mathematics

There are 8 big questions and 23 small questions in this paper, with full score of 150 and examination time of 120 minutes.

The total score of the topic is one two three four five six seven eight.

score

I. Multiple-choice questions (this is a small question entitled *** 10, with 4 points for each small question, out of 40 points)

Each item is given the same four options, code-named A, B, C and D, and only one option is correct. Please write the code name of the correct option in brackets after the item. If each item is selected correctly, get 4 points; if it is not selected, selected incorrectly or selected more than one code (whether written in brackets or not), get 0 point.

1.-2, 0, 2, -3, the largest of these four numbers is.

A.- 1 B.0 C. 1 D.2

At the end of 2.20 10, the forest area in Anhui province was 3804.2 thousand hectares. It is correct to express 3804200 hectares by scientific notation. .....................................................................................................................

a . 3804.2× 103 b . 380.42× 104 c . 3.842× 106d . 3.842× 105

3. The following figure shows several cubes made up of five identical cubes, and the left view is ………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….

4. Suppose A is between two adjacent integers, then these two integers are .....................

A. 1 and 2 B.2 and 3 C.3 and 4 D.4 and 5

5. From the five vertices of the lower Pentagon, any four vertices are connected to form a quadrilateral. For event m, "this quadrilateral is an isosceles trapezoid". The following inference is correct.

A. Event M is an impossible event B. Event M is an inevitable event.

C. the probability of event m is d. The probability of event m is

6 As shown in the figure, D is a point in △ABC, BD⊥CD, AD=6, BD=4, CD=3, E, F, G and H are the midpoint of AB, AC, CD and BD respectively, so the perimeter of the quadrilateral EFGH is ..............

A.7 B.9

C. 10 D. 1 1

7. As shown in the figure, ⊙ radius is 1, A, B and C are three points on the circumference, ∠ BAC = 36, then the length of the arc is .......................................

A.B. C. D。

8. The root of a quadratic equation is ..............

A.- 1b.2c. 1 and 2d. -1 and 2.

9. As shown in the figure, in the quadrilateral ABCD, ∠ bad = ∠ ADC = 90, AB=AD=, CD=, and point P is on the quadrilateral ABCD. If the distance from p to BD is, then the number of points of p is. ...............................

A. 1

10. As shown in the figure, P is a moving point on the diagonal AC of rhombic ABCD, and the straight line passing through P perpendicular to AC intersects with the edge of rhombic ABCD at two points, M and N. Let AC=2, BD= 1, AP=x, then the area of △AMN is Y, and the approximate shape of the function image of Y about X is ...............

Fill in the blanks (this is entitled ***4 small questions, with 5 points for each small question, with a full score of 20 points)

1 1. Factorization: = _ _ _ _ _ _.

12. According to the definition of the Richter scale, the relationship between the relative energy e released by the earthquake and the number of earthquakes n is:, so the relative energy released by the earthquake of magnitude 9 is a multiple of the relative energy released by the earthquake of magnitude 7.

13. As shown in Figure ⊙O, the two chords AB and CD are perpendicular to each other, and the vertical foot is E and AB=CD. Given CE= 1 and ED=3, the radius of ⊙O is _ _ _ _ _ _ _.

14. Define the operation, and some conclusions about this operation are given below:

① ②

③ If, then ④ If, then a=0.

The serial number of the correct conclusion is _ _ _ _ _. (Fill in the serial numbers of all the correct conclusions you think on the horizontal line)

Three. (There are ***2 small questions in this question, with 8 points for each small question, with a full score of 16.

15. Simplify before evaluating:

, where x =-2

solve

16. Jiangnan Eco-food Processing Factory purchased a batch of mountain products with the mass of 10000 kg, and carried out rough machining and fine machining according to market demand. It is known that the quality of finished products in mountain products is 3 times more than that of rough machining, and 2000 kg more. The quality of rough mountain products is necessary.

solve

Four, (this question ***2 small questions, 8 points for each small question, full score 16 points)

17. As shown in the figure, draw △ a 1 b1c1and △ a2b2c2 in the grid composed of small squares with side length of1;

(1) shift △ABC to the right by 4 units, and then shift 1 unit to get △ a1b1c1;

(2) With O as the potential center, transform the potential of △A 1B 1C 1 and amplify it to twice the original value to obtain △A2B2C2.

solve

18. In the plane rectangular coordinate system, an ant starts from the origin O and moves continuously in four directions: up, right, down and right, each time moving 1 unit. Its walking route is shown in the following figure.

