★ Examination time 120 minutes, full score on the paper 150.
1. Multiple choice questions (only one of the alternative answers to the following questions is correct, please fill in the serial number of the correct answer in the brackets after the question, with 3 points for each question and * * * 24 points).
1. The diameter of the sun is about 1390000 kilometers, which is expressed by scientific notation as ().
a . 0. 139× 107km b . 1.39× 106km c . 13.9× 105km d . 139× 104km。
2. The reciprocal of-6 is ()
From the 6th century to the 6th century.
3. The figure 1 is a geometry composed of several identical cubes, and its left view is ().
4. The solution set of inequality group is ()
a . x≤3 b . 1 < x≤3 c . x≥3d . x > 1
5. In the figure below, it is both an axisymmetric figure and a centrally symmetric figure ().
6. As shown in Figure 2, ∠ BDC = 98, ∠ C = 38, ∠ B = 23, and ∠A's degree is ()
6 1
C.37 D.39
7. Figure 3 is surrounded by four congruent right triangles. If the two right-angled sides are 3 and 4 respectively, a dart is thrown into the figure at random, and the probability that the dart falls in the shadow area is (regardless of the situation of falling on the line) ().
A.B. C. D。
8. As shown in Figure 4, in △ABC, AB=AC, M and N are the midpoint of AB and AC respectively, and D and E are points on BC, connecting d N and EM. If AB=5cm, BC=8cm, and DE=4cm, the area of the shaded part in the figure is ().
A. 1 cm2 b. 1.5 cm2
C. 2 square centimeters d. 3 square centimeters
Fill in the blanks (3 points for each small question, 24 points for * * *)
9. The value range of the independent variable X in the function is _ _ _ _ _ _ _.
10. Decomposition factor: a2b-2ab2+B3 = _ _ _ _ _ _ _ _ _ _ _ _ _
1 1. If the image of the inverse proportional function passes through the point (-2,3), then k is equal to _ _ _ _.
12. Xiao Liang practices shooting. After the first round of 10, his score is shown in Figure 5. The variance of his score 10 is _ _ _ _ _ _.
13. Rotate a triangular ruler with an angle of 30 around a longer right angle to get a cone. If the height of this cone is 3, then the side area of the cone is _ _ _ _.
14. In order to estimate the number of white balls in the opaque bag, first take out 10 balls from the bag and mark them, then put them back in the bag, shake them well and find out 10 balls, one of which is marked, so you can estimate that there are about _ _ _ _ _ _ white balls in the bag.
15. as shown in figure 6, point a and point b are on a straight line MN, AB= 1 1cm, and radii ⊙A and ⊙B are both 1cm. ⊙A moves from left to right at a speed of 2cm per second, at the same time.
16. The circle in Figure 7- 1 is tangent to all sides of the square. Let the area of this circle be s1; The four circles in Figure 7-2 have the same radius, which are circumscribed in turn and tangent to the sides of the square. Let the sum of the areas of these four circles be S2; The nine circles in Figure 7-3 have the same radius and are tangent to the sides of the square in turn. Let the sum of the areas of these nine circles be S3 ... According to this law, when the side length of a square is 2, the sum of the areas of all circles in the nth graph is Sn = _ _ _ _ _ _ _
Three. (8 points for each question, *** 16 points)
17. Simplify first, and then replace the evaluation with any number you like.
1 8. The position of △ ABC in the plane rectangular coordinate system is shown in Figure 8, where the side length of each small square is1unit length.
(1) Move △ABC to the right by two unit lengths, translate △ a1b1,and write the coordinates of each vertex of △ a1b1;
(2) If △ABC is rotated clockwise around point (-1, 0) 180, △A2B2C2 can be obtained, and the coordinates of each vertex of △A2B2C2 can be written;
(3) Observe △A 1B 1C 1 and △A2B2C2. Are they centrosymmetric about a certain point? If yes, please write down the coordinates of the center of symmetry; If not, explain why.
Iv. (Each question 10, ***20)
19. A school held an art activity with the theme of "Celebrating the 60th anniversary of the National Day" and held four competitions. They are: a lecture, b singing, c calligraphy and d painting. Each student must take part in one activity, and only one activity is allowed. Taking Class One, Grade Nine as a sample, the following two statistics are obtained. Please use the information given in Figure 9 to answer the following questions.
