20 13 Jinshan district third grade mathematics first semester final quality examination paper
(Examination time: 100 minutes, full mark: 150 minutes)
Note to candidates:
1. This paper contains three major questions, including ***25 questions. When answering questions, candidates must answer in the position specified in the answer sheet according to the requirements of answering questions. Answering questions on draft paper and this paper is invalid.
2. Except for the first and second questions, unless otherwise specified, the main steps of proof or calculation must be written in the corresponding position on the answer sheet.
1. Multiple choice questions: (There are 6 questions in this big question, 4 points for each question, out of 24 points).
In 1.Rt△ABC, ∠C = 90, and A, B and C are opposite sides of ∠A, ∠B and ∠ C respectively. If a=3 and b=4, then the following equation is correct ().
(1); (b) and: (c) and: (4).
2. As shown in the figure, it is known that AB‖CD, AD and BC intersect at point O, and AO∶DO= 1∶2.
Then the following formula is wrong ()
(A)BO∶CO = 1∶2； (B)CO∶BC = 1∶2；
(C)AD∶DO = 3∶2； (D)AB∶CD= 1∶2。
3. The analytical formula of the new parabola obtained by translating the parabola downward by 2 units is ().
(1); (b) and:
(c) and: (4).
4. The figure below is both an axisymmetric figure and a centrally symmetric figure ().
(a) an equilateral triangle; Parallelogram;
A square; A regular pentagon.
5. Among the following conditions, ‖ cannot be judged as ().
‖,‖； (b) and:
(C)=； (D)(B) =，=。
6. The radii of ⊙ and ⊙ are 1 and 3 respectively, so in the following four statements, the wrong one is ().
(a) When ⊙ and ⊙ have two things in common;
(b) When ⊙ and ⊙ have two things in common;
(c) When ≤, ⊙ and ⊙ have nothing in common;
(d) When ⊙ and ⊙ have nothing in common, ≤
Two. Fill in the blanks: (This topic is entitled *** 12, with 4 points for each question, out of 48 points)
7. It is known that line segment B is the median term in the ratio of line segments A and C, where a = 9 and c = 4, then B =.
8. If the area ratio of two similar triangles is 1: 4, then the ratio of their corresponding angular bisectors is.
9. Given that G is the center of gravity of △ABC, AD is the center line, and AG=6, DG =.
10. Evaluation:.
The vertex coordinates of 1 1. parabola are.
12. Please write a parabola with a straight line as the symmetry axis and rising on the left side of the symmetry axis. The expression of this parabola can be.
13. Xiao Li saw that Xiao Ming's depression angle at point A upstairs and point B downstairs was 35 degrees, so Xiao Ming at point B looked at Xiao Li's elevation angle at point A.
14. It is known that point P is outside ⊙O, and the radius ⊙O is 5. Let OP=x, then the range of x is.
15. In the plane rectangular coordinate system, the circle centered on point P(4,) is tangent to the X axis, so the positional relationship between the circle and the Y axis is.
16. The number of central angles of a regular decagon is.
17. The radii of two tangent circles are 4 and 6 respectively, so the distance between the centers of these two circles is.
18. In △ABC, AB=AC= 5, BC=6, and the circle with point A as the center and point R as the radius has two common points (including point B and point C), so the range of R is.
Third, answer: (This big question is ***7 questions, out of 78 points)
19. (The full mark of this question is 10)
As shown in the figure, two nonparallel vectors.
Simplify first, then strive for:
(The writing method is not required, but the vector indicating the conclusion in the diagram should be pointed out. )
20. (The full mark of this question is 10)
Knowing that the image of quadratic function passes through points (2) and (0), find the analytic expression of this quadratic function, and find the vertex coordinates and symmetry axis of its image.
2 1. (The full mark of this question is 10)
As shown in the figure, it is known that in the parallelogram ABCD, the point E is on the side AD, and the extension line of the line segment CE and the extension line of the line segment BA intersect at the point F, CD=6, AE= ED, and the length of BF is found.
22. (The full mark of this question is 10)
The picture shows a circular arch in the park. The center of the arch is point O, the distance from the highest point A of the arch to the ground is ah = 3m, and the width of the arch is BC = 2m. Find the radius of the arch.
23. (The full score of this question is 12, of which 6 points are given for each small question)
65438+February 22nd is the winter solstice of the China lunar calendar. On this day, the angle between the sun and the ground is the smallest, so the shadow of the building is the longest. On this day, the included angle between the sunlight at a certain time and the horizontal plane is 37, the distance between two buildings in a certain district is BD = 40m, and the height ED of the projection E of the roof A of the first building on the second building is 5m.
(1) Find the height of Building A;
(2) If the projection of the top of Building A is just at the bottom of Building B at this time, how many meters must the design distance between the two buildings be?
(Reference data:,,,)
24. (The full score of this question is 12, of which the first item (1) is 3 points, the second item (2) is 3 points, and the third item (3) is 6 points).
As shown in the figure, the images of both the proportional function and the quadratic function pass through point A(2, m).
(1) Find the analytic expression of this quadratic function;
(2) Find the coordinates and symmetry axis of the vertex P of this quadratic function image;
(3) If the symmetry axis of the quadratic function image intersects with the proportional function image at point B, and intersects with the X axis at point C, and point Q is a point on the positive semi-axis of the X axis, if △OBC is similar to △OAQ, find the coordinates of point Q. 。
25. (The full score of this question is 14, of which the first item (1) is 4, the second item (2) is 5, and the third item (3) is 5).
It is known that in Rt△ABC, ∠ ACB = 90, tan∠ABC=, AB=5, D is a point on line AB (not coincident with points A and B), straight line DP⊥AB intersects with line AC at point Q, intersects with ray BC at point P, and e is the midpoint of AQ.
