is correct)
1. The distance measured by laser rangefinder is 14000000 meters, and 14000000 is expressed by scientific notation as follows
A.B. C. D。
2. The point through which the function image passes is
A.B. C. D。
3. The range of independent variables of this function is
A.B. C. D。
4. As shown in the figure, the main view of the geometry is
5. The following are operational errors.
A.B. C. D。
6. If the radii of two circles are 2 and 3 respectively and the center distance is 5, the positional relationship between the two circles is
A. externalization B. externalization C. intersection D. internalization
7. A company * * * has 5 1 employees (including the manager), and the salary of the manager is higher than that of other employees. This year, the salary of the manager rose from 200,000 yuan last year to 225,000 yuan, and the salary of other employees was the same as last year. In this way, the average salary and median salary of all employees in this company will be lower than last year.
A. the average and median remain unchanged.
C. the average value remains unchanged and the median value increases.
8. As shown in the figure, there are two points A and B on the image of a linear function, the abscissa of point A is 2, the abscissa of point B is vertical lines passing through point A and point B respectively, the vertical feet are C and D, and the areas are respectively, so the size relationship is
A.b.c.d is not sure.
Fill in the blanks (this big question has 9 small questions, the ninth small question has 4 points, and the other 8 small questions have 2 points each, each small question has 20 points. There is no need to write a solution process. )
9. Calculation:,,,.
10. in Rt△ABC, ∠ C = 90, AC=2, BC= 1, then tanB=, sinA=.
1 1. the coordinate of point P( 1, 2) about the axis is, and the coordinate of point P( 1, 2) about the origin o is.
12. Given that the radius of the sector is 3cm, the area is cm2, the central angle of the sector is, and the arc length of the sector is cm (the result is reserved).
13. The scores of seven students in one exam (unit: points) are as follows: 6 1, 62,71,78,85,85,92. The extreme range of these seven students is points, and the mode is points.
14. Decomposition factor: =.
15. If the real number is satisfied, then.
16. As shown in the figure, AB is ⊙O in diameter, and the chord DC and AB intersect at point E. If ∠ ACD = 60 and ∠ ADC = 50, then
Abd =, CEB =.
17. As shown in the figure, the numbers 0, 12, 1, 2, 3, 4, …, 1 1 on the circle. Every time the electronic flea jumps, it can jump from one circle to the next. Now, an electronic flea starts from the circle marked with the number "0", jumps 20 10 times counterclockwise and falls into a circle. The number marked in the circle is.
Third, answer the question (this big question is ***2 small questions, *** 18 points. The solution should be written as a calculus step)
18. (The full score of this small question is 8) Simplification:
( 1) (2)
19. (Full score for this small question 10) Solve the equation:
( 1) (2)
Fourth, solve the problem (this big title is ***2 small questions, * *15 points, and the problem should be written in words or calculus steps)
20. (The full score for this short question is 7)
The statistics of all students in Class 8, Grade 7 in a middle school participating in extracurricular sports activities are as follows:
(1) Please fill in the following table according to the information in the above statistical chart:
The median number of people in these five activities and the average number of people in these five activities.
(2) Please complete the bar chart.
2 1. (Full score for this small question)
As shown in the picture, when Xiao Wu and Huang Xiao are playing roulette, they have prepared two roulette wheels A and B that can rotate freely. The cabinet wheel is divided into several sector areas with the same area, and each sector area is marked with numbers. Rules of the game: Rotate two roulette wheels at the same time. When the roulette wheel stops rotating and the sum of the numbers in the sector pointed by the pointer is 4, 5 or 6, Xiao Wu or Xiao Huang wins. (If the pointer happens to be on the dividing line, turn it again until the pointer points to a sector. )
(1) Are the rules of the game fair to both parties? Tell me your reasons;
(2) Please design a game rule that is fair to both parties.
Verb (abbreviation of verb) to solve problems (this big problem is ***2 small problems, * *12 points, and the idea of solving problems should be written in the proof process)
22. (The full score for this short question is 5)
As shown in the figure, in △ABC, point D and point E are on AC and AB sides respectively, BD=CE, ∠DBC=∠ECB.