(1) Find out the percentage of students participating in the painting competition in the class;
(2) Find out the degree of the fan-shaped central angle in the fan-shaped statistical chart where the students participating in the calligraphy competition are located;
(3) If there are 500 ninth-grade students in this school, please estimate how many students * * * will participate in the speech and singing of this activity?
In order to speed up the economic development of this city, a city plans to build a bridge across the north and south. As shown in Figure 10, the survey team observed a point C at the water edge on the other side of the river at point A, and it was measured that C was 60 north of due east, and reached B 30 meters along the river bank, and it was measured that C was 45 north of due east. Please help the survey team to calculate the width of the river according to the above data. ()
Verb (abbreviation of verb) (10 for each question, ***20 points)
2 1. Xiaogang and Xiaoming play games of "stone", "scissors" and "cloth". The rules of the game are: "stone" wins "scissors", "scissors" wins "cloth" and "cloth" wins "stone". If they make the same gesture, it's a draw.
(1) What is the probability of playing "Stone" once?
(2) What is the probability that Xiao Gang will win Xiao Ming once? Explain by listing or drawing a tree diagram.
22. According to the planning and design, a city engineering team is going to build a 300-meter-long blind road in the development zone. After laying 60 meters, due to the new construction method, the actual length of the blind road built every day is longer than the original plan 10 meter. It took eight days to finish the task. How many meters of blind roads will be laid every day after the engineering team improves its technology?
Six, (each question 10, ***20 points)
23. As shown in figure 1 1, AB is the diameter of ⊙O, and the bisector of AD ∠BAC intersects ⊙O at point D, DE intersects with AC at point E, and FB is the tangent of ⊙O and AD at point F. 。
(1) Verification: DE is the tangent of ⊙O;
(2) If DE=3 and the radius ⊙O is 5, find the length of BF.
24. When a shopping mall purchases a batch of goods with a unit price of 50 yuan, it is stipulated that the unit price at the time of sale shall not be lower than the purchase price, and the profit of each commodity shall not exceed 40%. The relationship between the sales volume y (pieces) and the selling unit price x (yuan) can be approximately regarded as a linear function, as shown in figure 12.
(1) Find the functional relationship between Y and X, and find the value range of X;
(2) Let the total profit (total profit = total sales-total cost) obtained by the company be W yuan, and find the functional relationship between W and X. What is the maximum profit when the unit sales price is what? What is the maximum profit?
Seven, (this question 12 points)
25. As shown in figure 13, the right-angled trapezoidal ABCD is on the same straight line with the sides BC and CG of the square EFGC, and ad∑BC and AB⊥BC are at point B, with AD=4, AB=6 and BC=8. The area of the right-angled trapezoidal ABCD is equal to the area of the square EFGC. Move the right-angled trapezoidal ABCD to the right along the BG parallel, when the point
(1) Find the side length of a square;
(2) Let the distance that the vertex C of the right-angled trapezoid ABCD moves to the right be X, and find the functional relationship between S and X;
(3) When the right-angled trapezoidal ABCD moves to the right, can the area s of the overlapping part with the square EFGC be equal to half the area of the right-angled trapezoidal ABCD? If yes, request to move the value of distance x at this time; If not, please explain why.
Eight, (this question 14 points)
26. as shown in figure 14, the parabola intersects the x axis at two points A(x 1 0) and B(X2, 0), and X 1 > x2 intersects the y axis at point C(0, 4), where x 1 and x2 are equations x2-2x.
(1) Find the analytical expression of this parabola;
(2) Point P is the moving point on line AB, passing point P is PE∑AC, passing BC at point E, connecting CP, and finding the coordinates of point P when the area of △CPE is the largest;
(3) Inquiry: If point Q is a point on the parabola symmetry axis, is there such a point Q that △QBC becomes an isosceles triangle? If yes, please directly write the coordinates q of all qualified points; If it does not exist, please explain why.
Reference answers and grading standards
First, multiple choice questions
1.B 2。 D 3。 A 4。 B 5。 B 6。 C 7。 D 8。 B
Second, fill in the blanks
9 . x > 3 10 . b(a-b)2 1 1。 -6 12.5.6
13.18 π14.10015.3 seconds1second13 seconds16.
I can't send the pictures and symbols with the root number. You can check them in "Chai Zhong Mathematics Network" and "2009 National Middle School Students Examination Questions".