(1) Verification: △ FBD ∽△ FDP;
(2) Find the value of BF∶BP;
(3) If ⊙A is tangent to the straight line BC and the radius of ⊙B is equal to the length of the line segment BF, let BD=x, and when ⊙A is tangent to ⊙B, find the value of X. 。
Jinshan district in 2009 the first semester junior high school ninth grade math final exam.
Reference answers and grading opinions 20 10. 1
I. Multiple-choice questions: (This big question is * * *, with a total of 6 questions, with 4 points for each question and a full score of 24 points).
1.d； 2.b； 3.a； 4.c； 5.b； 6.D。
Fill-in-the-blank question: (This big question * * has 12 questions, with 4 points for each question, out of * * *)48 points.
7.6; 8. 1∶2; 9.3; 10.； 1 1.( 1,-3); 12. and so on. 13.35; 14.； 15. Separation; 16.36 ; 17.2 and10; 18.。
Third, answer questions:
19. solution: ....................................... (4 points)
The picture is right (the picture is omitted). .................................................................................................................. (5 points)
Conclusion .................................................... (1)
20. Solution: According to the meaning of the question, you get ……2 points.
Solution ...................................... (2 points)
∴ The analytic formula of quadratic function is ......................................... (1 min).
∵ ................................. (2 points)
The vertex coordinate of the function image is (1, -4), and the symmetry axis is the straight line x =1.................................. (3 points).
2 1. solution: in the parallelogram ABCD, AB‖CD, ab = CD ................................................................ (2 points).
Ab CD, ∴ ............................................. (2 points)
* AE = ed, ∴ ................................. (3 points)
∴∴ AB = CD = 6bf = 9 ........................................ (3 points)
22. solution: add OB and set the radius as R. .................................... (2 points)
AH⊥BC can be obtained from the meaning of this question, and point O is right.
∴ BH = CH = .......................................... (2 points)
bc = 2m，∴ BH = 1m。
∠∠bho = 90，∴..........................( 1)
Get: ......................................... (2 points)
Solution: ................................................ (2 points)
A: the radius of the arch is m. ........................................................................................................................ (1 min).
23. solution: (1) the point passing through e is EH⊥AB, and the vertical foot is h.
cd⊥bd. ab⊥bd
∠ AEH = = 37，BD = EH = 40m，ED = BH = 5m。 ............................( 1)
In Rt△AHF, ∠ AHE = 90,
Tan ∠ AEH =, = EH Tan ∠ AEH = 30m, .......................... (3 points).
AB = AH+BH = 35m ...................................................................................................... (1min).
A: The height of Building A is 35 meters. ....................................( 1)
(2) Extended AE, ............................... (1) intersecting with straight line BD at point F.
In Rt△ABF, ∠ ABF = 90, ∠ AFB = = 37 ............................. (1).
Kurt ∠AFB=, BF = abcot∠AFB = 46.55 ............................. (3 points)
A: In the design, the distance between two buildings must reach 46.55 meters ................................................................. (1 min).
(2) Solution 2:
Extend AE, ....................................... (1) that intersects with straight line BD at point F.
∵AB⊥BD,EH⊥AB
∴∴ ......................................... (2 points)
Ab = 35, AH=30, EH=40 ∴ ∴ meter ................................................... (2 points).
Answer: When designing, the distance between two buildings must reach 100 meter .......................... (1).
24. Solution: (1)∫ The images of proportional function and quadratic function all pass through point A (2, m).
∴ ................................... (1min)
∴
∴ ........................................ (1min)
The analytic formula of this quadratic function is .................... (1 min).
(2) .............................. (1min)
∴ The coordinate of the vertex P of this quadratic function image is that the axis of symmetry is ................................ (2 points).
(3) setting. When,
∴ ....................................... (1min)
When △OBC∽△OAQ, right, for ....................... (2 points)
When △OBC∽△OQA, yes, get ……………………………………………………… (2 points).
∴ The coordinate of point Q is ................................. (1 min).
25. Solution: (1)≈ACB =∠pdb = 90, ∠ABC=∠PBD, ∴△BDP∽△ABC. ..
∴∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠873
∫∠ADQ = 90°, and E is the midpoint of AQ.
∴AE=EQ=DE
∴∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠ ......................................................................
∠∠FDB =∠ Ade.
∴∠FDB=∠FPD
∠∠DFB =∠PFD
∴△ FBD ∽△ FDP .......................................... (2 points)
(2) Solution 1:
∫△FBD∽△FDP，
∴ ................................... (1min)
∠∠PDB = 90°
∴ ................................. (1min)
∴ ..................................... (1min)
∴ ....................................... (1min)
BF: BP = 9: 7........................................( 1)
Solution 2:∫∠PDB = 90.
∴ ................................. (1min)
Let DP=4k and BD=3k, then BP = 5k ......................................................................... (1min).
∫△FBD∽△FDP，
∴
...................................( 1)
∴ ,
Solution: ........................................... (1)
∴ BF: BP = 9: 7.......................................( 1)
Solution 3:∫∠PDB = 90.
∴ ................................. (1min)
∫△FBD∽△FDP，
............................ (2 points)
∴ ....................................... (1min)
∴ BF: BP = 9: 7.......................................( 1)
(3) If ⊙A and ⊙B are circumscribed, ....................................... is not on the topic at this time (1+ 1).
If ⊙A and ⊙B are stems, then at this time, it is suitable for .................................................................... (1+ 1 min).
In a word, ....................................... (1 min)
I found one for you.
(handwritten)