Proof: AB=AC.
23. (The full score for this short question is 7)
As shown in the figure, in △ABC, AB=AC, D is the midpoint of BC, and the quadrilateral ABDE is a parallelogram. It is proved that the quadrilateral ADCE is a rectangle.
Exploration and drawing of intransitive verbs (this big topic is ***2 small topic, and *** 13 points. )
24. As shown in △ABC and △CDE, AB=AC=CE, BC=DC=DE, AB & gtBC, ∠BAC =∠DCE =∞, and points B, C and D are on the straight line L, so draw according to the following requirements (leaving traces of drawing);
(1) Draw the symmetry point E' of point E relative to the straight line L, and connect CE' and DE';
(2) Rotate the △ CDE ′ obtained in (1) counterclockwise with point C as the center of rotation, so that CE ′ and CA coincide, and get △ CD ′ e ′′′′′′′′′′′′′ (a). Draw △CD'E''(A). Solve the following problems:
① The positional relationship between AB line and CD' line is.
The reason is:
② Find the degree of ∞.
25. (The full score for this short question is 6)
Xiaoming was inspired by studying the interesting coordinate system published by the Soviet Union. He designed a coordinate system for the regular hexagon OABCDE, with O as the origin, straight line OA as the axis, straight line OE as the axis, and the side length of the regular hexagon OABCDE as the unit length. Any point P in the coordinate system is represented by an ordered real number pair (). We call this ordered real number pair () the coordinate of point P, and the coordinate of the midpoint in the coordinate system is determined as follows:
(i) The coordinate of point M on the axis is (), where is the real number represented by point M on the axis;
(2) The coordinate of the n point on the axis is (), where is the real number represented by the n point on the axis);
(iii) The coordinate of the point Q that is not on the axis is (), where the real number represented on the axis by the intersection of the straight line and the axis passing through the point Q is the real number represented on the axis by the intersection of the straight line and the axis passing through the point Q. ..
Then: (1) Write the coordinates of three points A, B and C respectively.
(2) the position of the marking point m (2,3);
(3) If this point is any point of ray OD, find the relationship between it and satisfaction.
Seven, answer (this big question ***3 small questions, ***26 points. The solution should be written in words, proving the process or calculation steps)
26. (The full score for this short question is 7)
Xiangyang Flower Base sells two kinds of flowers-lily and rose. The unit price is: rose 4 yuan/plant and lily 5 yuan/plant. If the number of roses purchased by the same customer exceeds 1 0,200, the price of each rose can be reduced by 1 yuan. First, a flower shop bought 1 0,000 roses and several lilies from Xiangyang Flower Base. This flower shop just spent 9000 yuan on roses and lilies this time. Then sell it at the price of Rose 5 yuan and Lily 6.3 yuan. Q: How should this flower shop purchase these two kinds of flowers to maximize gross profit?
(Note: 1 0,000 ~ 1 0,500, which means 1 0,000 and10,500. Gross profit = the total amount of lily roses sold by flower shops-the total amount needed to buy lily roses. )
27. (The full score for this short question is 9)
As shown in the figure, it is known that the image of quadratic function intersects the axis at points A and C, and intersects the axis at points B, a () and △AOB∽△BOC.
The relationship between the degree of (1)C point coordinate ∠ABC and quadratic function is:
(2) Whether there is a point m () on the line segment AC. So that the circle with the diameter of line segment BM intersects with side BC at point P (different from point B), and the triangle with points P, C and O as vertices is an isosceles triangle? If it exists, it is the calculated value; If it does not exist, please explain why.
28. (Full score for this small question 10)
As shown in the figure, in the rectangular ABCD, AB=8, AD=6, points P and Q are moving points on AB side and CD side respectively, point P moves from point A to point B, point Q moves from point C to point D, and AP-CQ remains unchanged. Let AP=
(1) When PQ∑AD, the value of;
(2) The range of required values when the vertical line of line PQ intersects with BC;
(3) When the perpendicular of the straight line PQ intersects BC, let the intersection point be E, connect EP and EQ, let the area of △EPQ be S, find the functional relationship of S, and write the range of S. ..