(1) fill in the coordinates of the following points: a1(_ _ _ _ _, _ _ _ _ _), A3 (_ _ _, _ _ _ _ _), a12 (_ _ _ _ _ _ _ _ _ _)

(2) Write the coordinates of point An (n is a positive integer);

solve

(3) Point out the moving direction of ants from point A 100 to point A10/.

solve

Five, (this question ***2 small questions, each small question 10, out of 20 points)

19. As shown in the figure, in the construction of an expressway, it is necessary to determine the length of tunnel AB. It is known that the plane at the height c is 1500m from the ground, and the surveyors measure that the depression angles of the two points A and B in front of it are 60 and 45 respectively, thus finding out the length of the tunnel AB.

solve

20. In a subject exam, students' scores are all integers, with full marks of 10. A score of 6 or above is qualified. If the score reaches 9, it is excellent. The histogram of students' scores in this exam is as follows.

(1) Please complete the following statistical analysis table:

(2) Students in Group A say that their passing rate and excellent rate are higher than those in Group B, so their grades are better than those in Group B. However, unlike students in Group A, students in Group B think that their grades are higher than those in Group A. Please give three reasons to support their views.

solve

Six, (full mark for this question 12)

2 1. As shown in the figure, the image of the function intersects with the image of the function (x > 0) at points A and B, and intersects with the Y axis at point C. It is known that the coordinates of point A are (2, 1) and that of point C are (0,3).

(1) Find the expression of the function and the coordinates of point B;

solve

(2) Observe the image and compare the sum when x > 0.

Seven, (this question is full 12)

22. At △ABC, ∠ ACB = 90, ∠ ABC = 30, rotate △ABC clockwise around vertex C at the rotation angle of θ (0 < θ < 180), and get △ A/B/C. 。

(1) As shown in Figure (1), when AB∑CB/, let AB and CB/ intersect at D. It is proved that △A/ CD is an equilateral triangle;

solve

(2) As shown in Figure (2), connect A/A and B/B, and let the areas of △ACA/ and △BCB/ be

S△ACA/ and S△BCB/. Verification: s △ ACA/∶ s △ BCB/=1∶ 3;

certificate

(3) As shown in Figure (3), let AC midpoint be E, A/ B/ midpoint be P, AC=a, and then E P. When θ = _ _ _ _ _ _, the length of EP is the largest, and the maximum value is _ _ _ _.

solve

Eight, (full mark for this question 14)

23. As shown in the figure, the four vertices of the square ABCD are on four parallel lines l 1, l2, l3 and l4, and the distances between two adjacent straight lines in these four straight lines are h 1, h2, H3(h 1 > 0, H2 > 0, H3 > 0) in turn.

(1) Verify h1= h3;

solve

(2) Let the area of square ABCD be S, and verify that S = (H2+H3) 2+h12;

solve

(3) If h 1 changes, it means that the area of square ABCD changes with h 1.

solve

20 1 1 Anhui junior high school graduation examination mathematics reference answer

1 ~ 5a cacb 6 ~ 10 dbdbbc

1 1.； 12. 100; 13. 14.①③.

15. Original formula =.

16. let the mountain products mass of rough machining be x kg, which is x+(3x+2000)= 10000 according to the meaning of the question.

The solution is x=2000.

Answer: The rough-machined mountain products has a mass of 2,000 kg.

17. The following figure

18.⑴A 1(0， 1) A3( 1，0) A 12(6，0)

⑵An(2n，0)

(3) upward

19. short answer: ∫OA, OB=OC= 1500,

∴AB= (male).

A: The AB tunnel is about 635 meters long.

20. (1) Group A: median 7; Group B: average 7, median 7.

(2) (The answer is not unique)

① Because the average scores of students in Group B are higher than those in Group A, the scores of students in Group B are better than those in Group A;

② Because the average scores of students in group A and group B are not much different, and the variance of students in group B is lower than that of students in group A, it shows that the fluctuation of students' scores in group B is smaller than that in group A, so students in group B are better than those in group A;

③ Because the lowest score of students in group B is higher than that in group A, students in group B are better than those in group A. 。

2 1.( 1) From the meaning of the question, we can get the solution VIII.

And point A is on the function, so the solution is like this.

solve an equation

So the coordinate of point B is (1, 2).

(2) when 0 < x < 1 or x > 2, y1< y2;

When 1 < x < 2, y1> y2;

When x= 1 or x=2, y 1=y2.

22.( 1) is easy to find, so it is proved.

(2) If it is easy to prove ∽ and the similarity ratio is equal, it can be proved.

(3) 120 ,

23.( 1) If point A passes, AF⊥l3 will cross at point E and point F respectively; if point C passes, CH ⊥ l2 will cross at point H and point G respectively.

Certificate △ Abe △ CDG is enough.

(2) It is easy to prove that △ Abbe △ BCH △ CDG △ DAF, two right-angled sides are h 1 and h 1+h2, and the quadrilateral EFGH is a square with a side length of h2.

So ...

3 by the meaning of the question, so.

0 < h 1

0 < h 1

When h 1=, s takes the minimum value; When < h 1