(Including Chengdu Grade Three Graduation Examination)
Count? study
Precautions:
1. The complete set of papers is divided into volume A and volume B, with a score of 100 and a score of 50. Examination time 120 minutes.
Before answering the questions, candidates must scribble their names and admission ticket numbers in the places specified in the test paper and answer sheet. At the end of the exam, the invigilator will take back the test paper and the answer sheet together.
3. Multiple choice questions must be filled in with 2B pencil; Non-multiple choice questions must also be written with a 0.5 mm black signature pen, with neat fonts and clear handwriting.
4. Please answer each question in the corresponding answer area on the answer sheet according to the question number, and the answer written beyond the answer area is invalid; The answer on the draft paper and test paper is invalid.
5. Keep the answer sheet clean and tidy without folding, pollution or damage.
Volume 1 (*** 100 point)
The first volume (multiple choice questions, ***30 points)
First, multiple-choice questions (this big question * * 10 small questions, 3 points for each small question, ***30 points, each small question has four options,
Only one of them meets the requirements of the topic, and the answer is drawn on the answer sheet)
1. Of the four numbers -2,-1, 0,2, the largest number is (? )
(1) -2? (B)- 1 (C)0？ (D)2
2. The main view of the following geometry is a triangle or (? )
(1) (2)? (3)? (4)
3. The second Chengdu Ring Expressway under construction, with a total length of more than 220 kilometers, connects the second and third floors of our city with surrounding areas such as Guanghan and Jianyang, with a total investment of 29 billion yuan. With scientific counting methods, 29 billion yuan should be (? )
(A)290× (B)290×？
(C)2.90×? (D)2.90 times
4. The following calculation is correct ()
(1)? (B)？
(C) (D)
5. In the following figure, the figure that is not axisymmetric is ().
(1) (2)? (3)? (4)
6. The value range of the independent variable in the function is ()
(1)? (2) (3)? (4)
7. As shown in the figure, put the right-angled vertex of the triangle on one side of the ruler. If ∠ 1 = 30, the degree of ∠2 is ().
60 people
50 people
40 people
30
8. In recent years, the persistent smog weather in China has made environmental protection and health issues the focus. In order to further popularize the knowledge of environmental protection and health, a school in our city held a knowledge contest of "building a livable Chengdu and paying attention to environmental protection". The statistics of students in a class are as follows:
Results (points)
60
70
80
90
100
People? count
four
eight
12
1 1
five
Then the mode and median of students' grades are () respectively.
(1) 70 points, 80 points? (2) 80 points, 80 points.
(3) 90 points, 80 points? 80 points, 90 points
9. Convert the quadratic function into the form of, and the result is ()
(1)? (2)
(3)? (4)
10. In a fan-shaped AOB with a central angle of120 and a radius of OA=6cm, the area of the fan-shaped AOB is (? )
(1) (2)? (3)? (4)
Volume 2 (multiple choice questions, ***70 points)
Fill in the blanks (there are 4 small questions in this big question, 4 points for each small question, *** 16 points, and the answer is written on the answer sheet).
1 1. Calculation: _ _ _ _ _ _.
12. As shown in the figure, in order to estimate the distance between point A and point B on both sides of the pond, choose point O on one side of the pond, go to the middle points M and N of OA and OB respectively, and measure MN=32 m, so the distance between point A and point B is _ _ _ _ _ _ _ _ m. 。
13. In the plane rectangular coordinate system, the image of a known function passes through two points. If so, then _ _ _ _ _ _. (Fill in ">;" , "< or" = ")
14. As shown in the figure, AB is ⊙O in diameter, point C is on the extension line of AB, and CD cuts ⊙O to point D to connect AD. If ∞= 25, then ∠ c = _ _ _ _ _ _ _ _
Three. Answer questions (this big topic is * * 6 small questions, with ***54 points, and the answer process is written on the answer sheet)
15. (Full score for this small question 12, 6 points for each question)
(1) calculation? .
(2) Solving inequality groups
16. (Full score for this small question)
As shown in the figure, in a math extracurricular exercise, Xiaowen measured that the elevation angle of tree top A at point C was 37, BC=20m, and the tree height AB was found.
(Reference data:,,)
17. (Full score for this small question)
Simplify before evaluating:, where,.
18. (Full score for this small question)
The 15th China West Expo will be held at the end of 20 14 and 10. At present, a sub-venue is going to take part in 20 volunteers, including 8 boys and 0/2 girls.
(1) If one of these 20 people is randomly selected as a liaison, find the probability of choosing a girl;
(2) If only one person is selected by Party A and Party B for a certain work at the sub-venue, it is ready to decide who will participate in the competition. The rules of the game are as follows: after washing four playing cards with numbers 2, 3, 4 and 5, put them face down on the table and choose two cards from them. If the sum of the cards is even, Party A will participate, otherwise Party B will participate. Is this game fair? Please explain the reasons in a tree diagram or list.
19. (Full score for this small question 10)
A
B
O
y
x
As shown in the figure, the image of the linear function (constant sum) and the image of the inverse proportional function intersect at two points. (1) Find the expression of linear function;
(2) If the straight line has only one common * * * point with the image of the inverse proportional function after being translated down by one unit length, the value of.
20. (Full score for this small question 10)
As shown in the figure, in the rectangle,, is the edge point,? (integer greater than 2), connect and make perpendicular bisector intersect at the point, and the intersection of sum is, connect and.
(1) Try to judge the shape of the quadrilateral and explain the reasons;
(2) When (is a constant), the length of When;
(3) Remember that the area of a quadrilateral is and the area of a rectangle is,
B
C
A
F
E
D
G
O
At that time, the value. (Write the result directly without writing the solution process)
Volume B (***50 points)
1. Fill in the blanks (there are 5 small questions in this big question, with 4 points for each small question and 20 points for * * *, and the answer is written on the answer sheet).
2 1. In order to know the extracurricular reading situation of the whole school 1300 students, a school randomly investigated the extracurricular reading time of 50 students in one week and drew a histogram as shown in the figure. It is estimated that _ _ _ _ _ _ _ _ _ _
22. It is known that the solution of the fractional equation is negative, so the value range of is _ _ _ _ _.
23. In the grid paper composed of small squares with a side length of 1, the vertices of the small squares are called "grid points", and the polygons with all vertices on the grid points are called "grid polygons". The area of a grid polygon is marked as S, the number of grid points inside it is marked as N, and the number of grid points on the boundary is marked as L. For example, the triangle in the figure is a grid triangle, where S=2, N = S corresponding to the polygon in the figure, and N and L are _ _ _ _ _ _ _. It is found that the area s of any polygon can be expressed as S=aN+bL+c, where a, b and c are constants, so when N=5 and L= 14, S = _ _ _ _.
24. As shown in the figure, in a diamond with a side length of 2, ∞= 60 is the midpoint of the side and a fixed point on the side, and the minimum length is _ _ _ _ _.
25. As shown in the figure, in the plane rectangular coordinate system xOy, a straight line and a hyperbola intersect at two points, which is a point on the hyperbola in the first quadrant, connecting and extending the intersection axis to this point. If the area of △ is 20, the coordinates of this point are _ _ _ _ _ _ _ _.
Second, answer the question (this small question * * three small questions, ***30 points. The answer is written on the answer sheet)
26. (The full score for this short question is 8)
In the activity of beautifying the campus, an interest group wants to enclose a rectangular garden with a 28-meter-long wall (only two sides) with a right angle (with long sides) as shown in the figure, so that M.
(1) If the area of the garden is 192, the value of;
(2) If there is a tree whose distances from the wall are 15m and 6m respectively, the tree should be enclosed in the garden (including the boundary, regardless of the thickness of the tree) to find the maximum area of the garden.
27. (Full score for this small question 10)
As shown in the figure, in the inscribed △ABC of ⊙, ∠ ACB = 90, AC=2BC, the vertical line passing through C is AB intersecting with ⊙O at another point D, the vertical foot is E, P is the moving point on ⌒AC different from A and C, and the ray AP intersects with F to connect PC and PD.
(1) Verification: △ PAC ∽△ PDF;
(2) If AB=5, ⌒AP=⌒BP, find the length of PD;
(3) In the process of P-point movement, set the functional relationship between,, and summation (the value range does not require writing).
28. (The full score of this short question is 12)
As shown in the figure, it is known that the parabola (constant sum) intersects the axis at two points A and B in turn from left to right, intersects the axis at point C, and the other intersection of the straight line passing through point B and the parabola is d 。
(1) If the abscissa of point D is -5, find the function expression of parabola;
(2) If there is a point P on the parabola of the first quadrant, which makes the triangle with vertices A, B and P similar to △ABC, then find its value;
(3) Under the condition of (1), let f be a point on the straight line BD (excluding the endpoint) and connect AF. The moving point M starts from the point A, moves along the line AF to F at a speed of 1 unit per second, and then stops along the line FD at a speed of 2 units per second. When the coordinates of point F are, point M spends the most time in the whole movement.
Reference answer
volume one
First, multiple choice questions
1、D 2、B 3、C 4、B 5、A
6、C 7、A 8、B 9、D 10、C
Second, fill in the blanks
1 1、 12、64 13、< 14、40
Third, answer questions.
15, (1) Original formula = 3-2+ 1-4 =-2.
(2)① x > 2, ② x < 3.
So the solution set of the original inequality is 2 < x < 3.
16, solution: tan 37 =, so AB = 0.75× 20 = 15 (m).
17, solution: original formula =,
When, when, the original formula = 2
18, solution: (1) The probability of choosing girls is: p =
(2) Any two may be: 23, 24, 25, 34, 35, 45, ***6,
Where the sum is even, there are: 24, 35, so the probability of A's participation is: and the probability of B's participation is:,
Therefore, the game is unfair.
19, solution: (1), solution: b = 4, k =,
So the linear function is: y = x+5.
(2) After moving down m unit lengths, the straight line is:
, become,
δ = (5-m) 2- 16 = 0, and the solution is: m = 1 or 9.
20, (1) rhombus
Because FG is the vertical line of BE, Fe = FB, GB = Ge, ∠ FE=FB = ∠ fbo,
And feb, so ∠ feb = ∠ gbo, so ∠ fbo = ∠ gbo, bo = bo, ∠ BOF = ∠ bog,
So, Δ δBOF?δBOG, so BF = BG,
Therefore, BG = ge = ef = FB, and BFEG is a diamond.
(2)AB=a，AD=2a，DE=a，AE=，BE=，OE=，
Let the side length of the rhombus BFEG be x, because AB2+AF2 = BF2,
So, the solution is: x =, so, of =,
So, fg =
(3)n=6
Volume II
Fill in the blanks
2 1、520
22, k > and K≠ 1
23、7、3、 10 1 1
24、- 1
25、
Second, answer the question.
26.( 1) 12m or16m; ; (2) 195
27.( 1) is inscribed on the circle o by APCB, and ∠ FPC = ∠ B,
And < b = < ace = 90-< BCE, < ace = < APD,
Therefore, ∠ APD = ∠ FPC, ∠ APD+∠ DPC = ∠ FPC+∠ DPC, that is.
∠ APC =∠ FPD and∠ PAC =∠ PDC,
So, △PAC∽△PDF
(2)
(3)x=2y
28( 1)k=
(2)k= or
(3)F(-2，2)